Equivalent sets of solutions of the Klein-Gordon equation with a constant electric field

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中国地质大学(北京)考博专业英复习材料

晶） is said to have a porphyritic texture（斑状结构）. The classification of fine-grained rocks, then, is based on the proportion of minerals which form phenocrysts and these phenocrysts （斑晶）reflect the general composition of the remainder(残留) of the rock. The fine-grained portion of a porphyritic（斑岩） rock is generally referred to as the groundmass（基质） of the phenocrysts. The terms "porphyritic" and "phenocrysts" are not restricted to fine-grained rocks but may also apply to coarse-grained rocks which contain a few crystals distinctly larger than the remainder. The term obsidian(黑曜岩) refers to a glassy rock of rhyolitic（流纹岩） composition. In general, fine-grained rocks consisting of small crystals cannot readily be distinguished from③ glassy rocks in which no crystalline material is present at all. The obsidians, however, are generally easily recognized by their black and highly glossy appearanceass of the same composition as obsidian. Apparently the difference between the modes of formation of obsidian and pumice is that in pumice the entrapped water vapors have been able to escape by a frothing（起泡） process which leaves a network of interconnected pore（气孔） spaces, thus giving the rock a highly porous （多孔的）and open appearance（外观较为松散）. ④ Pegmatite（结晶花岗岩） is a rock which is texturally（构造上地） the exact opposite of obsidian. ⑤ Pegmatites are generally formed as dikes associated with major bodies of granite （花岗岩） . They are characterized by extremely large individual crystals （单个晶体） ; in some pegmatites crystals up to several tens of feet in length（宽达几十英尺）have been identified, but the average size is measured in inches （英寸） . Most mineralogical museums contain a large number of spectacular（壮观的） crystals from pegmatites. Peridotite（橄榄岩） is a rock consisting primarily of olivine, though some varieties contain pyroxene（辉石） in addition. It occurs only as coarse-grained intrusives（侵入）, and no extrusive（喷出的） rocks of equivalent chemical composition have ever been found. Tuff （凝灰岩）is a rock which is igneous in one sense （在某种意义上） and sedimentary in another⑥. A tuff is a rock formed from pyroclastic （火成碎屑的）material which has been blown out of a volcano and accumulated on the ground as individual fragments called ash. Two terms（igneous and sedimentary） are useful to refer solely to the composition of igneous rocks regardless of their textures. The term silicic (硅质的)signifies an abundance of silica-rich（富硅） and light-colored minerals（浅色矿物）, such as quartz, potassium feldspar（钾长石）, and sodic plagioclase （钠长石） . The term basic （基性） signifies （意味着） an abundance of dark colored minerals relatively low in silica and high in calcium, iron, and

Flexible docking under pharmacophore type constraints

Journal of Computer-Aided Molecular Design,16:129–149,2002.KLUWER/ESCOM©2002Kluwer Academic Publishers.Printed in the Netherlands.129 Flexible docking under pharmacophore type constraintsSally A.Hindle∗,Matthias Rarey,Christian Buning&Thomas Lengauer†Fraunhofer Institute for Algorithms and Scientiﬁc Computing(FhI-SCAI),Schloss Birlinghoven,D-53754Sankt Augustin,GermanyReceived5December2001;Accepted6March2002Key words:constraint,ﬂexible docking,molecular modeling,pharmacophore,protein-ligand interaction,virtual screeningSummaryF LEX X-P HARM,an extended version of theﬂexible docking tool F LEX X,allows the incorporation of information about important characteristics of protein-ligand binding modes into a docking calculation.This information is introduced as a simple set of constraints derived from receptor-based type pharmacophore features.The constraints are determined by selected F LEX X interactions and inclusion volumes in the receptor active site.They guide the docking process to produce a set of docking solutions with particular properties.By applying a series of look-ahead checks during theﬂexible construction of ligand fragments within the active site,F LEX X-P HARM determines which partially built docking solutions can potentially obey the constraints.Solutions that will not obey the constraints are deleted as early as possible,often decreasing the calculation time and enabling new docking solutions to emerge.F LEX X-P HARM was evaluated on various individual protein-ligand complexes where the top docking solutions generated by F LEX X had high root mean square deviations(RMSD)from the experi-mentally observed binding modes.F LEX X-P HARM showed an improvement in the RMSD of the top solutions in most cases,along with a reduction in run time.We also tested F LEX X-P HARM as a database screening tool on a small dataset of molecules for three target proteins.In two cases,F LEX X-P HARM missed one or two of the active molecules due to the constraints selected.However,in general F LEX X-P HARM maintained or improved the enrichment shown with F LEX X,while completing the screen in considerably less run time.IntroductionAs the number of drug-like molecules stored in high-throughput libraries reaches into the millions,virtualscreening techniques offer a faster and more cost ef-fective alternative to conventional screening methods.Nowadays,especially in view of the expanding rateat which target protein structures are being solved,structure-based techniques such asﬂexible protein-ligand docking play an increasingly important role inthe identiﬁcation of potential lead compounds in thedrug discovery process.∗Author to whom correspondence should be addressed.Currentaddress:BioSolveIT GmbH,An der Ziegelei75,D-53757SanktAugustin,Germany.E-mail:hindle@biosolveit.de†Current address:Max-Planck Institut für Informatik,Stuhlsatzen-hausweg85,D-66123Saarbrücken,GermanyThere are various approaches used inﬂexibleprotein-ligand docking to model how a ligand maybind in the active site of a protein.For all approachesit is necessary to have a complete description of atleast the protein active site,often in the form of the3D structure as found in the Protein Data Bank(PDB)[1].Good[2]and Gane et al.[3]offer comprehensivereviews on the recent advances in structure-based vir-tual screening and structure-based rational drug designrespectively,includingﬂexible docking techniques,while a review of high-throughput docking has alsorecently been published by Abagyan et al.[4].Whendocking algorithms are used within a screening sce-nario,the emphasis has to be on speed.For this,thedocking program F LEX X[5]relies on an incrementalconstruction algorithm.In a virtual screening experi-ment,each molecule is docked and scored andﬁnally130the molecules in the database are re-ranked according to those scores.The main aim of a virtual screening experiment is to bring molecules predicted to be ac-tive with respect to the target protein to the top of the database hence giving an enrichment of potential leads.A pharmacophore is deﬁned as being a set of struc-tural features in a molecule that is recognized at a receptor site and is responsible for that molecule’s biological activity[6].It is used to represent the min-imal structural requirements which are essential for receptor recognition,receptor binding and biological response.A pharmacophore is usually generated from a set of known active ligands of a target protein,which infer likely binding conformations taken up by key bioreactive groups.Typically,a pharmacophore con-sists of three or four sites such as hydrogen bonding groups,charged centers or hydrophobic groups,along with a set of geometrical rules that describe how these features are related in3D space.Exclusion volumes are also often included to represent the presence of the protein.Pharmacophores are used as3D similar-ity search queries in virtual screening to identify new leads[7–9].These types of similarity searches identify compounds in a database that can adopt the correct conformation of bioreactive groups but,despite the use of exclusion volumes,they take no account of how the ligand may bind in the actual protein active site.The advantage ofﬂexible docking techniques is that they explore the conformational space of the lig-and within the active site of a protein,leading to a highly diverse docking solutions set.This could how-ever,in terms of screening applications,be seen as a drawback.Aﬂexible docking algorithm does not make use of any knowledge that might be available beforehand about the binding conformation of a sim-ilar ligand or about the properties of ligands that are already known to be active in the target molecule. When such beneﬁcial information is available,time and effort are wasted docking molecules in the wrong conformations or,of particular importance during a virtual screening experiment,docking molecules that should be rejected because they contradict the infor-mation at hand.By combining the advantages of3D similarity searching techniques and docking,it should be possible to reﬁne the results of virtual screen-ing.Furthermore,it should also be possible to speed up docking-based virtual screening;although docking algorithms are becoming increasingly faster,docking-based virtual screening is still not as fast as other3D searching techniques and timing remains critical.Relevant information may be available to the user in the form of an experimentally resolved structure of a similar protein-ligand complex to that in which they are interested.These structures show whereabouts in the site the ligand binds and in what conformation, and may also hold interesting clues about important interactions that are formed between ligands and the protein in the bound conformation.When such direct information is unavailable information can be derived from various sources.Analysis of active site properties allows the identiﬁcation of key interaction‘hotspots’[9–12]and the derivation of so-called receptor-based pharmacophores,while pharmacophore knowledge may be obtained from the study of the properties of known active ligands,using,for example,the active analogue approach,clique detection techniques and more recently genetic algorithms(for an overview of pharmacophore techniques in general see[9]).One important source of information that still plays a role in pharmacophore development comes from the un-derstanding the user themselves may have about the biochemical system.Previously,Fradera et al.[13]published a vari-ation of the DOCK4.0[14]program that uses the experimentally resolved structure of a protein-ligand complex to guide theﬂexible docking of similar lig-ands in the active site of that protein.During the docking process,the position of a ligand is com-pared to that of the crystal structure and the docking score is weighted according to the similarity of the two.Meanwhile,Thomas IV et al.[15]developed pharmacophore docking also within the DOCK pro-gram,in order to dock pharmacophores rather than ligands into protein active sites.This method was de-veloped as one way of incorporating conformational ligand information into the DOCK rigid body docking algorithm.For our purposes,a receptor-based pharmacophore type descriptor lends itself easily to application in docking.If pharmacophore information has been de-rived from the side of the ligand only,the pharma-cophore sites in the ligand can be translated on to the receptor site perhaps from an analysis of the results of docking calculations.With a receptor-based descrip-tor,interactions are deﬁned within the active site on the side of the protein rather than on the side of the ligand,while exclusion volumes are already described by the3D structure of the site itself.Consequently,as some description of the active site is a prerequisite for docking,a receptor-based pharmacophore provides an131ideal way of conferring information into the docking calculation.In the following we present F LEX X-P HARM,an extended version of theﬂexible docking program F LEX X,in which the user can incorporate pharma-cophore features as constraints into aﬂexible docking calculation.All docking solutions must possess the properties prescribed by the set of constraints.The F LEX X docking calculation is modiﬁed to accommo-date the constraints not by introducing penalties or weighting into the scoring scheme,but rather by using ﬁlters to keep or reject solutions in one of two ways. Firstly,and most simply,the set of constraints is used as a post-dockingﬁlter applied to theﬁnal set of dock-ing solutions generated by F LEX X.Or,secondly,the set of constraints is used as aﬁlter applied during the reconstruction of the ligand in the active site.This is the most advantageous method because solutions are ﬁltered out early in the course of the calculation.This leads not only to a more speciﬁc set of docking solu-tions but also to a speed-up in the calculation and the opportunity for novel docking solutions to appear due to a more intensive search of the conformational space deﬁned by the constraints.The following sections describe in detail the form of the pharmacophore type constraints used in F LEX X-P HARM,the implementation of various look-aheadﬁltering checks andﬁnally the application of F LEX X-P HARM in docking problems and in virtual screening scenarios.MethodsThe full details of the models and algorithms used in F LEX X are described in detail elsewhere[5,16,17]. However,a brief outline of the relevant points is given below.In F LEX X,the protein is referred to as the‘recep-tor’and therefore the term‘receptor’will be used in the text from here on.The receptor active site and the ligand interacting groups in F LEX X are described by the LUDI interaction model[18].An interacting group on the surface of the site is assigned an inter-action type and,accordingly,an interaction center and surface.The interaction center forms the center of a sphere on which the interaction surface lies.Interac-tions are formed when interaction groups on the ligand are matched with appropriate groups in the active site. If the interaction center of one group lies close to the interaction surface of the other,as in Figure1,Figure 1.A receptor-ligand interaction at the ideal geometry, formed between a hydrogen bond acceptor(left)and a hydrogen bond donor(right).then the interaction has an ideal geometry.(Devia-tions from the ideal geometry are tolerated in F LEX X but are penalized in the scoring function by a scaling factor.)The types of interaction currently available in F LEX X are listed in Table1.Note that for algorithmic purposes,the interaction surfaces on the receptor are approximated as aﬁnite set of discrete points during the calculation.The ligand is divided into fragments at rotatable bonds.Various base fragments are selected and placed independently into the active site.The remaining frag-ments are then built on to the base fragments in an iterative procedure.During each fragment place-ment,F LEX X identiﬁes the new interactions formed between the site and the fragment according to the interaction geometry parameters.The interactions are then used to optimize the ligand position and to score the placement by means of an empirical scoring func-tion based on that of Böhm[19].A greedy heuristic is used to retain the k best placements(default parame-ters give k=800for most F LEX X calculations)for the next iterative step.In F LEX X-P HARM,the set of pharmacophore fea-tures in the active site constrains the docking calcu-lation so that only solutions are produced that match the speciﬁed set of features.Thus,the term pharma-cophore constraint is here used to describe a feature in the site which will impose a restriction on the dock-ing calculation.Theﬁrst modiﬁcation of F LEX X is the inclusion of the pharmacophore constraints,the nature of which are described in the next section be-low.If the pharmacophore constraints are to be applied during the docking calculation then some pre-docking preparation steps are initiated.Firstly,all candidate countergroups for each constraint are located in the ligand.A candidate countergroup set contains one candidate countergroup for each bi-natorially,there is usually a list of possible candidate countergroup sets.A maximum distance look-up table132Table1.Interaction types in F LEX X.An interaction group on the receptor can be matched by any of the countergroups in the ligand and vice versaName Interaction Group CountergroupsDirected interactions(level3interactions-strong)h_don hydrogen bond donor h_acch_acc hydrogen bond acceptor h_donmetal metal atom metal_accmetal_acc metal ligand metalHydrophobic directed interactions(level2interactions)phenyl_center phenyl ring(centroid)phenyl_ring,ch3_phe,amide phenyl_ring atom in phenyl ring phenyl_centerch3_phe methyl group phenyl_centeramide amide bond phenyl_centerHydrophobic undirected interactions(level1interactions-weak)ch CH group ch,ch2,ch3,sulfur,aroch2CH2group ch,ch2,ch3,sulfur,aroch3methyl group ch,ch2,ch3,sulfur,aro sulfur sulfur atom ch,ch2,ch3,sulfur,aroaro aromatic C atom ch,ch2,ch3,sulfur,aro(MAXLT)is calculated for all the candidate coun-tergroups in the ligand,while a minimum distance look-up table(MINLT)is calculated for all the con-straints on the receptor.These are used to reduce the combinatorial list of candidate countergroup sets by eliminating impossible combinations of counter-groups.The resulting reduced list is referred to in the text as the master list.During the fragment placement,F LEX X-P HARM carries out an additional search for newly formed in-teractions with extended geometry parameters(larger distance and angle tolerances in deviations from the ideal geometries).These are stored separately and are not used in the optimization or scoring of the placement.The identiﬁcation of these interactions is important during the look-aheadﬁltering.The look-aheadﬁltering takes place after the base placement and each fragment building step.Theﬁl-tering consists of a series of three checks designed to assess whether each of the k retained solutions will be able to match the constraints.Theﬁlters;logical checks,distance checks and directed tweak checks,in-crease in complexity and are explained in more detail below.If a partial docking solution satisﬁes one check, it passes on to the next and if it satisﬁes all checks then it is retained for the next fragment building iteration.Deﬁnition of the Pharmacophore Constraints inF LEX X-P HARMIn F LEX X-P HARM two different types of constraint can be deﬁned in the active site,interaction con-straints and spatial constraints.For theﬁrst type, the user can specify a F LEX X interaction surface in the active site that must take part in an interaction with the ligand.For the second type,the user can specify inclusion volumes.In addition the constraints can be designated essential or optional.The follow-ing description makes reference to an example set of pharmacophore constraints built in the active site of carbonic anhydrase(PDB code1azm)which are listed in Table2and shown in Figure2.Interaction constraints.An interacting group and in-teraction type in the active site must be speciﬁed (along with an interaction surface if more than one surface exists for that interaction).F LEX X-P HARM ensures that an interaction is formed between the spec-iﬁed interacting group in the active site and the ligand in a valid docking solution.In Figure2,constraint1is a metal interaction on the zinc ion.A metal acceptor in the ligand must form an interaction with the zinc in a valid docking solution.A hydrogen donor(constraint133 Figure2.A set of four pharmacophore constraints in the active siteof carbonic anhydrase(1azm).Constraint1.essential metal inter-action at the zinc ion,constraint2.essential spatial constraint for acarbon atom,constraint3.optional h_don interaction at the back-bone nitrogen of THR199,constraint4.optional h_acc interactionat the gamma oxygen of THR199.P min=1and P max=2.Seetext for more details.3)and acceptor(constraint4)have also been selectedon the amide nitrogen and the hydroxy oxygen of THR199respectively.Spatial constraints.This constraint can be used toconstrict ligand position in the active site and consistsof a sphere plus an associated element type.For exam-ple,a carbon atom of the ligand must lie in the deﬁnedsphere of constraint2in Figure2.Essential constraints.A valid docking solution mustobey all essential constraints.Constraints1and2inFigure2are assigned essential priority.Optional constraints.The number of optional con-straints obeyed in a valid docking solution must liewithin a given interval[P min,P max].Optional con-straints allow for a partial pharmacophore match andhence provide a little moreﬂexibility in the overallpharmacophore deﬁnition.P min is useful,for exam-ple,when at least one interaction is required with theguanidinium group of Arginine.P max can be used tolimit the number of optional constraints found,spe-cially in the case of screening experiments where theremay be different classes of active molecules.Con-Figure3.The minimum distance m between two pharmacophoreconstraints.For the spatial constraint the minimum distance is mea-sured to the sphere(to the central point less the radius r)and forthe interaction constraint the minimum distance is measured to thenearest approximation point on the interaction surface.straints3and4in Figure2are optional.The associatedpartial deﬁnition prescribes that at least one of the twoconstraints is fulﬁlled in a valid docking solution.Pre-docking checks in F LEX X-P HARMIn order to gain the maximum potential from F LEX X-P HARM in terms of speed and optimal results,ligandsthat are bound to fail the pharmacophore constraintsshould be eliminated before the docking calculation.This can be achieved with some pre-docking checksin F LEX X-P HARM.If the ligand could potentiallyﬁtthe constraints then the information calculated duringthe pre-docking checks is used later in the dockingcalculation to delete incompatible docking solutionsas early as possible.Pre-docking preparation on the receptorThe MINLT(minimum distance look-up table for theconstraints)is created by calculating the minimum dis-tance between all pairs of constraints.The minimumdistance(m in Figure3)is calculated to a spatial con-straint by taking the nearest point on the sphere(i.e.the distance to the center less the radius r),whilethe minimum distance to an interaction constraint iscalculated to the nearest approximation point on theinteraction surface.Pre-docking preparation on the ligandThe MAXLT(maximum distance look-up table forthe candidate countergroups)is calculated for themaximum distances between all pairs of atoms andcandidate countergroups in the ligand.A candidatecountergroup for a spatial constraint is an atom of the134correct type,while a candidate countergroup for an interaction constraint is an interaction center of an ap-propriate countergroup for that interaction.Note that interaction centers are not atoms but deﬁned points in space.The MAXLT isﬁlled as follows.Firstly, all distances between each interaction center and an atom of the interacting group to which it belongs are calculated.A tolerance is added on to this distance to allow a little extra leeway in the MAXLT to accom-modate the formation of interactions that deviate from the ideal interaction geometry.Then the distances be-tween pairs of atoms are added to the table.Because all bond angles in F LEX X remainﬁxed,the distances between atom pairs separated by one and two bonds are taken directly from the original ligand conforma-tion.For any rotatable bonds,the maximum possible distance between atom pairs separated by three bonds is calculated by setting the torsion to180◦.For ring systems,distances are taken from the set of valid ring conformations stored by F LEX X(as calculated by the program CORINA[20]).The resulting table usually has gaps in it which are completed using the Floyd–Warshall all-pairs shortest path algorithm[21,22] (here applied in its variant for maximization of path length).This algorithmﬁlls a gap with the shortest distance between two points that is consistent with all the pairwise distance relationships already known.Finally,a list of candidate countergroup sets is compiled from all combinations of candidate coun-tergroups in the ligand.The candidate countergroups (plus the interaction surfaces)found in the ligand from the1azm complex are shown in Figure4.There are several candidates for each of the constraints(given in Figure2and Table2).F LEX X-P HARM determines whether the ligand can potentially meet the constraints by comparing the MAXLT and MINLT.A distance check is car-ried out for each candidate countergroup set.If the MAXLT distance between any two essential candi-date points is shorter than the corresponding MINLT distance,that candidate countergroup set is imme-diately deleted.Otherwise,the optional constraints are brought into play;if every MAXLT distance be-tween the optional candidate countergroup and each essential candidate countergroup is greater than the corresponding MINLT distance,that optional candi-date point satisﬁes the distance check.If the number of optional candidate countergroups which satisfy the check is greater than P min then this candidate counter-group set is retained.The distances between pairs of optional candidate countergroups are notconsidered Figure4.Candidate countergroups in the1azm complex ligand. Shown are the:(a)interaction surfaces of the six metal_acc coun-tergroups for constraint1,(b)four C atoms for constraint2,(c) interaction surfaces of the two h_don countergroups for constraint3, (d)interaction surfaces of the six h_acc countergroups for constraint 4.at this stage due to the very large number of compar-isons that would have to be made.If,ﬁnally,after the pre-docking distance checks the list of candidate countergroup sets is empty,it is impossible for any combination of candidate countergroups in the ligand to fulﬁll the constraints and the ligand is rejected.If not,the remaining list of candidate countergroups sets is stored as the master list.F LEX X-P HARM dockingﬁltersApplication of pharmacophore constraints during dockingThe actual placement of fragments by the F LEX X base placement and fragment building algorithms is not altered by F LEX X-P HARM.One incremental con-struction step begins with the set of partial docking solutions remaining from the previous step.A new fragment is added to the placed fragments in all pos-sible conformations providing there is no signiﬁcant overlap with the receptor.The F LEX X placement al-gorithm identiﬁes the new interactions between the fragment and the receptor which are used for opti-mization and scoring.Meanwhile,F LEX X-P HARM identiﬁes extra interactions with the extended angle and distance tolerance parameters.The use of these extended parameters is necessary because the posi-tion of the partial solutions may change during the rest of the incremental construction process due to lig-135and placement optimizations.F LEX X-P HARM could otherwise exclude a solution wrongly because the nec-essary interaction may later come to exist when groups on the ligand and receptor move closer together.The fragment building step is completed when a fragment has been added to all partial solutions,op-timized,scored and the k best solutions have been selected.The k best solutions are thenﬁltered against the constraints by F LEX X-P HARM before the next fragment building step begins.At this stage a valid solution is one in which the constraints are either ful-ﬁlled or can still be fulﬁlled during the placement of the remaining unplaced ligand.Logical checks.The logical checks ascertain whether the correct combinations of candidate countergroups exist in the placed and unplaced parts of the ligand. For each pharmacophore constraint,F LEX X-P HARM looks to see whether the constraint is already fulﬁlled in the placed part of the ligand or,if not,whether can-didate countergroups still exist in the unplaced part of the ligand(i.e.whether it is still possible to fulﬁll the constraint).An interaction constraint is fulﬁlled when an in-teraction containing the constraint interaction surface exists in amongst the interactions identiﬁed by F LEX X or F LEX X-P HARM(with extended parameters)dur-ing the fragment placement.A spatial constraint is fulﬁlled when a ligand atom of the correct type lies within the radius plus a tolerance of the constraint sphere.A tolerance is required on the sphere again to account for any movement of placed atoms during subsequent optimizations.Note that more than one candidate countergroup can fulﬁll one constraint.If a constraint is not fulﬁlled then it can be designated possible to fulﬁll if countergroups remain available in the unplaced part of the ligand.If the fragment added was theﬁnal fragment of the ligand then all constraints must be fulﬁlled(in accor-dance with the partial constraints deﬁnition).The extra interactions identiﬁed by F LEX X-P HARM and toler-ances on spatial constraint spheres are not included as there can be no further movement of the ligand atoms.Simple logical conditions are used to decide whether the partial docking solution can be retained. The solution is deleted if one of the following condi-tions is true:−any essential interaction constraint is not fulﬁlled or not possible;−fewer than P min optional constraints are fulﬁlled orpossible;Figure5.Schematic of the1azm active site with the pharmacophore constraints.After placement of two fragments of the ligand,con-straint1(essential)is fulﬁlled by one candidate countergroup in the ligand and constraint3(optional)is fulﬁlled by two.Constraints 2(essential)and4(optional)have not yet been fulﬁlled.It must be possible to fulﬁll constraint2as this is an essential constraint.It does not matter at this stage whether constraint4is still possible because the optional requirements are already satisﬁed by constraint3.−greater than P max optional constraints are fulﬁlled (this condition can only be applied if the fragment added was theﬁnal fragment because the num-ber of fulﬁlled optional constraints may otherwise change due to optimizations).The logical checks are illustrated by means of an imag-inary docking situation with the carbonic anhydrase active site,ligand and constraints in Figure5.If a partial(i.e.not aﬁnal)docking solution is retained then a list of candidate countergroup sets is created from the ligand placement.Several combi-natorial possibilities may exist due to the fact that constraints can be fulﬁlled by more than one counter-group and it may still be possible to fulﬁll constraints with more than one countergroup.All combination sets formed are checked against the master list;if that set is not present in the master list then it has al-ready been eliminated because the maximum possible distances between the candidate countergroups are al-ready too short for the constraints.This newly created list is local to that partial docking solution and the local lists vary from solution to solution.A solution with an empty local list is immediately deleted.Distance checks.The remainingﬁlter checks focus only on the constraints that remain possible and not those that are already fulﬁlled.This also means there is no further checking if the fragment added was the ﬁnal fragment.。

