Gravitation-Based Model for Information Retrieval

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非球面系数

非球面系数
非球面系数（non-spherical coefficients）是描述地球近似为椭球形的数学工具。

地球并非完全的球形，它的形状更接近于椭球，而非球面系数则是用来描述地球形状上的差异。

地球形状的研究一直是人类研究之一。

早在公元前3世纪，古希腊学者亚里士多德就已经提出了地球是一个球体的概念。

但是随着科学技术的进步，人们发现地球并非完全球形。

地球呈现椭球形状，拥有极半径和赤道半径等不同的参数，因此需要通过非球面系数对其进行描述。

非球面系数可用于地球测量学、地球物理学、大地测量学、地质学及地球大气科学等领域，如大气运动、海洋潮汐和地球重力场等都与非球面系数有着密切的关联。

目前，国际上应用较广泛的非球面系数是由欧洲航天局（ESA）推出的Earth Gravitational Model（EGM）系列数据。

该数据利用了全天球地球重力场模型，包括高低分辨率等不同版本，可广泛用于卫星测高、大地测量等方面，并在许多卫星导航系统中得到应用。

非球面系数的研究将有助于我们更深入地了解地球的形状及其变化，促进全球定位、导航和遥感技术的发展，进一步拓展地球科学的研究领域。

GravityModel

The Gravity Model∗James E.AndersonBoston College and NBERJanuary18,2011AbstractGravity has long been one of the most successful empirical models in economics.In-corporating deeper theoretical foundations of gravity into recent practice has led toa richer and more accurate estimation and interpretation of the spatial relations de-scribed by gravity.Wider acceptance has followed.Recent developments are reviewedhere and suggestions are made for promising future research.JEL Classiﬁcation:F10,R1.Contact information:James E.Anderson,Department of Economics,Boston Col-lege,Chestnut Hill,MA02467,USA.Keywords:Incidence,multilateral resistance,trade costs,migration.∗This review was prepared for Annual Review of Economics,vol.3.I thank Jeﬀrey H.Bergstrand,Keith Head,J.Peter Neary and Yoto V.Yotov for helpful comments.The gravity model in economics was until relatively recently an intellectual orphan,un-connected to the rich family of economic theory.This review is a tale of the orphan’s reunion with its heritage and the beneﬁts that continue toﬂow from connections to more distant relatives.Gravity has long been one of the most successful empirical models in economics,order-ing remarkably well the enormous observed variation in economic interaction across space in both trade and factor movements.The goodﬁt and relatively tight clustering of coeﬃ-cient estimates in the vast empirical literature suggested that some underlying economic law must be at work,but in the absence of an accepted connection to economic theory,most economists ignored gravity.The authoritative survey of Leamer and Levinsohn(1995)cap-tures the mid-90’s state of professional thinking:“These estimates of gravity have been both singularly successful and singularly unsuccessful.They have produced some of the clearest and most robust empiricalﬁndings in economics.But,paradoxically,they have had virtually no eﬀect on the subject of international economics.Textbooks continue to be written and courses designed without any explicit references to distance,but with the very strange im-plicit assumption that countries are both inﬁnitely far apart and inﬁnitely close,the former referring to factors and the latter to commodities.”Subsequently,gravityﬁrst appeared in textbooks in2004(Feenstra,2004),following on success in connecting gravity to economic theory,the subject of Section3.Reviews are not intended to be surveys.My take on the gravity model,thus licensed to be idiosyncratic,scants or omits some topics that others have found important while it emphasizes some topics that others have scanted.My emphases and omissions are intended to guide the orphan to maturity.An adoptive parent’s biases may have contaminated my judgment,caveat emptor.My focus is on theory.Incorporating the theoretical foundations of gravity into recent practice has led to richer and more accurate estimation and interpretation of the spatial relations described by gravity,so where appropriate I will point out this beneﬁt.The har-vest reaped from empirical work applying the gravity model is recently surveyed elsewhere (Anderson and van Wincoop,2004;Bergstrand and Egger,2011).From a modeling standpoint,gravity is distinguished by its parsimonious and tractable representation of economic interaction in a many country world.Most international economic theory is concentrated on two country cases,occasionally extended to three country cases with special features.The tractability of gravity in the many country case is due to its modularity:the distribution of goods or factors across space is determined by gravity forces conditional on the size of economic activities at each location.Modularity readily allows for disaggregation by goods or regions at any scale and permits inference about trade costs not dependent on any particular model of production and market structure in full general equilibrium.The modularity theme recurs often below,but is missing from some other prominent treatments of gravity in the literature.1Traditional GravityThe story begins by setting out the traditional gravity model and noting clues to its union with economic theory.The traditional gravity model drew on analogy with Newton’s Law of Gravitation.A mass of goods or labor or other factors of production supplied at origin i,Y i, is attracted to a mass of demand for goods or labor at destination j,E j,but the potential ﬂow is reduced by the distance between them,d ij.Strictly applying the analogy,X ij=Y i E j/d2ijgives the predicted movement of goods or labor between i and j,X ij.Ravenstein(1889) pioneered the use of gravity for migration patterns in the19th century UK.Tinbergen(1962) was theﬁrst to use gravity to explain tradeﬂows.Departing from strict analogy,traditional gravity allowed the exponents of1applied to the mass variables and of−2applied to bilateral distance to be generated by data toﬁt a statistically inferred log-linear relationship betweendata onﬂows and the mass variables and distance.Generally,across many applications,the estimated coeﬃcients on the mass variables cluster close to1and the distance coeﬃcients cluster close to−1while the estimated equationﬁts the data well:most data points cluster close to theﬁtted line in the sense that80−90%of the variation in theﬂows is captured by theﬁtted relationship.Theﬁt of traditional gravity improved when supplemented with other proxies for trade frictions,such as the eﬀect of political borders and common language.Notice that bilateral frictions alone would appear to be inadequate to fully explain the eﬀects of trade frictions on bilateral trade,because the sale from i to j is inﬂuenced by the resistance to movement on i’s other alternative destinations and by the resistance on move-ment to j from j’s alternative sources of supply.Prodded by this intuition the traditional gravity literature recently developed remoteness indexes of each country’s‘average’eﬀectivedistance to or from its partners(id ij/Y i was commonly deﬁned as the remoteness of coun-try j)and used them as further explanatory variables in the traditional gravity model,with some statistical success.The general problem posed by the intuition behind remoteness indexes is analogous to the N-body problem in Newtonian gravitation.An economic theory of gravity is required for an adequate solution.Because there are many origins and many destinations in any application,a theory of the bilateralﬂows must account for the relative attractiveness of origin-destination pairs.Each sale has multiple possible destinations and each purchase has multiple possible origins:any bilateral sale interacts with all others and involves all other bilateral frictions.This general equilibrium problem is neatly solved with structural gravity models.For expositional ease,the discussion focuses below on goods movements except when migration or investment is speciﬁcally treated.2Frictionless Gravity LessonsTaking a step toward structure,an intuitively appealing starting point is the description of a completely smooth homogeneous world in which all frictions disappear.Developing the implications of this structure yields a number of useful insights about the pattern of world trade.A frictionless world implies that each good has the same price everywhere.In a homoge-neous world,economic agents everywhere might be predicted to purchase goods in the same proportions when faced with the same prices.In the next section the assumptions on pref-erences and/or technology that justify this plausible prediction are the focus,but here the focus is on the implications for trade patterns.In a completely frictionless and homogeneous world,the natural benchmark prediction is that X ij/E j=Y i/Y,the proportion of spending by j on goods from i is equal to the global proportion of spending on goods from i,where Y denotes world spending.Any theory must impose adding up constraints,which for goods requires that the sum of sales to all destinations must equal Y i,the total sales by origin i,and the sum of purchases from all origins must equal E j,the total expenditure for each destination j.Total sales andexpenditures must be equal:i.e.,iY i=jE j=Y.One immediate payoﬀis an implication for inferring trade frictions.Multiplying both sides of the frictionless benchmark prediction X ij/E j=Y i/Y by E j yields predicted friction-less trade Y i E j/Y.The ratio of observed trade X ij to predicted frictionless trade Y i E j/Y represents the eﬀect of frictions along with random inﬂuences.(Bilateral trade data are notoriously rife with measurement error.)Fitting the statistical relationship between the ratio of observed to frictionless trade and various proxies for trade costs is justiﬁed by this simple theoretical structure as a proper focus of empirical gravity models.Thus far,the treatment of tradeﬂows has been of a generic good that most of the literature has implemented as an aggregate:the value of aggregate bilateral trade in goods for example.But the model applies more naturally to disaggregated goods(and factors)becausethe frictions to be analyzed below are likely to diﬀer markedly by product characteristics. The extension to disaggregated goods,indexed by k,is straightforward.X kij =Y kiE kjY k=s kib kjY k.(1)Here s ki =Y ki/Y k is country i’s share of the world’s sales of goods class k and b kj=E kj/Y kis country j’s share of the world spending on k,equal to the world’s sales of k,Y k.The notation and logic also readily apply to the disaggregation of countries into regions, and indeed a prominent portion of the empirical literature has examined bilateralﬂows between city pairs or regions,motivated by the observation that much economic interaction is concentrated at very short distances.The model can interpreted to reﬂect individual decisions aggregated with a probability model;see section5.1below.In aggregate gravity applications(i.e.,most applications),it has been common to use origin and destination mass variables equal to Gross Domestic Product(GDP).This is con-ceptually inappropriate and leads to inaccurate modeling unless the ratio of gross shipments to GDP is constant(in which case the ratio goes into a constant term).A possible direction for aggregate modeling is to convert trade to the same value-added basis as GDP,but this seems more problematic than using disaggregated gravity to explain the pattern of gross shipments and then uniting estimated gravity models within a superstructure to connect to GDP.That is the strategy of the structural gravity model research program reviewed here.Equation(1)generates a number of useful implications.1.Big producers have big market shares everywhere,2.small sellers are more open in the sense of trading more with the rest of the world,3.the world is more open the more similar in size and the more specialized the countriesare,4.the world is more open the greater the number of countries,and5.world openness rises with convergence under the simplifying assumption of balancedtrade.Implication1,that big producers have big market shares everywhere,follows because, reverting to the generic notation and omitting the k superscript,the frictionless gravity prediction is that:X ij/E j=s i.Implication2,that small sellers are more open in the sense of trading more with the rest of the world follows fromi=jX ij/E j=1−Y j/Y=1−s jusingjE j=iY i,which implies balanced trade for the world.Implication3is that the world is more open the more similar in size and the more special-ized the countries are.It is convenient to deﬁne world openness as the ratio of internationalshipments to total shipments,ji=jX ij/Y.Dividing(1)through by Y k and suppressingthe goods index k,world openness is given byji=jX ij/Y=jb j(1−s j)=1−jb j s j.Using standard statistical propertiesj b j s j=Nr bsV ar(s)V ar(b)+1/N,where N is the number of countries or regions,V ar denotes variance,r bs is the correlationcoeﬃcient between b and s and1/N=is i/N=jb j/N,the average share.This equationfollows from the shares summing to one and using standard properties of covariance.Here, V ar(s)and V ar(b)measures size dis-similarity and the correlation of s and b,r bs,is aninverse measure of specialization.Substituting into the expression for world openness:ji=jX ij/Y=1−1/N−Nr bsV ar(s)V ar(b)(2)Implication3follows from equation(2)because on the right-hand side the similarity of country size shrinks the variances while specialization shrinks the correlation r bs.The country-size similarity property has been prominently stressed in the monopolistic competition and trade literature.(It is sometimes taken as evidence for monopolistic com-petition in a sector rather than as a consequence of gravity no matter what explains the pattern of the b’s and s’s.)The specialization property has also been noted in that liter-ature as reﬂecting forces that make for greater net international trade,the absolute value of s j−b j.Making comparisons across goods classes,variation in the right-hand side of(2) results from variation in specialization and in the dispersion of the shipment and expenditure shares.Notice again that the cross-commodity variation in world openness arises here in a frictionless world,a reminder that measures of world home bias in a world with frictions must be evaluated relative to the frictionless world benchmark.Country-size similarity also tends to increase bilateral trade between any pair of countries, all else equal.This point(Bergstrand and Egger,2007)is seen most clearly with aggregate trade that is also balanced,hence s j=b j.Equation(1)can be rewritten asX ij=s iji s ijj(Y i+Y j)2Y,where s iji ≡Y i/(Y i+Y j),the share of i in the joint GDP of i and j.The product s ijis ijjis maximized at s iji =s ijj=1/2,so for given joint GDP size,bilateral trade is increasingin country similarity.(With unbalanced trade or specialization,an analogous similarity property holds for the bilateral similarity of income and expenditure shares.Letγj=E j/Y j. Then the same equation as before holds with the right-hand side multiplied byγj.)A more novel implication of equation(2)is implication4,that world openness is ordinarilyincreasing in the number of countries.Increasing world openness due to a rise in the number of countries reﬂects the property that smaller countries are more naturally open and division makes for more and smaller countries.This eﬀect is seen by diﬀerentiating the left-hand side ofji=jX ij/Y=1−jb j s j,yielding−j(b j ds j+s j db j).Increasing the number of countries tends to imply reducingthe share of each existing country while increasing the share(from zero)of the new country. The preceding diﬀerential expression should thus ordinarily be positive.The qualiﬁcation‘ordinarily’is needed because the pattern of share changes will depend on the underlying structure as revealed by the left-hand side of equation(2).On the one hand,the average share1/N decreases as N rises,raising world openness.On the otherhand,the change in the number of countries will usually change r bsin waysthat depend on the type of country division(or confederation)as well as indirect eﬀects on shares as prices change.(The apparent direct eﬀect of N in theﬁrst term on the right-handside of equation(2)vanishes because1/N scalesV ar(b)V ar(s).)A practical implication of this discussion is that inter-temporal comparisons of ratios of world international trade to world income,to be economically meaningful,should be con-trolled for changes in the size distribution and the number of countries,a correction of large practical importance in the past50to100years.Alternatively,measures of openness meant to reﬂect the eﬀects of trade frictions should be constructed in relation to the frictionless benchmark.Applied to aggregate trade data,gravity yields implication5,that world openness rises with convergence under the simplifying assumption of balanced trade for each country,b j= s j,∀j.The right-hand side of equation(2)becomes NV ar(s)+1/N under balanced trade, and per-capita income convergence lowers V ar(s)toward the variance of population.Baier and Bergstrand(2001)use the convergence property to partially explain postwar growth in world trade/income,ﬁnding relatively little action,although presumably more recent data inﬂuenced by the rise of China and India might give more action.Pointing toward a connection with economic theory,the shares s i and b j and the plau-sible hypothesis of the frictionless model must originate from an underlying structure of preferences and technology.Also,the deviation of observed X ij from the frictionless pre-diction reﬂects frictions as they act on the pattern of purchase decisions of buyers and the sales decisions of sellers,which originate from an underlying structure of preferences and technology.3Structural GravityModeling economies with trade costs works best if it moves backward from the end user. Start by evaluating all goods at user prices,applying demand-side structure to determine the allocation of demand at those prices.Treat all costs incurred between production and end use as being incurred by the supply side of the market,even though there are often signiﬁcant costs directly paid by the user.What matters economically in the end is the full cost between production and end use,and the incidence of that cost on the producer and the end user.Many of these costs are not directly observable,and the empirical gravity literature indicates the total is well in excess of the transportation and insurance costs that are observable(see Anderson and van Wincoop,2004,for a survey of trade costs).The supply side of the market under this approach both produces and distributes the delivered goods,incurring resource costs that are paid by end users.The factor markets for those resources must clear at equilibrium factor prices,determining costs that link to end-user prices.Budget constraints require national factor incomes to pay for national expenditures plus net lending or transfers including remittances.Below the national accounts,individual economic agents also meet budget constraints.Goods markets clear when prices are found such that demand is equal to supply for each good.The full general equilibrium requires a set of bilateral factor prices and bilateral goods prices such that all markets clear and all budget constraints are met.This standard description of general economic equilibrium is too complex to yield some-thing like gravity.A hugely useful simpliﬁcation is modularity,subordinating the economic determination of equilibrium distribution of goods within a class under the superstructure determination of the distribution of production and expenditure between classes of goods. Anderson and van Wincoop(2004)call this property trade separability.Observing that goods are typically supplied from multiple locations,even withinﬁne census commodity classes,it is natural to look for a theoretical structure that justiﬁes grouping in this way. The structural gravity model literature has uncovered two structures that work,one on the demand side and one on the supply side,detailed in sections3.1and3.2.Modularity(trade separability)permits the analyst to focus exclusively on inference about distribution costs from the pattern of distribution of goods(or factors)without having to explain at the same time what determines the total supplies of goods to all destinations or the total demand for goods from all origins.This is a great advantage for two reasons.First, it simpliﬁes the inference task enormously.Second,the inferences about the distribution of goods or factors is consistent with a great many plausible general equilibrium models of national(or regional)production and consumption.Modularity also requires a restriction on trade costs,so that only the national aggregate burden of trade costs within a goods class matters for allocation between classes.The most popular way to meet this requirement is to restrict the trade costs so that the distribution of goods uses resources in the same proportion as the production of those same goods.Samuel-son(1952)invented iceberg melting trade costs in which the trade costs were proportional to the volume shipped,as the amount melted from the iceberg is proportional to its volume. The iceberg metaphor still applies when allowing for aﬁxed cost,as if a chunk of the ice-berg breaks oﬀas it parts from the mother glacier.Mathematically,the generalized iceberg trade cost is linear in the volume shipped.Economically,distribution continues to require resources to be used in the same proportion as in production.Fixed costs are realistic and potentially play an important role in explaining why many potential bilateralﬂows are equalto zero.More general nonlinear trade cost functions continue to satisfy the production propor-tionality restriction and thus meet the requirements of modularity,but depart from the iceberg metaphor.Bergstrand(1985)derived a joint cost function that is homogeneous of degree one with Constant Elasticity of Transformation(CET).This setup allows for substi-tution eﬀects in costs between destinations rather than the cost independence due toﬁxed coeﬃcients in the iceberg model.Bilateral costs have a natural aggregator that is an iceberg cost facing monopolistically competitiveﬁrms.A nice feature of the joint cost model is its econometric tractability under the hypothesis of proﬁt maximizing choice of destinations. Although potentially more realistic,the joint cost reﬁnement turns out to make relatively little diﬀerence empirically.Arkolakis(2008)develops a nonlinear(in volume)trade cost function in which hetero-geneous customers are obtained byﬁrms with a marketing technology featuring aﬁxed-cost component(running a national advertisement)and a variable-cost component(leaﬂetting or telemarketing)subject to diminishing returns as the less likely customers are encountered. Because of the Ricardian production and distribution technology,resource requirements in distribution remain proportional to production resource requirements.Arkolakis shows that the marketing technology model can rationalize features of theﬁrm-level bilateral shipments data that cannot be explained with the linearﬁxed-costs model.His setup is not economet-rically tractable but is readily applicable as a simulation model.In all applications based on the preceding cost functions,proxies for costs are entered in some convenient functional form,usually loglinear in variables such as bilateral distance,con-tiguity,membership of a country,continent or regional trade agreement,common language and common legal traditions.See Anderson and van Wincoop(2004)for more discussion.More generality in trade costs that violates the production proportionality restriction comes at the price of losing modularity.See Matsuyama(2007)for recent exploration of the implications of non-iceberg trade costs in a2country Ricardian model.See Deardorﬀ(1980)for a very general treatment of the resource requirements of trade costs as a setting for his demonstration that the law of comparative advantage holds quite generally.3.1Demand-Side StructureThe second requirement for modularity can be met by restricting the preferences and/or technology such that the cross eﬀects in demand between classes of goods(either interme-diate orﬁnal)ﬂow only through aggregate price indexes.This demand property is satisﬁed when preferences or technology are homothetic and weakly separable with respect to a par-tition into classes whose members are deﬁned by location,a partition structure called the Armington assumption.Thus for example steel products from all countries are members of the steel class.Notice that the assumption implies that goods are purchased from multiple sources because they are evaluated diﬀerently by end users,and goods are diﬀerentiated by place of origin.It is usual to impose identical preferences across countries.Diﬀerences in demand across countries,such as a home bias in favor of locally produced goods,can be accommodated, understanding that‘trade costs’now include the eﬀect of a demand side home bias.In practice it is very diﬃcult to distinguish demand-side home bias from the eﬀect of trade costs, since the proxies used in the literature(common language,former colonial ties,or internal trade dummies,etc.)plausibly pick up both demand and cost diﬀerences.Henceforth trade cost is used without qualiﬁcation but is understood to potentially reﬂect demand-side home bias.Declines in trade costs can be understood as reﬂecting homogenization of tastes.Separability implies that each goods class has a natural quantity aggregate and a nat-ural price aggregate,with substitution between goods classes occurring as if the quantity aggregates were goods in the standard treatment.The separability assumption implies that national origin expenditure shares within the steel class are not altered by changes in the prices of non-steel products,though of course the aggregate purchase of steel is aﬀected by the aggregate cross eﬀect.Homotheticity ensures that relative demands are functions onlyof relative aggregate prices.Theﬁrst economic foundation for the gravity model was based on specifying the expendi-ture function to be a Constant Elasticity of Substitution(CES)function(Anderson,1979). Expenditure shares in the CES case are given byX ij E j =βi p i t ijP j1−σ(3)where P j is the CES price index,σis the elasticity of substitution parameter,βi is the ‘distribution parameter’for varieties shipped from i,p i is their factory gate price and t ij>1 is the trade cost factor between origin i and destination j.The CES price index is given byP j=i(βi p i t ij)1−σ1/(1−σ).(4)Notice that the same parameters characterize expenditure behavior in all locations;prefer-ences are common across the world by assumption.Notice also that the shares are invariant to income,preferences are homothetic.With frictionless trade,t ij=1,∀(i,j)and therefore all the buyers’shares of good i must equal the sellers share of world sales(at destination prices),Y i/Y.Thus the frictionless benchmark is justiﬁed by assuming identical homothetic preferences.For intermediate goods,the same logic works replacing expenditure shares with cost shares.The‘distribution parameters’βi bear several interpretations.They could be exogenous taste parameters.Alternatively,in applications to monopolistically competitive products,βi is proportional to the number ofﬁrms from i oﬀering distinct varieties(Bergstrand,1989). Countries with more activeﬁrms get bigger weights.In long run monopolistic competition the number ofﬁrms is endogenous.Due toﬁxed entry costs,bigger countries have more active ﬁrms in equilibrium,all else equal.The number of activeﬁrms contributes to determining the Y i’s that are given in the gravity module.The other building block in the structural gravity model is market clearance:at deliveredprices Y i=jX ij.Multiplying both sides of(3)by E j and summing over j yields a solutionforβi p1−σi,βi p1−σi =Y ij(t ij/P j)1−σE j.Deﬁne the denominator asΠ1−σi.Substituting into(3)and(4)yields the structural gravity model:Xij =EjYiYtijPjΠi1−σ(5)(Πi )1−σ=jtijPj1−σEjY(6)(Pj )1−σ=itijΠi.1−σYiY.(7)The second ratio on the right-hand side of(5)is a decreasing function(under the empirically valid restrictionσ>1)of direct bilateral trade costs relative to the product of two indexes of all bilateral trade costs in the system.Anderson and van Wincoop(2003)called the terms P j andΠi inward and outwardmultilateral resistance respectively.Note that{P1−σj ,Π1−σi}can be solved from(6)-(7)forgiven t1−σij’s,E j’s and Y i’s combined with a normalization.1Under the assumption of bilateral trade cost symmetry t ij=t ji,∀i,j and balanced trade E j=Y j,∀j,the natural normalization isΠi=P i.Anderson and van Wincoop estimated their gravity equation for Canada’s provinces and US states with a full information estimator that utilized(7)withΠi=P i. Subsequent research has focused mostly on estimating(5)with directional countryﬁxedeﬀects to control for E j/P1−σj and Y i/Π1−σi.Multilateral resistance is on the face of it an index of inward and outward bilateral trade costs,but because of the simultaneity of the system(6)-(7),all bilateral trade costs in the world contribute to the solution values.This somewhat mysterious structure has a simple1For any solution to the system{P0j ,Π0i},{λP0j,Π0i/λ}is also a solution.Thus a normalization is needed.Anderson and Yotov(2010a)ﬁnd that the system(6)-(7)solves quite quickly,not surprisingly because it is quadratic in the1−σpower transforms of the P’s andΠ’s.。

