A fractal-based model for the microstructure evolution of silicon bronze wires fabricated by die
材料断口中的分形(英文)
Fractals in Material BreaksWhen materials break, they often leave behind jagged and irregular surfaces. These surfaces, known as fracture surfaces, contain a wealth of information about the behavior of the material leading up to the break. One particular aspect that researchers have been studying is the presence of fractals in these surfaces.Fractals are mathematical patterns that repeat at different scales. They are often found in nature, such as in the branching of trees or the coastline of a beach. However, they can also be observed in man-made materials, especially when those materials are subjected to stress and strain.Researchers have found that the presence of fractals in material fracture surfaces can give valuable insights into the material's mechanical properties. By analyzing the fractal dimension of the surface, they can determine the level of complexity and irregularity in the material's structure.Fractals can also help predict the behavior of materials under different conditions. By studying the fractal patterns of a material before and after exposure to stress, researchers can better understand how the material responds to different forces and how it might fail under certain conditions.In addition to mechanical properties, fractals in material breaks can also be used for forensic analysis. By studying the fractal patterns left behind on a surface, investigators can determine the type and amount of force that was exerted on the material, helping to identify the cause of failure.Overall, the study of fractals in material fracture surfaces is an exciting area of research with many potential applications. By understanding the patterns and behaviors of materials on a fractal level, we can better design and utilize these materials in industry, while also gaining a deeper understanding of the world around us.。
A survey on the stability of fractional differential equations
Eur.Phys.J.Special Topics193,27–47(2011) c EDP Sciences,Springer-Verlag2011DOI:10.1140/epjst/e2011-01379-1T HE E UROPEANP HYSICAL J OURNAL S PECIAL T OPICSReviewA survey on the stability of fractionaldifferential equationsDedicated to Prof.Y.S.Chen on the Occasion of his80th BirthdayC.P.Li1,a and F.R.Zhang1,2,b1Department of Mathematics,Shanghai University,Shanghai200444,PR China2School of Mathematics and Computational Sciences,China University of Petroleum (East China),Dongying257061,PR ChinaReceived01December2010/Received infinal form27January2011Published online4April2011Abstract.Recently,fractional calculus has attracted much attentionsince it plays an important role in manyfields of science and engineer-ing.Especially,the study on stability of fractional differential equationsappears to be very important.In this paper,a brief overview on therecent stability results of fractional differential equations and the ana-lytical methods used are provided.These equations include linear frac-tional differential equations,nonlinear fractional differential equations,fractional differential equations with time-delay.Some conclusions forstability are similar to that of classical integer-order differential equa-tions.However,not all of the stability conditions are parallel to thecorresponding classical integer-order differential equations because ofnon-locality and weak singularities of fractional calculus.Some resultsand remarks are also included.1IntroductionFractional calculus has been300years old history,the development of fractional calculus theory is mainly focused on the pure mathematicalfield.The earliest more or less systematic studies seem to have been made in the19th century by Liouville, Riemann,Leibniz,etc.[1,2].In the last two decades,fractional differential equations (FDEs)have been used to model various stable physical phenomena with anomalous decay,say that are not of exponential type[3].We can refer to[4]for the recent history of fractional calculus.As we all know,many mathematical models of real problems arising in variousfields of science and engineering are either linear systems or nonlinear systems.Nevertheless,most differential systems used to describe physical phenomena are integer-order systems.With the development of fractional calculus, it has been found that the behavior of many systems can be described by using the fractional differential systems[5–9].It is worth mentioning that many physical phenomena having memory and genetic characteristics can be described by using the fractional differential systems.In fact,real world processes generally or most likelya e-mail:lcp@b e-mail:zhangfengrongsong@28The European Physical Journal Special Topicsare fractional order systems[10,11].That is to say,a lot of physical systems showfractional dynamical behavior because of special materials and chemical properties.Recently,the theory of FDEs has been studied and some basic results areobtained including stability theory.The question of stability is of main interest inphysical and biological systems,such as the fractional Duffing oscillator[12,13],frac-tional predator-prey and rabies models[14],etc.It is known that the chaotic sequenceis non-periodic and pseudo-random.Similar to integer-order differential equations,the stability theory of FDEs is also widely applied to chaos and chaos synchroniza-tion[15–19]due to its potential applications in control processing and secure com-munication.However,a few stability results rely on a restrictive modeling of FDEs:the basic hypothesis deals with commensurability,i.e.the fractional derivative ordershave to be an integer multiple of minimal fractional order.Owing to this hypothesis,some stability results are available,based on Matignon’s theorem[20].On the otherhand,the case of incommensurate fractional order can be referred to[21,22].In this paper,we present and discuss some basic results on stability of FDEsincluding linear FDEs,nonlinear FDEs,FDEs with time-delay and the analyticalmethods used.The analysis on stability of FDEs is more complex than that of clas-sical differential equations,since fractional derivatives are nonlocal and have weaklysingular kernels.The earliest study on stability of FDEs started in[23],the authorstudied the case of linear FDEs with Caputo derivative and the same fractional orderα,where0<α≤1.The stability problem comes down to the eigenvalue prob-lem of system matrix.Corresponding to the stability result in[23],Qian et al.[22]recently studied the case of linear FDEs with Riemann-Liouville derivative and thesame fractional orderα,where0<α<1.Then,in[24–26]authors derived thesame conclusion as[23]for the case1<α<2.[21]studied the linear system withmulti-order Caputo derivative and derived a sufficient condition on Lyapunov globalasymptotical stability.In the last decades,many researchers have more interests inthe stability of linear systems and various methods have emerged in succession.Forexample,there are frequency domain methods[27–32],Linear Matrix Inequalities(LMI)methods[25,26,33,34]and conversion methods[10],[35–37].By contrast,the development of stability of nonlinear FDEs is a bit slow.Thestructural stability was studied in[38],where the system with Riemann-Liouvillederivative was considered by using Taylor polynomial.In[39]authors investigatedthe system of nonautonomous FDEs involving Caputo derivative and derived theresult on continuous dependence of solution on initial conditions.The stability inthe sense of Lyapunov has also been studied[40]by using Gronwall’s lemma andSchwartz inequality.We can also refer to[14],[41–47],where the linearization method was considered.But the rigorous theoretical derivation has not been founded.Some researchers weakened the criterion of stability,such as[48]where the L p-stability properties of nonlinear FDEs were investigated.In[49,50],the Mittag-Leffler stability and the fractional Lyapunov’s second method were proposed.At last Deng[51]derived a sufficient stability condition of nonlinear FDEs.In engineering,a kind of system is also very important,namely,the time-delaysystem.In[52–55]authors considered thefinite-time stability of FDEs with time-delay on the basis of real problems.They studied the autonomous and nonau-tonomous fractional differential systems.For the time-delay system stability,we canrefer to[21],[56–58].In[59],Petr´aˇs gave a survey on the methods for stability investigation of a certainclass of fractional differential systems with rational orders and Caputo derivative in aviewpoint of control.To complement the literature,we will review the stability resultsof FDEs with Riemann-Liouville derivative or Caputo derivative and the analyticalmethods.Furthermore,the stability of FDEs with time-delay will also be covered.Thepaper is outlined as follows.In Sec.2,wefirst recall some definitions and propositions.Perspectives on Fractional Dynamics and Control29In Sec.3,some stability conditions of linear FDEs are presented,meanwhile,we give two results.In Sec.4,some stability conditions of nonlinear FDEs are described. Sec.5deals with the stability of FDEs with time-delay.Conclusions and comments are included in Sec.6.2PreliminariesLet us denote by R the set of real numbers,R+the set of positive real numbers and by Z+the set of positive integer numbers,denote by C the set of complex numbers. We denote the real part of complex numberαby Re(α).Two kinds of fractional derivatives,i.e.,the Riemann-Liouville derivative and Caputo derivative,have been often used in fractional differential systems.We briefly introduce these two definitions of fractional derivatives which will be frequently used throughout this paper.Firstly,we introduce the definition of fractional integral[60]. Definition1.The fractional integral(or,the Riemann-Liouville integral)D−αt0,t with fractional orderα∈R+of function x(t)is defined below:D−αt0,t x(t)=1Γ(α)tt0(t−τ)α−1x(τ)dτ,where t=t0is the initial time,Γ(·)is the Euler’s gamma function.Definition2.The Riemann-Liouville derivative with orderαof function x(t)is defined below:RL Dαt0,t x(t)=1Γ(m−α)d mdt mtt0(t−τ)m−α−1x(τ)dτ=d mdt mD−(m−α)t0,t,where m−1≤α<m∈Z+.Definition3.The Caputo derivative with orderαof function x(t)is defined below:C Dαt0,t x(t)=1Γ(m−α)tt0(t−τ)m−α−1x(m)(τ)dτ=D−(m−α)t0,td mdt mx(t),where m−1<α<m∈Z+.There are also two functions that play an important role in the study on stability of FDEs.Definition4.The Mittag-Leffler function is defined byEα(z)=∞k=0z kΓ(kα+1),where Re(α)>0,z∈C.The two-parameter Mittag-Leffler function is defined byEα,β(z)=∞k=0z kΓ(kα+β),where Re(α)>0andβ∈C,z∈C.One can see Eα(z)=Eα,1(z)from the above equations.30The European Physical Journal Special TopicsDefinition 5([61]).The α-exponential function is defined as follows:e λz α=zα−1E α,α(λz α),where z ∈C \0,Re (α)>0,and λ∈C .E α,α(·)is the two-parameter Mittag-Leffler function.Proposition 1.If 0<α<2,βis an arbitrary complex number,then for an arbitrary integer p ≥1the following expansions hold:E α,β(z )=1αz (1−β)/αexp(z 1/α)−p k =11Γ(β−αk )1z k +O 1|z |p +1 ,with |z |→∞,|arg(z )|≤απ2,andE α,β(z )=−pk =11Γ(β−αk )1z k +O 1|z |p +1 ,with |z |→∞,|arg(z )|>απ2.Proof.These results were proved in [60].The following relations for the α-exponential function follow from Definition 5and Proposition 1:Proposition 2[61].If 0<α<2,z ∈C ,then the following asymptotic equivalents for e λz αas |z |reaches infinity are valid:•for |arg(λ)|≤απ2,e λz α∼λ(1−α)/ααexp(λ1/α)z ,•for |arg(λ)|>απ2,e λz α∼−λ−2Γ(−α)1z α+1.In this paper,we will consider the following general type of FDEs involving Caputo derivative or Riemann-Liouville derivativeD ¯αt 0,t x (t )=f (t,x ),(1)with suitable initial values x k =[x k 1,x k 2,...,x kn ]T ∈R n (k =0,1,...,m −1),where x (t )=[x 1(t ),x 2(t ),...,x n (t )]T ∈R n ,¯α=[α1,α2,...,αn ]T ,m −1<αi <m ∈Z +(i =1,2,...,n ),D ¯αt 0,t x (t )=[D α1t 0,t x 1(t ),...,D αn t 0,t x n (t )]T ,f :[t 0,∞)×R n →R n ,D αi t 0,t denotes either C D αi t 0,t or RL D αi t 0,t .In particular,if α1=α2=···=αn =α,then Eq.(1)can be written asD αt 0,t x (t )=f (t,x ).(2)We call Eq.(2)the same order fractional differential system,otherwise,call Eq.