D=9 supergravity and p-brane solitons

a r X i v :h e p -t h /9703063v 1 8 M a r 1997CTP TAMU-15/97hep-th/9703063D =9supergravity and p -brane solitonsN.Khviengia and Z.KhviengiaCenter for Theoretical Physics,Texas A&M University,College Station,TX77843-4242AbstractWe construct the N =2,D =9supergravity theory up to the quartic fermionic terms and derive the supersymmetry transforma-tion rules for the ﬁelds modulo cubic fermions.We consider a class of p -brane solutions of this theory,the stainless p -branes,which cannot be isotropically oxidized into higher dimensions.The new stainless elementary membrane and elementary particle solutions are found.It is explicitly veriﬁed that these solutions preserve half of the supersym-metry.1IntroductionThe recent progress in the understanding of M-theory revived the interest in the supergravity theories in diverse dimensions.Much work has been done in constructing and classifying the p-brane solutions to these theories. However,the extended supergravity in nine dimensions has not yet been fully constructed and investigated.Purely bosonic N=2,D=9action in the context of type-II S-and T-duality symmetries has been discussed in[1,2], but the full action of the theory and the supersymmetry transformation rules has not appeared in the literature.The goal of this paper is toﬁll this gap and present an explicit construction of the N=2,D=9supergravity up to the quartic fermionic terms and provide an exhaustive classiﬁcation of stainless p-brane solutions of this theory.With few exceptions,the lower dimensional supergravity theories can be obtained by dimensional reduction of the eleven dimensional Cremmer-Julia-Scherk(CJS)supergravity[3].Some examples of such exceptions in D=10 are provided by type IIB and massive type IIA supergravity theories[4,5]. Dimensional reduction of CJS action,apart from massless supergravities, can also give massive theories in D≤8[6,7].As one descends through the dimensions to obtain lower dimensional supergravities,a plethora of isotropic p-brane solutions arises[8,9,10].Solutions of the dimensionally reduced theory are also solution of the higher-dimensional theory,however,in higher dimension these solutions may or may not exhibit isotropicity.The solutions which cannot be isotropically lifted to the higher dimension and,therefore, cannot be viewed as p-brane solutions in the higher dimension,are called stainless solutions[11].The extended N=2supergravity in nine dimensions can be truncated to N=1supergravity whose stainless solutions consist of an elementary particle and a solitonic5-brane[11].It turns out that,whilst the elementary particle remains stainless in N=2theory,the solitonic5-brane becomes rusty and can be obtained from the type IIA D=10solitonic 6-brane.We explain this phenomenon by employing a two-scalar5-brane solution of N=2supergravity.The paper is organised as follows.In sections2,using the ordinary Scherk-Schwarz dimensional reduction procedure[6],we obtain the bosonic Lagrangian of N=2,D=9supergravity theory by dimensionally reducing the eleven-dimensional CJS Lagrangian from eleven directly to nine dimen-sions.It is of interest to note that in D=9,unlike D=8case[12], nontrivial group manifolds do not arise.In section3,we perform an analo-gous dimensional reduction for fermions and obtain the fermionic part of the nine-dimensional supergravity up to quartic fermions.The supersymmetry transformation rules for the bosonic and fermionicﬁelds,modulo trilinear fermions,are derived in secion4.In section5,stainless solutions to the ob-tained N=2,D=9supergravity are analysed.New stainless elementaryparticle and elementary membrane solutions are found,and it is shown that they preserve half of the supersymmetry.A stainless solitonic6-brane is also discussed.It is noted that if one is to include type IIB chiral supergrav-ity into consideration,the solitonic6-brane and the elementary membrane solutions become rusty and can be treated as descendants of the type IIB solitonic7-brane and self-dual3-brane in D=10.2Bosonic SectorThe bosonic part of the N=1,D=11supergravity Lagrangian is given by [3]L=ˆe48ˆFˆµˆνˆρˆσˆFˆµˆνˆρˆσ+2κ(ˆeˆµˆrˆeˆνˆs−ˆeˆµˆsˆeˆνˆr)∂ˆµˆeˆtˆν.(5)2We shall now perform the ordinary Scherk-Schwarz dimensional reduction of CJS Lagrangian(1)directly to D=9dimensions.We begin by dimen-sionally reducing the Einstein-Hilbert term in(1).It is convenientﬁrst to consider reduction from an arbitrary D+d to D dimensions,and then apply obtained formulas to our case where D+d=11and D=9.The Lorentz invariance of the supergravity theory in D+d dimensions, enables one to cast the vielbein into the triangular formˆeˆrˆµ= ˆe rµˆA iµ0ˆe iα .(6)Hereµ,r=0,1,···,D−1;α,i=1,···,d,the hatted indices belong to (D+d)-dimensional space,andˆA iµare the vector gaugeﬁelds that give rise to2-indexﬁeld strengths in the dimensionally reduced theory.Then the inverse veilbein is given byˆeˆµˆr= ˆeµr−ˆAαr0ˆeαi ,(7) where internal indices are raised and lowered by the metricˆgαβ=ˆe iαˆe jβδij.(8) The components of the spin-connectionˆωˆrˆsˆt are given by[6]ˆωrsj=1ˆeαiˆeµr∂µˆe jα−(i↔j),2ˆωjrs=−ˆωrsj,(9)ˆωirj=−1ˆgαβˆFµναˆFβµν(11)4+1d L iα,(13)ˆAαµ=2κAαµ,where L iαis a unimodular matrix detL iα=1,andγis a free parameter that determines an exponential prefactor of the Einstein-Hilbert term in a lower dimensional theory.As a result of rescaling,the vielbeins are brought to the following form ˆeˆrˆµ= δγe rµ2κδ1d L iα ,ˆeˆµˆr= δ−γeµr−2κδ−γAαr0δ−1Under the rescaling of the type(13),the metric in D dimensions rescales asˆgµν=δ2γgµν,and a Ricci scalar changes asR→δ−2γ R−2γ(D−1)gµν∇µ∇νlnδ−γ2(D−1)(D−2)gµν∇µlnδ∇νlnδ .(15)Using(12)and(15),we obtain the expression for the dimensional reduction of the Einstein-Hilbert action from D+d to D dimensions(for d>1)that generalises the result of ref.[6]for the arbitrary value of parameterγ d D+d xˆeˆR= d D xeδγ(D−2)+1 R−κ2δ−2γ+2gµν∂µgαβ∂νgαβ ,(16)4where1β≡γ2(D−1)(D−2)+2γ(D−1)+1−d F rsj,ˆωrij=δ−γQ rij,ˆωjrs=−ˆωrsj,(18)ˆωijr=δ−γ(2P rij+1Lαi∂r Lαj+(i↔j),Qµij=12invariant under the general coordinate transformation[6].Upon compact-iﬁcation,this symmetry becomes D=9general coordinate transformation and a set of the[U(1)]2reparametrization transformations.Denoting a pa-rameter in D=11byξˆµ,one can show that under theξα-reparametrization transformation,the gaugeﬁelds deﬁned in(20)transform noncovariantly in-volving derivatives of the parameterξα.Nevertheless,the supersymmetry transformation rules and the dimensional reduction procedure is somewhat simpliﬁed by this choice[8,11].In order to obtain results in terms of the covariant gaugeﬁelds,used in[6],one has to change conventions by identi-fying the nine-dimensional gaugeﬁelds as B rst=δ3γˆA rst,B rsi=δ2γˆA rsi and B rij=δγˆA rij.This amounts to the following redeﬁnitions of theﬁelds:Bµνρ=Aµνρ−6κA i[µAνρ]i+12κ2A i[µA jνAρ]ij,Bµνi=Aµνi−4κA j[µAνi]j,(21)Bµij=Aµij.Dimensionally reducing theﬁeld strength,weﬁndˆF=δ−4γ F rstu−2kF rsti A i u+4k2F rsij A i t A j u ≡δ−4γF′rstu, rstuˆF=δ−3γ−12F′rsti,rstiˆF=δ−2γ−1F rsij,(22) rsijˆF=0,rijkˆF=0.ijklAbove rules reﬂect the fact that theﬁeld strengths in D=9do not transform covariantly under the U(1)transformations arising from eleven-dimensional general coordinate transformation.This U(1)reparametrization invariance should not be confused with another U(1)symmetry which is a gauge symmetry of the antisymmetricﬁeld in D=9.In D=11,the U(1)gauge transformation is given by[6]δΛˆAˆµˆνˆρ=3∂[ˆµΛˆνˆρ],(23) which upon reduction gives the following U(1)gauge transformationsin D=9:δΛAµνρ=3∂[µΛνρ],δΛAµνα=2∂[µΛν]α,(24)δΛAµαβ=∂µΛαβ.Notice that since we are performing the ordinary dimensional reduction, none of theﬁelds and parameters in D=9depend on extra compactiﬁcation coordinates,in other words,all∂αderivatives are identically zero.Turning to the kinetic term for the antisymmetric tensorﬁeld in(1)and performing the straightforward reduction of theﬁeld strengths using(22), we obtain−e(12)4εµ1···µ9εαβ 3Fµ1µ2µ3µ4Fµ5µ6µ7µ8Aµ9αβ+24Fµ1µ2µ3µ4Fµ5µ6µ7αAµ8µ9β−16Fµ1µ2µ3αFµ4µ5µ6βAµ7µ8µ9+12Fµ1µ2µ3µ4Fµ5µ6αβAµ7µ8µ9 ,(26) where the totally antisymmetric tensor in nine dimensions is deﬁned as εµ1···µ9εαβ=εµ1···µ9αβ.In order to have the canonical normalization of a scalarﬁeld kinetic term in(16),we introduce a dilaton in D dimensionsδ=e βκφ(27) and chooseγ=−1D−2=−174κ2R−1√2(∂µφ)2−148e47κφF′µνρσF′µνρσ−1√8e−87κφFµναβFµναβ+L F F A ,(28) where L F F A is given by(26).The bosonic action(28)is invariant under the Abelian U(1)gauge trans-formations(24).We shall consider the supersymmetry and Lorentz invari-ance of the full N=2,D=9ation in section4where the supersymmetry transformation rules for theﬁelds will be derived.Using the general expression for dimensional reduction of the Einstein-Hilbert term(16),one can rewrite the action(28)in the p-brane metric[8] which appears naturally in the p-braneσ-models and is related to the canon-ical gravitational matric in D dimensions as gµν(p−brane)=e a/(p+1)gµν, with[11]a2=∆−2(p+1)˜dwhere ˜d=D −p −3and ∆in maximal supergravity theories is equal to 4.Then for the p -brane metric,the parameter γis deﬁned by the equation:2κ(p +1)(7γ+1)(−2/β)1/2=−(D −2)a.(30)In the following,we use the canonical value of γ,which in D =9is −1/7.3Fermionic sectorWe shall now compactify the fermionic part of the elven-dimensional super-gravity Lagrangian which reads[3]LF =L (1)F +L (2)F +quartic fermions,(31)L (1)F =ˆe 98ˆ¯ψˆr ˆΓˆr ˆs ˆt ˆu ˆv ˆw ˆψˆs +12ˆ¯ψˆt ˆΓˆu ˆv ˆψˆwˆF ˆt ˆu ˆv ˆw ,(33)where the covariant derivative is given byˆD ˆs ˆψˆt=∂ˆs ˆψˆt +13√73√77Γr Γiχie 17κφ,ψi −→χi e17κφ.(39)In the kinetic term for the fermions,for example,the exponential in(39) cancels against the corresponding factors coming from the determinantˆe and the covariant derivativeˆDˆs,and the shift of the fermionicﬁeld ensures that the Lagrangian is diagonalised.In the arbitrary dimension D,one has to make the following redeﬁnitionsψr−→ ψr−12(γ(D−1)+1),(40)ψi−→χiδ−12¯ψµΓµνρDνψρ+e7ΓiΓj+δij Dµχj+κe√2¯ψρΓ[ρΓµνΓσ]Γjψσ+¯ψρΓµνΓρ 149¯χiΓµν −23Γkδij+59Γjδik χk ,(43)L(2)F=κe√7¯ψλΓµνρσΓλΓiχi+¯χiΓµνρσ 1124e−17κφF′µνρi −¯ψλΓ[λΓµνρΓσ]Γiψσ+2¯ψλΓµνρΓλ δij−27¯χk GammaµνρΓk δij−816e−47κφFµνij ¯ψλΓ[λΓµνΓσ]Γijψσ−2449ΓkΓi+δki χj ,(44)where the covariant derivetives Dµψν=e sµe tνD sψt and Dµχi=e sµD sχi are deﬁned asD sψt=∂sψt+14Q sijΓijψt,(45)D sχj=∂sχj+14Q sikΓikχj+Q sj kχk.(46) In deriving(43)and(44),we have used the followingﬂipping property of Majorana spinors in nine dimensions¯ψΓr1···r nη=(−1)n¯ηΓr n···r1ψ.(47)4Supersymmety transformationsIn this section,we obtain the supersymmetry transfomation laws in nine dimensions.In order to preserve the triangular form of the veilbeinˆe rα=0, one has to consider combined Lorentz and supersymmetry transformation laws.As we shall see,the requirement of the oﬀ-diagonal part of the veilbein be zero,imposes an additional constrain on the Lorentz group parameters. This,in its turn,aﬀects the supersymetry transformation laws of theﬁelds.Combining the supersymmetry and the Lorentz tranformation laws in eleven dimensions,we have[3]δˆeˆµˆr=−¯ηΓˆrˆψˆµ+Λˆrˆsˆeˆsˆµ,(48)δˆAˆµˆνˆρ=−3144 ˆΓˆνˆρˆσˆγˆµ+8ˆΓˆνˆρˆσδˆγˆµ ˆFˆνˆρˆσˆγη+13√¯εΓjχjδrs+Λ′rs,(52)3√7where symmetrization is performed with the unit strength andΛ′sr is the redeﬁned local SO(1,8)Lorentz transformation parameterΛ′sr=Λsr−¯εΓ[sψr]+1¯εe−37κφ Γiψµ+Γµ(δij+172κ−¯εΓ(iχj)A jµ+Λ′i j A jµ,(54)κδij(δφ)−¯εΓ(iχj)+Λ′ij,(55) LαjδLαi=−√3where the redeﬁned SO(2)Lorentz parameter isΛ′ij=Λij−¯εΓ[iχj].(56) Tracing(55)withδij,oneﬁnds the transformation law forδφ,which upon substitution into(52),puts the veilbein transformation law into canonical form.Suppressing theΛ′rs andΛ′ij transformations,we obtain the supersym-metry transformation rules for the bosonicﬁelds:δe rµ=−¯εΓrψµ,(57)δφ=−3¯εΓiχi,(58) 7κLαjδLαi=−¯ε Γ(iχj)−1¯εe−37kφ Γiψµ+Γµ(δij+12κ¯εe47κφΓαβψµ−¯εe47κφ 8√2¯εe17κφ ΓαΓ[µ−2κe37κφΓαγAγ[µ ψν]2−1√7ΓαΓβ χβ−4κ¯εe47κφ 6√¯εe−27κφΓ[µνψρ]+3√2√√√ΓαΓγ)+24√7κe37κφF iνρ Γµνρ+12Γνδρµ Γiε28−1√7Γνρσλµ+48e−17κφF′νρσj Γνρσµ+1542e−47κφFνρij 3Γνρµ+36Γνδρµ Γijε+cubics,7×24δχi=−1√7e27κφF′µνρσΓµνρσΓiε+1√144e−47κφFµνjiΓµνΓjε+cubics,(64)6whereDµε=∂µε+14QµijΓijε(65) 5Stainless p-brane solutionsMost supergravity theories in D<11dimensions can be obtained by dimen-sionally reducing D=11supergravity theory.Therefore,solutions of the dimensionally reduced theory are also solutions of the higher-dimensional theory.However,in higher dimension these solutions may or may not ex-hibit isotropicity.The solutions which cannot be isotropically lifted to the higher dimension and,therefore,cannot be viewed as p-brane solutions in the higher dimensions,are called stainless solutions[11].In other words,stain-less p-branes are genuinely new solutions of the supergravity theory in the given dimension and should not be treated on the same footing as solutions which are descendants of the higher dimensional p-branes.Weﬁrst brieﬂy review some of the main results on p-brane solutions [8,10,11]and then apply general results to constructing and classifying stainless p-branes in N=2,D=9theory.The p-brane solutions in general involve the metric tensor g MN,a dilatonφand an n-index antisymmetric .The Lagrangian for theseﬁelds takes the formtensor F M1M2···M ne−1L=R−12n!e−aφF2n,(66) where a is a constant given by(29)[8,11].In D=11,the absence of a dilaton implies that∆=4.The value of∆is preserved under the dimen-sional reduction procedure and,hence,all antisymmetric tensors in maximal supergravity theories have∆=4.However,if an antisymmetric tensor used in a particular p-brane solution is formed from a linear combination of the originalﬁeld strengths,then it will have∆<4.An example of this is a solitonic5-brane in N=1,D=10supergravity considered below.We shall be looking for isotropic p-brane solutions for which the metric ansatz is given by[8,11]ds2=e2A dxµdxνηµν+e2B dy m dy m,(67) where xµ(µ=0,···,d−1)are the coordinates of the(d−1)-brane world volume,and y m are the coordinates of the(9−d)-dimensional transverse space.The functions A and B,also the dilatonφ,depend only on r=√This ansatz for the metric preserves an SO(1,d−1)×SO(9−d)subgroup of the original SO(1,8)Lorentz group.For the elementary p-brane solutions,the ansatz for theﬁeld strenght isgiven by[8,11]F mµ1···µn−1=εµ1···µn−1∂m e C,(68)whereεµ1···µn−1≡gµ1ν1···εν1···withε012···=1,and C is a function of r only. The dimension of the brane world volume is d=n−1.For the solitonic p-brane solution,the ansatz for the antisymmetric tensor is given by[8,11]F m1···m n =λεm1···m n py p∆(D−2)ln 1+k˜d A,φ=7ǫa2˜d√√r˜d −1.(72)The solutions(70)-(72)are valid for an n-indexﬁld strength with n>1. When n=1,i.e.˜d=0,there only exists a solitonic solution described by (70)with kr−˜d→klogr and˜d→0.Stainlessness of a p-brane solution crucially depends on a degree of the antisymmtric tensor involved in a solution,and the value of constant a oc-curring in the exponential prefactor.There are two diﬀerent situations when a stainless p-brane solution may arise in a given dimension.In theﬁrst sce-nario,no(D+1)-dimensional theory contains the necessaryﬁeld strength for a brane solution.In particular,if in D dimensions the solution is elemen-tary,the(D+1)-dimensional theory must have aﬁeld strength of degree one higher than that in D dimensional theory.If it is a solitonic solution,the (D+1)-dimensional theory must contain aﬁeld strength of the same degree as in D dimensional theory.In the second case,the requiredﬁeld strengthexists in the (D +1)-dimensional theory,but a p -brane is stainless only if the constant ˆa of a corresponding antisymmtric tensor in (D +1)dimensions is not related to the constant a of the D -dimensional theory as [11]ˆa 2=a 2−2˜d24E 2e −2κϕ12e −2κϕe −2κϕ.(75)The internal metric (75)is not diagonal,therefore,the terms in the La-grangian containing g αβwill not be diagonal as well.To diagonalize theLagrangian,the following redeﬁnitions have to be made:F 2MN +E F 1MN →F (2)MN,F 1MN→F (1)MN ,F ′2MNP +EF ′1MNP →F ′(2)MNP ,F ′1MNP →F ′(1)MNP .(76)Here and throughout this subsection M,N,P =0,···,8denote the curvednine-dimensional world volume indices,whilst R,S,T =0,···,8denote the ﬂat indices.Then the Lagrangian (28)can be written ase −1L =R −12(∂ϕ)2−1√4e 37φ−ϕ(F (2)2)2−18e −47φ(F 2)2−1√12e −17φ−ϕ(F ′(2)3)2−1√whereF2n≡F M1M2···M n F M1M2···M ndenotes the square of an n-indexﬁeld strength,H M=∂M E and the parameter κis set to1/2.If in(77)one retains only oneﬁeld strength and a corresponding dilaton, which for F(i)2and F′(i)is a linear combination ofφandϕ,one arrives at the Lagrangian of the form(66).Then general results described above can be applied to constructing single p-brane solutions in the given supergravity theory.It should be noted that for the purposes ofﬁnding a purely elementary or a purely solitonic p-brane solution,the F F A-term in the Lagrangian and the Chern-Simons modiﬁcations of theﬁeld strengths can be disregarded due to the fact that the constraints implied by these terms are automatically satisﬁed in D=9.However,in general,for certain p-brane solutions,the L F F A term and the Chern-Simons modiﬁcations to theﬁeld strengths give rise to nontrivial equations in some dimensions[10].Good examples illustrating this point are dyonic p-branes in D=4and D=6dimensions.Since our principal interest lies in the stainless p-brane solutions,we have ﬁrst to determine which of the p-branes of N=2,D=9supergravity are stainless.For this,one recalls that the N=2,D=10supergravity contains a2-indexﬁeld strength,a3-indexﬁeld strength and a4-indexﬁeld stregthing the criteria for stainlessness with theˆa2values1,14of a p-brane and the equation(73),weﬁnd that the stainless solutions of N=2,D=9supergravity theory are an elementary particle,an elementary membrane and a solitonic6-brane.Applying(70),we obtain the metrics for these solutionsparticle:ds2= 1+k r6 2/7dy m dy m,(78) membrane:ds2= 1+k r4 3/7dy m dy m,(79) 6−brane:ds2=dxµdxνηµν+ 1+klogr 3/7dy m dy m.(80)It is of interest to note that a solitonic5-brane,which is stainless as a solution to N=1,D=9supergravity theory,does not remain stainless in N= 2,D=9supergravity.This seeming paradox can be resolved if we consider details of the truncation of N=2to N=1supergravity,which contains a dilaton,a2-indexﬁeld strength and a3-indexﬁeld strength.One cannot consistently truncate out either two2-index antisymmetric tensors or a scalar ﬁeld.Nonetheless,it is possible to make a consistent truncation if weﬁrst rotate the scalarﬁelds:ϕ= 8φ1− 8φ2,φ= 8φ1+ 8φ2(81)and then setφ2=F4=H1=F(1)3=F(1)2=0which now is consistent with the equations of motion.Deﬁning˜F2≡√2F(2)2,we get the Lagrangian for the bosonic sector of N=1,D=9supergravity[11,14]:L=eR−112ee−√7φ1(F(2)3)2−12r −1/7 1+k2r 6/7 1+k273e−A−B+C−27φ∂m Cγmγ9ǫijΓjε,δψ0=114e−B+C−27φ∂m CγmǫijΓijε,(85)δψm=∂mε+128e−A+C−27φ∂m Cγmnγ9ǫijΓijε+3√2Aε,γ9ε0=ε0,ǫijΓijε0=ε0,(86)whereε0is a constant spinor.Thus the elementary particle solution preserves half of the supersymmetry.To varify that the elementary membrane solution also preserves half of the supersymmetry,we make a3+9split of the gamma matrices:Γµ=γµ⊗γ7,Γm=1l⊗γm,(87) whereγ7=γ0γ1...γ5in the transverse space andγ1γ2γ3=1l on the world volume.The transformation rules for the fermions becomeδχi=−√6e−B∂mφγ7⊗γmΓiε−1√7e−B−3A+C+17φγµ⊗γ7γmε,(88)δψm=∂mε+128e−B−3A+C+17φ∂n C1l⊗γmnε+2√Scherk-Schwarz dimensional reduction procedure which gives an advantage of constructing the lower dimensional theory in one step,as opposed to the standard Kaluza-Klein step by step dimensional reduction,and also enables one to consider compactiﬁcation on a non-trivial group manifolds[12].We explored the stainless p-brane solutions to the obtained N=2supergravity in D=9.Having derived the supersymmetry transfornation laws for theﬁelds, we were in the position to examine the sypersymmetry of the found stainless p-branes.Discussing the relation of the N=2solutions to the N=1 stainless solutions,it was observed that the stainless solutions of truncated theory may or may not remain stainless in the extended supergravity.The notion of stainlessness was discussed in the case when,along with D=11 supergravity,type IIB supergravity was taken into consideration. AcknowledgementsWe are grateful to E.Sezgin,C.N.Pope,H.Lu and M.J.Duﬀfor useful discussions.References[1]E.Bergshoeﬀ,C.Hull and T.Ortin,Duality in the type-II superstringeﬀective action,QMW-PH-95-2,hep-th/9504081.[2]A.Das and S.Roy,On M-theory and the symmetries of type II stringeﬀective actions,Nucl.Phys.B482(1996)119,hep-th/9605073. [3]E.Cremmer,B.Julia and J.Scherk,Supergravity theory in eleven di-mensions,Phys.Lett.B76(1978)409.[4]L.Romans,Massive N=2a supergravity in ten dimensions,Phys.Lett.169B(1986)374.[5]E.Bergshoeﬀ,M.De Roo,M.B.Green,G.Papadopoulos andP.K.Townsend,Duality of type II7-branes and8-branes,UG-15-95, hep-th/9601150.[6]J.Scherk and J.H.Schwarz,How to get masses from extra dimensions,Nucl.Phys.B153(1979)61.[7]P.M.Cowdall,H.Lu, C.N.Pope,K.S.Stelle and P.K.Townsend,Domain walls in massive supergravities,CTP-TAMU-26-96A,hep-th/9608173.[8]M.J.Duﬀ,R.Khuri,J.X.Lu,Phys.Rept.String solitons259(1995)213.[9]N.Khviengia,Z.Khviengia,H.Lu and C.N.Pope,Intersecting M-branesand bound states,Phys.Lett.B388(1996)21,hep-th/9605077. [10]H.Lu and C.N.Pope,p-brane solitons in maximal supergravities,Nucl.Phys.B465(1996)127,hep-th/9512012.[11]H.Lu,C.N.Pope,E.Sezgin and K.S.Stelle,Stainless super p-branes,Nucl.Phys.B456,(1995)669,hep-th/9508042.[12]A.Salam and E.Sezgin,d=8supergravity,Nucl.Phys.B258(1985)284.[13]H.Lu and C.N.Pope,Multi-scalar p-brane solitons,CTP-TAMU-52/95,hep-th/9512153.[14]S.J.Gates,H.Nishino and E.Sezgin,Class.Quantum Grav.3(1986)21.。