格林定律英语词根词缀

格林定律英语词根词缀The Law of Gravitation, proposed by Isaac Newton in 1687,is known as the "Universal Law of Gravitation" or more commonly, "The Law of Gravity". The Law of Gravity states that "every object in the universe attracts every other object with a force proportional to the product of the two objects' masses and inversely proportional to the square of the distance between them." This can be expressed mathematically in the form of the famous equation:F =G (m₁m₂)/r²Where "F" is the force of attraction between two objects, "G" is the gravitational constant, "m₁" and "m₂" are the masses of the two objects, and "r" is the distance between them.The concept of gravitation is based on the Greek root "gravitas" which means "weight" or "heaviness". The prefix "gra-" means their tendency to come together or approach each other, while the suffix "-ation" implies action or process. Therefore, gravitation literally means to come near each other due to their weight.In physics, the root word "grav-", combined with the prefix "in-", forms the word "inertia" which means an object's tendency to remain at rest or in motion unless an outside force acts on it. Inertia is caused by an object's mass, and since gravitation is related to mass, it follows that inertia has something to do with gravitation. The Latin root word "levi-" means "to raise" or "to lift" and this forms the basis of the term "levity". Levity is the opposite ofgravity, and describes an object's ability to float or be suspended in the air as opposed to being pulled down by the force of gravity.Gravity is also related to the root word "cel-" which means "to move rapidly". This produces the words "acceleration" and "accelerate" which means to increase the speed of something, or to cause it to move faster. According to Newton's law of gravitation, an object will accelerate towards the source of the gravitational pull.Finally, the root word "cent-" which means "center" or "point" is related to gravity as well. This produces the word "centripetal" which means directed toward the center. According to Newton's law of gravitation, all objects in the universe are moving towards each other due to the gravitational pull they experience.In conclusion, the law of gravity is a universal law that governs all objects in the universe, and its concept is based on numerous English words that are derived from Latin and Greek roots. By understanding the roots of these words and their meanings, we can gain a better appreciation for the universality of gravitation.。