(1)multi-order fractional differential system.The following definitions are associated with the stability problem in the paper.Definition 6[49].The constant vector x eq is an equilibrium point of fractional dif-ferential system (1),if and only if f (t,x eq )=D ¯αt 0,t x (t )|x (t )=x eq for all t >t 0.Without loss of generality,let the equilibrium point be x eq =0,we introduce the following definition.Perspectives on Fractional Dynamics and Control31 Definition7.The zero solution of fractional differential system(1)is said to be stable if,for any initial values x k=[x k1,x k2,...,x kn]T∈R n(k=0,1,...,m−1), there exists >0such that any solution x(t)of(1)satisfies x(t) <εfor all t>t0. The zero solution is said to be asymptotically stable if,in addition to being stable, x(t) →0as t→+∞.Definition8.Let1≤p≤∞andΩ⊂[t0,∞),the same order system(2)with Riemann-Liouville derivative is L p(Ω)−stable if the solution x(t)=[x1(t),..., x n(t)]T defined by equationx(t)=x0Γ(α)(t−t0)α−1+1Γ(α)tt0(t−τ)α−1f(τ,x(τ))dτbelongs to L p(Ω).Where0<α<1,x0∈R n is the initial value,f∈C([t0,∞)×R n,R n+)is a continuous positive function.Definition9(Mittag-Leffler Stability)[49].Let B⊂R n be a domain containing the origin.The zero solution of the same order system(2)is said to be Mittag-Leffler stable ifx(t) ≤{m(x(t0))Eα(−λ(t−t0)α)}b,where t0is the initial time,α∈(0,1),λ>0,b>0,m(0)=0,m(x)≥0,and m(x)is locally Lipschitz on x∈B⊂R n with Lipschitz constant L.Definition10.A continuous functionα:[0,∞)→[0,∞)is said to belong to class-K if it is strictly increasing andα(0)=0.Definition11(Generalized Mittag-Leffler Stability).Let B⊂R n be a domain containing the origin.The zero solution of the same order system(2)is said to be generalized Mittag-Leffler stable ifx(t) ≤{m(x(t0))(t−t0)−γEα,1−γ(−λ(t−t0)α)}b,where t0is the initial time,α∈(0,1),−α<γ<1−α,λ≥0,b>0,m(0)=0,m(x)≥0,and m(x)is locally Lipschitz on x∈B⊂R n with Lipschitz constant L.We will also need the following definitions to analyze the case of FDEs with time-delay in Sec.5.First,we introduce the same order fractional differential system with multiple time delays represented by the following differential equation:⎧⎪⎨⎪⎩Dαt0,tx(t)=A0x(t)+mi=1A i x(t−τi)+B0u(t),0≤τ1<τ2<τ3<···<τi<···<τm=Δ(3)with the initial condition x(t0+t)=ψ(t)∈C[−Δ,0].Where0<α<1,Dαi t0,t denoteseither C Dαi t0,t or RL Dαi t0,t.x(t)∈R n is a state vector,u(t)∈R l is a control vector,A i(i=0,1,...,m),B0are constant system matrices of appropriate dimensions,and τi>0(i=1,2,...,m)are pure time delays.Definition12.The same order system(3)(u(t)≡0,∀t)satisfying initial condition x(t0+t)=ψ(t),−Δ≤t≤0,isfinite-time stable w.r.t.{t0,J,δ,ε,δ},δ<εif and only if:ψ c<δ,∀t∈J ,J =[− ,0]∈R32The European Physical Journal Special Topicsimplies:x (t ) <ε,∀t ∈J,where δis a positive real number and ε∈R +,δ<ε, ψ c =max −Δ≤t ≤0 ψ(t ) ,time interval J =[t 0,t 0+T ]⊂R ,quantity T may be either a positive real number or a symbol +∞.Definition 13.System given by (3)satisfying initial condition x (t 0+t )=ψ(t ),−Δ≤t ≤0,is finite-time stable w.r.t.{t 0,J,δ,ε,Δ,αu },δ<εif and only if:ψ c <δ,∀t ∈J ,J =[− ,0]∈Randu (t ) <αu ,∀t ∈Jimplies:x (t ) <ε,∀t ∈J,where δis a positive real number and ε∈R +,δ<ε,αu >0, ψ c =max −Δ≤t ≤0 ψ(t ) ,time interval J =[t 0,t 0+T ]⊂R ,quantity T may be either a positive real number or a symbol +∞.3Stability of linear fractional differential equationsIn this section,we consider the following linear system of FDEsD ¯αt 0,t x (t )=Ax (t ),(4)where x (t )=[x 1(t ),x 2(t ),...,x n (t )]T ∈R n ,matrix A ∈R n ×n ,¯α=[α1,α2,...,αn ]T ,D ¯αt 0,t x (t )=[D α1t 0,t x 1(t ),D α2t 0,t x 2(t ),...,D αn t 0,t x n (t )]T and D αi t 0,t is the Caputo derivativeor Riemann-Liouville derivative of order αi ,where 0<αi ≤2,for i =1,2,···,n .In particular,if α1=α2=···=αn =α,then fractional differential system (4)can be written as the following same order linear systemD αt 0,t x (t )=Ax (t ).(5)3.1The fundamental theoremsFor Eq.(5)and 0<α≤1,Matignon firstly gave a well-known stability result by an algebraic approach combined with the use of asymptotic results,where the necessary and sufficient conditions have been derived,the specific result is as follows [23].Theorem 1.The autonomous same order system (5)with Caputo derivative and initial value x 0=x (0),where 0<α≤1,is•asymptotically stable if and only if |arg(spec (A ))|>απ2.In this case the compo-nents of the state decay towards 0like t −α.•stable if and only if either it is asymptotically stable,or those critical eigenval-ues which satisfy |arg(spec (A ))|=απ2have geometric multiplicity one,spec (A )denotes the eigenvalues of matrix A .Perspectives on Fractional Dynamics and Control 33As we can see,in case α=1,the above stability result shows that roots of the equa-tion det(diag(λ,λ,...,λ)−A)=0lie outside the closed angular sector |arg(λ)|≤απ2,thus generalizing the well-known result for the integer case α=1.For the asymptot-ical stability in Theorem 1,the components of the state are anomalous decay,thus fractional systems have ‘memory’feature and its asymptotical stability is also called t −αstability.Exponential stability cannot be used to characterize the asymptotic stability of fractional differential systems.The case of zero eigenvalues of system matrix A is not included in Theorem 1,since the argument of zero in complex plane can be arbitrary.In view of this situation,Qian et al.recently studied the case of autonomous same order system (5)with Riemann-Liouville derivative by using the asymptotic expansions of Mittag-Leffler function,where 0<α<1.And they stated the zero eigenvalues case of Theorem 1,the corresponding conclusion is as follows [22].Theorem 2.The autonomous same order system (5)with Riemann-Liouville deriv-ative and initial value x 0=RL D α−1t 0,tx (t )|t =t 0,where 0<α<1and t 0=0,is •asymptotically stable if and only if all the non-zero eigenvalues of A satisfy |arg(spec (A ))|>απ2,or A has k -multiple zero eigenvalues corresponding to a Jordan block diag(J 1,J 2,...,J i ),where J l is a Jordan canonical form with order n l , i l =1n l =k ,and n l α<1,1≤l ≤i .•stable if and only if either it is asymptotically stable,or those critical eigenval-ues which satisfy |arg(spec (A ))|=απ2have the same algebraic and geometric multiplicities,or A has k -multiple zero eigenvalues corresponding to a Jordan block matrix diag(J 1,J 2,...,J i ),where J l is a Jordan canonical form with order n l , i l =1n l =k ,and n l α≤1,1≤l ≤i .The proof of Theorem 2is contained in [22].For the autonomous same order system(5)with Riemann-Liouville derivative and 0<α<1,if all the eigenvalues of system matrix A satisfy |arg(spec (A ))|>απ2,then the components of the state decay towards0like t −α−1which is different from the Caputo derivative case.And similar to the proof in [22],for the autonomous same order system (5)with Caputo derivative and 0<α≤1,if all the non-zero eigenvalues of A satisfy |arg(spec (A ))|≥απ2and the critical eigenvalues satisfying |arg(spec (A ))|=απ2have the same algebraic and geometric multiplicities,and the zero eigenvalue of A has the same algebraic and geometric multiplicities,then the zero solution of this system is stable from the representation of the solution.In addition,the zero solution of this system is never asymptotically stable as long as A has zero eigenvalue.The above two theorems dealt with the same order linear fractional differential system.For the multi-order linear fractional differential system (4),Deng et al.firstly studied the case that α,i s are rational numbers between 0and 1,for i =1,2,...,n ,where the following result [21,62]was introduced.Theorem 3.Suppose that α,i s are rational numbers between 0and 1,for i =1,2,...,n .Let M be the lowest common multiple (LCM)of the denominators u i of α,i s ,where αi =v i u i ,(u i ,v i )=1,u i ,v i ∈Z +,i =1,2,...,n ,and set γ=1M .Then the zero solution of system (4)with Caputo derivative and initial value x 0=x (0)is•asymptotically stable if and only if any zero solution of the polynomialdet(diag(λMα1,λMα2,...,λMαn )−A )satisfies |arg(λ)|>γπ/2,the components of the state variable (x 1(t ),x 2(t ),...,x n (t ))T ∈R n decay towards 0like t −α1,t −α2,...,t −αn ,respectively.34The European Physical Journal Special Topics•stable if and only if either it is asymptotically stable or those critical zero solutions λof the above polynomial satisfy |arg(λ)|=γπ/2have geometric multiplicity one.From Theorem 3,suppose α1=α2=···=αn =αare rational numbers between 0and 1,then the result of Theorem 3coincides with the one in Theorem 1.So,Theorem 3is an extension of Theorem 1in respect of rational orders.In [21],the authors used Laplace transform [63]and the final-value theorem to prove Theorem 3.Similarly,Odibat [64]also analyzed the stability of system (4)with 0<α=α1=α2=···=αn ≤1.In [64],the Mittag-Leffler functions and their integer-order derivatives which are analytic functions were used to obtain analytical solutions of the initial value problem (4),then the sufficient stability condition was derived by using the final-value theorem.This result [64]is consistent with the one in Theorem 1and Theorem 3.Matignon’s theorem is in fact the starting point of several results on the stability analysis.For example,Ralti et al.extended Theorem 1to the case 1<α<2[24].Remark 1.Similar to Theorem 2,if we assume that the conditions of Theorem 3hold except replacing C D ¯α0,t and the initial value x 0=x (0)by RL D ¯α0,t and the initial valuex 0=RL D ¯α0,t x (t )|t =0respectively,then the stability result which is an extension ofTheorem 2in respect of rational orders is still available.All the above conclusions are about the case of commensurate fractional order,in addition,some literatures such as [21,22]also involved the case of incommensurate fractional order.If α1,α2,...,αn are not rational numbers but real numbers between 0and 1in system (4),then we have the following result,which was introduced in [21,22]by using the final-value theorem of Laplace transform.Theorem 4.If all the roots of the characteristic equation det(diag(s α1,s α2,...,s αn )−A )=0have negative real parts,then the zero solution of system (4)is asymp-totically stable,where αi is real and lies in (0,1).From the above theorems and Proposition 2,we have the following result.Theorem 5.The autonomous same order system (5)with initial value x 0=x (0)and Riemann-Liouville derivative is asymptotically stable if and only if |arg(spec (A ))|>απ2,where n =2and 0<α≤1.Proof.From [65],this system has unique solution which can be expressed by a gen-eralization of the matrix α-exponential function as follows:x (t )=e At αC =t α−1∞k =0A kt αk Γ[(k +1)α]C.For A ,there exists an invertible matrix P from the algebra such that P −1AP =J,where J is the Jordan canonical form of the matrix A .Here are two cases to discuss:•for J = λ100λ2,x (t )=t α−1∞k =0P J k P −1t αk Γ[(k +1)α]C =P e λ1t α0e λ2t α P −1C.Perspectives on Fractional Dynamics and Control 35•for J =λ10λ,x (t )=t α−1∞k =0P J k P−1t αk Γ[(k +1)α]C =P e λt α∂∂λe λt α0e λt α P −1C.Thus,we have lim t →+∞ x (t ) =0if and only if |arg(spec (A ))|>απ2from Propo-sition 2,and the proof is complete.We can also extend Theorem 5to the case 1<α<2.Theorem 6.The autonomous same order system (5)with Riemann-Liouville deriv-ative and initial values x k =RL D α−k −10,t x (t )|t =0(k =0,1),is asymptotically stable if and only if |arg(spec (A ))|>απ2,where n =2and 1<α<2.Proof.Similar to the above proof,there exists an invertible matrix P such that P −1AP =J ,where J is the Jordan canonical form of matrix A .Let us denote y =P −1x and substitute into Eq.(5),the system can be described asRL D α0,t y (t )=Jy (t ),(6)with initial values RL D α−10,t y (t )|t =0=y 0=P −1x 0and RL D α−20,t y (t )|t =0=y 1=P −1x 1.Here are also two cases to discuss:•for J = λ100λ2,applying Laplace transform to Eq.(6),we have y i (t )=y 0i ·t α−1E α,α(λi t α)+y 1i ·t α−2E α,α−1(λi t α),where y 0i is the i -th component of y 0,y 1i is the i -th component of y 1,i =1,2.According to Proposition 1,y i (t )∼1αy 0i λ(1−α)/αi +y 1i λ(2−α)/αi exp λ1αi t ,with t →∞,|arg(λi )|≤απ2,andy i (t )∼−y 0i λ−2i Γ(−α)t −α−1−y 1i λ−2i Γ(−1−α)t −α−2,with t →∞and |arg(λi )|>απ2.•for J = λ10λ ,similarly,y 1(t )=y 01·t α−1E α,α(λt α)+y 11·t α−2E α,α−1(λt α)+y 02·t 2α−1E (1)α,α(λt α)+y 12·t 2α−2E (1)α,α−1(λt α),y 2(t )=y 02·t α−1E α,α(λt α)+y 12·t α−2E α,α−1(λt α).From Proposition 1,one getsy 02·t 2α−1E (1)α,α(λt α)+y 12·t 2α−2E (1)α,α−1(λt α)∼y 02+y 12α d dσ σ(1−α)/α+σ(2−α)/α exp σ1αt σ=λ,36The European Physical Journal Special Topicswith t→∞,|arg(λ)|≤απ2,andy02·t2α−1E(1)α,α(λtα)+y12·t2α−2E(1)α,α−1(λtα)∼2y02Γ(−α)λ−3t−α−1+2y12Γ(−1−α)λ−3t−α−2,with t→∞and|arg(λ)|>απ2.The proof is complete. Recently,the stability analysis of linear FDEs is much involved.Some new methods are presented,such as the popular Laplace transform methods(i.e.,the frequency domain methods)[27–32],the Linear Matrix Inequalities(LMI)methods[25,26,33, 34]and the conversion methods[10],[35–37].These summaries are as follows.3.2The frequency domain methods for stability analysis of linear FDEsThe stability analysis of linear FDEs is very important in the control area,where the frequency domain method is often used.It is known that the key point of the stability analysis for linear FDEs is to determine the location of the roots of charac-teristic equations in the complex plane.It seems difficult to calculate all the roots of the characteristic equations because of the equations with fractional power options. Therefore,the authors in[27]made the following variable substitution.In general, the characteristic equation of a linear fractional differential equation has the formni=1a i sαi=0,(7)where0<αi≤1,for i=1,2,...,n.Whenαi=u i vi is rational,where(u i,v i)=1,the above equation may be rewritten asni=1a i s i m=0,(8)where m is an integer and m=LCM{v1,v2,...,v n}.Translating this equation into the W-plane yields:ni=1a i W i=0,(9) where W=s1m.The steps for stability analysis are as follows[27,31]:1.For given a i,calculate the roots of Eq.