危险化学物质-甲醛安全数据单说明书

METHANOLThis dossier on methanol presents the most critical studies pertinent to the risk assessment of methanol in its use in drilling muds and hydraulic fracturing fluids. It does not represent an exhaustive or critical review of all available data. The information presented in this dossier was obtained primarily from the OECD-SIDS documents on methanol (OECD, 2004a,b), and the ECHA database that provides information on chemicals that have been registered under the EU REACH (ECHA). Where possible, study quality was evaluated using the Klimisch scoring system (Klimisch et al., 1997).Screening Assessment Conclusion – Methanol is classified as a tier 1 chemical and requires a hazard assessment only.1BACKGROUNDMethanol is a liquid at room temperature. It is readily bioavailable and will not bioaccumulate. Methanol exhibits a low toxicity concern for aquatic organisms, terrestrial invertebrates and plants. 2CHEMICAL NAME AND IDENTIFICATIONChemical Name (IUPAC): MethanolCAS RN: 67-56-1Molecular formula: CH4OMolecular weight: 32.04 g/molSynonyms: Methyl alcohol, carbinol, wood spirits, wood alcohol, methylol, wood, columbian spirits, colonial spirit, columbian spirit, methyl hydroxide, monohydroxymethane, pyroxylic spirit, wood naphtha.3PHYSICO-CHEMICAL PROPERTIESKey physical and chemical properties for the substance are shown in Table 1.Table 1 Physico-Chemical Properties of MethanolReference Property Value KlimischscorePhysical state at 20°C and 101.3 kPa Colourless liquid 2 ECHA Melting Point -97.8°********** 2 ECHA Boiling Point 64.7°********** 2 ECHA Density 790 Kg/m3 @ 20°C 2 ECHA Vapour Pressure 16927 Pa @ 25°C 2 ECHA Partition Coefficient (log Pow)-0.77 @ 20°C 2 ECHAProperty Value KlimischReferencescoreWater Solubility >1,000 g/L [miscible] 2 ECHA Viscosity 0.544 – 0.59 mPa s (dynamic) 2 ECHA Methanol is a highly flammable liquid.4DOMESTIC AND INTERNATIONAL REGULATORY INFORMATIONA review of international and national environmental regulatory information was undertaken (Table2). This chemical is listed on the Australian Inventory of Chemical Substances – AICS (Inventory). No conditions for its use were identified. No specific environmental regulatory controls or concerns were identified within Australia and internationally for methanol.Based on an assessment of environmental hazards, NICNAS identified methanol as a chemical of low concern to the environment (NICNAS, 2017). Chemicals of low concern are unlikely to have adverse environmental effects if they are released to the environment from coal seam gas operations.Table 2 Existing International ControlsConvention, Protocol or other international control Listed Yes or No?Montreal Protocol NoSynthetic Greenhouse Gases (SGG) NoRotterdam Convention NoStockholm Convention NoREACH (Substances of Very High Concern) NoUnited States Endocrine Disrupter Screening Program NoEuropean Commission Endocrine Disruptors Strategy No5ENVIRONMENTAL FATE SUMMARYA.SummaryMethanol is readily biodegradable. It has a low adsorptive capacity to soils and is unlikely to bioaccumulate.B.PartitioningMethanol is highly soluble in water. Based upon a Henry's Law constant of 0.461 Pa*m³/mol, it is expected to volatilise from water and moist soil surfaces. It is also expected to volatilise from dry soil surfaces based upon its vapour pressure(PubChem). Vapour-phase methanol will be degraded in the atmosphere by reaction with photochemically-produced hydroxyl radicals; the half-life for this reaction in air is estimated to be 17.2 days (ECHA).C.BiodegradationMethanol is readily biodegradable. In a closed bottle test using seawater, there was 84% and 95% degradation after 10 and 20 days, respectively (Price et al., 1974; ECHA). [Kl. score = 2]In a soil test using [14C]-methanol, there was 53.4% degradation under aerobic conditions after 5 days, as measured by CO2 evolution; and 46.3% degradation under anaerobic conditions after 5 days, as measured by CO2 evolution (Scheunert et al., 1987; ECHA). [Kl. score = 2]If a chemical is found to be readily biodegradable, it is categorised as Not Persistent since its half-life is substantially less than 60 days (DoEE, 2017).D.Environmental DistributionThe adsorption of methanol was investigated in three different soil types at 6°C (Lokke, 1984; ECHA). There was slight adsorption with the sandy soils tested (percentage organic matter of 0.09% and 0.1% in the samples) and with the clay soil (percentage organic matter was 0.22%). Methanol solutions of concentrations of 0.1, 1.0, 9 and 90 mg/L were used in one-hour exposure adsorption studies; the K oc values were between 0.13 and 0.61 for all soil types and at all concentrations. Based upon these K oc values, if released to soil, methanol is expected to have very high mobility. If released into water, due to its high water solubility and low K oc, methanol is not expected to adsorb to suspended solids and sediment in water.E.BioaccumulationThe BCF of methanol in Cyprinus carpio was determined to be 1.0 (Gluth et al. 1985); in Leuciscus idus, the BCF was <10 (Hansch and Leo, 1985; Freitag et al. 1985). Therefore, the potential for bioaccumulation is low.6ENVIRONMENTAL EFFECTS SUMMARYA.SummaryMethanol exhibits a low toxicity concern for aquatic organisms, terrestrial invertebrates, and plants.B.Aquatic ToxicityAcute StudiesTable 3 lists the results of acute aquatic toxicity studies conducted on methanol.Table 3 Acute Aquatic Toxicity Studies on MethanolTest Species Endpoint Results (mg/L)KlimischscoreReferenceBluegill 96-hour LC5015,400 1 Poirer et al. 1986 Salmo gairdneri 96-hour LC5020,100 1 Call et al., 1983 Pimphales promelas 96-hour LC50 28,100 1 Call et al., 1983Test Species Endpoint Results (mg/L)KlimischscoreReferenceDaphnia magna 96-hour EC50 18,260 2 Dorn et al., 2012; ECHA Daphnia magna 48-hour EC50 >10,000 2 Kuehn et al., 1989 Selenastrum capricornutum 96-hour EC50~22,000 2 Cho et al., 2008; ECHA Chlorella pyrenoidosa 10-14 day EC5028,400 2 Stratton and Smith, 1988Chronic StudiesNo adequate chronic studies were identified. Reported studies were either invalid or their reliability was questionable. Methanol belongs to the category of organic chemicals exerting toxicity for aquatic organisms with a non-specific mode of action. The acute and chronic toxicity may be estimated for such kind of chemicals using QSAR methods. The ECOSAR model (version 1.11, US EPA, July 2012) predicts for methanol a chronic toxicity value of about 450 mg/L (equivalent to a NOEC) for Pimephales promelas and a value of 208 mg/L for Daphnia magna (REACH) [Kl. score = 1].C.Terrestrial ToxicityThe terrestrial toxicity studies on methanol are listed below in Table 4.Table 4 Terrestrial Toxicity Studies on MethanolTest Species (Method)Endpoint Results(mg/kg soil dw)KlimischscoreReferenceEarthworm Eisenia fetida (OECD 222) 35-d EC5063-d EC5017,19926,6462 ECHAFolsomia candida (OECD 232) 28-d EC2528-d NOEC*(reproduction)2,8421,0001 ECHAHordeum vulgare (OECD 208)14-d EC5014-d NOEC*(seedling emergence)15,49212,0001 ECHA14-d EC2514-d NOEC*(shoot dry mass)2,5381,55514-d EC2514-d NOEC*(root dry mass)2,8232,59214-d EC2514-d NOEC*(shoot length)4,8852,59214-d EC2514-d NOEC*(root length)5,7524,320* Since only EC25 values were available from the test results, NOECs were derived graphically from the representing treatment means.7CATEGORISATION AND OTHER CHARACTERISTICS OF CONCERNA.PBT CategorisationThe methodology for the Persistent, Bioaccumulative and Toxic (PBT) substances assessment is based on the Australian and EU REACH Criteria methodology (DEWHA, 2009, ECHA, 2008). Methanol is readily biodegradable and thus it does not meet the screening criteria for persistence. Based on an experimental BCF of <10 in fish, methanol does not meet the criteria for bioaccumulation.There are no adequate chronic toxicity studies on methanol. Predicted toxicity based on QSAR methods indicates chronic values > 0.1 mg/L for fish and invertebrates. The acute EC50 values of methanol in fish, invertebrates and algae is >1 mg/L; thus, it does not meet the screening criteria for toxicity.The overall conclusion is that methanol is not a PBT substance.B.Other Characteristics of ConcernNo other characteristics of concern were identified for methanol.8SCREENING ASSESSMENTChemical Name CAS No.Overall PBTAssessment 1Chemical Databases of ConcernAssessment StepPersistence Assessment StepBioaccumulativeAssessment StepToxicity Assessment StepRisk Assessment ActionsRequired3 Listed as a COCon relevantdatabases?Identified asPolymer of LowConcernP criteriafulfilled?Other PConcernsB criteria fulfilled?T criteriafulfilled?AcuteToxicity2ChronicToxicity2Methanol 67-56-1 Not a PBT No No No No No No 1 1 1 Footnotes:1 - PBT Assessment based on PBT Framework.2 - Acute and chronic aquatic toxicity evaluated consistent with assessment criteria (see Framework).3 – Tier 1 – Hazard Assessment only.Notes:NA = not applicablePBT = Persistent, Bioaccumulative and ToxicB = bioaccumulativeP = persistentT = toxic9REFERENCES, ABBREVIATIONS AND ACRONYMSA.ReferencesCall, D.J. et al. (1983). Toxicity and metabolism studies with EPA priority pollutants and related chemicals in freshwater organisms, EPA-600/3-83-095, PB83-263665.Cho, C.-W. et al. (2008). The ecotoxicity of ionic liquids and traditional organic solvents on microalga Selenastrum capricornutum. Ecotoxicol. Environ. Saf. 71: 166-171.Department of the Environment, Water, Heritage and the Arts [DEWHA] (2009). Environmental risk assessment guidance manual for industrial chemicals, Department of the Environment,Water, Heritage and the Arts, Commonwealth of Australia.Department of the Environment and Energy [DoEE]. (2017). Chemical Risk Assessment Guidance Manual: for chemicals associated with coal seam gas extraction, Guidance manual prepared by Hydrobiology and ToxConsult Pty Ltd for the Department of the Environment and Energy, Commonwealth of Australia, Canberra.Dorn, N. et al. (2012). Discrepancies in the acute versus chronic toxicity of compounds with a designated narcotic mechanism. Chemosphere 87: 742-749.ECHA. ECHA REACH database: http://echa.europa.eu/information-on-chemicals/registered-substancesEuropean Chemicals Agency (ECHA). (2008). Guidance on Information Requirements and Chemical Safety Assessment, Chapter R11: PBT Assessment, European Chemicals Agency, Helsinki,Finland.Freitag, D., Lay, P. and Korte, F. (1985). Environmental Hazard Profile of Organic Chemicals: An experimental method for the assessment of the behaviour of organic chemicals in theecosphere by means of simple laboratory tests with 14C labelled chemicals. Chemosphere,14: 1589-1616.Gluth, G. et al. (1985). Accumulation of pollutants in fish. Comp. Biochem. Physiol., 81C: 273 – 277. Hansch, C. and Leo, A.J. (1985). Medchem. Project Issue No.26, Claremont CA, Pomona College.Klimisch, H.J., Andreae, M., and Tillmann, U. (1997). A systematic approach for evaluating the quality of experimental and toxicological and ecotoxicological data. Regul. Toxicol. Pharmacol. 25:1-5.Kuehn, R. et al. (1989). Water Research, 23: 495-499.Lokke, H. (1984). Leaching of ethylene glycol and ethanol in subsoils. Water, Air, and Soil Pollution 22: 373-387.OECD (2004a). IUCLID Data Set for Methanol (CAS No. 67-56-1). Available at:/Hpv/UI/SIDS_Details.aspx?id=39B5D34A-2F5D-4D53-B000-E497B3A3EE89OECD (2004b). Screening Information Dataset (SIDS) Initial Assessment Report for Methanol (CAS No. 67-56-1). Available at: /Hpv/UI/SIDS_Details.aspx?id=39B5D34A-2F5D-4D53-B000-E497B3A3EE89NICNAS. (2017). National assessment of chemicals associated with coal seam gas extraction in Australia,Technical report number 14 - Environmental risks associated with surface handling of chemicals used in coal seam gas extraction in Australia. Project report prepared by theChemicals and Biotechnology Assessments Section (CBAS), in the Chemicals and WasteBranch of the Department of the Environment and Energy as part of the NationalAssessment of Chemicals Associated with Coal Seam Gas Extraction in Australia,Commonwealth of Australia, Canberra.Poirer S.H., Knuth, L.M., Anderson-Buchou, C.D. et al. (1986). Comparative toxicity of methanol and N,N-dimethylformamide to freshwater fish. Bull. Environ. Contam. Toxicol., 37: 615-621.Price, K.S. et al. (1974). Brine shrimp bioassay and seawater BOD of petrochemicals. J. Water Pollution Control Fed. 46: 63-77.Scheunert, I. et al. (1987). Biomineralization rates of 14C-labelled organic chemicals in aerobic and anaerobic suspended soil. Chemosphere 16: 1031-1041.Stratton, G.W., and Smith, T.M. (1988). Interaction of organic solvents with the green alga Chlorella pyrenoidosa, Bull. Environ. Contam. Toxicol., 40: 736-742.B.Abbreviations and Acronyms°C degrees CelsiusBCF bioconcentration factorDEWHA Department of the Environment, Water, Heritage and the Artsdw dry weightEC effective concentrationECHA European Chemicals AgencyEU European Uniong/L grams per litrehPa hectopascalIUPAC International Union of Pure and Applied Chemistrykg/m3kilograms per cubic metrekPa kilopascalLC lethal concentrationmg/kg milligrams per kilogrammg/L milligrams per litremPa s millipascal secondNOEC no observed effective concentrationOECD Organisation for Economic Co-operation and Development Pa m3/mol Pascal metre cubed per gram molecular weightPBT Persistent, Bioaccumulative and ToxicQSAR Quantitative structure-activity relationshipSIDS Screening Information Data Set。