特斯拉动态引力理论原文

Introduction:
There is a new theory of gravity called Dynamic Theory of Gravity [DTG]. Based on classical thermodynamics Ref:[1] [2] [3] [9] it has been shown that the fundamental laws of Classical Thermodynamics also require Einstein’s
p 4 = mv 4 ,
(1a)
where the velocity in the fifth dimension is given by:
•
γ v4 = , αD
•
(1b)ቤተ መጻሕፍቲ ባይዱ
and γ is a time derivative where gamma itself has units of mass density or kg/m3, and αo is a density gradient with units of kg/m4. In the absence of curvature, (1) becomes:
(5)
and for orbiting Hubble telescope (ht) of a height h the following expression:
ln[1 + z ht ] = −
M em HL R⊕ G M⊕ − . + c 2 (R + h ) + R R h ⊕ c ⊕ em
Abstract:
In a new theory called Dynamic Theory of Gravity, the cosmological distance to an object and also its gravitational potential can be calculated. We first measure its redshift on the surface of the Earth. The theory can be applied as well to an object in orbit above the Earth, e.g., a satellite such as the Hubble telescope. In this paper, we give various expressions for the redshifts calculated on the surface of the Earth as well as on an object in orbit, being the Hubble telescope. Our calculations will assume that the emitting body is a star of mass M = MX-ray(source) = 1.6×108 Msolar masses and a core radius R = 80 pc, at a cosmological distance away from the Earth. We take the orbital height h of the Hubble telescope to be 450 Km.