(9)andfind the minimum absolute phaseof all roots|θW min|.2.The condition for stability is|θW min|>π2m,while the condition for oscillation is|θW min|=π2m,otherwise the system is unstable.3.Roots in the primary sheet of the W-plane which have corresponding roots in thes-plane can be obtained byfinding all roots which lie in the region|θW|<πm, then applying the inverse transformation s=W m.Evidently the time response of the system can be easily related to these roots.Recently,Trigeassou et al.[32]has presented a new frequency domain method based on Nyquist’s criterion to test the stability of FDEs.The stability of FDEs with one, two derivatives was investigated,some analytic results for systems with N fractional derivatives were given.The detailed analysis can be referred to[32].Thefirst fre-quency domain method is simple,but it is hard to calculate the roots of Eq.(9). The second frequency domain method is based on Nyquist’s criterion(a graphical approach),so the latter is more intuitive.3.3LMI conditions for stability analysis of linear FDEsIn what follows,we will survey the Linear Matrix Inequalities(LMI)conditions on stability of linear FDEs.LMI has played an important role in control theory since the1960s due to its particular form.The main issue when dealing with LMI is the convexity of the optimization set,however,the stability domain of the same order system described by Eq.(5)with order1≤α<2is a convex set,various LMI methods for defining such a region have already been developed[25,26,33,34].Hence a LMI-based theorem for the stability of fractional differential system(5)with order 1≤α<2can be introduced as follows[25,26,34]:Theorem7.A fractional differential system described by Eq.(5)with order1≤α< 2is asymptotically stable if and only if there exists a matrix P=P T>0,P∈R n×n,such that(A T P+P A)sin(απ2)(A T P−P A)cos(απ2)(P A−A T P)cos(απ2)(A T P+P A)sin(απ2)<0.Unfortunately,the stability domain is not convex when0<α<1.The LMI condi-tions can thus not be directly derived.Here there are three different ideas how one can apply these methods to obtain LMI conditions for the stability of linear FDEs. The following three theorems have also been proven in[25,26,34].Theorem8.A fractional differential system described by Eq.(5)with order0<α< 1is asymptotically stable if there exists a matrix P>0,P∈R n×n,such thatA1α TP+PA1α<0.The derivation of above Theorem8(see also[33])is based on an algebraic transfor-mation of the system(5)combined with Lyapunov’s second method.This method has conservatism(explanation can be seen in[26]),so it is a sufficient condition.In order to avoid the conservatism,a new stability theorem based on a geometric analysis of the stability domain was proposed as follows.Theorem9.A fractional differential system described by Eq.(5)with order0<α< 1is asymptotically stable if and only if there exists a positive definite matrix P∈S, where S denotes the set of symmetric matrices,such that−(−A)12−α TP+P−(−A)12−α<0.However,LMI of Theorem9is not linear in relation to matrix A,thus limiting its use in the more specific control problems.In order to overcome this problem,a third condition is proposed.It based on the fact that instability domain is a convex subset of the complex plane when0<α<1.Theorem10.A fractional differential system described by Eq.(5)with order0<α<1is asymptotically stable if and only if there does not exist any nonnegative rank one matrix Q∈C n×n such that(AQ+QA T)sin(απ2)(AQ−QA T)cos(απ2)(AQ−QA T)cos(απ2)(AQ+QA T)sin(απ2)≥0.The following statement is based on stability domain decomposition[34].。
Geometric Modeling
Geometric ModelingGeometric modeling is a fundamental concept in computer graphics and design, playing a crucial role in various industries such as architecture, engineering, and entertainment. It involves creating digital representations of physical objects or environments using mathematical and computational techniques. Geometric modeling allows designers and engineers to visualize, analyze, and manipulate complex shapes and structures, leading to the development of innovative products and solutions. However, it also presents several challenges and limitations that need to be addressed to ensure its effectiveness and efficiency. One of the key challenges in geometric modeling is the accurate representation of real-world objects and environments. This requires the use of advanced mathematical algorithms and computational methods to capture the intricate details and complexities of physical entities. For example, creating a realistic 3D model of a human face or a natural landscape involves precise measurements, surface calculations, and texture mapping to achieve a lifelike appearance. This level of accuracy is essential in industries such as animation, virtual reality, and simulation, where visual realism is critical for creating immersive experiences. Another challenge in geometric modeling is the efficient manipulation and editing of geometric shapes. Designers and engineers often need to modify existing models or create new ones to meet specific requirements or constraints. This process can be time-consuming and labor-intensive, especially when dealing with large-scale or highly detailed models. As a result, there is a constant demand for more intuitive and user-friendly modeling tools that streamline the design process and enhance productivity. Additionally, the interoperability of geometric models across different software platforms and systems is a persistent issue that hinders seamless collaboration and data exchange. Moreover, geometric modeling also faces challenges in terms of computational resources and performance. Generating and rendering complex 3D models requires significant computing power and memory, which can limit the scalability and accessibility of geometric modeling applications. High-resolution models with intricate geometries may strain hardware capabilities and lead to slow processing times, making it difficult for designers and engineers to work efficiently. This is particularly relevant in industries such as gamingand virtual reality, where real-time rendering and interactive simulations are essential for delivering engaging and immersive experiences. Despite these challenges, geometric modeling continues to evolve and advance through technological innovations and research efforts. The development of advanced modeling techniques such as parametric modeling, procedural modeling, and non-uniform rational B-spline (NURBS) modeling has significantly improved the accuracy and flexibility of geometric representations. These techniques enable designersand engineers to create complex shapes and surfaces with greater precision and control, paving the way for more sophisticated and realistic virtual environments. Furthermore, the integration of geometric modeling with other disciplines such as physics-based simulation, material science, and machine learning has expanded its capabilities and applications. This interdisciplinary approach allows for the creation of interactive and dynamic models that accurately simulate physical behaviors and interactions, leading to more realistic and immersive experiences. For example, in the field of architecture and construction, geometric modeling combined with structural analysis and environmental simulation enables the design and evaluation of sustainable and resilient buildings and infrastructure. In conclusion, while geometric modeling presents several challenges and limitations, it remains an indispensable tool for innovation and creativity in various industries. The ongoing advancements in geometric modeling techniques and technologies continue to push the boundaries of what is possible, enabling designers and engineers to create increasingly realistic and complex digital representations of the physical world. As computational power and software capabilities continue to improve, the future of geometric modeling holds great promise for revolutionizing the way we design, visualize, and interact with the world around us.。
fundamentals of microelectronics英文原版
The fundamentals of microelectronics refer to the basic principles and concepts that form the foundation of the field. Microelectronics deals with the study and application of small-scale electronic components, such as integrated circuits and transistors. This field has played a crucial role in the development of various technologies, including computers, smartphones, and medical devices.One of the key concepts in microelectronics is the idea of miniaturization. Microelectronic components are designed to be small and compact, allowing for increased functionality in a limited space. This miniaturization is made possible by advancements in semiconductor technology, which enables the production of smaller and more efficient electronic devices.Another fundamental principle is the understanding of electronic circuits. Microelectronics relies on the design and analysis of circuits that control the flow of electric current. These circuits can be composed of different components, such as resistors, capacitors, and inductors, which work together to perform specific tasks.The behavior of microelectronic devices is guided by the laws of physics, particularly quantum mechanics. At the nanoscale level, where microelectronics operates, particles exhibit quantum effects that can significantly impact the performance of electronic devices. Understanding these effects is essential for designing and optimizing microelectronic components.In addition to the physical principles, microelectronics also encompasses the study of fabrication techniques. The process of manufacturing microelectronic devices involves multiple steps, including deposition, lithography, etching, and doping. Each of these steps contributes to the creation of complex integrated circuits and other microelectronic components.The field of microelectronics also includes the study of electronic materials. Different materials exhibit unique properties that can be leveraged in microelectronic devices. For example, semiconductors, such as silicon, are widely used in microelectronics due to their ability to control the flow of electric current.Overall, the fundamentals of microelectronics cover a wide range of topics, including circuit design, semiconductor physics, fabrication techniques, and electronic materials. Understanding these principles is crucial for the development of new and innovative microelectronic devices that drive technological advancements in various industries.。
A model for the microstructure of calcium silicate hydrate in cement paste
ternal or interlayer surfaces that are not part of the pore system, and/or they miss some of the surface area. These results, reviewed recently by Thomas et al. [10], only broaden the debate about the “true” SSA and the implied microstructure. This paper describes a model for the microstructure of C-S-H at the scale between 1 and 100 nm. The model is for an underlying structure that is not directly observable, and it represents an attempt to reconcile several apparently disparate observations. It is a model that can be used to explain surface area, pore size distribution at the fine scale, and the density and the water content at various rh’s. Other characteristics such as fractal dimension are also considered. It is hoped that the hypothesis will serve as a basis for discussion and a motivation for experiments.
Characterization of fractal surfaces
J.-J. Wu r Wear 239 (2000) 36–47
37
where RŽt . is the auto-correlation function ŽACF. and 1
p D. sin Ž2 y D. p
The ACF and the structure function can be obtained from the spectral density by the following equations:
Keywords: Fractal surface; Root mean square; Asperity
1. Introduction
Surface roughness plays an important role in contact, friction and wear. Therefore, characterization of roughness is necessary in these studies.
Conventionally, a rough surface is assumed to be a random process. Statistical parameters, such as the standard deviations of the surface height s , slope sm and curvature sk , are used for characterizing surface roughness. These statistical parameters are used by the famous contact model established by Greenwood and Williamson w1x and other revised models w2,3x. However, these statistical parameters depend on the resolution and the scan length of the roughness-measuring instrument. They are not properties of the surface alone w4x. In spite of that, they are still valuable. Greenwood and Williamson’s contact model, which uses instrument-dependent statistical parameters, is surprisingly good at predicting elastic contact phenomena w5x.