药品国际注册相关英语词汇

1. toxicity [tɔk'sisəti]n. [毒物] 毒性2. content ['kɔntent]n. 内容，目录；满足；容量adj. 满意的vt. 使满足n. (content)人名；(法)孔唐3. substance ['sʌbstəns]n. 物质；实质；资产；主旨4. strictly ['striktli]adv. 严格地；完全地；确实地5. regulate ['reɡjuleit]vt. 调节，规定；控制；校准；有系统的管理6. monograph ['mɔnəɡrɑ:f, -ɡræf]n. 专题著作，专题论文vt. 写关于…的专著7. specified ['spesifaid]v. 指定；详细说明（specify的过去分词）adj. 规定的；详细说明的8. detectedv. 发现（detect的过去分词）；检测到；侦测到adj. 检测到的9. annex [ə'neks, 'æneks]n. 附加物；附属建筑物vt. 附加；获得；并吞10. validation [,væli'deiʃən]n. 确认；批准；生效11. degradation [,deɡrə'deiʃən]n. 退化；降格，降级；堕落；降解12. in-house ['in'haus]adj. 内部的adv. 内部地13. residual solvent剩余溶剂残留溶剂14. characterisation [,kærəktərai'zeiʃən, -ri'z-]n. （英）特性描述；性格化（等于characterization）15. elemental [,eli'mentəl]元素的16. spectrum ['spektrəm]n. 光谱；频谱；范围；余象17. infrared [,infrə'red]n. 红外线adj. 红外线的18. crossing over spectrum交叉谱，交换图谱19. COSY ['kəuzi]化学位移相关谱二维化学位移相关谱相关谱20. enlargement [in'lɑ:dʒmənt]n. 放大；放大的照片；增补物21. X-ray ['eks,rei]n. 射线；射线照片adj. x光的；与x射线有关的vt. 用x光线检查vi. 使用x光22. diffraction [di'frækʃən]n. （光，声等的）衍射，绕射23. chromatogram ['krəumətəɡræm]n. [分化] 色谱图；[分化] 色层分离谱24. comply with照做，遵守25. concentration [,kɔnsən'treiʃən]n. 浓度26. soluble ['sɒljʊb(ə)l]adj. [化学] 可溶的，可溶解的；可解决的27. residue on ignition炽灼残渣28. enantiomeric purity对映体纯度29. assay [ə'sei]n.含量测定30. injection volume进样量注入体积进样体积31. overhead tank压力罐；[化工] 高位槽，高位罐32. Deviation [diːvɪ'eɪʃ(ə)n]n. 偏差；误差；背离33. appendix [ə'pendɪks]n. 附录；阑尾；附加物34. Discharge the aqueous layer分掉水层35. agitator ['ædʒɪteɪtə]n. 搅拌器36. Adjust [ə'dʒʌst]vt. 调整，使…适合；校准vi. 调整，校准；适应37. crystallize ['kristə,laiz]vt. 使结晶；明确；使具体化；做成蜜饯vi. 结晶，形成结晶；明确；具体化38. as per proportion 2:1按2:1比例39. nomenclature [nə(ʊ)'meŋklətʃə; 'nəʊmən,kleɪtʃə]n. 命名法；术语40. molecular formulan. [化学] 分子式41. elucidation [ɪ,l(j)uːsɪ'deɪʃ(ə)n]n. 结构鉴定42. accordance [ə'kɔːd(ə)ns]n. 一致；和谐43. active substance活性物质；放射性物质；有效物质44. microbial [maɪ'krəʊbɪəl]adj. 微生物的；由细菌引起的45. spectrophotometry [,spektrəufəu'tɔmitri]n. [分化][光] 分光光度法；[分化] 分光光度测定法46. desiccator ['desɪkeɪtə]n. 干燥器；干燥剂；干燥工47. potassium bromide[无化] 溴化钾48. platinum crucible白金坩埚；铂坩埚49. mobile phase（色谱分析的）[分化] 流动相50. diluent ['dɪljʊənt]n. 稀释液；冲淡剂adj. 稀释的；冲淡的51. racemic [rə'siːmɪk; rə'semɪk]adj. 外消旋的；消旋酸的52. respectively [rɪ'spektɪvlɪ]adv. 分别地；各自地，独自地53. relative retention time相对保留时间54. resolution [rezə'luːʃ(ə)n]n. [物] 分辨率；决议；解决；决心55. RSDabbr. 无线电科学部（radio science division）56. consecutive [kən'sekjʊtɪv]adj. 连贯的；连续不断的57. average ['æv(ə)rɪdʒ]n. 平均；平均数；海损adj. 平均的；普通的vt. 算出…的平均数；将…平均分配；使…平衡vi. 平均为；呈中间色58. polypropylene plasticpolypropylene plastic: pp塑料|聚丙烯塑料PP-R(polypropylene) plastic: PP-R(聚丙烯)塑料pp-r (polypropylene) plastic: pp-r聚丙烯塑料59. vail [veɪl]？60. gradient ['greɪdɪənt]n. [数][物] 梯度；坡度；倾斜度adj. 倾斜的；步行的61. stock solution[分化] 储备溶液；原液；贮备溶液62. correction factor[数][分化] 校正因子；校正系数63. retention time[分化] 保留时间；[电子] 保持时间64. split [splɪt]n. 劈开；裂缝adj. 劈开的vt. 分离；使分离；劈开；离开；分解vi. 离开；被劈开；断绝关系65. head space[化学] 液面上空间；顶部空间；灌头顶隙66. LOOP [luːp]n. 回路67. flask [flɑːsk]n. [分化] 烧瓶；长颈瓶，细颈瓶；酒瓶，携带瓶68. bacterial [bæk'tɪərɪəl]adj. [微] 细菌的69. mould [məʊld]n. 模具；霉vt. 浇铸；用泥土覆盖vi. 发霉70. yeast [jiːst]n. 酵母；泡沫；酵母片；引起骚动因素71. filter cartridge滤芯；滤筒72. agar ['eɪgɑː]n. 琼脂（一种植物胶）73. perspective [pə'spektɪv]n. 观点；远景；透视图adj. 透视的74. disclaimer [dɪs'kleɪmə]n. 不承诺，免责声明；放弃，拒绝75. outline ['aʊtlaɪn]n. 轮廓；大纲；概要；略图vt. 概述；略述；描画…轮廓76. observation [ɒbzə'veɪʃ(ə)n]n. 观察；监视；观察报告77. regulatory ['reɡjulətəri]adj. 管理的；控制的；调整的78. formally ['fɔːməlɪ]adv. 正式地；形式上79. policy ['pɒləsɪ]n. 政策，方针；保险单80. guideline ['gaɪdlaɪn]n. 指导方针参考81. efficacy ['efɪkəsɪ]n. 功效，效力82. Developed by自行研制83. amendment [ə'men(d)m(ə)nt]n. 修正案；改善；改正84. be granted被授予85. provision [prə'vɪʒ(ə)n]n. 规定；条款；准备；[经] 供应品vt. 供给…食物及必需品86. assessment [ə'sesmənt]n. 评定；估价87. chronic ['krɒnɪk]adj. 慢性的；长期的；习惯性的n. (chronic)人名；(英)克罗尼克88. duration [djʊ'reɪʃ(ə)n]n. 持续，持续的时间，期间[语音学]音长，音延89. paediatric [,piːdɪ'ætrɪk]adj. [儿科] 儿科的；儿科学的90. category ['kætɪg(ə)rɪ]n. 种类，分类；[数] 范畴91. derived from来源于92. pharmacogenetics [,fɑːməkəʊdʒɪ'netɪks]n. 遗传药理学；药物基因学93. genomic [dʒiː'nəʊmɪk]adj. 基因组的；染色体的94. genomics [dʒə'nəumiks]n. 基因组学；基因体学95. expedite ['ekspɪdaɪt]vt. 加快；促进；发出adj. 畅通的；迅速的；方便的96. transmission [trænz'mɪʃ(ə)n; trɑːnz-; -ns-]n. 传动装置，[机] 变速器；传递；传送；播送97. implement ['ɪmplɪm(ə)nt]n. 工具，器具；手段vt. 实施，执行；实现，使生效98. implementation [ɪmplɪmen'teɪʃ(ə)n]n. [计] 实现；履行；安装启用99. pharmacovigilance药物警戒；药物安全监视100. dose-response ['dəusri,spɔns]n. 剂量反应；剂量效应101. ethnic ['eθnɪk]adj. 种族的；人种的102. addendum [ə'dendəm]n. 附录，附件；补遗；附加物103. geriatric [,dʒerɪ'ætrɪk]n. 老年病人；衰老老人adj. 老人的；老年医学的104. statistical [stə'tɪstɪk(ə)l]adj. 统计的；统计学的105. pediatric [,pi:dɪ'ætrɪk]adj. 小儿科的106. investigation [ɪn,vestɪ'geɪʃ(ə)n]n. 调查；调查研究107. therapeutic [,θerə'pjuːtɪk]n. 治疗剂；治疗学家adj. 治疗的；治疗学的；有益于健康的108. antihypertensive drugAntihypertensive drug: 抗高血压药|抗高血压药物|降压药central antihypertensive drug: 中枢性降压药centrally acting antihypertensive drug: 中枢降压药109. qualify ['kwɒlɪfaɪ]vi. 取得资格，有资格vt. 限制；使具有资格；证明…合格110. qualification [,kwɒlɪfɪ'keɪʃ(ə)n]n. 资格；条件；限制；赋予资格111. biomarker [,baiə'mɑ:kə]n. 生物标志物；生物标记；生物指标112. format ['fɔːmæt]n. 格式；版式；开本vt. 使格式化；规定…的格式vi. 设计版式113. submission [səb'mɪʃ(ə)n]n. 投降；提交（物）；服从；（向法官提出的）意见；谦恭114. multi-regional跨地区的，跨区域的115. character ['kærəktə]n. 性格，品质；特性；角色；[计] 字符vt. 印，刻；使具有特征116. characteristic [kærəktə'rɪstɪk]adj. 典型的；特有的；表示特性的n. 特征；特性；特色117. headspace vial顶空瓶118. sonication [,sɒnɪ'keɪʃən]n. 声波降解法119. pipette [pɪ'pet]n. 移液管；吸移管vt. 用移液器吸取120. slightly soluble微溶121. freely soluble易溶解的122. practically insoluble几乎不溶的123. in-process control中间过程控制124. potassium [pə'tæsɪəm]n. [化学] 钾125. carbonate ['kɑːbəneɪt]n. 碳酸盐vt. 使充满二氧化碳；使变成碳酸盐126. moisten ['mɒɪs(ə)n]vt. 弄湿；使…湿润vi. 潮湿；变潮湿127. hydrochloric acid[无化] 盐酸128. erlenmeyer flask ['ə:lən,maiə]锥形烧瓶；爱伦美氏烧瓶129. stopper ['stɒpə]n. 塞子；阻塞物；制止者；妨碍物vt. 用塞子塞住130. Carbon Dioxide–Free Wate无CO2水131. volatile ['vɒlətaɪl]n. 挥发物；有翅的动物adj. [化学] 挥发性的；不稳定的；爆炸性的；反覆无常的n. (volatile)人名；(意)沃拉蒂莱132. flammable ['flæməb(ə)l]n. 易燃物adj. 易燃的；可燃的；可燃性的133. aqueous ['eɪkwɪəs]adj. 水的，水般的134. nonvolatile matter不挥发物135. evaporate [ɪ'væpəreɪt]vt. 使……蒸发；使……脱水；使……消失vi. 蒸发，挥发；消失，失踪136. lustrous ['lʌstrəs]adj. 有光泽的；光辉的137. neutral ['njuːtr(ə)l]n. 中立国；中立者；非彩色；齿轮的空档adj. 中立的，中性的；中立国的；非彩色的138. turbidness ['tə:bidnis]n. 浓密；混浊139. constant ['kɒnst(ə)nt]n. [数] 常数；恒量adj. 不变的；恒定的；经常的n. (constant)人名；(德)康斯坦特140. thoroughly [ˈθʌrəli]adv. 彻底地，完全地141. vinegary fiavourvinegary fiavour: 醋味142. nasil[动] 鼻嗅143. ignite [ɪg'naɪt]vt. 点燃；使燃烧；使激动vi. 点火；燃烧144. platinum wire[材] 铂丝145. platinum filament铂丝146. equivalent [ɪ'kwɪv(ə)l(ə)nt]n. 等价物，相等物adj. 等价的，相等的；同意义的147. coliform ['kɒlɪfɔːm]n. 大肠菌（等于coliform bacillus）adj. 像大肠菌的；筛状的148. organoleptic test感官试验感官检验149. acidity or alkalinityAcidity or Alkalinity: 酸碱度|酸度或碱度|或碱的酸碱性150. immersed [ɪ'mɜːst]adj. 浸入的；专注的v. 浸（immerse的过去式和过去分词）；沉湎于151. deionized water[化学] 去离子水152. vertical axis[力] 垂直轴；纵轴153. vice versa [,vaisi'və:sə]反之亦然154. volumetric solutionn. 滴定液；标定溶液155. area normalization method面积归一化法156. sterilization [,sterəlaɪ'zeɪʃən]n. 消毒，杀菌157. sucker ['sʌkə]n. 吸管；乳儿；易受骗的人vt. 从……除去吸根vi. 成为吸根；长出根出条158. heatproof ['hi:t'pru:f]adj. 抗热的，耐热的vt. 使……隔热；使……耐热159. nitrate ['naɪtreɪt]n. 硝酸盐vt. 用硝酸处理160. ammonia-free waterAmmonia-Free Water: 不含氨的水161. membrane filtration methodmembrane filtration method: 薄膜过滤法|微孔滤膜法|滤膜法filter membrane filtration method: 滤膜过滤法centrifuging membrane filtration method: 离心薄膜过滤法162. declaration [deklə'reɪʃ(ə)n]n. （纳税品等的）申报；宣布；公告；申诉书申明163. genetically modified转基因的164. organism ['ɔːg(ə)nɪz(ə)m]n. 有机体；生物体；微生物165. genetically modified organism基因改造生物166. In accordance with依照；与…一致167. Melting range熔距；熔化范围；熔点区间168. Specific rotation[光] 旋光率；比旋度169. sodium hydroxiden. [无化] 氢氧化钠170. acetate ['æsɪteɪt]n. [有化] 醋酸盐；醋酸纤维素及其制成的产品171. Gradually ['grædʒʊlɪ; 'grædjʊəlɪ]adv. 逐步地；渐渐地172. tawny ['tɔːnɪ]n. 黄褐色；茶色adj. 黄褐色的；茶色的173. precipitate [prɪ'sɪpɪteɪt]n. [化学] 沉淀物vt. 使沉淀；促成；猛抛；使陷入adj. 突如其来的；猛地落下的；急促的vi. [化学] 沉淀；猛地落下；冷凝成为雨或雪等174. yellowish-brownn. 黄棕175. on standingon standing: 静置时|一经静置|静置以后176. on shaking振摇后177. be concordant with与……一致178. phosphorous pentoxide五氧化二磷179. under reduced pressureunder reduced pressure: 负压|在减压下Distillation under reduced pressure: 减压蒸馏concentrated under reduced pressure: 减压浓缩180. Residue on ignition炽灼残渣181. butyl acetate[有化] 乙酸丁酯；醋酸丁酯182. Pyrogensn. 致热源；焦精（pyrogen的复数）183. sonicate ['sɒnɪkeɪt]n. 对……进行声处理184. chloride ['klɔːraɪd]n. 氯化物185. sodium chloride[无化] 氯化钠，食盐186. hydroxide [haɪ'drɒksaɪd]n. [无化] 氢氧化物；羟化物187. parenteral administration肠胃外投药,注射给药188. rapidly ['ræpɪdlɪ]adv. 迅速地；很快地；立即189. persist [pə'sɪst]vi. 存留，坚持；持续，固执vt. 坚持说，反复说190. persist for持续到191. equivalent to等于，相当于；与…等值192. storage ['stɔːrɪdʒ]n. 存储；仓库；贮藏所193. preserve [prɪ'zɜːv]n. 保护区；禁猎地；加工成的食品vt. 保存；保护；维持；腌；禁猎194. hermetically [hə:'metikəli]adv. 密封地，不透气地；炼金术地195. granules [grænju:ls]n. 粒斑，颗粒（granule的复数）；颗粒剂196. spray [spreɪ]n. 喷雾；喷雾器；水沫vt. 喷射vi. 喷197. crystalline ['krɪst(ə)laɪn]adj. 透明的；水晶般的；水晶制的198. crystalline powdercrystalline powder: 晶体粉末|结晶性粉末|结晶粉末199. acetonitrile [ə,siːtə(ʊ)'naɪtraɪl; ,æsɪtəʊ-] n. [有化] 乙腈；氰化甲烷200. methanol ['meθənɒl]n. [有化] 甲醇（methyl alcohol）201. be identical with与…相同/一致202. principal peak主峰203. neutral solution[化学] 中性溶液204. liberate ['lɪbəreɪt]vt. 解放；放出；释放可用于化学反应中某种气味的产生205. mineral ['mɪn(ə)r(ə)l]n. 矿物；（英）矿泉水；无机物；苏打水（常用复数表示）adj. 矿物的；矿质的206. mineral acid矿物酸；[无化] 无机酸207. acetatesn. [有化] 醋酸盐，[有化] 乙酸盐；醋酸纤维素208. aluminium [æl(j)ʊ'mɪnɪəm]n. 铝adj. 铝的209. aluminium saltsaluminium salts: 铝盐|铝系絮凝剂aluminium and iron salts: 铝盐和铁盐210. ammonium [ə'məʊnɪəm]n. [无化] 铵；氨盐基211. ammonium salts【无机化学】铵盐212. antimony ['æntɪmənɪ]n. [化学] 锑（符号sb）213. barium ['beərɪəm]n. [化学] 钡（一种化学元素）214. barium salts215. benzoates ['benzəʊeɪt]n. 苯酸盐；安息香酸盐216. bismuth ['bɪzməθ]n. [化学] 铋217. bismuth salts铋盐218. borate ['bɔːreɪt]n. [无化][有化] 硼酸盐vt. 用硼酸处理；使与硼酸混合219. bromide ['brəʊmaɪd]n. [无化] 溴化物；庸俗的人；陈词滥调220. calcium ['kælsɪəm]n. [化学] 钙221. bicarbonate [baɪ'kɑːbəneɪt; -nət]n. 碳酸氢盐；重碳酸盐；酸式碳酸盐222. citrate ['sɪtreɪt]n. 柠檬酸盐223. copper ['kɒpə]n. 铜；铜币；警察adj. 铜的vt. 镀铜于n. (copper)人名；(英)科珀224. ferric ['ferɪk]adj. 铁的；[无化] 三价铁的；含铁的n. (ferric)人名；(法)费里克225. ferrous ['ferəs]adj. [化学] 亚铁的；铁的，含铁的226. iodide ['aɪədaɪd]n. [无化] 碘化物227. lactates [læk'teɪt]vi. 分泌乳汁；喂奶n. [有化] 乳酸盐228. lithium ['lɪθɪəm]n. 锂（符号li）229. magnesium [mæg'niːzɪəm]n. [化学] 镁230. malonylurea [,mæləniljuə'riə]n. 丙二酰脲；巴比土酸231. mercuric [mɜː'kjʊərɪk]adj. [无化] 汞的；水银的232. mercurous ['mɜːkjʊrəs]adj. 水银的；[无化] 亚汞的；含水银的233. organic fluorinated compounds含氟有机化合物234. fluorinate ['flʊərɪneɪt; 'flɔː-]vt. 使与氟素化合235. fluorine ['flʊəriːn; 'flɔː-]n. [化学] 氟236. phosphate ['fɒsfeɪt]n. 磷酸盐；皮膜化成237. primary aromatic amines初级芳香胺（primary aromatic amine的复数）238. aromatic amines芳香胺；芳香族碳氢基氨239. aromatic [ærə'mætɪk]n. 芳香植物；芳香剂adj. 芳香的，芬芳的；芳香族的240. amines [ə'mi:ns]n. 胺类；有机胺类（amine的复数）241. salicylate [sə'lɪsɪlət]n. [有化] 水杨酸盐242. silver ['sɪlvə]n. 银；银器；银币；银质奖章；餐具；银灰色adj. 银的；含银的；有银色光泽的；口才流利的；第二十五周年的婚姻vt. 镀银；使有银色光泽vi. 变成银色n. (silver)人名；(法)西尔韦；(英、德、芬、瑞典)西尔弗243. silver saltsn. 银盐244. sodium ['səʊdɪəm]n. [化学] 钠（11号元素，符号na）245. stannous ['stænəs]adj. 锡的；含锡的；含二价锡的246. stannous saltstannous salt: 亚锡盐|亚锡酸盐organic stannous salt: 有机亚锡盐247. sulfate ['sʌlfeɪt]n. [无化] 硫酸盐vt. 使成硫酸盐；用硫酸处理；使在上形成硫酸铅沉淀vi. 