动态称量

Dynamic Weighing Experiments -The Wayto New Physics of GravitationA. L. Dmitriev, E. M. Nikushchenko and S. A. BulgakovaSt-Petersburg State University of Information Technologies, Mechanics and Optics49, Kronverksky Prospect, St-Petersburg, 197101, Russia+7.812.3154071, alex@dmitriyev.ruAbstract. Dynamic weighing is a measuring of size of the average gravity force acting on a test body which is in the state of accelerated movement. The acceleration of a body, or its microparticles, can be caused both by forces of gravitation, and by a direct, electromagnetic in nature, influence on the part of other bodies. It is just dynamic weighing of bodies which is informative in studying the features of electromagnetic and gravitational forces interaction. The report gives a brief review of results of experiments with weighing of accelerated moving bodies –in case of shock phenomena, in state of rotation, and in heating. Special attention is given to measurements of free fall accelerations of a mechanical rotor. I n majority of the laboratory experiments executed with the purpose of checking the equivalence principle, the axis of a rotor was oriented verticallly. In our experiment we measured the free fall accelerations of the closed container inside which a mechanical rotor (gyroscope) with a horizontal axis of rotation was installed. There was observed an appreciable, essentially exceeding errors of measurements increase of acceleration of free falling of the container at angular speed of rotation of a rotor up to 20 000 rev/min. The physical conditions of free vertical falling ofa body essentially differ from conditions of rotary (orbital) movement of a body in the field of gravity and the resultobtained by us does not contradict the results of measurements of a gyroscope precession on satellites. Experiments with dynamic weighing of bodies give useful information on complex properties of the gravity force which are beyond the scope of well-known theories. Their careful analysis will allow to expand and supplement the concepts based on the general theory of relativity, and probably to open a way to new physics of gravitation and to new principles of movement.Keywords:Gravity Force, Weighing, Acceleration, Free Falling, Gyro, Equivalence Principle .PACS:, 04.80.-y.INTRODUCTIONThough physics is an experimental science, in modern physics of gravitation the scale of theoretical researches has considerably surpassed the scale of experiments. In a solid, over 600 pages, recently published review «100 Years of Gravity and Accelerated Frames » the experimental (and besides -astrophysical) tests of gravitational theories are given less than 30 pages(Hsu and Fine, 2005). Attempts to establish some new properties of gravitation in laboratory experiments, from the point of view of classical GR, are usually considered as unpromising. Meanwhile, the grounds for criticism of experimental basis of GR –equivalency principle –do exist. Thus, in all Eotvos-experiments the measurements of forces of gravitation were made in the extremely limited physical conditions, at constant temperature and small accelerations of test bodies (Chen and Cook, 1993;Haugan and Lammerzahl, 2001). The approximation of appropriate GR results in the area of high accelerations of bodies, strictly speaking, is incorrect. The interrelation of the external accelerations, for example, of elastic forces applied to a test body, and force of gravitation acting on this body, follows from the deep unity of electromagnetic and gravitational interactions and, according to the phenomenological description, can be considered as gravitational analogue of Faraday’ law of induction and Lentz’ rules (Dmitriev, 2001, 2009a). The search for non-classical effects in gravitation in experiments with precision weighing of accelerated moving bodies (oscillating, rotating, being heated up etc.) is logical and expedient. Yet Mendeleev(1950)pointed out: « I f it is possible to achieve something in understanding of gravitation and weight, then in no other way and most likely by the most precise weighings and observations of oscillations taking place at that time».CP1208, Space, Propulsion & Energy Sciences International Forum–SPESIF-2010, edited by G. A. Robertson© 2010 American Institute of Physics 978-0-7354-0749-7/10/$30.00There are distinguished two ways of exact weighing of bodies: static and dynamic. In static weighing the test body is motionless relative to the Earth and weight of the body is determined by the size of elastic or electromagnetic force compensating the gravity; this technique directly corresponds to definition of concept « weight of a body ». I n dynamic weighing the beam of weights and a test body make slowly fading oscillations, and average value of the weight measured is determined by elongations’method, by fixing and averaging some extreme values of readings displayed on the scale of weights; in that case the test body experiences some well marked accelerations, which are described by an infinite set of time derivatives from body displacement. Obviously, the physical conditions of dynamic and static weighing essentially differ, though in practical metrology of weight the results of both techniques of weighing are often believed to be identical. Just dynamic weighing is informative in researches into interrelation of gravitational and electromagnetic (elastic) forces.Of special interest are the measurements of acceleration of free falling of the test bodies underlying the ballistic methods of gravimetry. At free falling a body the interaction of gravitational and foreign forces, by definition, is excluded, but this ideal state is achieved only under condition of absence of own oscillatory or rotary movement of a test body.Preconditions of search of interaction of electromagnetic and gravitational forces are the results of various Gravity Electro-Magnetism theories which are based on modified GR’equations (Bini et al ., 2008;Schmid, 2009). Though the observable effects predicted in such theories are usually extremely small, some worthy positive results were obtained in some laboratory experiments (Tajmar et al .,2008;Woodward, 2009).The interrelation of gravitational and electromagnetic forces is especially important in the analysis of properties and reasons of inertia, propulsions’ problems, and search for new principles of movement. Correctly executed gravitational laboratory experiment can and should be the basis for formulations of new concepts in gravitation including, supplementing and developing the known GR approaches.ACCELERATION OF EXTERNAL FORCES, GRAVITYAND INERTIAL MASS OF A BODYIn distinction from "geometrical", the "field" concept of gravitation describes the gravitational interaction of bodies similarly to other kinds of physical interactions -electric and magnetic. Thus the concept of the "material" gravitational field related to sources -the gravitational mass -and characterized by the set of parameters (potential, velocity, impulse, moment) is considered. The advantage of the field, basically phenomenological concept of gravitation consists in an opportunity to use for its development some separate analogies of the gravitational and electromagnetic phenomena, and in their direct experimental check. Thus, gravitational fields, certainly, should have the properties similar, but not identical to properties of electromagnetic fields.I n (Dmitriev, 2001)on the basis of the noted analogies the assumption of original reaction of the gravity force acting on a test body, on its acceleration a G caused by action of external not gravitational (for example, elastic) forces is put forward. Change p,c g 'G of acceleration of the gravity, similar to the phenomenon of Faraday’s inductionlaw in view of Lenz’ rule, at simple linear approximation, is equal to p,c p,c g a ' D G G , (1)where indexes p,c indicate mutual, passing p or a contrary (opposite) c ,orientation of a vector 0g Gof normal acceleration of a gravity and vector a G of acceleration of external force, Figure 1.Rough estimations of the order of value of dimensionless factors p D and c D , which the gravitational interrelation ofgravitational and electromagnetic fields specify, were executed in mechanical experiments with weighing of two coupled mechanical rotors with the zero full moment, with a horizontal axis of rotation, and in the analysis of the shock phenomena (Dmitriev, 2002).For metal not magnetic test bodies it is 2c 10 D |,7p c ()10 D D |.By consideration of thermal chaotic movement of microparticles of solid bodies the consequence of equation (1), in view of an inequality p c D !D , is the negative temperature dependence of gravity, also observed in the experiment(Dmitriev, Nikushchenko and Snegov,2003; Dmitriev,2008).Measurements of anisotropy of weight of a crystalwith a big spatial difference of speeds of longitudinal acoustic waves also specify to nonzero value of a difference p c ()D D (Dmitriev and Chesnokov, 2004).(a) (b)FIGURE 1. a)Changes p g 'G in gravity force acceleration acting on test body while body is falling down with acceleration a G and b)Changes c g 'G in gravity force acceleration while body is moving up with acceleration a G .Definition of factors p D and c D of electromagnetic (elastic) and gravitational forces interaction has allowed to givea simple physical interpretation to inertial mass of a body. In (Dmitriev, 2008b;2009b)in the description of balance of the elastic (electromagnetic) and gravitational forces acting on the test mass on the part of remote mass (for example, stars), according to idea of Mach about the gravitational nature of inertial forces, the ratio between inertial i m and gravitational g m masses is obtained,i g p c m m () D D . (2)Equation (2)shows the direct proportionality of inertial and gravity masses of a body, and the relation of theses masses, contrary to the known postulate of "geometrical" model of gravitation, generally speaking, is not a constant. Equation (1)shows the relation of change of gravity acceleration with acceleration a Gof external forces, but in so doing it is necessary to take into account that the absolute size p,c g 'of an increment of acceleration should alsodepend on magnitude 0g of normal gravity acceleration. Generally, in view of influence of forces of the gravitationcaused by remote surrounding masses (stars), in movement of a test body on a vertical there should be carried out the equationp,c p,c 0A (g g )c D , (3)where g c -a projection of acceleration of forces of gravitation on the part of the remote masses located in a solid angle 2S , on the direction of the accelerated movement of body. Here the dimensional factors p,c A are universal andcharacterize the action on a test body of not only the gravitational field of the Earth, but also the fields of the gravitation created in all surrounding masses.The resultant forces of gravitation acting on the motionless or moving with the constant speed test body from direction of remote masses, uniformly distributed in space in a full solid angle 4S , it is approximately equal to zero, while the magnitude g c determines the inertial properties of a body, Figure 2, where the resulting accelerations ’ vectors g c G and g c c G , caused by action of the remote masses located in the left and the right half-spaces in the solid angles 2S , are equal in magnitude and are oppositely directed.Equations (2) and (3)are in agreement with the principle of Mach according to which the inertial properties of bodies are determined by action on them of forces of the gravitation created by all surrounding masses, including rather remote ones.FIGURE 2.Mutual orientation of a vector of acceleration of not gravitational forces a G and increments vectors p c g , g ''G G ofaccelerations of the gravitation forces acting on test mass from the direction of remote masses (stars).INERTIAL MASS ANISOTROPYAs is known, GR excludes the practical observablity of anisotropy of inertia (Hughes, 1960). Consequence of equations (2) and (3)is an appreciable difference of inertial mass of a test body at its accelerated movement relative to the Earth in horizontal and vertical directions (Dmitriev, 2009b). Let's show it on an example of harmonious oscillator.For the harmonious, caused by the action of external elastic force, oscillatory movement along a vertical, theaverage, for the period of oscillation, inertial mass i ˆmof a test body is equal to 0i g p c g ˆmm (A A )(g )2c . (4)In oscillatory movement of this test body along the horizontal, its average inertial mass i m is equal to i g p c m m (A A )g c . (5)In equations (4) and (5)the resulting magnitude g c of projections of accelerations of gravity forces created by the remote masses in a solid angle 2S , is believed approximately constant and independent from the direction in space. The relative difference of "vertical" and "horizontal" inertial masses, taking 0g g c !!, is equal to 0i i i i ˆg m m 2ˆmm 2g |c . (6)Experimental estimations of magnitude of inertial mass’ anisotropy of a body can be made, comparing the periods of oscillations of linear mechanical oscillator with vertical and horizontal orientations of its axis. For the same purpose it is convenient to use the rotation oscillator, for example a pendulum of high-quality mechanical balance watch, by changing orientation of the balance axis.The period T of free oscillations of system a balance -spiral of mechanical watch is equal toT 2 , (7)where I -the moment of inertia of balance i I m v and C -factor of elasticity of the spiral.According to equations (6) and (7)the period ˆTof oscillations of balance in a vertical plane should be more than the period T of oscillations of balance moving in a horizontal plane, that is the ideal mechanical watch in position « on an edge » goes more slowly, than in position "flatwise".The position-sensitivity of mechanical watch is influenced many factors, including, the moment of inertia and quality of a spiral, conformity of an axis of rotation and the centre of inertia of a pendulum, friction in axes of a suspension bracket of a pendulum etc (Paramonov, 1977). With high quality of watch and its careful adjustment,the influence of the specified factors can be reduced practically to zero, and in that case the comparison of daily motion of balance watch in vertical and horizontal positions can be used for an estimation of magnitude of anisotropy of inertial masses (equation 6).In view of equations (4)-(7), the relative difference J of the daily motion of an ideal watch is equal to 0ˆg T T 12ˆ4g TT J | . (8) In Figure 3,the results of measurements of position sensitivity of twenty one samples of mechanical watch «Raketa 2609 » manufactured by “Petrodvortsovy watch factory” are given. The difference of an average daily motion of watch in positions "flatwise" and « on an edge » was measured;each of them was measured as an average for two different positions of the head and plane of a dial of watch. The average magnitude of watch motion delay in position «on an edge» has come to about 15 seconds over one day which corresponds to 41.710 J |.specimen numberD i f f e r e n c e o f t i m e m o t i o n , s e c o n d i n 24 h o u r FIGURE 3. A difference of a daily motion of mechanical balance watch «Raketa 2609 » in positions "flatwise" and «on an edge».The question of what part of the given value J is caused by action of physical factors (anisotropy of inertial mass in a gravitational field of the Earth), and what –by technical imperfection of the mechanism of watch still remains open. The difficulty is that even with an appreciable influence on a motion of watch of anisotropy of inertial mass of the pendulum of watch, the position-dependence of a daily motion of watch can be reduced almost to zero by technical means of adjustment. Thus the "physical" delay of a watch motion can be artificially compensated by adjustment of watch,which complicates an objective estimation of magnitude of such effect.Therefore the careful analysis of all technical factors influencing the position sensitivity of balance watches and clockworks used in such experiments is necessary for obtaining of objective data. Nevertheless, the given average result is in agreement with physical preconditions noted above and can be the basis for setting up precision experiments with use of mechanical oscillators on measurements of prospective anisotropy of inertial mass.Note, if the result shown in Figure 3gives a true estimation of magnitude order of a relative difference of inertial mass in horizontal and vertical directions, then, according to equation (8), gravitational field-intensity g c created by all indefinitely remote masses located in a solid angle 2S relative to a point of observation, the said intensity is approximately one thousand times the magnitude of normal acceleration of gravity on the surface of the Earth. In view of gravitational analogue of the Faraday’s induction law (equation (1)), such rather strong "interstellar" gravitational field, apparently, is also the main physical reason of inertial properties of bodies.The precision measurements of anisotropy of inertial mass of bodies in a non-uniform gravitational field will confirm validity or a fallacy of the above estimation and as a consequence the validity of the phenomenological "field" concept of gravitation in the description of inertial properties of bodies.FREE FALLING OF A MECHANICAL ROTOR WITH A HORIZONTAL AXISIt is known, that weight of motionless bodies is directly determined by accelerationg of free falling. For ɨscillatingand rotating test bodies the measurement of such acceleration is not trivial.To laboratory weighings of rotors of mechanical gyroscopes the set of works (Nitschke and Wilmarth, 1990;Quinn and Picard, 1990;Faller et al., 1990) is devoted. Such measurements were usually carried out with the purpose of experimental check of an equivalence principle, or various gravitoelectric(gravitomagnetic)models. In most cases, in these experiments the axis of a rotor was oriented vertically and, as a whole, the positive effect was absent(Luo et al., 2002). In paper (Dmitriev and Snegov, 2001)the results of exact weighing of two coaxial rotors with a horizontal axis and with the zero total are given, and its weights which have shown little change, dependent on angular speed of rotation of a moment J6rotor. The explanation of these results the possible precession a gyroscope is complicated, connected to rotation the. Earth, which essentially could to influence indications of weights, owing to inexact performance of equality J06In much smaller degree the precession effects influence on results of measurement of size of acceleration by freely falling of rotor. Thus physical conditions of interaction of a falling rotating rotor with the centre of gravitation (Earth) essentially differ from conditions of weighing of a rotor on based laboratory weights.In described simple experiment (Dmitriev, Nikushchenko and Bulgakova, 2009)the acceleration of free falling of container with the two, located coaxially, rotors of mechanical gyroscopes placed inside it was measured Figure4; the device and characteristics of the container are given in (Dmitriev and Snegov, 2001).FIGURE4.The device of the container. 1 -electric coils of the engine of a gyroscope, 2 -a massive cylindrical part of a rotor, 3 -the case of the first gyroscope, 4 -plugs of power supplies of engines of gyroscopes, 5 -the case of the secondgyroscope (it is shown without a section), 6 -the case of the container.On the container the compact highly stable generator of pulses connected to two differ-coloured light-emitting diodes, located along a trajectory of falling of the container is fixed.Appearance of the container with the device for throwing down is shown in Figure5.Distance on centre to centre of aperture stop (holes), established before light-emitting diodes is l76.25mm, frequency of impulses F56.25Hz, duration of impulse optical signals0.13ms.The trajectory of the falling container was photographed by the digital camera with exposure0.60.8s.An example of such photos is shown in Figure6. Coordinates of marks (the centres of holes) were digitized by computer.FIGURE 5.Container with the device for throwing. FIGURE 6.An example of the container falling trajectory photo.The calculation of acceleration g of free falling container was carried out under the formula 2212()F g N ' ' , (9)where 12,''-absolute lengths of the next sites of the trajectories,containing N marks; the scale of the image wasdefined by distance A between light-emitting diodes.For reduction of influence of aberration of the image owing to distorsion, the average scale of the image paid off on three readout of length A -in the top, central and bottom parts of a trajectory. The size g in separate measurement was determined as average value of acceleration, designed on two trajectories appropriate to two groups of color marks on the image.The example of the measured values of acceleration of free falling container in conditions (1)0Z , (2)0Z z and (3)0Z (upon termination of time rotation of rotor) is shown in Figure 7.FIGURE 7.The example of the measured values of acceleration of free falling container. 1.0Z (N. 1-4 ), 20Z z ( N. 6-10 ), 3.0Z (N. 12-16 ).The maximal angular velocity of rotation of a rotor 20000rpm Z |, rotation time of rotor is 14-15 mines, duration of one cycle of measurements from 4-5 pictures about 2 minutes.It was processed over 200 pictures, thus the increase of acceleration of free falling of a rotor was regularly observed at transition from a condition (1) to a condition (2) with average size 2g 102ɫP V' r . At smooth reduction ofspeed Z of rotation of a rotor the size g'also decreased, falling up to zero at0Z. In the specified in figure measurements both rotors rotated in one direction and the maximal full moment of rotation of rotors was 2J0.2kg m/s6| .The reason of an appreciable divergence of the measured absolute value of acceleration g of a gravity at0Z(about 990 cm / s2) and standard, at latitude of Saint Petersburg (about 982 cm / s2 A ), apparently, are discrepancies indisplay of scale, errors of absolute value of frequency F of the generator and also the small local (technical) changes of g. Geographical orientation of a vector of the moment of rotation of a rotor, N-S or W-O, did not influence on results of measurements g'. Daily dependence of size g'also it was not observed.At horizontal orientation of an axis of rotation of a rotor the each of its particles simultaneously participates in two linear oscillations in horizontal and vertical planes.Thus of acceleration of particles at their vertical oscillations by an infinite set of derivatives on time from linear displacement are described. As it was marked in (Dmitriev, 2001;2008a;2009a)in these conditions it is possible to expect display of "nonclassical" properties of gravitation,which mentioned some more Mendeleev (1950).Free falling of masse oscillated along a vertical physically essentially differs from circular (orbital) movement of such masse. Therefore the result received by us does not contradict the results of exact measurements of precession a gyroscope in a circumterraneous orbit.Relative change g/g'of acceleration of free falling of the container in the described experiment is equal to210|. Taking into account that the mass of a rotor (500gram) amounts to1/3mass of the whole container, the relative change g/g'reduced to the rotor mass is equal to2310| . It is possible to assume that if in a capacity of such "rotors" to use the nuclei of atoms with spatially oriented spins(the set of such atoms forms a macro-dimensions test body) then at high concentration of oriented nuclei in a test body the spatial dependence of acceleration of free falling of a body on orientation of rotors will be much higher than the specified one.Further experimental researches into free falling of rotating (oscillating) in a vertical plane of either masses or samples of materials with oriented nuclear spins, with use of precision measuring instruments, for example, interferometric ones, seem rather expedient.CONCLUSIONSThe experimental results described above are obtained by simple technical means and are certainly of a preliminary character. At the same time, it is known that viable ideas in physics quite often prove themselves in technically simple experiments. Logical transition from statics to dynamics, realized in experimental gravitation, opens the prospect of establishment of new properties of gravitation which in the future can get the big scientific and practical values. It creates the prospects of effective solutions and propulsion-problems. The leading role in achievement of such targets belongs to experiment. The practical step to new physics of gravitation should be precision experimental researches into dynamic effects in gravitation. Among them it is necessary to note: x Measurement of temperature dependence of gravitation force;x Static and dynamic measurements of weights of test bodies rotating or oscillating in a vertical plane;x Measurement of anisotropy of crystals weights and measurements of anisotropy of inertial mass of bodies;x Measurement of acceleration of a free falling rotor at various orientations of axis of rotation, and also the samples with artificial orientation of nuclear moments (spins);x Measurements of spatial dependence of restitution coefficient at elastic impacts of solid bodies.Experiments with weighing of accelerated moving bodies will give useful information on complex, going beyond the scope of well-known theories properties of gravitation. Careful analysis of these results will allow to expand and complement the concepts based on the general theory of relativity, and probably to open the ways to new physics of gravitation and new principles of movement.NOMENCLATUREc A =coefficient of interaction of elastic and gravity forces by counter of a G and total vector of gravity force [-12m s ]p A = coefficient of interaction of elastic and gravity forces by passing of a G and total vector of gravity force [-12m s ]a G = acceleration vector of external force [-12m s ]c D =degree of interaction of elastic and gravity forces by counter of a G and 0g G (#)p D =degree of interaction of elastic and gravity forces by passing of a G and 0g G (#)C =factor of elasticity of the spiral [2-2kg m s ]g '=average difference of measured values of acceleration of free falling container [-2m s ]F =frequency [-1s ]g =acceleration of free falling container [-2m s ]g =average acceleration of free falling container [-2m s ]0g =normal acceleration of gravity [-2m s ]g c =resulting magnitude of projections of accelerations of gravity forces created by the remote masses in a solid angle 2S [-2m s ]J =the relative difference of the daily motion of an ideal watch (#)I =moment of inertia [2kg m ]J 6= full angular momentum [2-1kg m s ]A =distance [m ]g m =gravitational mass [kg ]i m =inertial mass [kg ] i m =average vertical inertial mass [kg ]i m =average horizontal inertial mass [kg ]N =number of marks (#)T =period of free oscillations [s ] T =period of oscillations of balance in a vertical plane [s ]T =period of oscillations of balance moving in a horizontal plane [s ]Ȧ=angular velocity [-1rad s ]12,''=lengths of the next sites of the trajectories [m ]'G c g ,'G p g = increments of acceleration of gravity [-2m s ]c G g ,c c G g =the resulting accelerations’ vectors, caused by action of the remote masses located in the left and the right half-spaces [-2m s ]REFERENCESBini, D., Cherubini, C., Chicone, C. and Mashhoon, B., “Gravitational I nduction,”/PS_cache/arxiv/pdf/0803/0803.0390v2.pdf,(2008).Chen, Y. T., and Cook, A., Gravitational Experiments in the Laboratory, Cambridge University Press, Cambridge, (1993).Dmitriev, A. L., “On the I nfluence of External Elastic (Electromagnetic) Forces on the Gravity,”Russian Physics Journal,44(12), (2001), pp.1323-1327.Dmitriev, A. L., and Snegov V. S., “Weighing of a Mechanical Gyroscope with Horizontal and Vertical Orientations of the SpinAxis,”Measurement Techniques ,44(8), (2001), pp.831-833.Dmitriev, A. L., “Inequality of the Coefficients of Restitution for Vertical and Horizontal Quasielastic Impacts of a Ball Against a Massive Plate,” International Applied Mechanics ,38(6), (2002), pp.747 –749.Dmitriev, A. L., Nikushchenko, E. M., and Snegov, V. S., “Influence of the Temperature of a Body on its Weight,” Measurement Techniques ,46(2), (2003), pp.115 –120.Dmitriev,A. L. and Chesnokov,N. N., “The effect of the orientation of an anisotropic crystal on its weight,”Measurement Techniques , 47(9),(2004), pp.899-901.Dmitriev, A. L., “Measurements of the Influence of Acceleration and Temperature of Bodies on their Weight,” in proceedings of Space Technology and Application International Forum (STAIF-2008), edited by M. El-Genk, AIP Conference Proceedings 969,New York, (2008a),pp. 1163-1169.Dmitriev, A. L., “On the Nature of Inertial Mass,”/ftp/arxiv/papers/0806/0806.0796.pdf,(2008b).。