基于石墨烯超表面的效率可调太赫兹聚焦透镜
DOI: 10.12086/oee.2021.200319基于石墨烯超表面的效率可调太赫兹聚焦透镜王俊瑶，樊俊鹏，舒 好，刘 畅，程用志*武汉科技大学信息科学与工程学院，湖北 武汉 430081摘要：本文提出了一种基于石墨烯超表面的效率可调太赫兹聚焦透镜。
该超表面单元结构由两层对称的圆形镂空石墨烯和中间介质层组成，其中镂空圆形中间由长方形石墨烯片连接。
该结构可实现偏振转换，入射到超表面的圆偏振波将以其正交的形式出射，如左旋圆到右旋圆偏振转换。
利用几何相位原理，通过旋转长方形条的方向，透射波会携带额外的附加相位并能满足2π范围内覆盖。
合适地排列石墨烯超表面的单元结构，以实现太赫兹聚焦透镜。
仿真结果表明：通过改变石墨烯的费米能级，可以对超表面圆偏振转换幅度进行调节，进而超透镜的聚焦效率也可以动态调节。
因此，这种基于石墨烯超表面的效率可调聚焦透镜不用改变单元结构的尺寸，只需通过改变费米能级便可实现，可以广泛地应用到能量收集、成像等太赫兹应用领域。
关键词：超表面；聚焦透镜；石墨烯；太赫兹中图分类号：TH74；TQ127.11 文献标志码：A王俊瑶，樊俊鹏，舒好，等. 基于石墨烯超表面的效率可调太赫兹聚焦透镜[J]. 光电工程，2021，48(4): 200319Wang J Y , Fan J P , Shu H, et al. Efficiency-tunable terahertz focusing lens based on graphene metasurface[J]. Opto-Electron Eng , 2021, 48(4): 200319Efficiency-tunable terahertz focusing lens based on graphene metasurfaceWang Junyao, Fan Junpeng, Shu Hao, Liu Chang, Cheng Yongzhi *School of Information Science and Engineering, Wuhan University of Science and Technology, Wuhan, Hubei 430081, China Abstract: This paper proposes an efficiency-tunable terahertz focusing lens based on the graphene metasurface. The unit cell is composed of two symmetrical circular graphene hollows and an intermediate dielectric layer, wherein the hollow circular middle is connected by a rectangular graphene sheet. This structure can realize polarization conversion, for example, when an incidence with left-hand circular polarization emitted on the metasurface the po-larization of the transmitted light is right-hand circular polarization. According to the principle of geometric phase, by rotating the direction of the rectangular bar, the transmitted wave will carry an additional phase and can cover the range of 2π. An THz focusing lens can be realized by properly arranging the unit structure of the graphene metasurface. The simulation results show that the conversion amplitude of circular polarized light can be adjusted by changing the Fermi level of graphene, and the focusing efficiency of the metalens can also be dynamically adjusted.LCPRCP(cross-polarization)xy zV g——————————————————收稿日期：2020-08-27； 收到修改稿日期：2020-10-26基金项目：湖北省教育厅科技研究计划重点项目(D2*******)；武汉科技大学研究生创新基金项目(JCX201959)；大学生创新基金项目资助课题(20ZA083)作者简介：王俊瑶(2000-)，女，主要从事电子科学与技术专业。
Directed Self-Assembly of Nanoparticl es 定向自组装纳米材料
Figure1.The universe of directed self-assembly by molecular interactions. Available building blocks are classified in terms of aspect ratio(AR),rang-ing from AR؍1(isotropic,mostly spheres(a؊g))through1ϽARϽ15(rod-like(h؊j))to ARϾ15(wires(k)).Self-assembly of gold nanoparticles on templates(macromolecules17(e);carbon nanotubes40(f);block-copolymers38(g))can lead to geometries that are complementary to those of the templates.In template-free self-assembly,stimuli responsive mol-ecules adsorbed on NPs surface induce controlled aggregation. Temperature-sensitive DNA can induce particles clustering28,29(a,b)viaH-bonding or induce formation of two-dimensional superlattices31(c), whereas light sensitive azobenzenes induce formation of colloidal crys-Figure2.Molecular level of directed self-assembly.Colloidal interfaces with distributed stimuli-sensitive molecules are for reversible self-assembly.(a)Electrochemically active host؊guest complexes can induce clustering17or aggregation polymeric sponges18via cooperative⌸؊⌸and H-bonding.(b)Solvent mediated aggregation of particles byH-bonding.19(c)Modulated concentration of H؉or metal ions induces reversible interparticle interactions by H-bonding metal-ion coordination.58(d)Photoisomerization of grafted molecules on the particles surface induces moleculardipole؊dipole interactions.47(e)Temperature induced denaturation of the DNA strain allows keeping particles dispersed, while a decrease in temperature causes aggregation.20Note,that some molecular forces are common for different stimuli.instance,H-bonding can be modulated by solvent nature,pH,or temperature.Such multistimuli response provides ditional control in assembly by competitive/cooperative interaction.Panel a reprinted from ref17.Copyright2009American Chemical Society.Panel d reprinted from ref47.Copyright2006American Chemical Society.Panel b reprinted with permis-from ref19.Copyright2000Nature Publishing Group.triangular lattices as shown in Figure4.127Self-assembly of bionanoparticles,such as rodlike viruses also reveals a complex interplay between electrostatic and capillary forces,with the easy formation of ordered structuresSeveral exciting developments in materials science exploit the self-assembly at interfaces in more complex designs.A clever method to generate novel materials is to induce phase separation in a solution or melt con-Figure3.Directed assembly of particles in externalfields(a),including the growth of microwires from gold nanoparticles,88assembly of micrometer-diameter colloidal particles into hexagonally close-packed arrays in AC electricfields,75assembly of metallo-dielectric ja-nus particles,90and ellipsoidal particles.84(b)Flow-field induced self-assembly.110,111Images reprinted with permission from the refer-ences as indicated.(a)Copyright2001AAAS;2004American Chemical Society;2007American Chemical Society;2008American Chemi-cal Society;2009American Physical Society;(b)2007American Chemical Society;2008American Chemical Society.Figure4.Two recent examples of capillary force driven self-assembly at liquid؊liquid interfaces.(Left)Charged ellipsoidalparticles assembling by shape-induced capillary interactions(seeref127,image courtesy of Dr.D.Madivala).(Right)TEM imageof a CdSe nanorod-stabilized water droplet after drying on amicrometer and submicrometer dimen-ellipsoid orientation is controlled duringby an external magneticfield,thus pre-from packing with random orienta-convected toward the drying front Similarly,Mittal et al.recently used AC elec-orient ellipsoidal titania nanoparticles dur-idly change the particle interactions,potentially to annealing methods that can be used jammed or kinetically frustrated states.OUTLOOK AND CONCLUSIONSIn the preceding review,we broadlyeral principal areas of directed self-assemblyrecent examples from ref134and135where the assembly of anisotropic particles was directedfields andflows.Such ordered structures have novel photonic and mechanical properties.Reprinted Copyright2009Wiley-VCH Verlag GmbH&Co.KGaA.。
基于群体平衡的汽轮机动叶表面盐析颗粒分布特性
2018年第37卷第2期 CHEMICAL INDUSTRY AND ENGINEERING PROGRESS·437·化 工 进展基于群体平衡的汽轮机动叶表面盐析颗粒分布特性胡鹏飞，李勇，曹丽华，吴雪菲（东北电力大学能源与动力工程学院，吉林 吉林 132012）摘要：为深入了解汽轮机动叶内盐析颗粒的微观行为，本文以某超临界汽轮机高压级动叶为研究对象，应用计算流体力学与群体平衡模型耦合方法，对汽轮机动叶内盐析颗粒在流场中的分布进行数值模拟研究，获得了盐析颗粒在动叶内的粒径分布及不同负荷时叶片尾缘处盐析颗粒数量密度分布规律。
模拟结果表明：在汽轮机动叶吸力面附近的盐析颗粒粒径较压力面附近盐析颗粒粒径小，且叶根处颗粒粒径小于叶顶处；动叶压力面的颗粒数量密度呈前缘点尾缘点处大、中间段小的分布规律，并且盐析颗粒在叶片上的数量密度分布最大值并不出现在组分数及粒径最大处，而是出现在平均粒径为110～150μm 的盐析颗粒沉积位置处；当汽轮机30%负荷运行时，粒径40μm 盐析颗粒的数量密度是其在汽轮机额定负荷运行时的1.5倍，而粒径140μm 盐析颗粒的数量密度仅为汽轮机额定负荷运行时的80%。
关键词：汽轮机动叶；盐析颗粒；群体平衡模型；两相流中图分类号：TK26 文献标志码：A 文章编号：1000–6613（2018）02–0437–07 DOI ：10.16085/j.issn.1000-6613.2017-1765Distribution characteristics of salting-out particles on the surface of steamrotor blade based on population balance model （PBM ）HU Pengfei ，LI Yong ，CAO Lihua ，WU Xuefei（School of Energy and Power Engineering ，Northeast Electric Power University ，Jilin 132012，Jilin ，China ）Abstract ：In order to get a better understanding of microscopic behavior of salting-out particles in a steam turbine ，a high-pressure grade rotor blade was employed in a supercritical steam turbine as a research object and the distribution of salting-out particles in the flow field from a steam turbine rotor blade was simulated using CFD-PBM method. The diameter distribution of salting-out particles in a rotor blade and the number density distribution of salting-out particles in the tailed-edge area of rotor blade with different load situations were obtained. The simulation results showed that the salting-out particle diameter near the suction side was smaller than that near the pressure side in a steam turbine rotor blade ，and the salting-out particle diameter at the blade bottom was smaller than that at the blade tip. The particle number density distribution law at the pressure side of rotor blade was presented that the particle number density was larger both at the leading edge and at the tailed-edge of rotor blade while the particle number density was smaller in the middle parts of rotor blade ，and the maximum value of salting-out particle number density distribution did not appear in the position having the maximum component number and particle diameter in the rotor blade ，but it appeared in the positionwhere salting-out particles with the average diameter 110—150μm deposit. When steam turbine was under 30% load operation ，the number density of salting-out particles with 40μm diameter was 1.5第一作者及通讯作者：胡鹏飞（1985—），男，博士研究生，讲师，主要研究方向为汽轮机节能技术与优化运行。
聚电解质多层膜包覆多孔碳酸钙药物控释体系
聚电解质多层膜包覆多孔碳酸钙药物控释体系王朝阳何成毅刘新星童真华南理工大学材料科学研究所，广州 510640关键词：多孔无机粒子，药物控释，逐层自组装随着现代医学的高度发展，药物控制释放体系在医学上的研究和应用日益受到人们的重视，并成为当今医学研究中最热门的领域之一。
无机多孔粒子由于具有巨大的内表面积，对药物分子有很强的吸附能力，并且具有生物稳定性和药物控释性等优点，近来正逐渐成为一种新型的药物载体[1]。
但是，如果不对装载药物的多孔粒子作适当的表面改性，在释放初期通常都会有比较明显的突释效应。
逐层自组装（Layer-by-Layer，LbL）技术是一种良好的表面改性技术，能在纳米尺度上对胶体粒子表面的组成、厚度、结构形态等进行准确控制[2-5]。
本工作的主要目的是将药物在无机多孔粒子中的装载技术与LbL技术相结合，以装载药物的粒子为模板进行逐层自组装制备一种新型的载药体系，并探讨这种载药体系的药物胶体粒子控制释放性能。
本研究的具体内容如下：1、制备单分散的多孔CaCO3(Figure 1)，表征多孔CaCO胶体粒子的比表面积、孔径、孔容等性能。
2、以多3胶体粒子为载体进行布洛芬的装载，研究溶剂、吸附次数对载药率的影响，孔CaCO3为布洛芬的装载选择合适的工艺条件；探讨药物在胶体粒子中的存在形态。
3、以胶体粒子为模板，研究硫酸鱼精蛋白（PRO）和聚苯乙烯磺酸钠（PSS）载药后的CaCO3在胶体粒子表面的逐层自组装，并对核-壳结构粒子的制备过程、表面形貌及其成胶体粒子中的布洛芬和核-壳囊性进行了探讨。
4、研究纯布洛芬晶体、多孔CaCO3结构粒子中的布洛芬在模拟胃液（Figure 2）及模拟肠液（Figure 3）中的释放行为，探讨这种新型的载药体系的药物控制释放性能, 发现聚电解质多层膜包覆多孔碳酸钙可以延缓药物释放。
a b c100 nm1 µm10 µmFigure 1.SEM photos of different magnifying powers for CaCO3 microparticles: (a) overview, (b) single particle, (c) enlarged part from a particle.C u m u l a t i v e r e l e a s e (%)Time (min)C u m u l a t i v e r e l e a s e (%)Time (min)参 考 文 献Figure 2. Release profiles of (a) bare IBU microcrystals, (b) IBU-loaded CaCO 3microparticles and (c) IBU-loaded microcapsules with 5 bilayers of PRO/PSS in the simulated gastric fluid (pH 1.2)Figure 3. Release profiles of (a) bare IBU microcrystals, (b) IBU-loaded CaCO 3microparticles and (c) IBU-loaded microcapsules with 5 bilayers of PRO/PSS in the simulated intestinal fluid (pH 7.4)[1] Li ZZ, Wen LX, Shao L, Chen JF. J Control Release, 2004, 98, 245.[2] Sun QL, Tong Z, Wang CY , Ren BY , Liu XX, Zeng F. Polymer, 2005, 46, 4958. [3] Liang ZP, Wang CY , Tong Z, Ye WH, Ye SQ. React Funct Polym, 2005, 63, 85. [4] Ye SQ, Wang CY , Liu XX, Tong Z. J Biomater Sci Polym Ed, 2005, 16, 909. [5] Ye SQ, Wang CY , Liu XX, Tong Z. J Control Release, 2005, in press.致谢：本工作得到国家自然科学基金（No: 90206010）、广东省基金（No: 031380）和广州市科技计划的资助。
毕业设计豆浆机外文翻译
Soy milk makerFrom Wikipe dia, the free encycl opedi aExampl e of one of the many differ ent kindsof soy milk makersA soy milk makeris a smallkitche n applia nce whichautoma tical ly cookssoy milk, a non-dairybevera gemade from soy beans. Soy milk makers work simila rly to a combin ation betwee n a home blende r and an automa tic coffee maker. Some soy milk makers can also be progra mmedto make almond milk, rice milk andothervegeta ble-basedsteepe d bevera ges.Home-made soy milk can be made to the drinke rs' tastes and nutrit ional requir ement s, provid ing addedvalue.Soy pulp or okara, a health y by-produc t of soy milkprepar ation, can be used as an ingred ientin manyrecipe s and food produc ts.Ordina ry method s for making soy milk at home are oftenvery labor-intens ive (requir ing beansto be soaked, ground in a blende r, strain ed, and then cooked). Soy milk machin es perfor m many of thesestepsautoma tical ly, greatl y simpli fyinghome-basedsoy milk produc tion.Standa rd operat ionBefore use, driedbeansare rinsed with waterto remove partic ulate debris, soaked for 6–10 hoursto moiste n and soften the driedbeans, and then rinsed againbefore use. The moiste ned soy beansare placed into the grindi ng chambe r, wherethey are ground into a fine paste, and fall into a finely screen ed strain er chambe r immers ed in a pot of water.The pasteis steepe d in the waterin a proces s simila r to that of tea making; the pot of wateris heated, fullycookin g both the dissol ved soy milk and the strain ed soy solids, whichbecome okara. The new models on the market now have no filter cup—soy beansare placed direct ly inside the machin e jug.Most soy milk makers includ e a mechan ism to stop the boilin g soy milk fromoverfl owing. The heater is turned off as the waterlevelapproa chesthe top of the chambe r, and then turned back on as the soy milk return s to an accept ablelevel. This proces s is repeat ed for the length of the cookin g period, whichlastsfor approx imate ly fiftee n minute s.When the soy milk has fullycooked, the machin e will automa tical ly turn off, leavin g the okarain the filter cup and the soy milk in the waterchambe r. Many machin es will beep to inform the user of the soy milk's comple tion.Review of popula r soy milk makersomMaki ng your own soy milk with a soymil k makeris very easy, allows you to save a lot of moneyand you know exactl y what the ingred ients are. If needed, you can add extraingred ients such as sugar, sweete ners, flavou rs, thicke nersand salt to make it tastemore like indust rialsoy milk. Making soy milk with normal kitche n toolsis also possib le, but requir es more time and result s in a loweryield. Basica lly you have to add the soaked soybea ns and waterto the soy milk makerand pressthe startbutton. We have tested the follow ing soy milk makers with filter cup: SoyQui ck, VeganStar, SoyaJo y,SoyaPo wer, SoyWon der and QT400, and two filter lesssoy milk makers: Premiu m SoyQui ck and SoyaDi rect. The SoyaDi rectbelong s to the newest genera tionof soy milk makers that use no filter cups or grindi ng cover, making cleani ng and handli ng easier. You can orderthis machin e from the UK basedcompan y Soyadi rect. When orderi ng, please do not forget to mentio n our specia l promot ion code SYBE09, whichgivesyou an extradiscou nt of 10% off produc t sale price.Compon entsof a soymil k makerMost models are compos ed of the follow ing parts:∙Heatin g elemen t: this can be a heatin g elemen t whichis submer ged in the liquid or a heatin g bottom plate. Both system s also existwith normal waterboiler.