硫酸盐化248. sulfite ['sʌlfaɪt]n. [无化] 亚硫酸盐（等于sulphite）249. bisulfite [,baɪ'sʌlfaɪt]n. [无化] 重亚硫酸盐；酸性亚硫酸盐250. tartrate ['tɑːtreɪt]n. [有化] 酒石酸盐251. tropane托品烷252. alkaloide生物碱253. tropane alkaloidstropane alkaloids: 烷类生物碱|烷生物碱|莨菪烷类生物碱254. zinc [zɪŋk]n. 锌vt. 镀锌于…；涂锌于…；用锌处理255. feed Port进料口256. orifice ['ɒrɪfɪs]n. [机] 孔口257. inlet ['ɪnlet]n. 入口，进口；插入物258. potassium dihydrogen phosphate[肥料] 磷酸二氢钾259. dihydrogen二氢260. phosphoric [fɒs'fɒrɪk]adj. 磷的，含磷的261. phosphoric acid磷酸262. full scale全尺寸；原大的；完全的；全刻度的；满量程263. attenuation [ə,tenjʊ'eɪʃən]n. [物] 衰减；变薄；稀释264. disregard [dɪsrɪ'gɑːd]n. 忽视；不尊重vt. 忽视；不理；漠视；不顾265. vacuum ['vækjʊəm]n. 真空；空间；真空吸尘器adj. 真空的；利用真空的；产生真空的vt. 用真空吸尘器清扫266. bonded silica gelbonded silica gel: 键合硅胶bonded silica gel adsorption: 吸附stearyl bonded silica gel: 十八烷基键合硅胶267. particle size[岩] 粒度；颗粒大小268. octadecylsilaneoctadecylsilane: 十八烷基硅烷n-octadecylsilane: 正十八烷基硅烷octadecylsilane chemically bonded silica: 十八烷基硅烷键合硅胶269. silane ['sɪleɪn]n. [无化][电子] 硅烷；矽烷270. pack with塞进；挤进；塞满了东西；某地方挤满了人271. neutralize ['nju:trəlaiz]vt. 抵销；使…中和；使…无效；使…中立vi. 中和；中立化；变无效272. with reference to关于，根据（等于in reference to）273. external [ɪk'stɜːn(ə)l; ek-]n. 外部；外观；外面adj. 外部的；表面的；[药] 外用的；外国的；外面的274. external standard method[分化] 外标法275. capsule ['kæpsjuːl; -sjʊl]n. 胶囊；[植] 蒴果；太空舱；小容器adj. 压缩的；概要的vt. 压缩；简述276. apart from远离，除…之外；且不说；缺少277. other than除了；不同于278. reflux condenser[化工] 回流冷凝器；回龄凝器279. sachet ['sæʃeɪ]n. 香囊；小袋280. instrument ['ɪnstrʊm(ə)nt]n. 仪器；工具；乐器；手段；器械281. EDQMEDQM: 欧洲药品质量管理局(European Directorate For Quality Medicines) 282. compression [kəm'preʃ(ə)n]n. 压缩，浓缩；压榨，压迫283. extract [ˈekstrækt]n. 汁；摘录；榨出物；选粹vt. 提取；取出；摘录；榨取284. certificate [sə'tɪfɪkət]n. 证书；执照，文凭vt. 发给证明书；以证书形式授权给…；用证书批准285. supersede [,suːpə'siːd; ,sjuː-]vt. 取代，代替；紧接着……而到来vi. 推迟行动286. subsequent ['sʌbsɪkw(ə)nt]adj. 后来的，随后的287. carton ['kɑːt(ə)n]n. 纸板箱；靶心白点vt. 用盒包装vi. 制作纸箱n. (carton)人名；(英、西)卡顿；(法)卡尔东288. aluminium foil铝箔（作包装材料）；锡箔纸289. dossier ['dɒsɪə; -ɪeɪ; -jeɪ]n. 档案，卷宗；病历表册n. (dossier)人名；(法)多西耶290. in accordance with依照；与…一致291. render ['rendə]n. 打底；交纳；粉刷vt. 致使；提出；实施；着色；以…回报vi. 给予补偿n. (render)人名；(英、德)伦德尔292. void [vɒɪd]n. 空虚；空间；空隙adj. 空的；无效的；无人的vt. 使无效；排放n. (void)人名；(俄)沃伊德293. grant [grɑːnt]n. 拨款；[法] 授予物vt. 授予；允许；承认vi. 同意n. (grant)人名；(瑞典、葡、西、俄、罗、英、塞、德、意)格兰特；(法)格朗294. establish [ɪ'stæblɪʃ; e-]vi. 植物定植vt. 建立；创办；安置295. notification [,nəʊtɪfɪ'keɪʃn]n. 通知；通告；[法] 告示296. manufacturer [,mænjʊ'fæktʃ(ə)rə(r)]n. 制造商；[经] 厂商297. performing partyperforming party: 履约方|参与履约方298. responsible party责任方299. consultedv. 请教，咨询（consult过去式）300. release [rɪ'liːs]n. 释放；发布；让与vt. 释放；发射；让与；允许发表301. respective [rɪ'spektɪv]adj. 分别的，各自的302. territory ['terɪt(ə)rɪ]n. 领土，领域；范围；地域；版图303. generate ['dʒenəreɪt]vt. 使形成；发生；生殖304. refrigeration [rɪ,frɪdʒə'reɪʃən]n. 制冷；冷藏；[热] 冷却305. Equivalent [ɪ'kwɪv(ə)l(ə)nt]n. 等价物，相等物adj. 等价的，相等的；同意义的306. capillary [kə'pɪlərɪ]n. 毛细管adj. 毛细管的；毛状的307. Vaporizer ['veɪpəraɪzə]n. 汽化器；喷雾器；蒸馏器308. general noticesgeneral notices: 凡例|相应的总要求General Notices and Accelerated Revision: 凡例修订Notices of General Meetings: 股东大会召开公告309. general principles通则；总则310. abbreviation [əbriːvɪ'eɪʃ(ə)n]缩写，缩写词311. enact [ɪ'nækt; e-]vt. 制定法律；颁布；扮演；发生312. promulgate ['prɒm(ə)lgeɪt]vt. 公布；传播；发表313. enforce [ɪn'fɔːs; en-]vt. 实施，执行；强迫，强制314. enforcement [en'fɔːsm(ə)nt]n. 执行，实施；强制315. issue for enforcementissue for enforcement: 颁行316. national standard[标准] 国家标准317. quote [kwəʊt]n. 引用vi. 报价；引用；引证vt. 报价；引述；举证318. compendium [kəm'pendɪəm]n. 纲要；概略319. denote [dɪ'nəʊt]vt. 表示，指示320. in addition to除…之外(同besides)321. so as to以便；以致322. serve as担任…，充当…；起…的作用323. interpretation [ɪntɜːprɪ'teɪʃ(ə)n]n. 解释；翻译；演出324. obviate ['ɒbvɪeɪt]vt. 排除；避免；消除325. replication [replɪ'keɪʃ(ə)n]n. 复制；回答；反响326. replica ['replɪkə]n. 复制品，复制物327. adopt [ə'dɒpt]vi. 采取；过继vt. 采取；接受；收养；正式通过328. adopt inadopt in: 采用adopt in time: 及时采取329. admit [əd'mɪt]vi. 承认；容许vt. 承认；准许进入；可容纳330. cite [saɪt]vt. 引用；传讯；想起；表彰331. be specified for针对……而言332. medicament [mɪ'dɪkəm(ə)nt; 'medɪk-]n. 药剂；医药vt. 用药物治疗333. violate ['vaɪəleɪt]vt. 违反；侵犯，妨碍；亵渎334. in spite尽管335. airtight container密封容器336. humidity [hjʊ'mɪdɪtɪ]n. [气象] 湿度；湿气337. illumination [ɪ,ljuːmɪ'neɪʃən]n. 照明；[光] 照度；启发；灯饰（需用复数）；阐明338. Oxidative ['ɒksɪdeɪtɪv]adj. [化学] 氧化的339. Commitment [kə'mɪtm(ə)nt]n. 承诺，保证；委托；承担义务；献身340. apparatus [ˌæpəˈreɪtəs]n. 装置，设备；仪器；器官341. monitor ['mɒnɪtə]n. 监视器；监听器；监控器；显示屏；班长vt. 监控342. editorial [edɪ'tɔːrɪəl]n. 社论adj. 编辑的；社论的343. editorial board编辑委员；编辑部344. preface ['prefəs]n. 前言；引语vt. 为…加序言；以…开始vi. 作序345. designation [dezɪg'neɪʃ(ə)n]n. 指定；名称；指示；选派头衔，职位346. production capacity生产能力；生产力347. expansion [ɪk'spænʃ(ə)n; ek-]n. 膨胀；阐述；扩张物348. expiration date[贸易] 截止日期349. initiate [ɪ'nɪʃɪeɪt]n. 开始；新加入者，接受初步知识者vt. 开始，创始；发起；使初步了解adj. 新加入的；接受初步知识的350. monotherapy单药治疗单一疗法351. genotype ['dʒenətaɪp; 'dʒiːn-]n. 基因型；遗传型352. dosage regimen给药方案353. interferon [,ɪntə'fɪərɒn]n. [生化][药] 干扰素354. peginterferon聚乙二醇干扰素α-2a355. prescribe [prɪ'skraɪb]vt. 规定；开处方vi. 规定；开药方356. infection [ɪn'fekʃ(ə)n]n. 感染；传染；影响；传染病357. ineligible [ɪn'elɪdʒɪb(ə)l]n. 无被选资格的人adj. 不合格的；不适任的；无被选资格的358. interferon-based therapy基于干扰素治疗359. assessment of the potential benefits and risks 潜在利益与风险评估360. hepar ['hi:pɑ:]n. [解剖] 肝361. liver ['lɪvə]n. 肝脏；生活者，居民362. hepatic [hɪ'pætɪk]adj. 肝的；肝脏色的；治肝病的363. hepatocyte ['hepətəʊsaɪt; he'pætə(ʊ)-] n. [细胞] 肝细胞364. hepatocellular [,hepətəu'seljulə]adj. 肝细胞的365. carcinoma [,kɑːsɪ'nəʊmə]n. [肿瘤] 癌366. hepatocellular carcinoma肝细胞癌；肝细胞性肝癌367. renal ['riːn(ə)l]adj. [解剖] 肾脏的，[解剖] 肾的368. kidney ['kɪdnɪ]n. [解剖] 肾脏；腰子；个性n. (kidney)人名；(英)基德尼369. severe [sɪ'vɪə]adj. 严峻的；严厉的；剧烈的；苛刻的370. drug interactions药物相互作用371. convert [kən'vɜːt]n. 皈依者；改变宗教信仰者vt. 使转变；转换…；使…改变信仰vi. 转变，变换；皈依；改变信仰n. (convert)人名；(法)孔韦尔372. predominant [prɪ'dɒmɪnənt]adj. 主要的；卓越的；支配的；有力的；有影响的373. circulate ['sɜːkjʊleɪt]vt. 使循环；使流通；使传播vi. 传播，流传；循环；流通374. metabolite [mɪ'tæbəlaɪt]n. [生化] 代谢物375. account for对…负有责任；对…做出解释；说明……的原因；导致；（比例）占376. substrate ['sʌbstreɪt]n. 基质；基片；底层（等于substratum）；酶作用物377. breast cancer乳腺癌378. resistance [rɪ'zɪst(ə)ns]耐受性，抗性n. 阻力；电阻；抵抗；反抗；抵抗力379. inducer [ɪn'djuːsə]n. [遗] 诱导物；引诱者；导流片；电感器380. coadministration同时服用381. inhibit [ɪn'hɪbɪt]vt. 抑制；禁止382. alteration [ɔːltə'reɪʃ(ə)n; 'ɒl-]n. 修改，改变；变更383. comment ['kɒment]n. 评论；意见；批评vi. 发表评论；发表意见vt. 为…作评语n. (comment)人名；(德)科门特；(法)科芒384. clinical comment临床评价385. impairment [ɪm'peəm(ə)nt]n. 损伤，损害386. renal impairment肾损害387. undergo [ʌndə'gəʊ]vt. 经历，经受；忍受388. as professionally prescribed遵医嘱389. cold symptomsCold Symptoms: 感冒症状alleviate cold symptoms: 缓解感冒症状common cold symptoms: 感冒症状390. pregnant ['pregnənt]adj. 怀孕的；富有意义的391. breastfeeding ['brest,fi:diŋ]n. 母乳哺育v. 用母乳喂养（breastfeed的现在分词）392. consult [kən'sʌlt]vi. 请教；商议；当顾问vt. 查阅；商量；向…请教393. preservatives [prɪ'zɝvətɪv]n. 防腐的（preservative的复数）；[助剂] 防腐剂；保存剂394. artificial [ɑːtɪ'fɪʃ(ə)l]adj. 人造的；仿造的；虚伪的；非原产地的；武断的395. flavour ['fleɪvə]n. 香味；滋味vt. 给……调味；给……增添风趣396. sweetenersn. 甜味剂（sweetener的复数形式）397. artificial flavoursArtificial flavours: 香味No artificial flavours: 不含人工香料|不含野生香料|无添加香料Artificial Colours Or Flavours: 人工色素香料398. wound [wuːnd]n. 创伤，伤口vt. 使受伤vi. 受伤，伤害399. expiry [ɪk'spaɪrɪ; ek-]n. 满期，逾期；呼气；终结400. expiring date到期日；有效期限；失效日期401. regardless of不顾，不管402. diameter [daɪ'æmɪtə]n. 直径403. anhydrous [æn'haɪdrəs]adj. 无水的404. hygroscopic [haɪgrə(ʊ)'skɒpɪk]adj. 吸湿的；湿度计的；易潮湿的405. multiply ['mʌltɪplaɪ]adj. 多层的；多样的vt. 乘；使增加；使繁殖；使相乘vi. 乘；繁殖；增加adv. 多样地；复合地406. pharmaceutical excipients药用辅料407. excipient [ek'sɪpɪənt]n. [药] 赋形剂408. vehicles ['viɪkl]赋形剂n. [车辆] 车辆（vehicle的复数形式）；交通工具409. hypochlorite [,haɪpəʊ'klɔːraɪt]n. [无化] 次氯酸盐；低氧化氯410. thiosulfate [,θaɪəʊ'sʌlfeɪt]n. [无化] 硫代硫酸盐411. sodium thiosulfate[无化] 硫代硫酸钠412. quench [kwen(t)ʃ]急冷vt. 熄灭，[机] 淬火；解渴；结束；冷浸vi. 熄灭；平息413. dehydration [,diːhaɪ'dreɪʃən]n. 脱水，干燥414. filter ['fɪltə]n. 滤波器；[化工] 过滤器；筛选；滤光器vt. 过滤；渗透；用过滤法除去vi. 滤过；渗入；慢慢传开n. (filter)人名；(德)菲尔特415. dimethyl sulfoxide二甲亚砜416. centrifuge ['sentrɪfjuːdʒ]n. 离心机；[机][化工] 离心分离机vt. 用离心机分离；使…受离心作用417. saturated ['sætʃəreɪtɪd]v. 使渗透，使饱和（saturate的过去式）adj. 饱和的；渗透的；深颜色的418. brine [braɪn]n. 卤水；盐水；海水n. (brine)人名；(阿拉伯)布里内；(英)布赖恩vt. 用浓盐水处理（或浸泡）419. sampling ['sɑːmplɪŋ]n. 取样；抽样v. 取样；抽样（sample的ing形式）420. evacuate [ɪ'vækjʊeɪt]vt. 疏散，撤退；排泄vi. 疏散；撤退；排泄421. evacuate air排出空气422. juge endpoint判断终点423. developing solvent[分化] 展开剂；显影溶剂424. catalyst ['kæt(ə)lɪst]n. [物化] 催化剂；刺激因素425. milligram ['miliɡræm]n. 毫克426. litre升427. millilitre ['mili,li:tə]n. [计量] 毫升428. methylamine [miː'θaɪləmiːn]n. [有化] 甲胺429. conical ['kɒnɪk(ə)l]adj. 圆锥的；圆锥形的430. conical flask锥形烧瓶；锥形瓶431. methyl ['miːθaɪl; 'meθ-; -θɪl]n. [有化] 甲基；木精432. sulphuric [sʌl'fjʊərɪk]adj. 硫磺的；含多量硫磺的433. odor ['əudə]n. 气味；名声n. (odor)人名；(匈)欧多尔434. evaporation [ɪ,væpə'reɪʃən]n. 蒸发；消失435. evaporation pan[分化] 蒸发皿436. oven ['ʌv(ə)n]n. 炉，灶；烤炉，烤箱(也可用作蒸发皿)437. turbid ['tɜːbɪd]adj. 浑浊的；混乱的；雾重的438. filtrate ['fɪltreɪt]n. [化学] 滤液vt. 过滤；筛选vi. 过滤439. phenolphthalein [,fiːnɒl'(f)θæliːn; -'(f)θeɪl-] n. [试剂] 酚酞（一种测试碱性的试剂，可作刺激性泻剂）440. and vice versa反之亦然；反过来也一样441. hydrolysis [haɪ'drɒlɪsɪs]n. 水解作用442. prospectivelyadv. 盼望中；可能；潜在；预期前瞻性443. administration route给药途径444. topical ['tɒpɪk(ə)l]adj. 局部的；论题的；时事问题的；局部地区的445. eliminate [ɪ'lɪmɪneɪt]vt. 消除；排除446. attain [ə'teɪn]n. 成就vt. 达到，实现；获得；到达vi. 达到；获得；到达447. raw material[材] 原料448. reassessment [,ri:ə'sesmənt]n. 重新评估；[经] 重新估价；重新考虑449. as well as也；和…一样；不但…而且450. conventional [kən'venʃ(ə)n(ə)l]adj. 符合习俗的，传统的；常见的；惯例的451. conventional testsconventional tests: 常规试验方法|常规试验conventional indoor tests: 室内常规试验conventional tests of physical properties: 常规452. viscosity [vɪ'skɒsɪtɪ]n. [物] 粘性，[物] 粘度453. sterility [stə'rɪlɪtɪ]n.无菌；[泌尿] 不育；[妇产] 不孕；不毛；内容贫乏454. pyrogen ['paɪrədʒ(ə)n]n. 热原质；发热源455. endotoxin ['endəʊ,tɒksɪn]n. [病理] 内毒素456. bacterial endotoxin细菌内毒素457. adjacent [ə'dʒeɪs(ə)nt]adj. 邻近的，毗连的458. gelatinous [dʒə'lætinəs]adj. 凝胶状的，胶状的459. vapour ['veɪpə]n. 蒸气（等于vapor）；水蒸气460. litmus ['lɪtməs]n. [试剂] 石蕊461. red litmus paper红色石蕊纸462. filter paper滤纸（尤制定量滤纸）463. nonluminous [nɔn'lju:minəs]adj. 无光的；不发光的464. nonluminous flame无色火焰465. charring ['tʃɑ:riŋ]n. 炭化v. 烧焦（char的ing形式）466. sublimate ['sʌblɪmeɪt]n. 升华物vt. 使升华；使高尚vi. 升华；纯化adj. 纯净化的；理想化的；高尚的467. turmeric ['tɜːmərɪk]n. 姜黄；姜黄根粉末468. turmeric paper[分化] 姜黄试纸；姜黄纸469. curdy ['kɜːdɪ]adj. 凝结了的；成凝乳状的470. pale [peɪl]n. 前哨；栅栏；范围adj. 苍白的；无力的；暗淡的vt. 使失色；使变苍白；用栅栏围vi. 失色；变苍白；变得暗淡n. (pale)人名；(塞)帕莱471. pale yellowadj. 淡黄色，浅黄色472. violet ['vaɪələt]n. 紫罗兰；堇菜；羞怯的人adj. 紫色的；紫罗兰色的n. (violet)人名；(西)比奥莱特；(法)维奥莱；(印、匈、英)维奥莱特473. portion ['pɔːʃ(ə)n]n. 部分；一份；命运vt. 分配；给…嫁妆474. emission [ɪ'mɪʃ(ə)n]n. （光、热等的）发射，散发；喷射；发行n. (emission)人名；(英)埃米申475. calibrate ['kælɪbreɪt]vt. 校正；调整；测定口径476. coefficient [,kəʊɪ'fɪʃ(ə)nt]n. [数] 系数；率；协同因素adj. 合作的；共同作用的477. equation [ɪ'kweɪʒ(ə)n]n. 方程式，等式；相等；[化学] 反应式478. mechanism ['mek(ə)nɪz(ə)m]n. 机制；原理，途径；进程；机械装置；技巧479. exclusion [ɪk'skluːʒ(ə)n; ek-]n. 排除；排斥；驱逐；被排除在外的事物480. affinity [ə'fɪnɪtɪ]n. 密切关系；吸引力；姻亲关系；类同481. adsorbantadsorbant: 吸附剂Adsorbant affinity: 吸着力Broken adsorbant: 意即已被破碎的482. eluted洗脱483. successively [sək'sesivli]adv. 相继地；接连着地484. distribution [dɪstrɪ'bjuːʃ(ə)n]n. 分布；分配485. stationary ['steɪʃ(ə)n(ə)rɪ]n. 不动的人；驻军adj. 固定的；静止的；定居的；常备军的486. stationary phase[物化][分化] 固定相；稳定期487. steering ['stiəriŋ]n. 操纵；指导；掌舵v. 驾驶；掌舵（steer的ing形式）488. steering committee指导委员会。