科技英语翻译___课后答案

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工业用机器人与数控机床有许多共同的特性。

第1节翻译练习2With non-changeover control both the boiler plant and the chiller plant operate to provide simultaneous heating and cooling throughout the year.The online service delivers substantially more value to our global audience of e-business professionals in the chemical, plastics and allied industries.This device can mimic photosynthesis to produce usable energy from sunlight.采用非转换控制，锅炉设备和制冷装置都在运行，全年可同时供暖和制冷。

该网络服务主要向全球从事化学、塑料及相关工业的专业电子商务用户提供更有价值的服务。

这种装置能够模拟光合作用，利用阳光产生可用的能源。

第1节翻译练习3The longitudinal axis of the turbine generator is perpendicular to the axis of the steam generator. In the right conditions, membranes are self-assembling.Winding of the spring induces residual stresses through bending.汽轮发电机的纵轴与锅炉轴线垂直。

a little history of science 蓝思值

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深空探测中的轨道设计和轨道力学

深空探测中的轨道设计和轨道力学一、本文概述Overview of this article《深空探测中的轨道设计和轨道力学》这篇文章旨在深入探讨深空探测任务中轨道设计和轨道力学的关键要素和实际应用。

随着人类探索宇宙的步伐不断加快，深空探测已成为空间科学领域的重要研究方向。

轨道设计和轨道力学作为深空探测任务的核心技术，对于实现高效、精确的探测任务具有至关重要的作用。

The article "Orbital Design and Orbital Mechanics in Deep Space Exploration" aims to delve into the key elements and practical applications of orbital design and mechanics in deep space exploration missions. With the accelerating pace of human exploration of the universe, deep space exploration has become an important research direction in the field of space science. Orbital design and mechanics, as the core technologies of deep space exploration missions, play a crucial role in achieving efficient and accurate exploration tasks.本文首先将对深空探测任务进行简要介绍，阐述轨道设计和轨道力学在深空探测中的重要性和应用背景。

随后，文章将重点讨论轨道设计的基本原理和方法，包括轨道选择、轨道优化、轨道转移等方面的内容。

归纳、演绎、类比等逻辑思维方法

归纳、演绎、类比等逻辑思维方法Inductive, deductive, and analogical reasoning are three important methods of logical thinking. These methods play a crucial role in various fields such as science, mathematics, philosophy, and everyday problem-solving. Each method has its unique characteristics and applications, contributing to the development of human knowledge and understanding. In this essay, we will explore these three methods from multiple perspectives, highlighting their definitions, processes, and real-world examples.Inductive reasoning is a form of logical thinking that involves drawing general conclusions based on specific observations or patterns. It starts with specific instances and then generalizes them into broader principles or theories. This method is often used in scientific research, where scientists collect data, analyze patterns, and make generalizations about the natural world. For example, after observing several instances of objects falling to the ground when released, Isaac Newton formulated the law ofuniversal gravitation, which states that every object in the universe attracts every other object with a force proportional to their masses and inversely proportional to the square of the distance between them.On the other hand, deductive reasoning is a logical thinking process that starts with general principles or theories and applies them to specific situations to draw specific conclusions. It involves reasoning from the general to the particular. Deductive reasoning is commonly used in mathematics and formal logic, where a set of axioms or premises are used to derive new statements or theorems. For instance, in geometry, the Pythagorean theorem is deduced from the axioms of Euclidean geometry. The theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.Analogical reasoning is a method of logical thinking that involves drawing conclusions by finding similarities between different situations or objects. It relies on the assumption that if two or more things are similar in somerespects, they are likely to be similar in other respects as well. Analogical reasoning is often used in problem-solving, decision-making, and creative thinking. For example, when faced with a new problem, one might try to find similarities with previously encountered problems and apply similar solutions. This method is also used in legal reasoning, where judges may consider previous cases as precedents to guide their decisions in similar cases.In addition to their definitions and applications, it is important to understand the processes involved in these methods of logical thinking. Inductive reasoning typically involves several steps, including observation, pattern recognition, hypothesis formation, and conclusion drawing. It requires careful data collection, analysis, and evaluation to ensure the validity of the generalization. Deductive reasoning, on the other hand, follows a more structured process. It starts with a set of premises or axioms, applies logical rules or principles, and derives specific conclusions. This process is often represented in the form of syllogisms or logical arguments. Analogical reasoning involves identifying similarities betweendifferent situations or objects, extracting relevant information, and applying it to the current problem or situation.To illustrate the practical relevance of these logical thinking methods, let's consider some real-world examples. In the field of medicine, doctors often use inductive reasoning to diagnose patients. They collect specific symptoms and observations, analyze patterns, and make generalizations about the underlying medical conditions. Deductive reasoning is employed in computer programming, where programmers use predefined rules or algorithms to solve specific problems. They start with general programming principles and apply them to write code for specific tasks. Analogical reasoning is commonly used in marketing and advertising. Marketers often draw on successful campaigns from the past and apply similar strategies to promote new products or services.In conclusion, inductive, deductive, and analogical reasoning are three important methods of logical thinking that have diverse applications in various fields. Inductivereasoning involves generalizing from specific observations, deductive reasoning applies general principles to specific situations, and analogical reasoning draws conclusions by finding similarities between different situations. Understanding the processes and examples of these methods can enhance problem-solving, decision-making, and creative thinking abilities. These methods are essential tools for advancing human knowledge and understanding the complexities of the world we live in.。

天文学的英语作文

天文学的英语作文The Fascinating World of Astronomy。

Astronomy, the study of celestial objects and phenomena, has captured the imagination of humans for centuries. From the ancient civilizations who used the stars for navigation to the modern scientists who explore the depths of the universe, astronomy has always been a source of wonder and fascination. In this essay, we will explore the history of astronomy, its importance in our lives, and the exciting discoveries that have been made in recent years.The history of astronomy dates back to ancient times, with civilizations such as the Babylonians, Egyptians, and Greeks making significant contributions to the field. These early astronomers observed the movements of the stars and planets, developed calendars based on celestial events, and even made rudimentary measurements of the Earth's size.Their observations and calculations laid the groundwork for the development of modern astronomy.One of the most important figures in the history of astronomy is Nicolaus Copernicus, whose heliocentric model of the solar system revolutionized our understanding of the universe. Prior to Copernicus, it was widely believed that the Earth was the center of the universe, with the sun and other planets revolving around it. Copernicus's model, which placed the sun at the center of the solar system, was a groundbreaking concept that laid the foundation for the modern understanding of planetary motion.The invention of the telescope in the early 17th century further revolutionized astronomy, allowing scientists to observe celestial objects in greater detail. Galileo Galilei, using a telescope of his own design, made several groundbreaking discoveries, including the moons of Jupiter and the phases of Venus. His observations provided compelling evidence for the heliocentric model and helped to cement the telescope as an essential tool for astronomers.In the centuries that followed, astronomers continuedto make important discoveries about the nature of the universe. Sir Isaac Newton's laws of motion and universal gravitation provided a theoretical framework for understanding the motions of celestial bodies, while the development of spectroscopy allowed scientists to analyze the composition of stars and galaxies. The 20th century saw the development of powerful telescopes and the launch of space probes, which allowed astronomers to study the universe in unprecedented detail.Today, astronomy continues to be a vibrant and exciting field of study. Modern astronomers use a variety of tools and techniques to explore the universe, from ground-based telescopes and space-based observatories to computer simulations and data analysis. Recent discoveries, such as the detection of exoplanets orbiting other stars and the observation of gravitational waves from colliding black holes, have expanded our understanding of the cosmos and raised new questions about the nature of the universe.In addition to its scientific importance, astronomy also holds a special place in our culture and society. Thebeauty and majesty of the night sky have inspired artists, poets, and musicians for centuries, while the practical applications of astronomy, such as GPS technology and weather forecasting, have become essential parts of our daily lives. Furthermore, the search for extraterrestrial life and the exploration of other planets have captured the public's imagination and sparked widespread interest in space exploration.In conclusion, astronomy is a fascinating and important field of study that has deep roots in human history and continues to make significant contributions to our understanding of the universe. From the ancientcivilizations who gazed at the stars in wonder to the modern scientists who probe the depths of space, astronomy has always been a source of inspiration and discovery. As we continue to explore the cosmos, we can look forward to new and exciting revelations about the nature of the universe and our place within it.。