∙ A contai ner whichwill hold the soy milk plus some extraair spaceto preven t overco oking. This contai ner can be plasti c or stainl ess steel.∙ A filter cup whichholdsthe soy beans. The surfac e consis ts of a screen whichallows wateror soy milk to pass throug h. Thereare two typesof screen s: a thin platewith very smallroundholes(Soyajo y, SoyaPo wer and VeganStar) and a fine mesh screen (SoyWon der).∙Sensor s to preven t the overco oking of the soymil k.∙Motorwith stainl ess steelstirri ng bladeto mix the soybea ns.∙ A microp roces sorsto contro l the proces s of heatin g and mixing.∙Some automa tic soy milk makers have additi onalpartsor option s: a feedin g window or openin g whichallows you to add the beansto the fullyassemb led soy milk maker(Soyajo ys and SoyaPo wer) or a kit to make tofu.Operat ion of an authom aticsoy milk makerThe operat ion instru ction s differ slight ly betwee n the differ ent brands but basica lly they work like this:∙Weighor measur e 80 to 100 gramsof dry soybea ns for each literof soy milk.Normal ly a measur ing cup is provid ed.∙Rinsethe soybea ns and soak for about8 hoursor overni ght. Rinsethe soaked soybea ns againwith water. Some manufa cture rs of soy milk makers claimthat theirmachin e can make soy milk direct ly from unsoak ed soybea ns. Howeve r, the tastewill not be that good and yieldwill be lower.∙Put the soybea ns in filter cup and monthit in the soy milk maker.∙Add cold waterin the contai ner of the soy milk maker. Normal ly the desire d levels are marked on the inside or outsid e of the contai ner.∙Plug the powercord in and pressthe startbutton. The soy milk makerwill firstheat the waterto about80 degree C (180 degree F) and then startto grindthesoybea ns.∙Afterabout15 minute s the soy milk makerwill indica te that the cycleis comple ted and that you can pour the soy milk in anothe r contai ner. The pulp, orokara, whichremain s in the filter cup can be used as an health y ingred ientin breador soups. This okarais very rich in fibrebut will also contai n otherhealth y ingred ients such as soy protei n, isofla vones, saponi ns and vitami ns.Soy Milk Makers at Factor y-Direct PricesGet nutrit iousnon-dairymilksfrom harves ts of the nature: Beans, nuts, seeds, and grainsMemori al Day Sale!! Ends May 20th!SoyaJo y is the origin al soy milk maker. It has won all head-to-head testsconduc tedbut import ant improv ement s so that SoyaJo y and the SoyaPo wer soymil k makers stay aheadof the compet ition. Now we are introd ucing our SoyaJo y G3, the thirdgenera tionof our award-winnin g SoyaJo y Soy Milk Makers.The SoyaPo wer Plus Soy Milk Makeris the most review ed soy milk makers and the only one with an averag e of 5-Star rating by Amazon as of Dec. 22, 2011. It is also inTop-10 list, togeth er with such namesas Kitche nAid Artisa n Series Mixer,and Zojiru shi Rice Cooker. Not a single otherbrandof soy milk makers has made it to even in the Top-100 list!We recomm end that you consid er the follow ing when making your purcha se decisi on:1. Make sure the soymil k makeris UL listed. UL has strict requir ement s for produc tdesign and manufa cturi ng proces s. It is no surpri se that knocko ff manufa cture rs can't meet UL qualit y and safety requir ement s.2. Making soymil k from soaked soybea n is more health ier. Read why3. Pay attent ion to the capaci ty of the machin e - how much soymil k it makesin one batch.4. Carefu lly read the featur es of the soymil k maker.5. Consid er shippi ng cost and warran ty cost as part of totalcost.6. Checkout how long has the brandand the compan y been around. We have seen so many soymil k makerbrands and market ers come and go over the years, you don't want to see the compan y is alread y gone when you need theirservic e.You can find just aboutanythi ng on soy milk, tofu, and soy milk makers at this web site. Checkout the subjec ts in the menu bar at the right.Featur es and benefi ts of SoyaJo y/SoyaPo wer soy milk makersClickthe pictur e of each modelto see more detail s∙Microp roces sor-contro lledcookin g; no "beany" taste!∙Easy to use - add waterand soybea ns, pressone button!∙Fullyautoma tic plus manual settin gs for maximu m flexib ility, such as making raw milk (no heatin g), see detail s of each model.∙Stainl ess steelconstr uctio n - lastin g qualit y!∙Six-glass, 1.5-liter(50 oz) capaci ty - 6 glasse s in one batch!∙The best machin e, best servic e - read indepe ndent review s!∙90-day full refund return policy. One-year warran ty!∙UL approv ed with all safety featur es builtinto the machin e.∙Five-year warran ty on grindi ng bladeand pitche r!∙Free recipe bookle t, cleani ng kit, sample soybea ns,and more.AboutSoyaPo wer Plus:From the compan y that pionee red soymil k makers with the best-sellin g SoyaJo y soy milk makercomesthis newest, third-genera tionmilk maker! "SoyaPo wer Plus offersa revolu tiona ry leap in milk making techno logy" review ed by Vickil ynnHaycra ft Clickto read full review.The only milk makerwith four push-buttonoperat ions, each optimi zed for making milk from soybea ns, grains, seedsor unlimi ted combin ation s of beans, grains and seeds.SoyaPo wer Plus is the most advanc ed and versat ile milk makertoday. It boasts thequiete st operat ion and highes t energy effici encythanks to its thermo-plasti c outlin erover the stainl ess steelbody. With unique safety featur es such as safety latchandthermo-isolat ion, the SoyaPo wer Plus is aboutthe only UL approv ed filter-lesssoymil k makeron the market. The SoyaPo wer Plus gets the highes t user rating. Clickhere for detail ed review s of SoyaPo wer Plus soy milk maker.The Tornad o Grindi ng System (TM) enable s not only the highes t milk yieldandeasies t soymil k making operat ion availa ble, but also the capabi lityfor makingnon-dairymilksand porrid ges from any type of beans, rice, grains, seedsand nuts,such as soybea ns, mung beans, brownrice, whiterice, oats, millet, wheatgroats,almond s, hazeln uts, hemp seeds, or any combin ation s of them. It can even makebroths and soupslike soy-pumpki n soup and rice and sweetpotato es soup.For more detail s, clickthe SoyaPo wer Plus pictur e, or clickhereSanlin x Return/Refund PolicyAs the exclus ive US wholes ale distri butor, Sanlin x Inc. will provid e its custom ers with warran ty servic e even if the SoyaJo y is purcha sed from our resell ers, provid ed that the warran ty is regist eredwith Sanlin x within 30 days of purcha se. If you buy the SoyaJo y from a SoyaJo y resell er, the resell er may have its own return and refund policy, in whichcase the resell er must be contac ted for return/refund.If this same machin e is sold with a resell er's own brand, Sanlin x is NOT respon sible for return/refund or warran ty servic e. Refund Policy豆浆机来自Wikipedia,免费百科全书例如，众多不同种类的豆浆机制造商之一豆浆机是一种小的厨房设备用于自动研磨豆浆，是一种用黄豆制成的非乳制品家用电器。
大学科技英语课文例句和课后部分答案
1.把激光射束射向地球Laser beams are emitted at the moon2.这个模型描述了原子的情况This model is descriptive of the behavior of an atom3.那位教授将做有关移动通讯方面的讲座That professor will deliver a lecture on mobile communication4.她给本科生上C++程序设计语言课She gives undergraduates lessons in the C++programming language5.这些学生在做物理实验These students are making an experiment in physics6.他们在做电学实验They are doing an experiment on electricity7.该教授对沃氏函数的研究起了重要作用The professor has played an important role in the research on the Walsh Functions8.无线电波朝四面八方传播Radio waves travel in all directions9.为此，我们必须在负载两端接一个电容器For this purpose,we must connect a capacitor across the load10.在这个温度上该金属就会融化At this temperature the metai will melt11.该专家将在会议上宣读一篇重要的学术论文The expert will read an important academic paper at the conference12.速度等于距离与时间之比Speed is the ratio of distance to time13.太阳离地球的距离是很远的The distance of the sun from the earth is very great14.温度对金属导电率的影响是很小的The effect of temperature on conductivity of metals is small15.本节论述晶体管与电子管相比的优点This section deals with the advantages of transistors over electron tubes16.重力加速度随纬度的变化，部分原因是由于地球的自转The variation of g with latitude is due in part to the earth’s rotation17.Y对x的依从关系用y=f(x)表示The dependence of y on x is expressed by y=f(x)18.人们用椭圆来描述行星绕太阳的运行情况Ellipses are used to describe the motions of the planets around the sun19.我们讨论了电流通过酸碱盐溶液的情况We have discussed the passage of an electric current through liquid solutions of acids,bases,and salts20.物体对净力F的影响就是正比于F的加速度a The response of a body to a net force F is an acceleration a proportional to F21.把式（4）与式（6）相比较，我们就能的得到一下几个关系式A comparison of Eq.(4)with Eq.(6)Leads to the following relations22.我们可以把一个力分解成x和y分量The resolution force into x and y components is possible23.应避免使人体接触有潜在毒性的物质Exposure of the body to potentially toxic substances should be avoided24.这些特殊问题是有把原子能用作为能源而产生的These special problems arise from the use of atomic energy as a source of power25.把电流定义为电荷的运动对我们大家都是熟悉的The definition of an electric current as the flow of electric charge is familiar to all of us26.哥伦布发现美洲是在哪一天What is the date of the discovery of America by Columbus27.爱因斯坦确立了相对论是20世纪最重要的事件之一The formation of the theory ofrelativity by Einstein is one of the most significant events of the 20th century28.门捷列夫于1869年发现了周期表使人们有了计算原子质量的另一种方法The discovery of the periodic table by Mendeleev in 1869 suggested another way of estimating atomic masses29.这个工厂和那个一样大The factory is as large as that one30.铜的导电能力几乎和银一样好Copper conducts electricity almost as well as silver31.这台计算机的体积是一台打印机的3倍The size of this computer is there times as large as that of a typewriter32.那根导线长达100米That wire is as long as 100meters33.这根导线不如那根长This wire is not as long as that one(is)34.这台计算机的性能不如那台好This computer dose not work so well as that one35.导线越长，电阻越大The longer the wire ,the greater the resistance36.电压越大，电流就越大The greater the voltage,the larger the current37.电流越大，在导线中产生的热量就越多The larger the current,the more heat will be produced in the wire38.你学习越努力，你的进步就会越大The harder you study ,the greater progress you will make39.在无线电接收机中，一部分功率转变成了声波In a radio receiver,some power is converted to song waves40.绝缘体可以被用在导体之间来防止电流在他们之间流动Insulators may be used between conductors in order to prevent the flow of electric current between them41.把理论应用于实践是非常重要的To apply theory to practice is very important42.制作这样的电感器需要许多这样的线匝和铁芯To construct such inductors requires many turns of wire and iron cores43.现在能够把太阳光直接转变成电It is now possible to convert sunlight directly into electricity44.我们似乎能求出这个电流It seems possible to find out this current45.操作这台机器并不是件容易的事It is not an easy job to operate this machine46.做实验是极为重要的It is of great importance to make experiments47.解这个方程将要花费我们许多时间It will take us a lot of time to solve this equation48.我们发现用弧度而不是用度数表示角度是比较方便的It is found convenient to express angles in radians rather than in degrees49.当电流流过电路时，要损耗掉一部分能量Flowing through a circuit,the current will lose part of its energy50.若已知电流和电阻，我们就能求出电压Given current and resistance,we can find out voltage51.由于铜具有大量的自由电子，所以它是良导体Having a large number of free electrons,copper is a good conductor52.若用公式表示的话，电路中的电压，电流，电阻之间的关系可写成V=IR Expressed in a formula,the relationship between voltage,current and resistance in a circuit can be written as V=IR53.由于铜是电的良导体，所以被广泛的用在电工技术中Being a good conductor of electricity,copper is widely used in electrical engineering54.银是最好的导体，其次是铜Silver is the best conductor,followed by copper55.Σ是希腊字母“西格玛”，它的意思是“...之和”Σis the Greek letter sigma,meaning“the sum of”56.当机车拉着火车跑时，它就会做功A locomotive does work while pulling a moving train57.将物体置于水中，就会感觉到他比较轻When placed in water,everything will be foundlighter58.这一设备，如果设计得当就可以用无线电控制This device,properly designed,can be controlled by radio59.当把雷达信号发向月球时，由于月球是固体，所以能反射信号When radar signals are sent to the moon,the moon,being solid,reflects them60.若该电流发生变化，磁场也将变化This current changing,the magnetic field will change as well61.