Open Quantum Systems

Minisymposium15OperatortheorieLeiter des Symposiums:Prof.Dr.Birgit Jacob Dr.Carsten TrunkTechnical University Delft Technische Universit¨at BerlinFac.EWI/TWAP.O.Box5031Straße des17.Juni1362600GA Delft,The Netherlands10623Berlin,GermanyDie Operatortheorie besch¨aftigt sich mit der Analyse linearer Abbildungen auf unend-lichdimensionalen R¨aumen.Einen besonderen Schwerpunkt bildet dabei die Spektral-theorie,die Erweiterungstheorie symmetrischer Operatoren,die Fredholmtheorie und die Theorie der Halbgruppen.148Minisymposium15Montag,18.SeptemberHS IV,Hauptgeb¨aude,Regina-Pacis-Weg14:30–15:20Klaus-Jochen Engel(University of L’Aquila,Italy) Boundary control ofﬂows in networks15:30–15:50Andras B´atkai(ELTE TTK/Institute of Mathematics) Differenzialgleichungen mit Verz¨ogerung in L p Phasenr¨aumen16:00–16:20Peer Kunstmann(Karlsruhe)L q-Eigenschaften elliptischer Randwertprobleme16:30–16:50Markus Biegert(Ulm)Elliptic Problems on Varying DomainsDienstag,19.SeptemberH¨orsaal411AVZ I,Endenicher Allee11-1315:00–15:50Christiane Tretter(Bremen)Spectral problems for block operator matrices in hydrodynamics16:00–16:20Matthias Langer(University of Strathclyde,Glasgow) Variational principles for eigenvalues of the Klein–Gordon equation16:30–16:50Monika Winklmeier(Bremen)Estimates for the eigenvalues of the angular part of the Dirac equation in the Kerr-Newman metric17:00–17:20Annemarie Luger(TU Berlin)On a result for differential operators with singular potentials17:30–17:50Jussi Behrndt(University of Groningen)Open Quantum SystemsOperatortheorie149 Mittwoch,20.SeptemberH¨orsaal411AVZ I,Endenicher Allee11-1315:00–15:50Hagen Neidhardt(WIAS Berlin)Perturbation theory of semi-groups and evolution equations16:00–16:20Bernhard Haak(TU Delft)A stochastic Datko-Pazy theorem16:30–16:50Tanja Eisner(T¨ubingen)Fast schwache Konvergenz von Operatorhalbgruppen17:00–17:20Carsten Trunk(TU Berlin)Location of the spectrum of operator matrices which are associated to second order equations17:30–17:50Birgit Jacob(TU Delft)A resolvent test for admissibility of Volterra observation operators150Minisymposium15Vortragsausz¨ugeKlaus-Jochen Engel(University of L’Aquila,Italy)Boundary control ofﬂows in networksWe investigate a boundary control problem on a network.We study a transport equation in the network,controlling it in a single vertex.We describe all the possible reachable states and prove a criterium of Kalman type for the vertices in which the problem is controllable.This is joint work with Marjeta Kramar Fijav(Ljubljana),Rainer Nagel(T¨ubingen)and Eszter Sikolya(Budapest).Andras B´atkai(ELTE TTK/Institute of Mathematics) Differenzialgleichungen mit Verz¨ogerung in L p Phasenr¨aumenIm Vortrag wird ein halbgruppentheoretischer Zugang zu Differenzialgleichungen mit Verz¨ogerung in L p Phasenr¨aumen pr¨asentiert.Dies erm¨oglicht uns die Verz¨ogerung in eine additive St¨orung zu verwandeln und erm¨oglicht dadurch die Anwendung der reichen St¨orungstheorie der Halbgruppen.Neben diesem Zugang werden auch die Er-gebnisse neuester spektraltheoretischer Untersuchungen gezeigt.Referenzen:B´atkai,A.,Piazzera,S.,“Semigroups for Delay Equations in L p-Phase Spaces”,Rese-arch Notes in Mathematics vol.10,A.K.Peters:Wellesley MA,2005.B´atkai,A.,Eisner,T.,Latushkin,Y.,The spectral mapping property of delay semigroups, submittedPeer Kunstmann(Karlsruhe)L q-Eigenschaften elliptischer RandwertproblemeWir untersuchen L q-Eigenschaften elliptischer Randwertproblemeλu−Au=f inΩ⊂R nBu=g auf∂Ω.Operatortheorie151 Hierbei ist im einfachsten Fall A= jk a jk∂j∂k ein Differentialoperator mit a jk∈L∞, B= j b j∂j ein Differentialoperator erster Ordnung mit b j∈C0,1,sowie f∈L q(Ω)und g∈W1,q(Ω).Ausgehend von Absch¨atzungen wie|λ| u q+ ∇2u q≤C( f q+|λ|1/2 g q+ ∇g q)f¨ur ein festes q∈(1,∞)und hinreichend großeλin einem geeigneten Sektor zei-gen wir verallgemeinerte Gauß-Absch¨atzungen und mit deren Hilfe weitere Eigenschaf-ten wie R-Sektorialit¨at,R-Beschr¨anktheit der L¨osungsoperatoren und maximale L p-L q-Regularit¨at f¨ur die induzierte analytische Halbgruppe.Markus Biegert(Ulm)Elliptic Problems on Varying DomainsThe aim of this talk is to show optimal results on local and global uniform convergence of solutions to elliptic equations with Dirichlet boundary conditions on varying domains. We assume that the limit domain be stable in the sense of Keldyˇs.We further assume that the approaching domains satisfy a necessary condition in the inside of the limit domain,and only require L2-convergence outside.As a consequence,uniform and L2-convergence are the same in the trivial case of homogenisation of a perforated domain.Christiane Tretter(Bremen)Spectral problems for block operator matrices in hydrodynamicsIn the linear stability analysis of hydrodynamics,the spectra of non-symmetric systems of coupled differential equations have to be studied.As examples,we consider the Ekman boundary layer problem and the Hagen Poiseuilleﬂow with non-axisymmetric disturbances.In both cases we investigate the essential spectrum by means of operator theoretic methods.(joint work with M.Marletta,Cardiff)152Minisymposium15Matthias Langer(University of Strathclyde,Glasgow)Variational principles for eigenvalues of the Klein–Gordon equationWe consider eigenvalues of the Klein–Gordon equation,which can be written as a quadratic eigenvalue problem.Under certain assumptions the continuous spectrum has a gap and we can characterise eigenvalues in this gap even in the presence of complex eigenvalues.This quadratic eigenvalue problem can also be linearised in a Pontryagin space.Connections between the negative index of the Pontryagin space and the index shift in the variational principle are presented.Monika Winklmeier(Bremen)Estimates for the eigenvalues of the angular part of the Dirac equation in theKerr-Newman metricThe radial part of the Dirac equation describing a fermion in the Kerr-Newman back-ground metric has an operator theoretical realisation as a block operator matrix A= −D B B∗D with domain D(A)=D(B∗)⊕D(B)in the Hilbert space H=L2(0,π)2.It can be shown that the spectrum of A consists of eigenvalues only.We will show that the expression A−λallows for a factorisation into three factors such that all the information about the spectrum of A is contained in a scalar operator valued function.From this function we obtain a lower bound for the smallest eigenvalue in modulus of A.Another method to obtain such a bound is to use techniques related to the quadratic nuermical range of block operator matrices.Annemarie Luger(TU Berlin)On a result for differential operators with singular potentialsWe explore the connection between a(generalized)Titchmarsh-Weyl-coefﬁcient for the singular Sturm-Liouville operator(y):=−y (x)+ q0x2+q1x y(x)on x∈(0,∞),with q0>3and q1∈R,and a certain singular perturbation of this operator.This talk is based on joint work with Pavel Kurasov(Lund).Operatortheorie153 Jussi Behrndt(University of Groningen)Open Quantum SystemsOpen quantum systems are often described with a maximal dissipative operator A D, a so-called pseudo-Hamiltonian,and a self-adjoint operator A0in some Hilbert space H.If L denotes a minimal self-adjoint dilation of A D,i.e.,L acts in a Hilbert space H⊕L2(R,K)such that P H(L−λ)−1|H=(A D−λ)−1,and L0=A0⊕−i d dx,then thescattering matrix of the closed system{L,L0}can be recovered from the scattering matrix of the dissipative system{A D,A0}.Since in this model L is not semibounded from below serious doubts arise from a physical point of view.We propose a slightly different approach where instead of aﬁxed pseudo-Hamiltonian A D a family of energy dependent pseudo-Hamiltonians{A−τ(λ)}is considered.The outer space L2(R,K)is replaced by some Hilbert space K and the Hamiltonian L in H⊕K satisﬁes P(L−λ)−1|H=(A−τ(λ)−λ)−1and is often semibounded from below. We show that the scattering matrix of the closed system can be recovered in a similar way as above and that the model with oneﬁxed pseudo-Hamiltonian can be regarded as an approximation.The abstract theory is illustrated with some examples.The talk is based on joint work with Mark M.Malamud(Donetsk National University, Ukraine)and Hagen Neidhardt(WIAS,Berlin).Hagen Neidhardt(WIAS Berlin)Perturbation theory of semi-groups and evolutionequationsThe aim of the present talk is to develop an approach to the Cauchy problem for linear evolution equations of type∂u(t)+A(t)u(t)=0,u(s)=u s,a<s≤t<b,∂ton a separable Banach space X,where(a,b)is aﬁnite open interval and{A(t)}t∈(a,b)is a family of closed linear operators on the separable Banach space X.The main questi-on concerning the Cauchy problem is toﬁnd a so-called“solution operator”or propaga-tor U(t,s).We are going to solve this problem embedding it into a perturbation problem for generators of semi-groups in the Banach space L p([0,T],X),1<p<∞.The ab-stract existence results are applied to Schr¨odinger operators with time-dependent point interactions.154Minisymposium15Bernhard Haak(TU Delft)A stochastic Datko-Pazy theoremThe well-known Datko-Pazy theorem states that if(T(t))t≥0is a strongly continuous semigroup on a Banach space E such that all orbits T(·)x belong to the space L p(R+,E) for some p∈[1,∞),then(T(t))t≥0is uniformly exponentially stable,or equivalently, there exists an >0such that all orbits t→e t T(t)x belong to L p(R+,E).We show that a similar result also hold for so-calledγ–radonifying operators,namely the equivalence of1.For all x∈E,T(·)x∈γ(R+,E).2.There exists an >0such that for all x∈E,t→e t T(t)x∈γ(R+,E).If E is a Hilbert space,γ(R+,E)=L2(R+,E)and we reobtain Datko’s theorem mentio-ned above.γ–radonifying operators play an important role in the study abstract stocha-stic Cauchy problems on E whence the result can also be seen as a perturbation result for stochastic Cauchy problems.References:B.Haak,M.Veraar,J.van Neerven:A stochastic Datko-Pazy theorem,submitted; avaiable on ArXiv.Tanja Eisner(T¨ubingen)Fast schwache Konvergenz von OperatorhalbgruppenF¨ur C0-Halbruppen auf Banachr¨aumen diskutieren wir den Zusammenhang zwischen Spektraleigenschaften des Generators und der Konvergenz der Halbgruppe f¨ur t→∞(insbesondere f¨ur die schwache Topologie).Carsten Trunk(TU Berlin)Location of the spectrum of operator matrices which are associated to second order equationsWe study second order equations of the form¨z(t)+A o z(t)+D˙z(t)=0.Operatortheorie155 Here the stiffness operator A o is a possibly unbounded positive operator on a Hilbert space H,which is assumed to be boundedly invertible,and D,the damping operator,is an unbounded operator,such that A−1/2o DA−1/2o is a bounded non negative operatoron H.This second order equation is equivalent to the standardﬁrst-order equation ˙x(t)=Ax(t),where A:D(A)⊂D(A1/2o)×H→D(A1/2o)×H,is given byA= 0I−A o−D ,D(A)= [z w]∈D(A1/2o)×D(A1/2o)|A o z+Dw∈H .This block operator matrix has been studied in the literature for more than20years.It is well-known that A generates a C0-semigroup of contraction,and thus the spectrum of A is located in the closed left half plane.We are interested in a more detailed study of the location of the spectrum of A in the left half plane.In general the(essential)spectrum of A can be quite arbitrary in the closed left half plane.Under various conditions on the damping operator D we describe the location of the spectrum and the essential spectrum of A.The talk is based on joint work with Birgit Jacob(Delft).Birgit Jacob(TU Delft)A resolvent test for admissibility of Volterra observation operatorsNecessary and sufﬁcient conditions are given forﬁnite-time admissibility of a linear sy-stem deﬁned by a Volterra integral equation when the underlying semigroup is equiva-lent to a contraction semigroup.These necessray and sufﬁcient conditions are in terms of a pointwise bound on the resolvent of the inﬁnitesimal generator.This generalizes an analogous result known to hold for the standard Cauchy problem.The talk is based on joint work with Jonathan R.Partington(University of Leeds).。

Vitali’s theorem and WWKL

VITALI’S THEOREM AND WWKLDOUGLAS K.BROWNMARIAGNESE GIUSTOSTEPHEN G.SIMPSONAbstract.Continuing the investigations of X.Yu and others,westudy the role of set existence axioms in classical Lebesgue mea-sure theory.We show that pairwise disjoint countable additivityfor open sets of reals is provable in RCA0.We show that sev-eral well-known measure-theoretic propositions including the VitaliCovering Theorem are equivalent to WWKL over RCA0.1.IntroductionThe purpose of Reverse Mathematics is to study the role of set ex-istence axioms,with an eye to determining which axioms are needed in order to prove speciﬁc mathematical theorems.In many cases,it is shown that a speciﬁc mathematical theorem is equivalent to the set existence axiom which is needed to prove it.Such equivalences are often proved in the weak base theory RCA0.RCA0may be viewed as a kind of formalized constructive or recursive mathematics,with full clas-sical logic but severely restricted comprehension and induction.The program of Reverse Mathematics has been developed in many publica-tions;see for instance[5,10,11,12,20].In this paper we carry out a Reverse Mathematics study of some aspects of classical Lebesgue measure theory.Historically,the subject of measure theory developed hand in hand with the nonconstructive, set-theoretic approach to mathematics.Errett Bishop has remarked that the foundations of measure theory present a special challenge to the constructive mathematician.Although our program of Reverse Mathematics is quite diﬀerent from Bishop-style constructivism,we feel that Bishop’s remark implicitly raises an interesting question:Which nonconstructive set existence axioms are needed for measure theory?VITALI’S THEOREM AND WWKL 2This paper,together with earlier papers of Yu and others [21,22,23,24,25,26],constitute an answer to that question.The results of this paper build upon and clarify some early results of Yu and Simpson.The reader of this paper will ﬁnd that familiarity with Yu–Simpson [26]is desirable but not essential.We begin in section 2by exploring the extent to which measure theory can be developed in RCA 0.We show that pairwise disjoint countable additivity for open sets of reals is provable in RCA 0.This is in contrast to a result of Yu–Simpson [26]:countable additivity for open sets of reals is equivalent over RCA 0to a nonconstructive set existence axiom known as Weak Weak K¨o nig’s Lemma (WWKL).We show in sections 3and 4that several other basic propositions of measure theory are also equivalent to WWKL over RCA 0.Finally in section 5we show that the Vitali Covering Theorem is likewise equivalent to WWKL over RCA 0.2.Measure Theory in RCA 0Recall that RCA 0is the subsystem of second order arithmetic with∆01comprehension and Σ01induction.The purpose of this section is toshow that some measure-theoretic results can be proved in RCA 0.Within RCA 0,let X be a compact separable metric space.We deﬁne C (X )= A,the completion of A ,where A is the vector space of rational “polynomials”over X under the sup-norm, f =sup x ∈X |f (x )|.For the precise deﬁnitions within RCA 0,see [26]and section III.E of Brown’s thesis [4].The construction of C (X )within RCA 0is inspired by the constructive Stone–Weierstrass theorem in section 4.5of Bishop and Bridges [2].It is provable in RCA 0that there is a natural one-to-one correspondence between points of C (X )and continuous functions f :X →R which are equipped with a modulus of uniform continuity ,that is to say,a function h :N →N such that for all n ∈N and x ,y ∈Xd (x,y )<12n .Within RCA 0we deﬁne a measure (more accurately,a nonnegative Borel probability measure)on X to be a nonnegative bounded linear functional µ:C (X )→R such that µ(1)=1.(Here µ(1)denotes µ(f ),f ∈C (X ),f (x )=1for all x ∈X .)For example,if X =[0,1],the unit interval,then there is an obvious measure µL :C ([0,1])→R given by µL (f )= 10f (x )dx ,the Riemann integral of f from 0to 1.We refer to µL as Lebesgue measure on [0,1].There is also the obvious generalization to Lebesgue measure µL on X =[0,1]n ,the n -cube.VITALI’S THEOREM AND WWKL 3Deﬁnition 2.1(measure of an open set).This deﬁnition is made in RCA 0.Let X be any compact separable metric space,and let µbe any measure on X .If U is an open set in X ,we deﬁneµ(U )=sup {µ(f )|f ∈C (X ),0≤f ≤1,f =0on X \U }.Within RCA 0this supremum need not exist as a real number.(Indeed,the existence of µ(U )for all open sets U is equivalent to ACA 0over RCA 0.)Therefore,when working within RCA 0,we interpret assertions about µ(U )in a “virtual”or comparative sense.For example,µ(U )≤µ(V )is taken to mean that for all >0and all f ∈C (X )with 0≤f ≤1and f =0on X \U ,there exists g ∈C (X )with 0≤g ≤1and g =0on X \V such that µ(f )≤µ(g )+ .See also [26].Some basic properties of Lebesgue measure are easily proved in RCA 0.For instance,it is straightforward to show that the Lebesgue measure of the union of a ﬁnite set of pairwise disjoint open intervals is equal to the sum of the lengths of the intervals.We deﬁne L 1(X,µ)to be the completion of C (X )under the L 1-norm given by f 1=µ(|f |).(For the precise deﬁnitions,see [5]and[26].)In RCA 0we see that L 1(X,µ)is a separable Banach space,but to assert within RCA 0that points of the Banach space L 1(X,µ)represent measurable functions f :X →R is problematic.We shall comment further on this question in section 4below.Lemma 2.2.The following is provable in RCA 0.If U n ,n ∈N ,is a sequence of open sets,then µ∞ n =0U n ≥lim k →∞µ k n =0U n .Proof.Trivial.Lemma 2.3.The following is provable in RCA 0.If U 0,U 1,...,U k is a ﬁnite,pairwise disjoint sequence of open sets,then µ k n =0U n ≥k n =0µ(U n ).Proof.Trivial.An open set is said to be connected if it is not the union of two disjoint nonempty open sets.Let us say that a compact separable metric space X is nice if for all suﬃciently small δ>0and all x ∈X ,the open ballB (x,δ)={y ∈X |d (x,y )<δ}VITALI’S THEOREM AND WWKL4 is connected.Such aδis called a modulus of niceness for X.For example,the unit interval[0,1]and the n-cube[0,1]n are nice, but the Cantor space2N is not nice.Theorem2.4(disjoint countable additivity).The following is prov-able in RCA0.Assume that X is nice.If U n,n∈N,is a pairwise disjoint sequence of open sets in X,thenµ∞n=0U n=∞n=0µ(U n).Proof.Put U= ∞n=0U n.Note that U is an open set.By Lemmas2.2and2.3,we have in RCA0thatµ(U)≥ ∞n=0µ(U n).It remainsto prove in RCA0thatµ(U)≤ ∞n=0µ(U n).Let f∈C(X)be suchthat0≤f≤1and f=0on X\U.It suﬃces to prove thatµ(f)≤∞n=0µ(U n).Claim1:There is a sequence of continuous functions f n:X→R, n∈N,deﬁned by f n(x)=f(x)for all x∈U n,f n(x)=0for all x∈X\U n.To prove this in RCA0,recall from[6]or[20]that a code for a continuous function g from X to Y is a collection G of quadruples (a,r,b,s)with certain properties,the idea being that d(a,x)<r im-plies d(b,g(x))≤s.Also,a code for an open set U is a collection of pairs(a,r)with certain properties,the idea being that d(a,x)<r im-plies x∈U.In this case we write(a,r)<U to mean that d(a,b)+r<s for some(b,s)belonging to the code of U.Now let F be a code for f:X→R.Deﬁne a sequence of codes F n,n∈N,by putting(a,r,b,s) into F n if and only if1.(a,r,b,s)belongs to F and(a,r)<U n,or2.(a,r,b,s)belongs to F and b−s≤0≤b+s,or3.b−s≤0≤b+s and(a,r)<U m for some m=n.It is straightforward to verify that F n is a code for f n as required by claim1.Claim2:The sequence f n,n∈N,is a sequence of elements of C(X). To prove this in RCA0,we must show that the sequence of f n’s has a sequence of moduli of uniform continuity.Let h:N→N be a modulus of uniform continuity for f,and let k be so large that1/2k is a modulus of niceness for X.We shall show that h :N→N deﬁned by h (m)=max(h(m),k)is a modulus of uniform continuity for all of the f n’s.Let x,y∈X and m∈N be such that d(x,y)<1/2h (m). To show that|f n(x)−f n(y)|<1/2m,we consider three cases.Case1:VITALI’S THEOREM AND WWKL5 x,y∈U n.In this case we have|f n(x)−f n(y)|=|f(x)−f(y)|<1VITALI’S THEOREM AND WWKL 6From (1)we see that for each >0there exists k such that µ(f )− ≤ kn =0µ(f n ).Thus we haveµ(f )− ≤kn =0µ(f n )≤k n =0µ(U n )≤∞ n =0µ(U n ).Since this holds for all >0,it follows that µ(f )≤ ∞n =0µ(U n ).Thus µ(U )≤ ∞n =0µ(U n )and the proof of Theorem 2.4is complete.Corollary 2.5.The following is provable in RCA 0.If (a n ,b n ),n ∈N is a sequence of pairwise disjoint open intervals,then µL ∞ n =0(a n ,b n ) =∞ n =0|a n −b n |.Proof.This is a special case of Theorem 2.4.Remark 2.6.Theorem 2.4fails if we drop the assumption that X is nice.Indeed,let µC be the familiar “fair coin”measure on the Cantor space X =2N ,given by µC ({x |x (n )=i })=1/2for all n ∈N and i ∈{0,1}.It can be shown that disjoint ﬁnite additivity for µC is equivalent to WWKL over RCA 0.(WWKL is deﬁned and discussed in the next section.)In particular,disjoint ﬁnite additivity for µC is not provable in RCA 0.3.Measure Theory in WWKL 0Yu and Simpson [26]introduced a subsystem of second order arith-metic known as WWKL 0,consisting of RCA 0plus the following axiom:if T is a subtree of 2<N with no inﬁnite path,thenlim n →∞|{σ∈T |length(σ)=n }|VITALI’S THEOREM AND WWKL 7see also Sieg [18].In this sense,every mathematical theorem provable in WKL 0or WWKL 0is ﬁnitistically reducible in the sense of Hilbert’s Program;see [19,6,20].Remark 3.2.The study of ω-models of WWKL 0is closely related to the theory of 1-random sequences,as initiated by Martin-L¨o f [16]and continued by Kuˇc era [7,13,14,15].At the time of writing of [26],Yu and Simpson were unaware of this work of Martin-L¨o f and Kuˇc era.The purpose of this section and the next is to review and extend the results of [26]and [21]concerning measure theory in WWKL 0.A measure µ:C (X )→R on a compact separable metric space X is said to be countably additive if µ∞ n =0U n =lim k →∞µ k n =0U n for any sequence of open sets U n ,n ∈N ,in X .The following theorem is implicit in [26]and [21].Theorem 3.3.The following assertions are pairwise equivalent over RCA 0.1.WWKL.2.(countable additivity)For any compact separable metric space Xand any measure µon X ,µis countably additive.3.For any covering of the closed unit interval [0,1]by a sequence of open intervals (a n ,b n ),n ∈N ,we have ∞n =0|a n −b n |≥1.Proof.That WWKL implies statement 2is proved in Theorem 1of [26].The implication 2→3is trivial.It remains to prove that statement 3implies WWKL.Reasoning in RCA 0,let T be a subtree of 2<N with no inﬁnite path.PutT ={σ i |σ∈T,σ i /∈T,i <2}.For σ∈2<N put lh(σ)=length of σanda σ=lh(σ)−1n =0σ(n )2lh(σ).Note that |a σ−b σ|=1/2lh(σ).Note also that σ,τ∈2<N are incompa-rable if and only if (a σ,b σ)∩(a τ,b τ)=∅.In particular,the intervals (a τ,b τ),τ∈ T,are pairwise disjoint and cover [0,1)except for some of the points a σ,σ∈2<N .Fix >0and put c σ=a σ− /4lh(σ),d σ=a σ+ /4lh(σ).Then the open intervals (a τ,b τ),τ∈ T,(c σ,d σ),VITALI’S THEOREM AND WWKL 8σ∈2<N and (1− ,1+ )form a covering of [0,1].Applying statement 3,we see that the sum of the lengths of these intervals is ≥1,i.e. τ∈ T12lh(τ)=1.From this,equation (2)follows easily.Thus we have proved that state-ment 3implies WWKL.This completes the proof of the theorem.It is possible to take a somewhat diﬀerent approach to measure the-ory in RCA 0.Note that the deﬁnition of µ(U )that we have given (Deﬁnition 2.1)is extensional in RCA 0.This means that if U and V contain the same points then µ(U )=µ(V ),provably in RCA 0.An alternative approach is the intensional one,embodied in Deﬁnition 3.4below.Recall that an open set U is given in RCA 0as a sequence of basic open sets.In the case of the real line,basic open sets are just intervals with rational endpoints.Deﬁnition 3.4(intensional Lebesgue measure).We make this deﬁni-tion in RCA 0.Let U = (a n ,b n ) n ∈N be an open set in the real line.The intensional Lebesgue measure of U is deﬁned by µI (U )=lim k →∞µL k n =0(a n ,b n ) .Theorem 3.5.It is provable in RCA 0that intensional Lebesgue mea-sure µI is countably additive on open sets.In other words,if U n ,n ∈N ,is a sequence of open sets,then µI∞ n =0U n =lim k →∞µI k n =0U n .Proof.This is immediate from the deﬁnitions,since ∞n =0U n is deﬁned as the union of the sequences of basic open intervals in U n ,n ∈N .Returning now to WWKL 0,we can prove that intensional Lebesgue measure concides with extensional Lebesgue measure.In fact,we have the following easy result.Theorem 3.6.The following assertions are pairwise equivalent over RCA 0.VITALI’S THEOREM AND WWKL91.WWKL.2.µI(U)=µL(U)for all open sets U⊆[0,1].3.µI is extensional on open sets.In other words,for all open setsU,V⊆[0,1],if∀x(x∈U↔x∈V)thenµI(U)=µI(V).4.For all open sets U⊇[0,1],we haveµI(U)≥1.Proof.This is immediate from Theorems3.3and3.5.4.More Measure Theory in WWKL0In this section we show that a good theory of measurable functions and measurable sets can be developed within WWKL0.Weﬁrst consider pointwise values of measurable functions.Our ap-proach is due to Yu[21,24].Let X be a compact separable metric space and letµ:C(X)→R be a positive Borel probability measure on X.Recall that L1(X,µ)is deﬁned within RCA0as the completion of C(X)under the L1-norm.In what sense or to what extent can we prove that a point of the Banach space L1(X,µ)gives rise to a function f:X→R?In order to answer this question,recall that f∈L1(X,µ)is given by a sequence f n∈C(X),n∈N,which converges to f in the L1-norm; more preciselyf n−f n+1 1≤12nfor all n,and|f m(x)−f m (x)|≤12k.VITALI’S THEOREM AND WWKL10 Then for x∈C fnand m ≥m≥n+2k+2we have|f m(x)−f m (x)|≤m −1i=m|f i(x)−f i+1(x)|≤∞i=n+2k+2|f i(x)−f i+1(x)|≤12k.We need a lemma:Lemma4.2.The following is provable in RCA0.For f∈C(X)and >0,we haveµ({x|f(x)> })≤ f 1/ .Proof.Put U={x|f(x)> }.Note that U is an open set.If g∈C(X),0≤g≤1,g=0on X\U,then we have g≤|f|, hence µ(g)=µ( g)≤µ(|f|)= f 1,henceµ(g)≤ f 1/ .Thus µ(U)≤ f 1/ and the lemma is proved.Using this lemma we haveµ(X\C fnk )=µx∞i=n+2k+2|f i(x)−f i+1(x)|>12i=1VITALI’S THEOREM AND WWKL 11hence by countable additivityµ(X \C f n )≤∞ k =0µ(X \C f nk )≤∞k =012n .This completes the proof of Proposition 4.1.Remark 4.3(Yu [21]).In accordance with Proposition 4.1,forf = f n n ∈N ∈L 1(X,µ)and x ∈ ∞n =0C f n ,we deﬁne f (x )=lim n →∞f n (x ).Thus we see thatf (x )is deﬁned on an F σset of measure 1.Moreover,if f =g in L 1(X,µ),i.e.if f −g 1=0,then f (x )=g (x )for all x in an F σset of measure 1.These facts are provable in WWKL 0.We now turn to a discussion of measurable sets within WWKL 0.We sketch two approaches to this topic.Our ﬁrst approach is to identify measurable sets with their characteristic functions in L 1(X,µ),accord-ing to the following deﬁnition.Deﬁnition 4.4.This deﬁnition is made within WWKL 0.We say that f ∈L 1(X,µ)is a measurable characteristic function if there exists a sequence of closed setsC 0⊆C 1⊆···⊆C n ⊆...,n ∈N ,such that µ(X \C n )≤1/2n for all n ,and f (x )∈{0,1}for all x ∈ ∞n =0C n .Here f (x )is as deﬁned in Remark 4.3.Our second approach is more direct,but in its present form it applies only to certain speciﬁc situations.For concreteness we consider only Lebesgue measure µL on the unit interval [0,1].Our discussion can easily be extended to Lebesgue measure on the n -cube [0,1]n ,the “fair coin”measure on the Cantor space 2N ,etc .Deﬁnition 4.5.The following deﬁnition is made within RCA 0.Let S be the Boolean algebra of ﬁnite unions of intervals in [0,1]with rational endpoints.For E 1,E 2∈S we deﬁne the distanced (E 1,E 2)=µL ((E 1\E 2)∪(E 2\E 1)),the Lebesgue measure of the symmetric diﬀerence of E 1and E 2.Thus d is a pseudometric on S ,and we deﬁne S to be the compact separable metric space which is the completion of S under d .A point E ∈ S is called a Lebesgue measurable set in [0,1].VITALI’S THEOREM AND WWKL 12We shall show that these two approaches to measurable sets (Deﬁ-nitions 4.4and 4.5)are equivalent in WWKL 0.Begin by deﬁning an isometry χ:S →L 1([0,1],µL )as follows.For 0≤a <b ≤1deﬁneχ([a,b ])= f n n ∈N ∈L 1([0,1],µL )where f n (0)=f n (a )=f n (b )=f n (1)=0and f n a +b −a 2n +1=1and f n ∈C ([0,1])is piecewise linear otherwise.Thus χ([a,b ])is a measurable characteristic function corresponding to the interval [a,b ].For 0≤a 1<b 1<···<a k <b k ≤1deﬁneχ([a 1,b 1]∪···∪[a k ,b k ])=χ([a 1,b 1])+···+χ([a k ,b k ]).It is straightforward to prove in RCA 0that χextends to an isometryχ: S→L 1([0,1],µL ).Proposition 4.6.The following is provable in WWKL 0.If E ∈ Sis a Lebesgue measurable set,then χ(E )is a measurable characteristic function in L 1([0,1],µL ).Conversely,given a measurable characteristic function f ∈L 1([0,1],µL ),we can ﬁnd E ∈ Ssuch that χ(E )=f in L 1([0,1],µL ).Proof.It is straightforward to prove in RCA 0that for all E ∈ S , χ(E )is a measurable characteristic function.For the converse,let f be a measurable characteristic function.By Deﬁnition 4.4we have that f (x )∈{0,1}for all x ∈ ∞n =0C n .ByProposition 4.1we have |f (x )−f 3n +3(x )|<1/2n for all x ∈C f n .Put U n ={x ||f 3n +3(x )−1|<1/2n }and V n ={x ||f 3n +3(x )|<1/2n }.Then for n ≥1,U n and V n are disjoint open sets.Moreover C n ∩C f n ⊆U n ∪V n ,hence µL (U n ∪V n )≥1−1/2n −1.By countable additivity(Theorem 3.3)we can eﬀectively ﬁnd E n ,F n ∈S such that E n ⊆U n and F n ⊆V n and µL (E n ∪F n )≥1−1/2n −2.Put E = E n +5 n ∈N .It is straightforward to show that E belongs to S and that χ(E )=f in L 1([0,1],µL ).This completes the proof.Remark 4.7.We have presented two notions of Lebesgue measurable set and shown that they are equivalent in WWKL 0.Our ﬁrst notion (Deﬁnition 4.4)has the advantage of generality in that it applies to any measure on a compact separable metric space.Our second no-tion (Deﬁnition 4.5)is advantageous in other ways,namely it is more straightforward and works well in RCA 0.It would be desirable to ﬁnd a single deﬁnition which combines all of these advantages.VITALI’S THEOREM AND WWKL 135.Vitali’s TheoremLet S be a collection of sets.A point x is said to be Vitali covered by S if for all >0there exists S ∈S such that x ∈S and the diameter of S is less than .The Vitali Covering Theorem in its simplest form says the following:if I is a sequence of intervals which Vitali covers an interval E in the real line,then I contains a countable,pairwise disjoint set of intervals I n ,n ∈N ,such that ∞n =0I n covers E except for a set of Lebesgue measure 0.The purpose of this section is to show that various forms of the Vitali Covering Theorem are provable in WWKL 0and in fact equivalent to WWKL over RCA 0.Throughout this section,we use µto denote Lebesgue measure.Lemma 5.1(Baby Vitali Lemma).The following is provable in RCA 0.Let I 0,...,I n be a ﬁnite sequence of intervals.Then we can ﬁnd a pair-wise disjoint subsequence I k 0,...,I k m such thatµ(I k 0∪···∪I k m )≥1VITALI’S THEOREM AND WWKL 14I =[2a −b,2b −a ].)Thusµ(I 0∪···∪I n )≤µ(I k 0∪···∪I k m )≤µ(I k 0)+···+µ(I k m )=3µ(I k 0)+···+3µ(I k m )=3µ(I k 0∪···∪I k m )and the lemma is proved.Lemma 5.2.The following is provable in WWKL 0.Let E be an in-terval,and let I n ,n ∈N ,be a sequence of intervals.If E ⊆ ∞n =0I n ,then µ(E )≤lim k →∞µ k n =0I n .Proof.If the intervals I n are open,then the desired conclusion follows immediately from countable additivity (Theorem 3.3).Otherwise,ﬁx >0and let I n be an open interval with the same midpoint as I n andµ(I n )=µ(I n )+µ(E \A ).(3)VITALI’S THEOREM AND WWKL 15To prove the claim,use Lemma 5.2and the Vitali property to ﬁnd a ﬁnite set of intervals J 1,...,J l ∈I such that J 1,...,J l ⊆E \A andµ(E \(A ∪J 1∪···∪J l ))<13µ(J 1∪···∪J l ).We then have µ(E \(A ∪I 1∪···∪I k ))<212µ(E \A )≤212µ(E \A )=34nµ(E ).Then by countable additivity we have µ E \∞ n =1A n =0and the lemma is proved.Remark 5.4.It is straightforward to generalize the previous lemma to the case of a Vitali covering of the n -cube [0,1]n by closed balls or n -dimensional cubes.In the case of closed balls,the constant 3in the Baby Vitali Lemma 5.1is replaced by 3n .Theorem 5.5.The Vitali theorem for the interval [0,1](as stated in Lemma 5.3)is equivalent to WWKL over RCA 0.Proof.Lemma 5.3shows that,in RCA 0,WWKL implies the Vitali theorem for intervals.It remains to prove within RCA 0that the Vitali theorem for [0,1]implies WWKL.Instead of proving WWKL,we shall prove the equivalent statement 3.3.3.Reasoning in RCA 0,suppose thatVITALI’S THEOREM AND WWKL 16(a n ,b n ),n ∈N ,is a sequence of open intervals which covers [0,1].Let I be the countable set of intervals (a nki ,b nki )= a n +i k(b n −a n ) where i,k,n ∈N and 0≤i <k .Then I is a Vitali covering of [0,1].By the Vitali theorem for intervals,I contains a sequence of pairwise disjoint intervals I m ,m ∈N ,such that µ ∞ m =0I m ≥1.By disjoint countable additivity (Corollary 2.5),we have∞m =0µ(I m )≥1.From this it follows easily that∞n =0|a n −b n |≥1.Thus we have 3.3.3and our theorem is proved.We now turn to Vitali’s theorem for measurable sets.Recall our discussion of measurable sets in section 4.A sequence of intervals I is said to almost Vitali cover a Lebesgue measurable set E ⊆[0,1]if for all >0we have µL (E \O )=0,where O = {I |I ∈I ,diam(I )< }.Theorem 5.6.The following is provable in WWKL 0.Let E ⊆[0,1]be a Lebesgue measurable set with µ(E )>0.Let I be a sequence of intervals which almost Vitali covers E .Then I contains a pairwise disjoint sequence of intervals I n ,n ∈N ,such that µ E \∞ n =0I n =0.Proof.The proof of this theorem is similar to that of Lemma 5.3.The only modiﬁcation needed is in the proof of the claim.Recall from Deﬁnition 4.5that E =lim n →∞E n where each E n is a ﬁnite union of intervals in [0,1].Fix m so large thatµ((E \E m )∪(E m \E ))<1VITALI’S THEOREM AND WWKL 17andµ(E m \(A ∪J 1∪···∪J l ))<136µ(E \A )<236µ(E \A )≤236µ(E \A )<236µ(E \A )=3,The Baire category theorem in weak subsystems of second order arith-metic ,Journal of Symbolic Logic 58(1993),557–578.7.O.Demuth and A.Kuˇc era,Remarks on constructive mathematical analysis ,[3],1979,pp.81–129.8.H.-D.Ebbinghaus,G.H.M¨u ller,and G.E.Sacks (eds.),Recursion Theory Week ,Lecture Notes in Mathematics,no.1141,Springer-Verlag,1985,IX +418pages.VITALI’S THEOREM AND WWKL189.Harvey Friedman,unpublished communication to Leo Harrington,1977.10.Harvey Friedman,Stephen G.Simpson,and Rick L.Smith,Countable algebraand set existence axioms,Annals of Pure and Applied Logic25(1983),141–181.11.,Randomness and generalizations ofﬁxed point free functions,[1],1990, pp.245–254.15.,Subsystems of Second Order Arithmetic,Perspectives in Mathematical Logic,Springer-Verlag,1998,XIV+445pages.21.Xiaokang Yu,Measure Theory in Weak Subsystems of Second Order Arithmetic,Ph.D.thesis,Pennsylvania State University,1987,vii+73pages.22.,Riesz representation theorem,Borel measures,and subsystems of sec-ond order arithmetic,Annals of Pure and Applied Logic59(1993),65–78. 24.,A study of singular points and supports of measures in reverse mathe-matics,Annals of Pure and Applied Logic79(1996),211–219.26.Xiaokang Yu and Stephen G.Simpson,Measure theory and weak K¨o nig’slemma,Archive for Mathematical Logic30(1990),171–180.E-mail address:dkb5@,giusto@dm.unito.it,simpson@ The Pennsylvania State University。