The gravitational field energy density for symmetrical and asymmetrical systems

The gravitational field energy density for symmetrical and asymmetrical systemsRoald SosnovskiyTechnical University, 194021, St. Petersburg, RussiaE-mail:rosov2@yandexAbstract. The relativistic theory of gravitation has the considerable difficulties by description of the gravitational field energy. Pseudotensor t 00 in the some cases cannot be interpreted as energy density of the gravitational field. In [1] the approach was proposed, which allow to express the energy density of such a field through the components of a metric tensor. This approach based on the consideration of the isothermal compression of the layer consisted of the incoherent matter. It was employ to the cylindrically and spherically symmetrical static gravitational field. In presented paper the approach is developed.1. Introduction. The problem of the gravitational field energy discussed a long time [2], [3]. However, pseudotensor differs from author to author reflecting the ambiguity in defining gravitational field energy density [3]. In [1] the approach has proposed allows one to express the energy density of such a field through the components of a metric tensor. This approach based on the consideration of the isothermal compression of a layer consisted of the incoherent matter in the field of the infinitesimal thin material shell by fulfillment of the requirements [4]: (a) the local energy conservation law should be fulfilled and (b) the correspondence principle should be fulfilled including the energy part.µνt In the presented paper proved, that this approach can be used for asymmetrical systems. Here proved, that the requirement of the invariance of the gravitational field energy density [4] fulfilled. For the cylindrically and spherically symmetrical systems is obtained field energy density formulas, contained only the metric tensor component and his derivative.2. The differential of the gravitational field energyIn [1] has obtained the formulas of the gravitational field energy for the special coordinates, connected with type of symmetry. Here it considered the formula of the field energy for the arbitrary static coordinates systems. The solution is analogous to one in[1].2.1. The isothermal compression. Here it considered the movement of the particles layers when acquired energy of particles has eradiated or dissipated. The movement considered as consisted of discrete infinitesimal steps, when the particles fall free, and in end of step energy of particles has dissipated. Concrete ways of dissipation no discussed. Sufficiently to suppose that such way can be on principle approximately realized. For example, free fall of particles in thin lay on the solid surface with following cooling of the solid.The particles considered as test-particles. However, the change of field, caused with accumulation of the matter on solid surface, calculated after every step. Assume αx is the initial coordinate system, admissible for the system configuration, with metric .0,0=µµνg g Let us consider the displacement of the particles layer from position 111x x = to position 1111x d x x +=. The free particles fall equations are[5] 0=∂∂−⎟⎠⎞⎜⎝⎛∂∂µµτxL x L d d & (1) where τ is the intrinsic time, ·τµµd x d x =& and()νµµνσσx x g x x L &&&21,=, ()321,,x x x g g µνµν= (2) For static system (1),(2) lead to 0000g C x =& (3) where C 0 is constant on all step. From (3) and from equationk i ik x x g xg c &&&+=02002 (4) we get, so far as i x&is small, 000g c C = (5) From formulas (1), (2) for i, k =1,2,3 result02,0021x g xg i k ik &&&= (6) and from (5),(6)002,0021g c g g x i ik kδτ=& (7) where τ is the intrinsic time of particles movement. Components k u of the maximum velocity of free particles fall near by point ),,(321x x x x r may written00,00g g g u iik k β= (8)where ß is infinitesimal coefficient.2.2. The static gravitational field energy. General formulas. The energy of the particles by free fall can obtained from the relation [6]0002g g u mc E ννδ=, τννcd x d u = (9) where δm is rest mass of the particles group. From (3) and so far as 0000g g ννδ= the change of particles energy on way i x d isi i x d g g mc dE ,000022δ−= (10) This energy has dissipated on way i x d . If the local energy conservation law fulfilled then the energy change of particles must result from change of field energy dE f on way i x d . Thereforei i f x d g mc dE ,000022δ= (11)From (8) follow, that the components of the of the particle coordinates mean change is00,00g g g x d kik i λ= (12)and scalar displacement is equalk i ik g g g g dl ,00,0000λ= (13) wherek i ik g g g dlg ,00,0000=λ (14)If substitute λ in (12) and then i x d in (11) then we get dl g g g g mc E d k i ik f ,00,000022δδ−= (15)Here δm and δl are scalars, 00g by 00=i g no depend on the space coordinates transformation. The quantity k i ik g g g ,00,00 is invariant by the space coordinates transformation k i k i x A x = (16)Therefore, d δE f is also invariant.3. Energy of the asymmetrical gravitational field.3.1. The object. Considered the static field of the asymmetric convex smooth infinitesimally thin material shell with surface mass density σc .The quantity σc is a single-valued function of the coordinates of shell point ()3211,x x x x c c =, ()32,x x c c σσ=. It considered the space between a shell and some convex smooth external surface ()3211,x x x x e e = with surface mass density ()32,x x e e σσ=. Assumed, that it known how the metric ik g of the space region between c x and e x to find. This is possible at least by miens of the computer methods [7].3.2. The calculations order. Is considered the motion of N j discrete test particles layers from the external surface to the shell. The motion is discrete; the number of steps is N q . For every layer position, the calculations made for N k · N n points. The every point position determined in coordinate system i x . For every point P(k,n,q) the volume element is built at the vectors ),,(321ii i i i x d x d x d z d z d r r =, i =1,2,3. Let this vectors create the coordinate system ()0000,,,,g g x d j q n k B dz k i k i == (17)One side (dz 2,dz 3) of this element is disposed at the layer position q and the opposite side at the layer position q+1. The vector l d r describe the fall of particle from point P(k,n,q) up to point F(k',n',q+1) at the layer position q+1. For every point P(k,n,q) and every layer j are calculated from (15) the field energy differential d δE f and masse density σ(k',n',q+1,j) for point P(k',n',q+1). Afterwards the layer j arrive the position q = N q metric components g ik calculated for all points P(k,n,q) . The method of such calculation no considered because that does not matter for the purpose of this paper.3.3. The gravitational field integral energy and energy density invariance. Let the volume element is built at the vectors dz i .The mass of the particles group, passed through this element, is equal()()()j q n k dS j q n k j q n k m ,,,,,,,,,⋅=δσδ (18)where δσ(k,n,q,j) is the matter density in the particles layer j and dS(k,n,q,j) – the area of the element (dz 2,dz 3). The mass δm of this element, which is considered as in the one point concentrated, fall from point P(k,n,q) in point F(k,n,q+1) with coordinates z i + dl i . Components dl i can be calculated in coordinates dz i from (12), (17). Component dl 1 = dz 1 andq q pkp k g g g g dl dl ,001,001=,k=2,3 (19)By means interpolation can be calculate the mass δm(n,q+1,j) and mass density δσ(n,q+1,j) for points P(k,n,q+1). Consider the successive pass of the layers through the element of area ()32,dz dz with point P(k,n,q). From (15),(17) after step j = N j the field energy change in volume element is equal ()j q n k s i isN j f g g g g dl dS c q n k dE j ,,,,00,0000222,,⎥⎦⎤⎢⎣⎡⋅⋅=∑δσ (20) where [] depend on (k,n,q,j). The quantities under the symbol Σ are the invariants, therefore dE f (k,n,q) is invariant. The sum of energy in all points of the field is also invariant.The energy density in point P(n,q) is given by()()),(,,,q n dV q n dE q n k w f =, 321dz dz dz g dV я= (21)where dV(n,q) is the volume of the volume element, built at the vectors ()321,,z d z d z d r r r for step j=N j ; z g is determinant of the metric components. The quantity dV is scalar, therefore w(n,q) is invariant.Thus, the approach based on the consideration of the isothermal compression of the layer consisted of the incoherent matter, can be used for asymmetrical systems.4. The transformation of the formulas for field energy density of the symmetrical systems.The formulas for these quantities in the paper [1] maintain, besides the metric tensor components, the field source mass M and the distance to symmetry centre R. As the metric tensor components are the functions of M and R, it is possible to except M and R from these formulas.4.1. The cylindrical symmetry. In [1] there are the formulas000a R R g ⎟⎟⎠⎞⎜⎜⎝⎛=, 204c GM a z = (22) where R – radius, R 0 – radius of the field source, M z – the linear mass density. From (23) followRc GM g g z 2001,004= (23) and energy density 002001,0040022322g g g G c g R GM w z ⎟⎟⎠⎞⎜⎜⎝⎛−=−=ππ (24)4.2. The spherical symmetry. From [1] in this caseRc GM g 20021−=; dx 1=dR; dx 2=Rd θ; dx 3=RSin θd φ (25) and energy density⎥⎦⎤⎢⎣⎡+⎟⎠⎞⎜⎝⎛−=R c GM R c GM GR g сw 2222221ln 1600π (26)or from (25) []G g c g g g GR g g сw ππ321ln 11621,004000020020021,004−≅−+−= (27)4.References1.R.Sosnovskiy.gr-qc 05070162.K.S.Virbhadra.A comment on the energy-momentum pseudotensor of Landau and Lifshitz. Phys. Lett.A 157(1991)1953.J.Katz. gr-qc 05100924. N.V.Mitzkevitsch. Physical fields in general relativity. Nauka, Moskow, 19695.J.L.Martin. General Relativity . N.Y.,19886.A.Logunov. Lectures in relativity and gravitation. A modern Look. Nauka, Moskow,19907. L.Lehner. gr-qc 0106072。

Geometric Modeling

Geometric ModelingGeometric modeling is a crucial aspect of computer graphics, engineering, and design. It involves creating digital representations of objects and environments using mathematical and computational techniques. Geometric modeling plays a significant role in various industries, including architecture, automotive design, video game development, and virtual reality. The process of geometric modeling allows designers and engineers to visualize and analyze complex structures, simulate real-world scenarios, and create realistic visualizations of their ideas. One of the key challenges in geometric modeling is achieving a balance between accuracy and efficiency. Designers and engineers often need to create highly detailed models with complex geometries, which can be computationally expensiveand time-consuming. At the same time, they also need to ensure that the models can be manipulated and rendered in real-time for interactive applications. This trade-off between accuracy and efficiency requires careful consideration of the modeling techniques and algorithms used to represent and manipulate geometric data.Another important consideration in geometric modeling is the representation of curved surfaces and freeform shapes. While simple geometric primitives such as cubes, spheres, and cylinders can be easily defined using mathematical equations, representing more complex shapes like human bodies, organic forms, and natural landscapes requires more advanced techniques. B-spline and NURBS (Non-Uniform Rational B-Splines) are commonly used to represent and manipulate curved surfacesin geometric modeling, allowing for smooth and flexible deformation of shapes. Geometric modeling also involves the creation of 3D models from 2D sketches or images. This process, known as 3D reconstruction, requires the use of computer vision and image processing techniques to extract depth and spatial information from 2D data. 3D reconstruction has applications in fields such as medical imaging, remote sensing, and augmented reality, where 3D models are generated from 2D images to facilitate analysis and visualization. In addition to creating static3D models, geometric modeling also encompasses the simulation and animation of dynamic objects and environments. Physics-based modeling techniques are used to simulate the behavior of physical systems, such as the motion of rigid bodies, the deformation of elastic materials, and the interaction of fluids and gases. Thesesimulations are essential for applications like virtual prototyping, computer-aided engineering, and special effects in movies and video games. Moreover, geometric modeling is closely related to the field of computational geometry, which focuses on the development of algorithms and data structures for solving geometric problems. Computational geometry has applications in areas such as computer-aided design, robotics, geographic information systems, and computer graphics. It addresses fundamental problems like geometric intersection, proximity queries, convex hull computation, and mesh generation, which are essential for many geometric modeling tasks. In conclusion, geometric modeling is a multifaceted discipline that encompasses a wide range of techniques and applications. It plays a critical role in various industries and research fields, enabling the creation, analysis, and visualization of complex geometric data. The challenges in geometric modeling, such as balancing accuracy and efficiency, representing curved surfaces, reconstructing 3D models from 2D data, simulating dynamic systems, and solving fundamental geometric problems, require innovative solutions and advancements in computational and mathematical techniques. As technology continues to evolve, geometric modeling will continue to be anessential tool for shaping the virtual and physical world around us.。

生物医学工程专业英语词汇

百度文库- 让每个人平等地提升自我1. electronic 电的（与电有关的）2. engineering 工程，工程学3. circuit 电路4. common-base 共基极5. common-emitter 共发射极6. common-collector 共集电极7. transistor 晶体管，三极管8. impedance阻抗9. ohm 欧姆10. megohm 兆欧11. voltage 电压12. rectifier 整流器13. diode 二极管14. current 电流15. cycle 周期16. pulsate 博动，波动17. amplitude幅度18. frequency 频率19. in series 串联20. in parallel 并联21. pulse 波，脉冲22. positive正的23. negative 负的24. baseline 基线25. waveform 波形26. rectangular 矩形的，直角的27. sawtooth 锯齿28. capacitance 电容值，容抗29. electric 电的（靠电工作的）30. condenser 电容器，电容31. capacitor 电容器32. metallic 金属的33. dielectric 电介质34. terminal 电极，终端，套管35. accumulate 蓄电，储电，积累36. electron 电子37. potential 电势38. charge 充电，电荷39. discharge 放电40. farad 法拉41. volt 伏特42. ampere安培43. microfarad 微法44. gravitation 重力，引力，万有引力45. mass 质量46. matter 物质47. resistance 电阻48. cathode 负极49. anode 正极50. short circuit 短路51. open circuit 断路52. germanium 锗53. crystal 晶体⏹LED ( Light Emitting Diode ) 发光二极管⏹probe 探针⏹mains 电源，干线⏹buffer 缓冲器⏹ultrasound 超声⏹ultrasonography 超声波检查法⏹tissue 组织⏹bone 骨⏹organ 器官⏹dimensional 维的⏹transducer 传感器keyboard 键盘⏹cursor 光标⏹piezoelectric 压电的⏹quartz 石英⏹acoustic lens 声学透镜⏹microprocessor 微处理器⏹memory 存储器⏹power supplies 电源⏹amplifier 放大器⏹archive 存档⏹fetus 胎，胎儿⏹cancerous 癌的，恶性肿瘤的⏹benign tumors 良性肿瘤⏹prostate 前列腺⏹gland腺⏹colon 结肠⏹rectum 直肠⏹breast 胸⏹breast lesions 乳腺病变⏹biopsies 活组织检查⏹limb 肢⏹blood 血⏹artery 动脉⏹radiation（辐射，放射）.radiographic （放射照相的）⏹Obstetrics （产科学）and gynecology （妇科学）breech（臀部）⏹Checking the position o the placenta（胎盘）⏹uterus（子宫）⏹Seeing tumors of the ovary （卵巢）and breast⏹Cardiology 心脏病学blood vessels （血管）⏹Urology （泌尿学）⏹Measuring blood flow through the kidney （肾）pregnancy(怀孕).⏹multifunctional⏹多功能的⏹portable⏹便于携带的，可移动的⏹electrocardiogram (ECG)⏹心电图⏹monitor⏹监护仪Study and Design of a Multifunctional Portable Electrocardiogram (ECG) Monitor Based on SPCE061A基于SPCE061A多功能便携式心电监护仪的研究与设计⏹wireless 无线的fetal 胎儿的Design of a Wireless Fetal Electrocar-diogram Monitoring System Based on S3C2410 基于S3C2410的无线胎儿心电监护仪的设计⏹microcontroller 单片机⏹instrument 仪器The Development of Embedded ECG Monitor Instrument Using C8051F040 Microcontroller基于C8051F040单片机的便携式心电监护仪的低功耗设计R & D (Research and Development ) 研究与开发，简称研发On R & D of an ECG Bedside Monitor心电床边监护仪的研制cardiac 心脏(病)的Performance Test for Cardiac Monitor心电监护仪的性能测试⏹liquid crystal display (LCD) 液晶显示器Development of a Portable ECG Monitor with Liquid Crystal Display便携式液晶显示心电监护仪的研制⏹maintenance 维护，维修⏹equipment 设备The Research of Remote Intelligent Monitoring, Diagnosis and Maintenance System for Complicated Equipment 复杂装备远程智能监测、诊断与维护系统研究⏹oxygen saturation 血氧饱和度⏹non-invasively 无创地This paper describes the measuring principle and instrument structure characteristic of the Multi-parameter Patient Monitor which is able to ECG, heart rate, blood pressure, breath rate, body temperature and oxygen saturation non-invasively.介绍了能测量心电图、心率、脉搏、无创血氧、无创血压、体温、呼吸等多参数监护仪的测量原理和仪表结构特点resolution 分辨率acquisition 采集conversion card 转换卡The resolution of the system has reached % and the real-time display has been realized by the data acquisition and processing with A/D/A conversion card controlled by the software.用软件控制A/D/A转换卡进行数据采集与处理,系统分辨率达%,实现了实时显示。