若其他情况相同，电阻将正比于导体的长度Other things being equal,the resistance is directly proportional to the length of the conductor62.当阳光照在光电电池上时，该设备就会自动工作起来The sunlight falling upon photo-electric cells,the device will automatically go into operation63.由于原子很小，所以我们看不见它们Atoms being extremely small,we cannot see them64.几乎所有的金属都是良导体，而银为最好Almost all metals are good conductors,silver being the best65.每当导体内的电流发生变化时就会在到体内感应出一个电动势，因而这种电动势就成为自感电动势Whenever there is a change of current in a conductor,an emf is induced in the conductor,thus this kind of emf being called a self-induced emf66.银在金属中电阻率最低，而铜的电阻率比他高不了很多Silver has the smallest resistivity of any metal,with that of copper not much greater67.若电路中没有电阻，电流就会无限增大With no resistance in the circuit,the current would increase forever68.我们周围的一切东西均是物质这一事实是大家都知道的The fact that everything around us is matter is known to all P（127）69.在这种情况下，该函数必须存在这一条件并没有满足In this case ,the condition that the function must exist is not satisfied70.等式只是某个量等于另一个量的一种陈述An equation is simply a statement that a certain quantity ia equal to another one71.欧姆观察到这一事实：如果电压保持不变，则电阻越大，电流就越小Ohm observed the fact that if the voltage remains the same,the greater the resistance,the smaller the current72.质子和电子之间所观察到的作用力，就导致了大家所熟悉的说法;同种电荷相互排斥，一中电荷相互吸引The observed forces between protons and electrons then lead to the familiar statement that like charges repel one another,unlike charges attract one another73.这些实验用来证实吉尔伯特的结论：电荷有两种There experiments serve to confirm Gilbert's conclusion that there are two kinds of electric charge74.电子学的诞生，是从发现了真空二极管中的电流，可以通过引入第三个电极来加以控制这个时候算起的The advent of electronics is reckoned from the discovery that the current in a vacuum diode can be controlled by introducing a third electrode75.十九世纪科学上最显著的成就之一是人们认识到了光是由电磁波构成的Among the most noteworthy achievements of 19th century science was the realization that light consist of electromagnetic waves76.现在人们越来越认识到这些技术在诸如控制系统和仪表测量这样的领域中也是很有价值的There is a growing awareness that these techniques are also of value in such areas as system control and instrumentation77.这两个带电球之间的斥力表明具有同种电荷的物体相互排斥The repulsion between these two charged balls is evidence that bodies having like charges repel each other78.由图2可以看出这一现象与反射有关That this phenomenon has connection with reflection may be seen from Fig.2 P（137）79.每个电路的工作原理在这一章进行了详细的讨论How each circuit works is discussed in detail in this chapter80.我们用哪个式子，将取决于在题目中给出了那些数据Which equation we want to use will depend on what data we have been given in a problem81.我们可以用计算机解决这些复杂的题目It is possible that we use a computer to solve these complicated problems82.有趣的是，每个函数均可用一些简单函数来近似It is interesting that every function can be approximated by simply functions83.那个问题是如何解决的还是个谜It is a mystery how the problem was solved84.众所周知我们周围的一切东西均为物质It is known that everything around us is matter85.在很久以前人们就发现电流的方向与电子的方向相反It was found long ago that the direction of the current is just opposite to that of the electron flow86.我们已经知道接收到的信号一般是很微弱的，其通常的功率约为几皮瓦It has been known that the signal received is generally quite weak,powers of the order of picowatts being common87.尚不了解有那些因素决定这种灯丝的尺寸It is not yet understood which factors determine the size of filaments of this kind88.我们无法预言这种现象何时发生It cannot be predicted when this phenomenon will take place89.朝哪个方向运用NPN晶体管基本上是没什么区别的It does not basically make any difference in which direction an NPN transistor is operated90.我们知道磁场能对电流施加一个力We have known that a magnetic field is able to exert a force on an electric current91.我们可以说物体的能量就是物体做功的能力One may say that the energy of a body is the ability of that body to do work92.我们往往想要知道这一误差是否可以忽略不计We often want to know whether this error may be neglected93.事实是无线电波的传播速度和光速一样The fact is that radio waves travel as fast as light dose94.其结果将是在导线两端之间将会存在这种电位差The result will be that this potential difference will exist between the ends of the conductor95.温度是与物体的体积无关的一种物质性质Temperature is a property of the body not concerned with how large the body is96.上面所讲的就是欧姆定律What has been described is Ohm's law97.我们能够学会我们原来不懂的东西We can learn what we did not know98.计算机能够做人们告诉它要做的事A computer can do what it has been told to do99.发电机的功能是把机械能转换成电能What a generator dose is convert mechanical energy into electrical energy100.作用在载流导线上的磁力就是使电机工作的力The magnetic force on current-carrying wires is what makes electric motors work101.我们想要获得对于A、B两点之间所发生的情况的详细描述We wish a detailed picture of what happens between points A and B102.所得到的是同样的那些表达式What result are the same expressions103.这个能量就是给自感电动势供能的能量This energy is what powers the self-induced emf 104.众所周知（的是）光是一种电磁波What is well know is that light is a kind of electromagnetic wave105.这就是我们通常所说的力This is what we call a force106.电子计算机能懂得所谓的机器语言The electronic computer is able to understand what is known as the machine language107.电流随所谓的电阻变化Current changes with what is described as resistance108.反射回来的那部分电流形成了所谓的回波信号The reflected portion of waves forms what is referred to as the echo signal109.存在有许多自由电子的物质被称为导体The substance in which there are many free electrons is called a conductor110.电流流过的闭合通道被称为电路The close path though which current flows is referred to as the electric circuit111.电动机是把电能转换成机械能的一种机器An electric motor is a machine by which electric energy is chang into mechanical energy112.存储电荷的器件称为电容器The devices on which charges are stored are called capacitors 113.光传播的速度是极快的The spend at which light travels is extremely great114.用来把热能转换成功的任何机械装置均称为热机Any mechanical device by means of which heat is converted into work is called a heat engine115.惯性是物质的一种特性，由于这种特性，要使物体加速就必须对该物体施加一个力Inertia is that property because of which a force must be exerted on a body in order to accelerate it116.正如标题所示本章论述数字计算机的原理As the title indicates,this chapter deals with the principles of digital computers117.我们知道,电子是微小的负电荷Electrons,as one knows,are minute negative charges of electricity118.我们已讲过晶体管是电流控制器件As has been described,transistors are current-control devices119.晶体管体积小效率高这是大家所熟知的Transistors are small & efficient,as is well known to us120.顾名思义流体是一种容易流动的物质Fluid,as the name shows,is a substance that flows readily121.一根导线可用作为天线A wire can serve as an antenna122.作为通讯工具，卫星是最先进的As a means of communication,a satellite is the most advanced123.能量被定义为物体做功的能力Energy is defined as the ability of a body to do work124.我们把g这个量定义为重力加速度We refer to the quantity g as gravity125.一个常数无论有多大，均不可能称为无穷大A constant number,no matter how large it may be,is never spoken of as infinite126.把能量定义为物体做功的能力是合理的The definition of energy as the ability of a body to do work is reasonable127.当电流流动时电池的能量就给电阻消耗了As the current flows,energy from the battery goes to the resistance128.两物体间的万有引力,随他们之间的距离的增加而减弱The force of gravitational attraction between two bodies decreases as the distance between them increases129.由于空气有重量所以它对处于其中的任何物体均要施加一个力As air has weight,it exerts force on any object immersed in it130.电子绕原子核旋转，就像行星绕太阳运行一样Electrons move round the nucleus just as the planets moves round the sun131.这台计算机与那台一样重This computer is as heavy as that one(is)132.原子虽小,却是由一些更小的单元组成Small as they are,atoms are made up of still smaller units133.正如早已证明的那样，若使负的各项变为正，该级数就发散If the negative terms are made positive the series becomes divergent,as has been shown already134.我们必须记住用以表示化学元素的那些符号We must remember such symbols as are used to represent chemical elements135.我们也可以用计算机解这道题A computer can be used as well to solve this problem 136.我们能求出流过这个电阻的电流及两端的电压It is possible to find out the current through this resistor as well as the voltage across it137. 这台计算机的工作性能与那台一样好This computer works as well as that one dose 138.数学是一种非常有用的工具，因此它广泛用在工程的各个领域之中Mathematics is a very useful tool.As a result,it is widely used in various fields of engineering139.只要外加电压保持不变在电路中流动的电流与该电路中的电阻成反比The current flowing in a circuit is inversely proportional to the resistance in the circuit as long as the applied voltage remains constant140.若地面没有摩擦，就不可能停止任何物体的运动Were there no friction on the ground,it would be impossible to stop the motion of any body141..若电压不那么高的话，那台仪器也就不会被烧坏了That instrument would not have been damaged had the voltage not been so high142.如果在导线中有很强的电流，那么只要用一匝大号导线就可以制成磁性很强的电磁铁A powerful electromagnet can be made with only one turn of a large-sized wire,should a very large current flow in the wire143.若没有地球的引力，地球上的一切东西都要失重Everything on the earth will lose its weight provided there be no gravity144.若没有半导体，就不可能有卫星通讯这类事情Some things,like satellite communications,would be impossible without semiconductors145.要不是二进制，电子计算机可能要比现在复杂得多But for the binary system,the electronic computer might have been much more complicated146.我们本来可以用定理（6）来导出式（5）We could also have used Theorem(6)to derive equation(5)147.为了使电流在电路中流动，必须保持一个电位差It is necessary that potential difference be maintained for current to flow in a circuit148.数字电路设计人员必须很熟悉布尔代数的实用知识It is essential that the digital designers should have a good working knowledge of Boolean algebra149.我们希望机器都不要有能量消耗It is desired that any machine have no energy loss150.有人建议在太空制造药物It is suggested that drugs be made in space151.我们建议读者最好用袖珍计算器来做基础电子学中的所需的数学计算It is recommended that the reader use a pocket calculator to do mathematical work required in basic electronics 152.经济方面要求电力以高压传送Economy demands that electric power be transmitted at high voltage153.实验要求测量应精确Experiments require that accurate measurements be made154.我们建议把这一点接地Our suggestion is that this point be grounded155.这是由于输出必须稳定的原因This comes from the necessary that the output be stable 156.这根传输线的作用就好像它是开路似的This transmission line acts as though it were open-circuit157.在这种情况下金质叶片就会散离开来，就好像它们由通过接触而起电的物体而带电一样Under this condition the gold leaves will diverge just as if they had been charged from a body electrified by contact158.电位差使电流在电路中流动The potential different causes an electric current to flow in the circuit159.正是电位差使得电流在电路中流动It is the potential difference that causes as electric current to flow in the circuit160.物体的惯性质量与重力质量是成正比的，这是一个极为重要的实验事实It is very significant empirical fact that the inertial and gravitational masses of a body are proportional to each other161.是硬件在很大程度上确定了该系统的能力It is the hardware which determines to a large degree the capabilities of the system162.正是这些优点使阿拉伯数字为全世界人们所接受It is these strong points that make the Arabic figures accepted by people all over the world163.直到1925年才证实了电离层的存在It was not until 1925 that the existence of the ionosphere was proved164.是法拉第首先发现了电磁感应现象It was Faraday who first discovered electromagnetic induction165.正是这些力导致产生了磁现象It is these forces which lead to magnetic phenomena 166.天平所度量的实际上是质量不是重量It is actually mass not weight which the balance measures167.正是在那儿发射了第一颗卫星It was there that the first satellite was launched168.正是在这个意义上数学有时被称为科学的语言It is in this sense that mathematics is sometimes called the language of science169.正是当导线切割磁力线时在导体上感应出一个电动势来It is when lines of force are being cut by the wire that an emf is induced in it170.并不是科学家使用的工具而是他使用工具的方法使他成为科学家It is not the tool a scientist uses but how he uses these tools that makes him a scientist171.没人知道到底是什么东西构成了场本身No one knows what it is that composes the field itself172.大多数数字电路是与其它数字电路对接的。
英文超晶格
英文超晶格Here is a 1,000-word essay on the topic of "English Superlattice":The concept of the English superlattice has fascinated linguists and language researchers for decades. A superlattice, in the context of language, refers to a structured arrangement of linguistic elements, such as sounds, words, or grammatical patterns, that exhibit periodic repetition and emergent properties beyond those of the individual components. In the case of the English superlattice, this phenomenon manifests in the intricate and multifaceted nature of the English language, which has evolved over centuries to become a remarkably versatile and adaptable mode of communication.At the heart of the English superlattice lies the rich diversity of the language's vocabulary. English has a vast lexicon, drawing from a multitude of linguistic sources, including Germanic, Romance, and Latinate roots. This linguistic melting pot has endowed the language with an extraordinary capacity for nuance, precision, and expressiveness. Each word in the English superlattice carries with it a unique history, connotation, and contextual significance, allowing speakers to convey complex ideas and emotions with remarkable subtlety.Moreover, the grammatical structure of the English language further enhances the complexity of the superlattice. The combination of rigid syntactical rules, flexible word order, and a range of grammatical constructions, such as tenses, moods, and voice, enables English speakers to craft intricate and sophisticated sentences. This structural versatility allows for the seamless expression of diverse communicative intentions, from the objective and factual to the imaginative and poetic.One of the most intriguing aspects of the English superlattice is its ability to accommodate and assimilate new linguistic elements. As the world becomes increasingly interconnected, English has absorbed words, phrases, and idioms from countless languages, further expanding the boundaries of the superlattice. This dynamic process of linguistic cross-pollination has enriched the language, making