世卫组织饮用水硬度标准

世卫组织饮用水硬度标准The World Health Organization (WHO) sets guidelines for drinking water quality, including standards for water hardness. Water hardness is primarily determined by the concentration of calcium and magnesium ions in the water. These ions are essential minerals for human health, but excessive levels can cause problems such as scale buildup in pipes and appliances.世界卫生组织（WHO）制定了饮用水质量标准，包括水硬度标准。

水硬度主要由水中钙和镁离子的浓度决定。

这些离子是人体健康所必需的矿物质，但过高的水平可能会导致管道和家电中的水垢积聚。

The WHO recommends that the hardness of drinking water should not exceed 200 milligrams per liter (mg/l), which is equivalent to grains per gallon (gpg). This guideline is based on the potential health effects of consuming hard water over a long period of time. High levels of calcium and magnesium in drinking water have been associated with increased risk of cardiovascular disease and kidney stones.世卫组织建议饮用水的硬度不应超过每升200毫克（mg/l），相当于每加仑颗粒（gpg）。

学术英语(社科)Unit2二单元原文及翻译

UNIT 2 Economist1.Every field of study has its own language and its own way of thinking. Mathematicians talk about axioms, integrals, and vector spaces. Psychologists talk about ego, id, and cognitive dissonance. Lawyers talk about venue, torts, and promissory estoppel.每个研究领域都有它自己的语言和思考方式。

数学家谈论定理、积分以及向量空间。

心理学家谈论自我、本能、以及认知的不一致性。

律师谈论犯罪地点、侵权行为以及约定的禁止翻供。

2.Economics is no different. Supply, demand, elasticity, comparative advantage, consumer surplus, deadweight loss—these terms are part of the economist’s language. In the co ming chapters, you will encounter many new terms and some familiar words that economists use in specialized ways. At first, this new language may seem needlessly arcane. But, as you will see, its value lies in its ability to provide you a new and useful way of thinking about the world in which you live.经济学家也一样。

等同理论的核心要义

等同理论的核心要义如以权利主体、权利客体、权利内容、权利变动、权利变动原因的分析范式来考察专利制度，则专利法的主要研究领域在于客体与内容，而主体、变动以及变动原因方面可援用民法的相应制度。

在专利诉讼中，大部分案件纠结于专利权保护范围的确定，可以佐证上述判断。

专利权保护范围的确定居于专利诉讼的核心地位，基于权利要求文字的局限性，以等同理论弥补字面保护范围，成为不少国家专利制度的选择。

等同理论在法院的司法实践中发展起来，用于适当超越专利权利要求的文字来确定专利权保护范围，使专利法保持弹性，其适用标准日益精细化，也随着工业化和技术革新的步伐不断调整其政策走向。

范围而非侵权国内一般将“infringement”译为侵权，实际上该词一般专指侵害知识产权的行为，并不包括主观过错。

大陆法系下所谓的“侵权”要符合“侵害行为、主观过错、因果关系、损害后果”之构成要件，英美专利法上的“infringement”应译为“落入专利权保护范围”或“侵害行为”，如译为“侵权”，易使人误解知识产权之侵权构成不需要主观过错要件（这大概就是为什么持知识产权侵权无过错责任论者不在少数的原因）。

专利侵权（其他知识产权侵权也是如此）仍属于侵权（tort）之一种，使用infringement这一用语，恰恰意味着专利权保护乃至版权、商标权保护的关键问题之一在于确定权利边界，这是由知识产权客体的无形性决定的，边界确定之后一旦认定被告行为落入保护范围，则不论有无主观过错，权利人均可基于绝对权请求排除妨碍及不当得利之返还；如认定被告存在主观过错，才涉及到侵权赔偿问题。

严格地说，只有不当得利以外的赔偿才属于真正的侵权损害赔偿范畴，否则只是返还不当得利。

英美专利法著作一般说patent infringement包括两步，先是解释权利要求，再是将被控产品或方法与权利要求进行比对，判断专利权的范围是否覆盖了被控的产品或方法，可见判定是否构成infringement本来就无需考虑行为人的主观状态。

Ground states of the Wick-Cutkosky model using light-front dynamics

NT@UW-99-63
Ground states of the Wick-Cutkosky model using light-front dynamics
Jason R. Cooke and Gerald A. Miller
Department of Physics University of Washington Box 351560 Seattle WA 98195-1560, USA (FREVTEX 1
I. INTRODUCTION
Recent experiments at Thomas Jeﬀerson National Accelerator Facility have measured the A(Q2 ) structure function of the deuteron for momentum transfers up to 6 (GeV/c)2 [1], and measurements for B (Q2 ) are planned. At such large momentum transfers, a relativistic description of the deuteron is required. One approach that gives such a description is light-front dynamics, which we will examine here. To separate the eﬀects of the using lightfront dynamics from the eﬀects of the model, we choose to use the massive Wick-Cutkosky model. This is a “toy model” investigation, instead of the full nuclear theory calculation. Using this model, the light-front Hamiltonian approach is used to solve for the bound-state wavefunction. The results of our calculation can then be compared to other calculations done with the same model but diﬀerent approaches. The simplest observable that can be compared is the relationship between the bound-state mass and the coupling constant. The utility of the light-front dynamics was ﬁrst discussed by Dirac [2]. We start by expressing the four-vector xµ in terms of the light-front variables xµ = (x+ , x− , x1 , x2 ), where x± = x0 ± x3 . This is simply a change of variables, but an especially convenient one. Using this coordinate system and deﬁning the commutation relations at equal light-front time (x+ = tLF ), we obtain a light-front Hamiltonian [3–5]. The Hamiltonian is used in the light-front Schr¨ odinger equation to solve for the ground state. There are many desirable features of the light-front dynamics and the use of light-front coordinates. First of all, high-energy experiments are naturally described using light-front coordinates. The wave front of a beam of high-energy particles traveling in the (negative) three-direction is deﬁned by a surface where x+ is (approximately) constant. Such a beam can probe the wavefunction of a target described in terms of light-front variables [3,6]: the Bjorken x variable used to describe high-energy experiments is simply the ratio of the plus momentum of the struck constituent particle to the total plus momentum (p+ ) of the bound state. Secondly, the vacuum for a theory with massive particles can be very simple on the light front. This is because all massive particles and anti-particles have positive plus momentum, and the total plus momentum is a conserved quantity. Thus, the na¨ ıve vacuum + (with p = 0) is empty, and diagrams that couple to this vacuum are zero. This greatly reduces the number of non-trivial light-front time-ordered diagrams. Thirdly, the generators of boosts in the one, two, and plus directions are kinematical, meaning they are independent of the interaction. Thus, even when the Hamiltonian is truncated, the wavefunctions will transform correctly under boosts. Thus, light-front dynamics is useful for describing form factors at high momentum transfers. A drawback of the light-front formalism is that the Hamiltonian is not manifestly rotationally invariant, since the generators of rotations about the one and two directions are dynamical. A study of the eﬀects of the loss of rotational invariance of the excited states in the model being used here was made in Ref. [7], which shows that there is less breaking of the degeneracy in the spectrum when higher order potentials are used as opposed to lower order potentials. There are other approaches that can be used to obtain relativistic wavefunctions and bound-state energies, including the Feynman-Schwinger representation (FSR) of the twoparticle Green’s function [8] and the Bethe-Salpeter equation (BSE) [9–12]. The FSR is useful since it can be constructed so it is equivalent to the Bethe-Salpeter equation using a kernel where all two-particle-to-two-particle ladder and crossed ladder diagrams are included. 2

【工程学科英语(整合第二稿)】参考答案

Unit OneTask 1⑩④⑧③⑥⑦②⑤①⑨Task 2① be consistent with他说，未来的改革必须符合自由贸易和开放投资的原则。

② specialize in启动成本较低，因为每个企业都可以只专门从事一个很窄的领域。

③ d erive from以上这些能力都源自一种叫机器学习的东西，它在许多现代人工智能应用中都处于核心地位。

④ A range of创业公司和成熟品牌推出的一系列穿戴式产品让人们欢欣鼓舞,跃跃欲试。

⑤ date back to置身硅谷的我们时常淹没在各种"新新"方式之中，我们常常忘记了，我们只是在重新发现一些可追溯至涉及商业根本的朴素教训。

Task 3T F F T FTask 4The most common viewThe principle task of engineering: To take into account the customers ‘ needs and to find the appropriate technical means to accommodate these needs.Commonly accepted claims:Technology tries to find appropriate means for given ends or desires;Technology is applied science;Technology is the aggregate of all technological artifacts;Technology is the total of all actions and institutions required to create artefacts or products and the total of all actions which make use of these artefacts or products.The author’s opinion: it is a viewpoint with flaws.Arguments: It must of course be taken for granted that the given simplified view of engineers with regard to technology has taken a turn within the last few decades. Observable changes: In many technical universities, the inter‐disciplinary courses arealready inherent parts of the curriculum.Task 5① 工程师对于自己的职业行为最常见的观点是：他们是通过应用科学结论来计划、开发、设计和推出技术产品的。

英文翻译原件

1
where t is a new variable. Next we deﬁne the Generalized Gram’s Polynomials of A as the coeﬃcients of the characteristic polynomial of A A◦ , which are Laurent polynomials in the variable t. From the Generalized Gram’s Polynomials it is possible in a very uniform and compact way: 1. to characterize the rank of A and, 2. once the rank of A is ﬁxed, to determine: (a) matrices associated with precise projections of K(t)m onto Im A and of K(t)n onto Ker A respectively, (b) the equations of Im(A), (c) a Generalized Moore–Penrose Inverse of A, and (d) given v ∈ Im(A), a solution of A x = v generalizing the classical Cramer’s Rule to the underdetermined and overdetermined cases via our Generalized Moore–Penrose Inverse. This provides a generalization of the classical Moore-Penrose Inverse and Gram’s Coeﬃcients in the real or complex cases. The surprising fact is that for non real ﬁelds (e.g., ﬁelds of characteristic p) the rank of any matrix and a uniform generalized inverse of the matrix can be also controlled by a small number of sums of squares of minors. In fact our Generalized Gram’s Polynomials are only slight variants of the polynomials that appear in Mulmuley’s Algorithm. A consequence of this method is, as in [16], that the characterization of a full rank matrix in Km×n (for any ﬁeld K) can be done by using less than min(n, m)|n − m| + 1 polynomials in the entries of A: each one of these polynomials is a sum of squares of maximal minors of A. If n = 2m then n min(n, m)|n − m| + 1 = m2 + 1, which is clearly far from the consideration of the m maximal minors of A. In general, the total number of sums of squares of minors to be used for characterizing the rank is 1 smaller than 2 p(p + 1)p , where p = min(m, n) and p = max(m, n), so it is bounded by O(p p2 ); note p 2 that the total number of minors is clearly bigger than 2p ( p p) . Compared to Mulmuley’s Method, an important (and new) characteristic of the proposed method is the generalization of Moore–Penrose Inverses for each possible rank r. This allows us to obtain a uniform solving of linear systems of equations once the rank is known. Moreover, this is particularly useful when linear systems of equations depend on some parameters (avoiding thus any discussion on the vanishing or not of the pivots to be used; see the last section for enlightening examples). Our method requires a complexity similar to the one given in [11], where the parameterized Gauss elimination is analyzed, and it is proved that with k parameters, the complexity of parametric solving of A x = v is in nO(k) . The paper is organized as follows. The ﬁrst section recalls the classical theory about generalized inverses matrices. In the second section, we introduce a generalization of both Gram Coeﬃcients and of Moore–Penrose Inverse matrix for an arbitrary ﬁeld. Finally, the third section presents three diﬀerent examples, where we apply the diﬀerent results described in the second section.