电子信息工程专业英语翻译清华出版社English for IT and EE-03

已经证明电磁场的量子描述是非常成功的，引出了量子电动力学，一种描述电磁辐射与带电物体之间的相互作用的量子场理论。
11
8 Dynamics of the electromagnetic field
In the past, electrically charged objects were thought to produce two types of field associated with their charge property. An electric field is produced when the charge is stationary with respect to an observer measuring the properties of the charge and a magnetic field (as well as an electric field) is produced when the charge moves (creating an electric current) with respect to this observer.
例如，振荡电荷产生电场和磁场，可看成平滑的、连续的波动方式。
7
5
In this case, energy is viewed as being transferred
continuously through the electromagnetic field between any
two locations. For instance, the metal atoms in a radio
电磁场在空间无限延伸，并描述电磁相互作用。
4
2
The field can be viewed as the combination of an electric field

想要了解的事物英语作文

想要了解的事物英语作文Things I Yearn to Understand The world is an intricate tapestry woven with threads of knowledge, both known and unknown. While I find myself fascinated by the vast amount of information we’ve accumulated as a species, I am acutely aware of the vast, uncharted territories of understanding that lie before me. There are several key areas that spark a deep curiosity within me, areas I yearn to explore and grasp with greater clarity. Firstly, I am captivated by the complex workings of the human mind. The brain, a three-pound universe contained within our skulls, is a marvel of intricate networks and electrochemical signals that give rise to consciousness, emotion, and behavior. How do neurons fire in symphony to create our perceptions of the world? What are the mechanisms behind memory formation and retrieval? How does our unique blend of genetics and environment shape our personalities and predispositions? Unraveling the mysteries of the mind holds the key to understanding the very essence of what makes us human. The vast universe, with its swirling galaxies, enigmatic black holes, and the tantalizing possibility of life beyond Earth, also ignites my imagination. I long to understand the fundamental laws that govern the cosmos, from the delicate dance of subatomic particles to the majestic movements of celestial bodies. What is the true natureof dark matter and dark energy, the unseen forces shaping the universe's evolution? Are we alone in this vast cosmic expanse, or does life, in all its wondrous forms, exist elsewhere? The pursuit of answers to these questions is a quest to understand our place in the grand scheme of existence. Closer to home, the interconnected web of life on our planet fascinates me. The intricate ecosystems teeming with biodiversity, the delicate balance of predator and prey, theintricate cycles of energy and nutrients - these are all testament to the awe-inspiring power of evolution and adaptation. I yearn to understand the complex interactions within these ecosystems, the delicate balance that sustains them, and the impact of human activities on this delicate web. Understanding these complexities is crucial for our responsible stewardship of the planet and the preservation of its irreplaceable biodiversity. Furthermore, I am drawn to the intricacies of human history and its impact on our present reality. From the rise and fall of civilizations to the struggles for freedom and equality, historyoffers a lens through which we can examine the triumphs and failures of humankind.I crave a deeper understanding of the forces that have shaped our social,political, and economic systems, the ideologies that have fueled conflicts and cooperation, and the enduring legacies of past events. By studying history, wecan learn from our ancestors' mistakes and successes, equipping ourselves to navigate the challenges of the present and build a better future. The ever-evolving world of technology, with its rapid advancements in artificial intelligence, biotechnology, and space exploration, also holds a powerful allure.I am driven to understand the principles behind these innovations, their potential to address global challenges, and the ethical implications that accompany them. How can we harness the power of artificial intelligence for the betterment of society while mitigating potential risks? What are the ethical considerations surrounding genetic engineering and its impact on future generations? How can space exploration contribute to scientific advancements and inspire future generations? Exploring these frontiers of technology is essential for shaping a future where innovation serves humanity and the planet. Finally, I yearn to understand the very essence of creativity and its power to inspire, challenge, and transform. From the evocative brushstrokes of a painter to the soaring melodiesof a composer, creativity speaks a universal language that transcends cultural boundaries. What are the cognitive processes that underpin artistic expression? How does creativity foster innovation and problem-solving across disciplines? How can we nurture and cultivate our own creative potential to contribute to the world in meaningful ways? Understanding the nature of creativity is key to unlockingour own potential and enriching the human experience. In conclusion, the pursuit of knowledge is a lifelong journey, an insatiable thirst for understanding that fuels my curiosity and motivates my exploration. From the inner workings of the human mind to the vast expanses of the cosmos, from the intricate web of life on Earth to the enduring legacies of human history, from the frontiers of technology to the power of creative expression - these are the areas I yearn to understand with greater depth and clarity. This quest for knowledge is not merely an academic pursuit but a fundamental aspect of what makes us human - the desire to learn, grow, and contribute to the betterment of ourselves and the world around us.。

爱因斯坦英语名言

爱因斯坦英语名言一个从不犯错误的人，一定从来没有尝试过任何新鲜事物。

2. Intellectuals solve problems; geniuses prevent them.智者解决问题，天才预防问题。

3. Science is a wonderful thing if one does not have to earn one’s living at it.科学是个美妙的东西——如果无须靠它维生的话。

4. The hardest thing in the world to understand is the income tax.世界上最让人难以理解的东西就是个人所得税。

5. I am convinced that He (God) does not play dice.我确信上帝不玩赌博游戏。

6. Reality is merely an illusion, albeit a very persistent one.现实不过是幻象，尽管这幻象挥之不去。

7. I never think of the future. It comes soon enough.我从不去想未来。

因为它来得已经够快的了。

8. The only thing that interferes with my learning is my education. 妨碍我学习的唯一障碍就是我的教育。

9. Two things are infinite: the universe and humanstupidity; and I’m not sure abo ut the universe.宇宙中唯有两件事物是无限的：宇宙的大小与人的愚蠢。

我不能确定的是宇宙的大小。

10. I know not with what weapons World War III will be fought, but World War IV will be fought with sticks and stones.我不知道第三次世界大战会用哪些武器，但第四次世界大战中人们肯定用的是木棍和石块。

卫星轨道外推：第一部分(英文批注)

Orbital Propagation: Part I轨道外推：第一部分By Dr. T.S. KelsoWelcome to the Computers and Satellites column of Satellite Times. We are about to embark on an adventure of discovery—an adventure I have been looking forward to for quite some time. I only hope you will enjoy the experience as much as I and want to follow along with each new episode.欢迎来到《卫星时刻》计算机与卫星专栏，我们即将踏上我期待已久的探索之旅。

我谨希望你能和我一同享受这份经历并追随每一段新的旅程。

Along the way, I hope to enlighten you, the reader—whether novice or expert—on the subtleties involved in the theory and practical application of computers to the process of tracking satellites in earth orbit. Whether you simply want to be able to know where to point your TVRO antenna to pick up your favorite television shows, are curious as to where to look to see the Mir space station on a twilight pass, or want to know when you will be able to DX with the space shuttle on the next SAREX mission, we'll cover it all.一路上，我希望无论新手还是专家的每一位读者在卫星地球轨道计算的详细理论和实际应用方面能有所启迪。