it a truly global medium of communication.The superlattice metaphor also extends to the contextual and pragmatic dimensions of the English language. The appropriate use of English often depends on the social, cultural, and situational factors at play. Mastering the nuances of register, tone, and communication styles is essential for effective language use, as the same words and grammatical structures can convey vastly different meanings and intentions depending on the context.Furthermore, the English superlattice is not limited to the written and spoken forms of the language. It also encompasses the diverse range of non-verbal communication modes, such as body language, facial expressions, and gestures, which play a crucial role in shaping the overall communicative experience. These paralinguistic elements seamlessly integrate with the linguistic components of the superlattice, creating a multidimensional tapestry of expression.The complexity of the English superlattice is further amplified by the dynamic nature of the language. English is continuously evolving, with new words, idioms, and grammatical constructions constantly emerging, while others fall out of use or undergo semantic shifts. This ongoing process of linguistic transformation ensures that the superlattice remains a living, breathing entity, constantly adapting to the changing needs and preferences of its users.Mastering the English superlattice is a lifelong endeavor, as the depth and breadth of the language defy easy categorization or complete understanding. Even the most proficient speakers and writers of English often encounter novel linguistic challenges, requiring them to navigate the intricate web of the superlattice with creativity, flexibility, and a deep appreciation for the language's nuances.In conclusion, the English superlattice is a remarkable linguistic phenomenon that defies simple explanation. It is a multifaceted and dynamic system that encompasses a vast array of linguistic elements, each with its own unique history, meaning, and contextual significance. The superlattice metaphor captures the extraordinary complexity and adaptability of the English language, which continues to captivate and inspire language enthusiasts, scholars, and communicators around the world.。
评语大全之英语专业论文评语
英语专业论文评语【篇一：英文论文审稿意见汇总】英文论文审稿意见汇总以下12点无轻重主次之分。
每一点内容由总结性标题和代表性审稿人意见构成。
1、目标和结果不清晰。
it is noted that your manuscript needs careful editing by someone with expertise in technical english editing paying particular attention to english grammar, spelling, and sentence structure so that the goals and results of the study are clear to the reader.2、未解释研究方法或解释不充分。
◆ in general, there is a lack of explanation of replicates and statistical methods used in the study.◆ furthermore, an explanation of why the authors did these various experiments should be provided.3、对于研究设计的rationale:also, there are few explanations of the rationale for the study design.4、夸张地陈述结论/夸大成果/不严谨：the conclusions are overstated. for example, the study did not showif the side effects from initial copper burst can be avoid with the polymer formulation.5、对hypothesis的清晰界定：a hypothesis needs to be presented。
(完整word版)英文审稿意见
在比较高级别的会议、期刊等，评审系统中包括给编辑的和给作者的评审意见.本文就这两部分评审以及进行汇总第一部分:给作者的审稿意见1、目标和结果不清晰。
It is noted that your manuscript needs careful editing by someone with expertise in technical English editing paying particular attention to English grammar， spelling， and sentence structure so that the goals and results of the study are clear to the reader.2、未解释研究方法或解释不充分。
◆ In general， there is a lack of explanation of replicates and statistical methods used in the study.◆Furthermore, an explanation of why the authors did these various experimentsshould be provided。
3、对于研究设计的rationale:Also， there are few explanations of the rationale for the study design.4、夸张地陈述结论/夸大成果/不严谨：The conclusions are overstated。
For example, the study did not show if the side effects from initial copper burst can be avoid with the polymer formulation。
5、对hypothesis的清晰界定：A hypothesis needs to be presented。
美国国家自然科学基金
英文审稿意见汇总
1、目标和结果不清晰。
It is noted that your manuscript needs careful editing by someone with expertise in technical English editing paying particular attention to English grammar, spelling, and sentence structure so that the goals and results of the study are clear to the reader.2、未解释研究方法或解释不充分。
◆In general, there is a lack of explanation of replicates and statistical methods used in the study.◆Furthermore, an explanation of why the authors did these various experiments should be provided.3、对于研究设计的rationale:Also, there are few explanations of the rationale for the study design.4、夸张地陈述结论/夸大成果/不严谨：The conclusions are overstated. For example, the study did not showif the side effects from initial copper burst can be avoid with the polymer formulation.5、对hypothesis的清晰界定：A hypothesis needs to be presented。
6、对某个概念或工具使用的rationale/定义概念：What was the rationale for the film/SBF volume ratio?7、对研究问题的定义：Try to set the problem discussed in this paper in more clear,write one section to define the problem8、如何凸现原创性以及如何充分地写literature review:The topic is novel but the application proposed is not so novel.9、对claim,如A＞B的证明，verification:There is no experimental comparison of the algorithm with previously known work, so it is impossible to judge whether the algorithm is an improvement on previous work.10、严谨度问题：MNQ is easier than the primitive PNQS, how to prove that.11、格式（重视程度）：◆In addition, the list of references is not in our style. It is close but not completely correct. I have attached a pdf file with "Instructions for Authors" which shows examples.◆Before submitting a revision be sure that your material is properly prepared and formatted. If you are unsure, please consult the formatting nstructions to authors that are given under the "Instructions and Forms" button in he upper right-hand corner of the screen.12、语言问题（出现最多的问题）：有关语言的审稿人意见：◆It is noted that your manuscript needs careful editing by someone with expertise in technical English editing paying particular attention to English grammar, spelling, and sentence structure so that the goals and results of the study are clear to the reader.◆The authors must have their work reviewed by a proper translation/reviewing service before submission; only then can a proper review be performed. Mostsentences contain grammatical and/or spelling mistakes or are not complete sentences.◆As presented, the writing is not acceptable for the journal. There are problems with sentence structure, verb tense, and clause construction.◆The English of your manuscript must be improved before resubmission. We str ongly suggest that you obtain assistance from a colleague who is well-versed in English or whose native language is English.◆Please have someone competent in the English language and the subject matter of your paper go over the paper and correct it. ?◆the quality of English needs improving.来自编辑的鼓励：Encouragement from reviewers:◆I would be very glad to re-review the paper in greater depth once it has been edited because the subject is interesting.◆There is continued interest in your manuscript titled "……" which you submitted to the Journal of Biomedical Materials Research: Part B - Applied Biomat erials.◆The Submission has been greatly improved and is worthy of publication.•The paper is very annoying to read as it is riddled with grammatical errors and poorly constructed sentences. Furthermore, the novelty and motivation of the work is not well justified. Also, the experimental study is shallow. In fact, I cant figure out the legends as it is too small! How does your effort compares with state-of-the-art??•The experiment is the major problem in the paper. Not only the dataset is notpublished, but also the description is very rough. It is impossible to replicate the experiment and verify the claim of the author. Furthermore, almost no discussion for the experimental result is given. E.g. why the author would obtain this result? Which component is the most important? Any further improvement?•the author should concentrated on the new algorithm with your idea and explained its advantages clearly with a most simple words.•it is good concept, but need to polish layout, language.•The authors did a good job in motivating the problem studied in the introduction.The mathematic explanation of the proposed solutions is also nice. Furthermore, the paper is accompanied by an adequate set of experiments for evaluating the effectiveness of the solutions the authors propose.•Apparently，Obviously ,Innovation ,refine ,In my humble opinion如果仍然有需要修改的小毛病，一般你可以用you paper has been conditionally accepted. Please revise .....according to review comments.如果是接受，你可以用We are very pleased to inform you that your paper "xxxxx" has been accepted by [journal name]. Please prepare your paper by journal template...............At a first glance, this short manuscript seems an interesting piece ofwork, reporting on ×××. Fine, good quality, but all this has been done and published, and nearly become a well-known phenomenon. Therefore, there is insufficient novelty or significance to meet publication criteria. Also, I did not see any expermental evidence how the ** is related with **, except for the hand-waving qualitativediscussion. Therefore, I cannot support its publication in JPD in its present form. It should be rejected.建议去小木虫问问，那里有一些资源。
microclass包的说明文档说明书
Package‘microclass’October13,2022Encoding UTF-8Type PackageTitle Methods for Taxonomic Classification of ProkaryotesVersion1.2Date2020-08-11Author Kristian Hovde Liland,Hilde Vinje,Lars SnipenMaintainer Lars Snipen<*******************>Description Functions for assigning16S sequence data to ataxonomic level in the tree-of-life for prokaryotes.License GPL(>=2)Depends R(>=3.5.0),microseq,microcontax,dplyr,stringr,rlangImports Rcpp(>=0.11.1),RcppParallel,tibbleLinkingTo Rcpp(>=0.11.1),RcppEigen,RcppParallelSystemRequirements GNU makeRoxygenNote7.1.1Suggests knitr,rmarkdownVignetteBuilder knitrNeedsCompilation yesRepository CRANDate/Publication2020-08-2812:20:08UTCR topics documented:microclass-package (2)blastClassify16S (2)blastDbase16S (4)KmerCount (5)multinomClassify (6)multinomTrain (7)rdpClassify (8)1rdpTrain (10)setParallel (11)small.16S (12)taxMachine (12)Index15 microclass-package Methods for16S based taxonomic classification of prokaryotesDescriptionThe package provides functions for assigning16S sequence data to a taxonomic level in the tree-of-life for prokaryotes.Usagemicroclass()DetailsPackage:microclassType:PackageVersion: 1.0.1Date:2016-08-31License:GPL-2Author(s)Hilde Vinje,Kristian Hovde Liland,Lars Snipen.Maintainer:Lars Snipen<*******************>blastClassify16S Classifying using BLASTDescriptionA16S based classification based on BLAST.UsageblastClassify16S(sequence,bdb)Argumentssequence Character vector of16S sequences to classify.bdb Name of BLAST data base,see blastDbase16S.DetailsA vector of16S sequences(DNA)are classified byfirst using BLAST blastn against a databaseof16S DNA sequences,and then classify according to the nearest-neighbour principle.The nearest neighbour of a query sequence is the hit with the largest bitscore.The blast+software https: ///Blast.cgi?PAGE_TYPE=BlastDocs&DOC_TYPE=Download must be installed on the system.Type system("blastn-help")in the Console window,and a sensible Help-text should appear.The database must contain16S sequences where the Header starts with a token specifying the taxon.More specifically,the tokens must look like:<taxon>_1<taxon>_2...etcwhere<taxon>is some proper taxon e blastDbase16S to make such databases.The identity of each alignment is also computed.This should be close to1.0for a classification to be trusted.Identity values below0.95could indicate uncertain classifications,but this will vary between taxa.ValueA data.frame with two columns:Taxon is the predicted taxon for each sequence and Identity isthe corresponding identity-value.If no BLAST hit is seen,the sequence is"unclassified". Author(s)Lars Snipen.See AlsoblastDbase16S.Examplesdata("small.16S")##Not run:dbase<-blastDbase16S("test",small.16S$Sequence,word(small.16S$Header,2,2))reads<-str_sub(small.16S$Sequence,100,550)blastClassify16S(reads,dbase)%>%bind_cols(small.16S)->tbl##End(Not run)4blastDbase16S blastDbase16S Building a BLAST databaseDescriptionBuilding a BLAST database for16S based classification.UsageblastDbase16S(name,sequence,taxon)Argumentsname The name of the database(text).sequence A character vector with16S sequence data.taxon A character vector with taxon information.DetailsThis functions builds a database using the makeblastdb program of the BLAST+software https: ///Blast.cgi?PAGE_TYPE=BlastDocs&DOC_TYPE=Download.Thus,this software must be available on the system when using this function.If you type system("makeblastdb -help")in the Console window some meaningful Help-text should be displayed.This function is most typically used prior to blastClassify16S to set up the database before searching and