Quanta Without Quantization

a rXiv:h ep-th/975235v129M a y1997Quanta without quantization James T.Wheeler Department of Physics,Utah State University,Logan,UT 84322Abstract The dimensional properties of ﬁelds in classical general relativity lead to a tangent tower structure which gives rise directly to quantum mechanical and quantum ﬁeld theory structures without quantization.We derive all of the fundamental elements of quantum mechanics from the tangent tower structure,including fundamental commuta-tion relations,a Hilbert space of pure and mixed states,measurable expectation values,Schr¨o dinger time evolution,“collapse”of a state and the probability interpretation.The most central elements of string theory also follow,including an operator valued mode expansion like that in string theory as well as the Virasoro algebra with central charges.Introduction The detailed structure of quantum systems follows by fully developing the scaling structure of spacetime.Thus quantum systems -de-spite their Hilbert space of states,operator-valued observables,interferingcomplex quantities,and probabilities -are rendered in terms of classical spacetime variables which simultaneously form a Lie algebra of operators on the space of conformal weights.This remarkable result follows from the tangent tower structure implicit in general relativity.We develop this structure,cite a central theorem,then examine some properties of tensors over the tangent tower.Finally,we apply these ideas to quantum mechanics and string theory,showing how the core elements of both arise classically.1The weight tower and weight maps Consider a spacetime(M,g)with dynamicalﬁelds,{ΦA|A∈A}of various conformal weights and tensorial types.Under a global change of units byλ,letΦA→(λ)w AΦA(1) where w A is called the conformal weight ofΦA.Normally,physicists simply insert these scale factors by hand when needed,without mentioning the im-plicit mathematical structures their use requires,but these structures turn out to be interesting and important.The tower structure begins with the set of conformal weights,W≡{w A| A∈A},which must be closed under addition of any two diﬀerent elements. Possible sets include the reals R,the rationals Q,the integers J,and the ﬁnite set{0,1,−1}.For most physical problems we can choose the unit-weight objects to give W=J.Next,deﬁne the equivalence relationΦA∼=ΦB if w A=w B and∃ηsuch thatΦA=ηΦB(2) which partitions the tangent space T M into a tower of projective Minkowski spaces,P M,one copy for each n∈J=W.This partition enlarges the linear transformation group of the tangent space into the direct product of the Lorentz group and the group of weight maps.While the Lorentz trans-formations have their usual eﬀect,general weight maps act on conformal weight.To see that the group is a direct product,consider the product of an n-weight scalarﬁeld with an m-weight vectorﬁeld.Since the linear trans-formations preserve the Lorentz inner product between arbitrarily weighted vectors,the resulting(n+m)-weight vectorﬁeld remains parallel to the orig-inal m-weight vectorﬁeld under Lorentz transformation.Therefore,Lorentz transformations map diﬀerent weight vectors in the same way.We now investigate weight maps.Just as the only measurable Lorentz objects are scalars,the only measurable tangent tower quantities are zero weight scalars1.Therefore,to readily form zero weight scalars,we classify weight maps and tensors over W by their conformal weights.The generator of global scale changes,D,determines the weights ofﬁelds according to2DΦA=w AΦA(3)while the generators Mαof deﬁnite-weight maps satisfy[D,Mα]=nαMα(4) where nα∈J.Then Mαmaps n-weightﬁelds to(n+nα)-weightﬁelds,making the construction of0-weight quantities straightforward.The following theorem now holds[1]:Theorem.Let V be a maximally non-commuting Lie algebra consisting of exactly one weight map of each conformal weight.Then V is the Virasoro algebra with central charge,[M(m),M(n)]=(m−n)M(m+n)+cm(m2−1)δ0m+n1(5) The lengthy proof relies on explicit construction through a series of induc-tive arguments.It is highly signiﬁcant to note that the real-projective tangent tower produces the same central charge for V as unitarily-projective string theory,despite its classical character.This is theﬁrst concrete evidence that some phenomena widely regarded as“quantum”can be understood from a classical standpoint.Tensors over the weight tower Having understood the algebraic char-acter of deﬁnite-weight weight maps,we next look at the tensors they act on.Since Lorentz transformations decouple from weight maps,the Lorentz and conformal ranks are independent.ThusT a1···a rn1···n s:(P M)r⊗J s→R(6) is a typical rank(r,s)tensor.Weight maps act linearly on each label n i.Particularly relevant to quantum systems are(0,1)tensors.Withηk a k-weight scalar,Dηk=kηk,a general(0,1)tensor is an indeﬁnite-weightlinear combinationΦ=∞k=−∞φkηk(7)We immediately see the need for some convergence criterion.Imposing a norm provides such a criterion,and with a norm these objects form a Hilbert space,H.The simplest norm uses a continuous representation for the(0,1)tensors deﬁned byΦ(x)≡∞n=−∞φn e inx.(8) 3Clearly,Φ(x)exists only under appropriate convergence conditions,provided by including as the(0,1)tensors those vectors satisfying1δ(x−y)+c1(11)∂xfor D andM(k)(x,y)=e ikx(−i∂x−k)δ(x−y)(12) for the k-weight Virasoro operator.In eq.(11),D(x,y)requires the central distribution c to cancel surface terms from the product integral.Such terms are an artifact of the continuous representation.Physical eﬀects of the tangent tower Now we describe physical eﬀects of the tangent tower.We replace the usual(r,0)tensors of quantum mechan-ics and quantumﬁeld theory by(r,1)or(r,2)tensors.In the remaining two sections we do this in detail for quantum mechanics,then brieﬂy for string theory.Conformal weight and quantum mechanics The tangent tower under-pinning of all axiomatic features of quantum mechanics now follows imme-diately:commutation relations of operator-valued position and momentum vectors,a Hilbert space of pure and mixed states,measurable expectation values,Schr¨o dinger time evolution,“collapse”of a state and the probability interpretation.First,consider canonical commutators.Since w x=1and w p/h=−1, canonical coordinates lie in the subalgebra determined by W0={0,1,−1}⊂W.We temporarily consider operators in this subspace,replacing symplectic coordinates Q A=(q i,πj)by weight-map-valued6-vectorsˆQ A=(ˆq i,ˆπj)∈T a nm forming the Lie algebra[ˆQ A,ˆQ B]=c AB1(13)4where projective representation allows arbitrary central charges c AB.The only invariant antisymmetric symplectic tensor is the symplectic2-formΩAB= 0−δi jδj i0 (14)so we set[ˆQ A,ˆQ B]=ΩAB1(15) Furthermore,the natural symplectic metricK AB= 0δi jδj i0 (16)may be diagonalized by a symplectic transformation to new variablesˆR A= (ˆX i,ˆP j)such that˜K AB= δij−δij (17) or equivalentlyˆR′A=(ˆX i,iˆP j)with˜K′AB= δijδij (18)The zero signature of the symplectic metric requires an imaginary unit in relatingˆR′A toˆP j because the physicalˆX i andˆP j have the same metric, +δij.The projective algebra ofˆX i andˆP j is the canonical one[ˆX i,ˆP j]=iδij1(19)[ˆX i,ˆX j]=[ˆP i,ˆP j]=0(20) Thus,“quantum”(ˆX i,ˆP j)commutators follow from classical scaling consid-erations by replacing classical variables with weight tower operators in the {0,1,−1}subalgebra,and using the natural symplectic structure.Other quantum structures follow easily.Thus,deﬁnite weight scalars replace pure quantum states,while indeﬁnite weight objects such asΦ(x)∈H replace mixed states.The construction of expectation values is simply a rule to generate a0-weight scalar.The rule works by matching elements of5H with their complex conjugates but the deﬁnition ofΦ(x)above translates this into the manifestly0-weight sumΦ,Ψ =1dτinﬂat spacetime while uµWµΦgives the action ofa weight map H≡uµWµon the weight superpositionΦ(xν;x).Identifying H as the Hamiltonian operator[2],eq.(22)becomes the Schr¨o dinger equation. The free-particle form for H is the zero-weight quantityH= dˆX jL ,L2φ−2,etc.,with L some standard unitof length.Therefore the rules of quantum mechanics have natural classical interpre-tations in terms of the scale-invariance properties of spacetime.6Conformal weight and quantumﬁeld theory Just asﬁeld theory emerges as the limiting case of multiparticle dynamics,and quantumﬁeld theory emerges as a blend of quantum mechanics and special relativity[3], we can imagine retracing the preceding arguments to derive the principles of quantumﬁeld theory.After all,the quantum state is aﬁeld,even in quantum mechanics.Thus,we may anticipate a classical tangent tower in-terpretation of quantumﬁeld theory.As striking as this conjecture seems, we now demonstrate a more striking claim:the tangent tower contains the essential elements of string theory[4].Minor manipulations of a deﬁnite weight(1,2)tensorαµ(k)(x,y)found bywriting theδ-function in D asδ(x−y)=1References[1]Wheeler,J.T.,String without strings,in preparation.[2]Wheeler,J.T.,Phys.Rev.D44(1990);Wheeler,J.T,Proceedings ofthe Seventh Marcel Grossman Meeting on General Relativity,R.T.Jantzen and G.M.Keiser,editors,World Scientiﬁc,London(1996)pp 457-459.[3]Weinberg,S.,The quantum theory ofﬁelds,Cambridge University Press(1995).[4]Green,M.B.,J.H.Schwarz and E.Witten,Superstring theory,Cam-bridge University Press(1987).[5]Kuchar,K.V.and C.G.Torre,J.Math.Phys.30(8),August1989.8。

数学专业英语(吴炯圻)翻译5-A

5-A The coordinate system of Cartesian geometryAs mentioned earlier, one of the applications of the integral is the calculation of area. Ordinarily we do not talk about area by itself, instead, we talk about the area of something.就像前面提到的，积分的一个应用就是计算面积. 通常我们不讨论面积本身, 相反, 是讨论某物的面积.This means that we have certain objects (polygonal regions, circular regions, parabolic segments etc.) whose areas we wish to measure.这意味着我们想测量一些物体的面积（多边形区域，圆域，抛物弓形等。

If we hope to arrive at a treatment of area that will enable us to deal with many different kinds of objects, we must first find an effective way to describe these objects.如果我们希望获得面积的计算方法以便能够用它来处理各种不同类型的图形，我们就必须首先找出表述这些图形的有效方法。

The most primitive way of doing this is by drawing figures, as was done by the ancient Greeks.描述图形最原始的方法是画图, 就像古希腊人做的那样A much better way was suggested by Rene Descartes, who introduced the subject of analytic geometry (also known as Cartesian geometry).R.笛卡儿提出了一种好得多的办法，并建立了解析几何（也称为笛卡儿几何）这个学科。

Scattering of a Klein-Gordon particle by a Hulth'en potential

a r X i v :0710.2575v 1[q u a n t -p h ] 13 O c t 2007Scattering of a Klein-Gordon particle by a Hulth´e n potentialJian You Guo,1,∗Xiang Zheng Fang,1and Chuan Mei Xie 11School of physics and material science,Anhui university,Hefei 230039,P.R.ChinaThe Klein-Gordon equation in the presence of a spatially one-dimensional Hulth´e n potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions.The transmission coeﬃcient is derived by the matching conditions on the wavefunctions and the condition for the existence of transmission resonances are investigated.It is shown how the zero-reﬂection condition depends on the shape of the potential.PACS numbers:03.65.Nk,03.65.PmThe study of low-momentum scattering in the Schr¨o inger equation in one-dimensional even potentials shows that,as momentum goes to zero,the reﬂection coeﬃcient goes to unity unless the potential V (x )supports a zero-energy resonance[1].In this case the transmission coeﬃcient goes to unity,becoming a transmission resonance[2].Recently,this result has been generalized to the Dirac equation[3],showing that transmission resonances at k =0in the Dirac equation take place for a potential barrier V =V (x )when the corresponding potential well V =−V (x )supports a supercritical state.This conclusion is demonstrated in both special examples as square potential and Gaussian potential,where the phenomenon of transmission resonance is exhibited clearly in Dirac spinors in the appropriate shapes and strengths of the potentials.Except for the both special examples,the transmission resonance is also investigated in the realistic physical system.In Ref.[4],a key potential in nuclear physics is introduced,and the scattering and bound states are obtained by solving the Dirac equation in the presence of Woods-Saxon potential,which has been extensively discussed in the literature[5,6,7,8,9].The transmission resonance is shown appearing at the spinor wave solutions with a functional dependence on the shape and strength of the potential.The presence of transmission resonance in relativistic scalar wave equations in the potential is also investigated by solving the one-dimensional Klein-Gordon equation.The phenomenon of resonance appearing in Dirac equation is reproduced at the one-dimensional scalar wave solutions with a functional dependence on the shape and strength of the potential similar to those obtained for the Dirac equation[10].Due to the transmission resonance appearing in the realistic physical system for not only Dirac particle but also Klein Gordon particle as illustrated in the Woods-Saxon potential,it is indispensable to check the existence of the phenomenon in some other ﬁelds.Considering that the Hulth´e n potential[11]is an important realistic model,it has been widely used in a number of areas such as nuclear and particle physics,atomic physics,condensed matter and chemical physics[12,13,14,15].Hence,to discuss the scattering problem for a relativistic particle moving in the potential is signiﬁcant,which may provide more knowledge on the transmission resonance.Recently,there have been a great deal of works to be put to the Hulth´e n potential in order to obtain the bound and scattering solutions in the case of relativity and non relativity[16].However,the transmission resonance is not still checked for particle moving in the potential in the relativistic case.In this paper,we will derive the scattering solution of the Klein-Gordon equation in the presence of the general Hulth´e n potential,and show the phenomenon of transmission resonance as well as its relation to the parameters of the potential.Following Ref.[10],one-dimensional Klein-Gordon equation,minimally coupled to a vector potential A µ,is written asηαβ(∂α+ieA α)(∂β+ieA β)φ+φ=0,(1)where the metric ηαβ=diag(1,-1).For simplicity,the natural units =c =m =1are adopted,and Eq.(1)is simpliﬁed into the following formd 2φ(x )e −ax −q+Θ(x )V 0∗Electronicaddress:jianyou@where all the parameters V0,a,and q are real and positive.To remove oﬀthe divergence of Hulth´e n potential,q<1 is required.If q=−1is taken,the Hulth´e n potential turns into a Woods-Saxon potential.Θ(x)is the Heaviside step function.The form of the Hulth´e n potential is shown in Fig.1and2at diﬀerent values of parameters.From Fig.1and2one readily notices that for a given value of the potential strength parameter V0,as q increases, the height of potential barrier increases.When q−→1,the height of potential barrier goes to inﬁnity.Similarly,the potential becomes more diﬀusible with the decreasing of the diﬀuseness parameter a.In order to obtain the scattering solutions for x<0with E2>1,we solve the diﬀerential equationd2φ(x)e−ax−q 2−1 φ(x)=0.(4)On making the substitution y=qe ax,Eq.(4)becomesa2y2d2φdy+ E−V01−y 2−1 φ(x)=0.(5)In order to derive the solution of Eq.(5),we putφ=yµ(1−y)λf,then Eq.(5)reduces to the hypergeometric equationy(1−y)f′′+[1+2µ−(2µ+2λ+1)y]f′− λ(1+2µ)+2EV0E2−1,λ±=12 µ2+λ2−λ−2EV0dx2+ E−V0dz2+a2zdφq(1−z) 2−1φ(x)=0.(11)Putφ=zµ(1−z)λg,Eq.(11)reduces to the hypergeometric equationz(1−z)g′′+[1+2µ−(2µ+2λ+1)z]g′− λ(1+2µ)+2EV02m φdφ∗dx .(16)The current as x−→−∞can be decomposed as j L=j in−j reﬂwhere j in is the incident current and j reﬂis the reﬂected one.Analogously we have that,on the right side,as x−→∞the current is j R=j trans,where j trans is the transmitted ing the reﬂected j reﬂand transmitted j trans currents,we have that the reﬂection coeﬃcient R,and the transmission coeﬃcient T can be expressed in terms of the coeﬃcients A,B,and D asR=j reﬂ|A|2,(17)T=j trans|A|2.(18)Obviously,R and T are not independent;they are related via the unitarity conditionR+T=1.(19)In order to obtain R and T we proceed to equate at x=0the rightφR and leftφLwave functions and theirﬁrstderivatives.From the matching condition we derive a system of equations governing the dependence of coeﬃcients A and B on D that can be solved numerically.The calculated transmission coeﬃcient T varying with the energy E is displayed in Figs.3-6at the diﬀerent values of the parameters in the Hulth´e n potential.From Figs.3-6,one can see that the transmission resonance appears in all the Hulth´e n potential considered here.But the intensity and width of resonance as well as the condition for the existence of resonance are diﬀerent,and they depend on the shape of the pared Fig.3with Fig.4,it can be seen that the width of resonance decreases as the decreasing of diﬀuseness a,which is similar to that of Woods-Saxon potential as shown in Figs.3and5in Ref.[10].The same dependence can also be observed from Figs.5and6. Compared Fig.3with Fig.5,one canﬁnd that the condition for the existence of transmission resonance does also relate to the parameter q.As q decreases,the height of potential barrier increases,the widths of the transmission resonance increases.The conclusion can also be obtained by comparing Fig.4with Fig.6.In order to obtain more knowledge on the dependence of transmission resonance on the shapes of the potential,the transmission coeﬃcient T varying with the strength of potential V0is plotted in Figs.7and8.Beside of the phenomenon of transmission resonance,similar to the Fig.3and4,the width of resonance decreasing as the decreasing of diﬀuseness a is disclosed.All these show the transmission resonances in Hulth´e n potential for Klein-Gordon particle possess the same rich structure with that we observe in Woods-Saxon potential.AcknowledgmentsThis work was partly supported by the National Natural Science Foundation of China under Grant No.10475001and 10675001,the Program for New Century Excellent Talents in University of China under Grant No.NCET-05-0558,the Program for Excellent Talents in Anhui Province University,and the Education Committee Foundation of Anhui Province under Grant No.2006KJ259B[1]R.Newton,Scattering Theory of Waves and Particles (Springer-Verlag,Berlin,1982).[2]D.Bohm,Quantum Mechanics (Prentice-Hall,Englewood Cliﬀs,NJ,1951).[3]N.Dombey,P.Kennedy,and A.Calogeracos,Phys.Rev.Lett.85,1787(2000).[4]P.Kennedy,J.Phys.A 35,689(2002).[5]J.Y.Guo,X.Z.Fang,and F.X.Xu,Phys.Rev.A 66,062105(2002).[6]V.Petrillo and D.Janner,Phys.Rev.A 67,012110(2003).[7]G.Chen,Phys.Scr.69,257(2004).[8]J.Y.Guo,J.Meng,and F.X.Xu,Chin.Phys.Lett.20,602(2003).[9]A.D.Alhaidari,Phys.Rev.Lett.87,210405(2001);88,189901(E)(2002).[10]C.Rojas and V.M.Villalba,Phys.Rev.A 71,052101(2005).[11]L.Hulth´e n,Ark.Mat.Astron.Fys.A 28,5(1942).[12]Y.P.Varshni,Phys.Rev.A 41,4682(1990).[13]M.Jameelt,J.Phys.A:Math.Gen.19,1967(1986).[14]R.Barnana and R.Rajkumar R,J.Phys.A:Math.Gen.20,3051(1987).[15]L.H.Richard,J.Phys.A:Math.Gen.25,1373(1992).[16]C.-Y.Chen,D.-S.Sun,F.-L.Lu,Phys.Lett.A,(2007)(in press),and the Reﬀerences there.[17]W.-C.Qiang,R.-S.Zhou,Y.Gao,Phys.Lett.A,(2007)(in press).42024X510152025303540VFIG.1:Hulth´e n potential for a=1.0and q=0.9with V 0=4,of which the peak of barrier reaches 40.0.42024X12345678VFIG.2:Hulth´e n potential for a=0.5and q=0.5with V 0=4,of which the peak of barrier reaches 8.0.246810E0.20.40.6T FIG.3:The transmission coeﬃcient for the relativistic Hulth´e n potential barrier.The plot illustrate T for varying energy E with V 0=4,a =1,and q =0.9.246810E0.20.40.60.81T FIG.4:Similar to Fig.3,but with V 0=4,a =0.5,and q =0.9.246810E0.20.40.60.81T FIG.5:Similar to Fig.3,but with V 0=4,a =1,and q =0.5.246810E0.20.40.6T FIG.6:Similar to Fig.3,but with V 0=4,a =0.5,and q =0.5.1234V00.20.40.60.81T FIG.7:The transmission coeﬃcient for the relativistic Hulth´e n potential barrier.The plot illustrate T for varying barrier height V 0with E =2,a =1,and q =0.9.1234V00.20.40.60.81T FIG.8:Similar to Fig.7,but with E =2,a =0.5,and q =0.9.。

Sparse Linear Least Squares Problems in Optimization

PONTUS MATSTOMS
at@math.liu.se
Department of Mathematics, Link¨ oping University, S-581 82 Link¨ oping, Sweden.
Abstract. Numerical and computational aspects of direct methods for large and sparse least squares problems are considered. After a brief survey of the most often used methods, we summarize the important conclusions made from a numerical comparison in matlab. Signiﬁcantly improved algorithms have during the last 1015 years made sparse QR factorization attractive, and competitive to previously recommended alternatives. Of particular importance is the multifrontal approach, characterized by low ﬁll-in, dense subproblems and naturally implemented parallelism. We describe a Householder multifrontal scheme and its implementation on sequential and parallel computers. Available software has in practice a great inﬂuence on the choice of numerical algorithms. Less appropriate algorithms are thus often used solely because of existing software packages. We brieﬂy survey software packages for the solution of sparse linear least squares problems. Finally, we focus on various applications from optimization, leading to the solution of large and sparse linear least squares problems. In particular, we concentrate on the important case where the coefﬁcient matrix is a ﬁxed general sparse matrix with a variable diagonal matrix below. Inner point methods for constrained linear least squares problems give, for example, rise to such subproblems. Important gains can be made by taking advantage of structure. Closely related is also the choice of numerical method for these subproblems. We discuss why the less accurate normal equations tend to be sufﬁcient in many applications. Keywords: Least squares problem, Sparse matrices, QR factorization, Multifrontal method

英文机器人

Journal of lntelligent and Robotic Systems 14: 43-68, 1995. © 1995 Kluwer Academic Publishers. Printed in the Netherlands.
43
Overview of Damped Least-Squares Methods for Inverse Kinematics of Robot Manipulators
ARATI S. DEO and IAN D. WALKER Department of Electrical and Computer Engineering, Rice University, Houston TX 77251, U.S.A. (Received: 28 December 1993)
Abstract. In this paper, we present a tutorial report of the literature on the damped-least squares method which has been used for computing velocity inverse kinematics of robotic manipulators. This is a local optimization method that can prevent infeasible joint velocities near singular configurations by using a damping factor to control the norm of the joint velocity vector. However, the exactness of the inverse kinematic solution has to be sacrificed in order to achieve feasibility. The damping factor is an important parameter in this technique since it determines the trade-off between the accuracy and feasibility of the inverse kinematic solution. Various methods that have been proposed to compute an appropriate damping factor are described. Redundant manipulators, possessing extra degrees of freedom, afford more choice of inverse kinematic solutions than do non-redundant ones. The damped least-squares method has been used in conjunction with redundancy resolution schemes to compute feasible joint velocities for redundant arms while performing an additional subtask. We outline the different techniques that have been proposed to achieve this objective. In addition, we introduce an iterative method to compute the optimal damping factor for one of the redundancy resolution techniques. Key words. Robotics, kinematics, redundancy, damped least squares singularity robustness.