classifying.It can be seen as the’training step’of a BLAST-based classification procedure.The sequence must be a vector of DNA-sequences(16S sequences).The taxon is a vector of the same length as sequence,containing the correpsonding taxon information.ValueThe databasefiles are created,and the name of the database(name)is returned.Author(s)Lars Snipen.See AlsoblastClassify16S.Examples#See examples for blastClassify16S.KmerCount5 KmerCount K-mer countingDescriptionCounting overlapping words of length K in DNA/RNA sequences.UsageKmerCount(sequences,K=1,s=FALSE)Argumentssequences Vector of sequences(text).K Word length(integer).s Logical indicating if the words should be added as columns names.DetailsFor each input sequence,the frequency of every word of length K is counted.Counting is done with overlap.The counting itself is done by a C++function.With s=TRUE the K-mers are added as column names,but this makes the computations slower.ValueA matrix with one row for each sequence in sequences and one column for each possible word oflength K.Author(s)Kristian Hovde Liland and Lars Snipen.See AlsomultinomTrain,multinomClassify.ExamplesKmerCount("ATGCCTGAACTGACCTGC",K=2)6multinomClassify multinomClassify Classifying with a Multinomial modelDescriptionClassifying sequences by a trained Multinomial model.UsagemultinomClassify(sequence,trained.model,post.prob=FALSE,prior=FALSE)Argumentssequence Character vector of16S sequences to classify.trained.model A list with a trained model,see multinomTrain.post.prob Logical indicating if posterior log-probabilities should be returned.prior Logical indicating if classification should be done byflat priors(default)or with empirical priors(prior=TRUE).DetailsThe classification step of the Multinomial method(Vinje et al,2015)means counting K-mers on all sequences,and computing the posterior probabilities for each taxon in the trained model.The predicted taxon for each input sequence is the one with the maximum posterior probability for that sequence.By setting post.prob=TRUE you will get the log-probability of the best and second best taxon for each sequence.This can be used for evaluating the certainty in the classifications,see taxMachine.The classification is parallelized through RcppParallel employing Intel TBB and TinyThread.By default all available processing cores are used.This can be changed using the function setParallel. ValueIf post.prob=FALSE a character vector of predicted taxa is returned.If post.prob=TRUE a data.frame with three columns is returned.Taxon is the vector of predicted taxa,one for each sequence in sequence.The Post.prob.1and Post.prob.2are vectors with the maximum and second largest posterior log-probabilities for each sequence.Author(s)Kristian Hovde Liland and Lars Snipen.ReferencesVinje,H,Liland,KH,Almøy,T,Snipen,L.(2015).Comparing K-mer based methods for improved classification of16S sequences.BMC Bioinformatics,16:205.multinomTrain7See AlsoKmerCount,multinomTrain.Examplesdata("small.16S")seq<-small.16S$Sequencetax<-sapply(strsplit(small.16S$Header,split=""),function(x){x[2]})##Not run:trn<-multinomTrain(seq,tax)primer.515f<-"GTGYCAGCMGCCGCGGTAA"primer.806rB<-"GGACTACNVGGGTWTCTAAT"reads<-amplicon(seq,primer.515f,primer.806rB)predicted<-multinomClassify(unlist(reads[nchar(reads)>0]),trn)print(predicted)##End(Not run)multinomTrain Training multinomial modelDescriptionTraining the multinomial K-mer method on sequence data.UsagemultinomTrain(sequence,taxon,K=8,s=FALSE,n.pseudo=100)Argumentssequence Character vector of16S sequences.taxon Character vector of taxon labels for each sequence.K Word length(integer).s Logical indicating if column names should be added to the trained model matrix.n.pseudo Number of pseudo-counts to use(positive numerics,need not be integer).Spe-cial case-1will only return word counts,not log-probabilities.DetailsThe training step of the multinomial method(Vinje et al,2015)means counting K-mers on all se-quences and compute the multinomial probabilities for each K-mer for each unique taxon.n.pseudo pseudo-counts are added,divided equally over all K-mers,before probabilities are estimated.The optimal choice of n.pseudo will depend on K and the training data set.The default value n.pseudo=100 has proven good for K=8and the contax.trim data set(see the microcontax R-package).Adding the actual K-mers as column names(s=TRUE)will slow down the computations.The relative taxon sizes are also computed,and may be used as an empirical prior in the classifica-tion step(see"prior"below).ValueA list with two elements.Thefirst element is Method,which is the text"multinom"in this case.Thesecond element is Fitted,which is a matrix of probabilities with one row for each unique taxon and one column for each possible word of length K.The sum of each row is1.0.No probabilities are 0if n.pseudo>0.0.The matrix Fitted has an attribute attr("prior",),that contains the relative taxon sizes. Author(s)Kristian Hovde Liland and Lars Snipen.ReferencesVinje,H,Liland,KH,Almøy,T,Snipen,L.(2015).Comparing K-mer based methods for improved classification of16S sequences.BMC Bioinformatics,16:205.See AlsoKmerCount,multinomClassify.Examples#See examples for multinomClassifyrdpClassify Classifying with the RDP classifierDescriptionClassifying sequences by a trained presence/absence K-mer model.UsagerdpClassify(sequence,trained.model,post.prob=FALSE,prior=FALSE)Argumentssequence Character vector of sequences to classify.trained.model A list with a trained model,see rdpTrain.post.prob Logical indicating if posterior log-probabilities should be returned.prior Logical indicating if classification should be done byflat priors(default)or with empirical priors(prior=TRUE).DetailsThe classification step of the presence/absence method known as the RDP classifier(Wang et al 2007)means looking for K-mers on all sequences,and computing the posterior probabilities for each taxon using a trained model and a naive Bayes assumption.The predicted taxon is the one producing the maximum posterior probability,for each sequence.The classification is parallelized through RcppParallel employing Intel TBB and TinyThread.By default all available processing cores are used.This can be changed using the function setParallel. ValueA character vector with the predicted taxa,one for each sequence.Author(s)Kristian Hovde Liland and Lars Snipen.ReferencesWang,Q,Garrity,GM,Tiedje,JM,Cole,JR(2007).Naive Bayesian Classifier for Rapid Assign-ment of rRNA Sequences into the New Bacterial Taxonomy.Applied and Enviromental Microbiol-ogy,73:5261-5267.See AlsordpTrain.Examplesdata("small.16S")seq<-small.16S$Sequencetax<-sapply(strsplit(small.16S$Header,split=""),function(x){x[2]})##Not run:trn<-rdpTrain(seq,tax)primer.515f<-"GTGYCAGCMGCCGCGGTAA"primer.806rB<-"GGACTACNVGGGTWTCTAAT"reads<-amplicon(seq,primer.515f,primer.806rB)predicted<-rdpClassify(unlist(reads[nchar(reads)>0]),trn)print(predicted)##End(Not run)10rdpTrain rdpTrain Training the RDP classifierDescriptionTraining the RDP presence/absence K-mer method on sequence data.UsagerdpTrain(sequence,taxon,K=8,cnames=FALSE)Argumentssequence Character vector of16S sequences.taxon Character vector of taxon labels for each sequence.K Word length(integer).cnames Logical indicating if column names should be added to the trained model matrix.DetailsThe training step of the RDP method means looking for K-mers on all sequences,and computing the probability of each K-mer being present for each unique taxon.This is an attempt to re-implement the method described by Wang et tal(2007),but without the bootstrapping.See that publications for all details.The word-length K is by default8,since this is the value used by Wang et rger values may lead to memory-problems since the trained model is a matrix with4^K columns.Adding the K-mers as column names will slow down all computations.The relative taxon sizes are also computed,and returned as an attribute to the model matrix.They may be used as empirical priors in the classification step.ValueA list with two elements.Thefirst element is Method,which is the text"RDPclassifier"in thiscase.The second element is Fitted,which is a matrix with one row for each unique taxon and one column for each possible word of length K.The value in row i and column j is the probability that word j is present in taxon i.Author(s)Kristian Hovde Liland and Lars Snipen.ReferencesWang,Q,Garrity,GM,Tiedje,JM,Cole,JR(2007).Naive Bayesian Classifier for Rapid Assign-ment of rRNA Sequences into the New Bacterial Taxonomy.Applied and Enviromental Microbiol-ogy,73:5261-5267.setParallel11 See AlsordpClassify.Examples#See examples for rdpClassify.setParallel Set number of parallel threadsDescriptionSimple function to set the number of threads to use in parallel computations.The default equals all available logical cores.An integer is interpreted as the number of threads.A numeric<1is interpreted as a proportion of the avialable logical cores.UsagesetParallel(C=NULL)ArgumentsC a scalar indicating the number of threads,default=NULL(#available logicalcores)ValueNULL,returned silently.Examples##Not run:setParallel()#Use all available logical cores.##End(Not run)small.16S A small example data setDescriptionA tibble object(data.frame)with some16S sequences with taxon information.Usagedata(small.16S)DetailsThis is a tibble object(data.frame)with71sequences used in some examples.The taxonomy information for each sequence follows the ConTax format,see the microcontax package for more details.Author(s)Hilde Vinje,Kristian Hovde Liland,Lars Snipen.Examplesdata(small.16S)str(small.16S)taxMachine Classifying16S sequencesDescriptionOptimized classification of16S sequence data.UsagetaxMachine(sequence,model.in.memory=TRUE,model.on.disk=FALSE,verbose=TRUE,chunk.size=10000)Argumentssequence Character vector with DNA sequences.model.in.memoryLogical indicating if model should be cached in memory(default=TRUE).model.on.disk Logical or text,for reading/saving models,see Deatils below(default=FALSE).verbose Logical,if TRUE progress is reported during computations(default=TRUE).chunk.size The number of sequence to classify in each iteration of the loop(default=10000). DetailsThis function provides optimized taxonomy classifications from16S sequence data.All sequences are classified to the genus level based on a Multinomial model(see multinomTrain) trained on the designed consensus taxonomy data set contax.trim found in the R-package microcontax.The word length K=8has been used in the model.To avoid savingfitted models in the package,a model is trained thefirst time you run taxMachine in an R session.This takes only a few seconds,and the result is cached for latter use if model.in.memory is TRUE.If a path to an existingfile with a trained model is supplied in model.on.disk,this Multinomial model is read from thefile and used.If a path to a newfile is supplied,the trained Multinomial model will be saved to thatfile.The default(model.on.disk=FALSE),means nofiles are read/saved, while model.on.disk=TRUE will attempt to load/save models from the microclass/extdata di-rectory.Both verbose and chunk.size are used to monitor the progress,which is nice when classifying huge data sets,since this will take some time.ValueA data.frame with one row for each sequence.The columns are Genus,D.score,R.score andP.recognize.Genus is the predicted genus for each sequence.Note that all sequences get a prediction,but may still be more or less reliable.The D.score is a measure of how the predicted genus wins over all other genera in the race for being the chosen one.A large D.score means the winner stands out clearly,and we can be confident it is the correct genus.A D.score close to0means we have an uncertain classification.Only D.scores below1.0,should be of any concern,see Liland et al(2016)for details.The R.score is a measure of the models ability to recognize the sequence.The more negative the R.score gets,the more unusual the sequence is compared to the training set(the contax.trim data set).The P.recognize is a rough probability of seing an R.score this small,or smaller,given the training data.Thus,a very small P.recognize means the sequence is not really recognized,and the classification is worthless.A very negative R.score indicates either not16S at all,many sequencing errors that has destroyed the read,or a completely new taxon never seen before.See Liland et al (2016)for details.Author(s)Lars Snipen and Kristian Hovde LilandReferencesLiland,KH,Vinje,H,Snipen,L(2016).microclass-An R-package for16S taxonomy classifica-tion.BMC Bioinformatics,xx:yy.See AlsoKmerCount,multinomClassify.Examples##Not run:data(small.16S)tax.tab<-taxMachine(small.16S$Sequence)##End(Not run)Index∗packagemicroclass-package,2blastClassify16S,2,4blastDbase16S,3,4contax.trim,7,13KmerCount,5,7,8,14microclass(microclass-package),2 microclass-package,2microcontax,12multinomClassify,5,6,8,14multinomTrain,5–7,7,13rdpClassify,8,11rdpTrain,8,9,10setParallel,6,9,11small.16S,12taxMachine,6,1215。