中科院博士研究生英语精读教材翻译及原文整理解读

第1课知识的悖论The Paradox of KnowledgeThe greatest achievement of humankind in its long evolution from ancient hominoid ancestors to its present status is the acquisition and accumulation of a vast body of knowledge about itself, the world, and the universe. The products of this knowledge are all those things that, in the aggregate, we call "civilization," including language, science, literature, art, all the physical mechanisms, instruments, and structures we use, and the physical infrastructures on which society relies. Most of us assume that in modern society knowledge of all kinds is continually increasing and the aggregation of new information into the corpus of our social or collective knowledge is steadily reducing the area of ignorance about ourselves, the world, and the universe. But continuing reminders of the numerous areas of our present ignorance invite a critical analysis of this assumption.In the popular view, intellectual evolution is similar to, although much more rapid than, somatic evolution. Biological evolution is often described by the statement that "ontogeny recapitulates phylogeny"--meaning that the individual embryo, in its development from a fertilized ovum into a human baby, passes through successive stages in which it resembles ancestral forms of the human species. The popular view is that humankind has progressed from a state of innocent ignorance, comparable to that of an infant, and gradually has acquired more and more knowledge, much as a child learns in passing through the several grades of the educational system. Implicit in this view is an assumption that phylogeny resembles ontogeny, so that there will ultimately be a stage in which the accumulation of knowledge is essentially complete, at least in specific fields, as if society had graduated with all the advanced degrees that signify mastery of important subjects.Such views have, in fact, been expressed by some eminent scientists. In 1894 the great American physicist Albert Michelson said in a talk at the University of Chicago:While it is never safe to affirm that the future of Physical Science has no marvels in store even more astonishing than those of the past, it seems probable that most of the grand underlying principles have been firmly established and that further advances are to be sought chiefly in the rigorous application of these principles to all the phenomena which come under our notice .... The future truths of Physical Science ate to be looked for in the sixth place of decimals.In the century since Michelson's talk, scientists have discovered much more than the refinement of measurements in the sixth decimal place, and none is willing to make a similar statement today. However, many still cling to the notion that such a state of knowledge remains a possibility to be attained sooner or later. Stephen Hawking, thegreat English scientist, in his immensely popular book A Brief History of Time (1988), concludes with the speculation that we may "discover a complete theory" that "would be the ultimate triumph of human reason--for then we would know the mind of God." Paul Davies, an Australian physicist, echoes that view by suggesting that the human mind may be able to grasp some of the secrets encompassed by the title of his book The Mind of God (1992). Other contemporary scientists write of "theories of everything," meaning theories that explain all observable physical phenomena, and Nobel Laureate Steven Weinberg, one of the founders of the current standard model of physical theory, writes of his Dreams of a Final Theory (1992).Despite the eminence and obvious yearning of these and many other contemporary scientists, there is nothing in the history of science to suggest that any addition of data or theories to the body of scientific knowledge will ever provide answers to all questions in any field. On the contrary, the history of science indicates that increasing knowledge brings awareness of new areas of ignorance and of new questions to be answered.Astronomy is the most ancient of the sciences, and its development is a model of other fields of knowledge. People have been observing the stars and other celestial bodies since the dawn of recorded history. As early as 3000 B.C. the Babylonians recognized a number of the constellations. In the sixth century B.C., Pythagoras proposed the notion of a spherical Earth and of a universe with objects in it chat moved in accordance with natural laws. Later Greek philosophers taught that the sky was a hollow globe surrounding the Earth, that it was supported on an axis running through the Earth, and chat stars were inlaid on its inner surface, which rotated westward daily. In the second century A.D., Ptolemy propounded a theory of a geocentric (Earth-centered) universe in which the sun, planets, and stars moved in circular orbits of cycles and epicycles around the Earth, although the Earth was not at the precise center of these orbits. While somewhat awkward, the Ptolemaic system could produce reasonably reliable predictions of planetary positions, which were, however, good for only a few years and which developed substantial discrepancies from actual observations over a long period of time. Nevertheless, since there was no evidence then apparent to astronomers that the Earth itself moves, the Ptolemaic system remained unchallenged for more than 13 centuries.In the sixteenth century Nocolaus Copernicus, who is said to have mastered all the knowledge of his day in mathematics, astronomy, medicine, and theology, became dissatisfied with the Ptolemaic system. He found that a heliocentric system was both mathematically possible and aesthetically more pleasing, and wrote a full exposition of his hypothesis, which was not published until 1543, shortly after his death. Early inthe seventeenth century, Johannes Kepler became imperial mathematician of the Holy Roman Empire upon the death of Tycho Brahe, and he acquired a collection of meticulous naked-eye observations of the positions of celestial bodies chat had been made by Brahe. On the basis of these data, Kepler calculated that both Ptolemy and Copernicus were in error in assuming chat planets traveled in circular orbits, and in 1609 he published a book demonstrating mathematically chat the planets travel around the sun in elliptical orbits. Kepler's laws of planetary motion are still regarded as basically valid.In the first decade of the seventeenth century Galileo Galilei learned of the invention of the telescope and began to build such instruments, becoming the first person to use a telescope for astronomical observations, and thus discovering craters on the moon, phases of Venus, and the satellites of Jupiter. His observations convinced him of the validity of the Copernican system and resulted in the well-known conflict between Galileo and church authorities. In January 1642 Galileo died, and in December of chat year Isaac Newton was born. Modern science derives largely from the work of these two men.Newton's contributions to science are numerous. He laid the foundations for modem physical optics, formulated the basic laws of motion and the law of universal gravitation, and devised the infinitesimal calculus. Newton's laws of motion and gravitation are still used for calculations of such matters as trajectories of spacecraft and satellites and orbits of planets. In 1846, relying on such calculations as a guide to observation, astronomers discovered the planet Neptune.While calculations based on Newton's laws are accurate, they are dismayingly complex when three or more bodies are involved. In 1915, Einstein announced his theory of general relativity, which led to a set of differential equations for planetary orbits identical to those based on Newtonian calculations, except for those relating to the planet Mercury. The elliptical orbit of Mercury rotates through the years, but so slowly that the change of position is less than one minute of arc each century. The equations of general relativity precisely accounted for this precession; Newtonian equations did not.Einstein's equations also explained the red shift in the light from distant stars and the deflection of starlight as it passed near the sun. However, Einstein assumed chat the universe was static, and, in order to permit a meaningful solution to the equations of relativity, in 1917 he added another term, called a "cosmological constant," to the equations. Although the existence and significance of a cosmological constant is still being debated, Einstein later declared chat this was a major mistake, as Edwin Hubble established in the 1920s chat the universe is expanding and galaxies are receding fromone another at a speed proportionate to their distance.Another important development in astronomy grew out of Newton's experimentation in optics, beginning with his demonstration chat sunlight could be broken up by a prism into a spectrum of different colors, which led to the science of spectroscopy. In the twentieth century, spectroscopy was applied to astronomy to gun information about the chemical and physical condition of celestial bodies chat was not disclosed by visual observation. In the 1920s, precise photographic photometry was introduced to astronomy and quantitative spectrochemical analysis became common. Also during the 1920s, scientists like Heisenberg, de Broglie, Schrodinger, and Dirac developed quantum mechanics, a branch of physics dealing with subatomic particles of matter and quanta of energy. Astronomers began to recognize that the properties of celestial bodies, including planets, could be well understood only in terms of physics, and the field began to be referred to as "astrophysics."These developments created an explosive expansion in our knowledge of astronomy. During the first five thousand years or more of observing the heavens, observation was confined to the narrow band of visible light. In the last half of this century astronomical observations have been made across the spectrum of electromagnetic radiation, including radio waves, infrared, ultraviolet, X-rays, and gamma rays, and from satellites beyond the atmosphere. It is no exaggeration to say chat since the end of World War II more astronomical data have been gathered than during all of the thousands of years of preceding human history.However, despite all improvements in instrumentation, increasing sophistication of analysis and calculation augmented by the massive power of computers, and the huge aggregation of data, or knowledge, we still cannot predict future movements of planets and other elements of even the solar system with a high degree of certainty. Ivars Peterson, a highly trained science writer and an editor of Science News, writes in his book Newton's Clock (1993) that a surprisingly subtle chaos pervades the solar system. He states:In one way or another the problem of the solar system's stability has fascinated and tormented asrtonomers and mathematicians for more than 200 years. Somewhat to the embarrassment of contemporary experts, it remains one of the most perplexing, unsolved issues in celestial mechanics. Each step toward resolving this and related questions has only exposed additional uncertainties and even deeper mysteries.Similar problems pervade astronomy. The two major theories of cosmology, general relativity and quantum mechanics, cannot be stated in the same mathematical language, and thus are inconsistent with one another, as the Ptolemaic and Copernicantheories were in the sixteenth century, although both contemporary theories continue to be used, but for different calculations. Oxford mathematician Roger Penrose, in The Emperors New Mind (1989), contends that this inconsistency requires a change in quantum theory to provide a new theory he calls "correct quantum gravity."Furthermore, the observations astronomers make with new technologies disclose a total mass in the universe that is less than about 10 percent of the total mass that mathematical calculations require the universe to contain on the basis of its observed rate of expansion. If the universe contains no more mass than we have been able to observe directly, then according to all current theories it should have expanded in the past, and be expanding now, much more rapidly than the rate actually observed. It is therefore believed that 90 percent or more of the mass in the universe is some sort of "dark matter" that has not yet been observed and the nature of which is unknown. Current theories favor either WIMPs (weakly interacting massive particles) or MACHOs (massive compact halo objects). Other similar mysteries abound and increase in number as our ability to observe improves.The progress of biological and life sciences has been similar to that of the physical sciences, except that it has occurred several centuries later. The theory of biological evolution first came to the attention of scientists with the publication of Darwin's Origin of Species in 1859. But Darwin lacked any explanation of the causes of variation and inheritance of characteristics. These were provided by Gregor Mendel, who laid the mathematical foundation of genetics with the publication of papers in 1865 and 1866.Medicine, according to Lewis Thomas, is the youngest science, having become truly scientific only in the 1930s. Recent and ongoing research has created uncertainty about even such basic concepts as when and how life begins and when death occurs, and we are spending billions in an attempt to learn how much it may be possible to know about human genetics. Modern medicine has demonstrably improved both our life expectancies and our health, and further improvements continue to be made as research progresses. But new questions arise even more rapidly than our research resources grow, as the host of problems related to the Human Genome Project illustrates.From even such an abbreviated and incomplete survey of science as this, it appears that increasing knowledge does not result in a commensurate decrease in ignorance, but, on the contrary, exposes new lacunae in our comprehension and confronts us with unforeseen questions disclosing areas of ignorance of which we were not previously aware.Thus the concept of science as an expanding body of knowledge that will eventually encompass or dispel all significant areas of ignorance is an illusion. Scientists and philosophers are now observing that it is naive to regard science as a process that begins with observations that are organized into theories and are then subsequently tested by experiments. The late Karl Popper, a leading philosopher of science, wrote in The Growth of Scientific Knowledge (1960) chat science starts from problems, not from observations, and chat every worthwhile new theory raises new problems. Thus there is no danger that science will come to an end because it has completed its task, clanks to the "infinity of our ignorance."At least since Thomas Kuhn published The Structure of Scientific Revolutions (1962), it has been generally recognized that observations are the result of theories (called paradigms by Kuhn and other philosophers), for without theories of relevance and irrelevance there would be no basis for determining what observations to make. Since no one can know everything, to be fully informed on any subject (a claim sometimes made by those in authority) is simply to reach a judgment that additional data are not important enough to be worth the trouble of securing or considering.To carry the analysis another step, it must be recognized that theories are the result of questions and questions are the product of perceived ignorance. Thus it is chat ignorance gives rise to inquiry chat produces knowledge, which, in turn, discloses new areas of ignorance. This is the paradox of knowledge: As knowledge increases so does ignorance, and ignorance may increase more than its related knowledge.My own metaphor to illustrate the relationship of knowledge and ignorance is based on a line from Matthew Arnold: "For we are here as on a darkling plain...." The dark chat surrounds us, chat, indeed, envelops our world, is ignorance. Knowledge is the illumination shed by whatever candles (or more technologically advanced light sources) we can provide. As we light more and more figurative candles, the area of illumination enlarges; but the area beyond illumination increases geometrically. We know chat there is much we don't know; but we cannot know how much there is chat we don't know. Thus knowledge is finite, but ignorance is infinite, and the finite cannot ever encompass the infinite.This is a revised version of an article originally published in COSMOS 1994. Copyright 1995 by Lee Loevinger.Lee Loevinger is a Washington lawyer and former assistant attorney general of the United States who writes frequently for scientific c publications. He has participated for many years as a member, co-chair, or liaison with the National Conference of Lawyers and Scientists, and he is a founder and former chair of the Science andTechnology Section of the American Bar Association. Office address: Hogan and Hartson, 555 Thirteenth St. NW, Washington, DC 20004.人类从古类人猿进化到当前的状态这个长久的进化过程中的最大成就是有关于人类自身、世界以及宇宙众多知识的获得和积聚。

博世汽车SPC

4th Edition, 07.20053rd Edition dated 06.19942nd Edition dated 05.19901st Edition dated 09.19872005 Robert Bosch GmbHTable of ContentsIntroduction (5)1. Terms for Statistical Process Control (6)2. Planning .........................................................................................................................................................8 2.1 Selection of Product Characteristics .................................................................................................8 2.1.1 Test Variable ........................................................................................................................8 2.1.2 Controllability ......................................................................................................................9 2.2 Measuring Equipment .......................................................................................................................9 2.3 Machinery .........................................................................................................................................9 2.4 Types of Characteristics and Quality Control Charts ......................................................................10 2.5 Random Sample Size ......................................................................................................................11 2.6 Defining the Interval for Taking Random Samples (11)3. Determining Statistical Process Parameters ................................................................................................12 3.1 Trial Run .........................................................................................................................................12 3.2 Disturbances ....................................................................................................................................12 3.3 General Comments on Statistical Calculation Methods ..................................................................12 3.4 Process Average ..............................................................................................................................13 3.5 Process Variation . (14)4. Calculation of Control Limits ......................................................................................................................15 4.1 Process-Related Control Limits ......................................................................................................15 4.1.1 Natural Control Limits for Stable Processes ......................................................................16 4.1.1.1 Control Limits for Location Control Charts .........................................................16 4.1.1.2 Control Limits for Variation Control Charts ........................................................18 4.1.2 Calculating Control Limits for Processes with Systematic Changes in the Average .........19 4.2 Acceptance Control Chart (Tolerance-Related Control Limits) .....................................................20 4.3 Selection of the Control Chart .........................................................................................................21 4.4 Characteristics of the Different Types of Control Charts . (22)5. Preparation and Use of Control Charts ........................................................................................................23 5.1 Reaction Plan (Action Catalog) .......................................................................................................23 5.2 Preparation of the Control Chart .....................................................................................................23 5.3 Use of the Control Chart .................................................................................................................23 5.4 Evaluation and Control Criteria ......................................................................................................24 5.5 Which Comparisons Can be Made? (25)6. Quality Control, Documentation .................................................................................................................26 6.1 Evaluation .......................................................................................................................................26 6.2 Documentation .. (26)7. SPC with Discrete Characteristics ...............................................................................................................27 7.1 General ............................................................................................................................................27 7.2 Defect Tally Chart for 100% Testing . (27)8. Tables (28)9. Example of an Event Code for Mechanically Processed Parts ....................................................................29 9.1 Causes .............................................................................................................................................29 9.2 Action ..............................................................................................................................................29 9.3 Handling of the Parts/Goods ...........................................................................................................30 9.4 Action Catalog .. (30)10. Example of an x -s Control Chart (32)11. Literature (33)12. Symbols (34)Index (35)IntroductionStatistical Process Control (SPC) is a procedure for open or closed loop control of manufacturing processes, based on statistical methods.Random samples of parts are taken from the manufacturing process according to process-specific sampling rules. Their characteristics are measured and entered in control charts. This can be done with computer support. Statistical indicators are calculated from the measurements and used to assess the current status of the process. If necessary, the process is corrected with suitable actions.Statistical principles must be observed when taking random samples.The control chart method was developed by Walter Andrew Shewhart (1891-1967) in the 1920´s and described in detail in his book “Economic Control of Quality of Manufactured Product”, published in 1931.There are many publications and self-study programs on SPC. The procedures described in various publications sometimes differ significant-ly from RB procedures.SPC is used at RB in a common manner in all divisions. The procedure is defined in QSP0402 [1] in agreement with all business divisions and can be presented to customers as the Bosch approach.Current questions on use of SPC and related topics are discussed in the SPC work group. Results that are helpful for daily work and of general interest can be summarized and published as QA Information sheets. SPC is an application of inductive statistics. Not all parts have been measured, as would be the case for 100% testing. A small set of data, the random sample measurements, is used to estimate parameters of the entire population.In order to correctly interpret results, we have to know which mathematical model to use, where its limits are and to what extent it can be used for practical reasons, even if it differs from the real situation.We differentiate between discrete (countable) and continuous (measurable) characteristics. Control charts can be used for both types of characteristics.Statistical process control is based on the concept that many inputs can influence a process.The “5 M´s” – man, machine, material, milieu, method – are the primary groups of inputs. Each “M” can be subdivided, e.g. milieu in temperature, humidity, vibration, contamination, lighting, ....Despite careful process control, uncontrolled, random effects of several inputs cause deviation of actual characteristic values from their targets (usually the middle of the tolerance range).The random effects of several inputs ideally result in a normal distribution for the characteristic.Many situations can be well described with a normal distribution for SPC.A normal distribution is characterized with two parameters, the mean µ and the standard deviation σ.The graph of the density function of a normal distribution is the typical bell curve, with inflection points at σµ− and σµ+.In SPC, the parameters µ and σ of the population are estimated based on random sample measurements and these estimates are used to assess the current status of the process.1. Terms for Statistical Process ControlProcessA process is a series of activities and/or procedures that transform raw materials or pre-processed parts/components into an output product.The definition from the standard [3] is: “Set of interrelated or interacting activities which trans-forms inputs into outputs.”This booklet only refers to manufacturing or assembly processes.Stable processA stable process (process in a state of statistical control) is only subject to random influences (causes). Especially the location and variation of the process characteristic are stable over time (refer to [4])Capable processA process is capable when it is able to completely fulfill the specified requirements. Refer to [11] for determining capability indices. Shewhart quality control chartQuality control chart for monitoring a parameter of the probability distribution of a characteristic, in order to determine whether the parameter varies from a specified value.SPCSPC is a standard method for visualizing and controlling (open or closed loop) processes, based on measurements of random samples.The goal of SPC is to ensure that the planned process output is achieved and that corresponding customer requirements are fulfilled.SPC is always linked to (manual or software supported) use of a quality control chart (QCC). QCC´s are filled out with the goal of achieving, maintaining and improving stable and capable processes. This is done by recording process or product data, drawing conclusions from this data and reacting to undesirable data with appropriate actions.The following definitions are the same as or at least equivalent to those in [6].Limiting valueLower or upper limiting valueLower limiting valueLowest permissible value of a characteristic (lower specification limit LSL)Upper limiting valueHighest permissible value of a characteristic (upper specification limit USL)ToleranceUpper limiting value minus lower limiting value:LSLUSLT−=Tolerance rangeRange of permissible characteristic values between the lower and upper limiting valuesCenter point C of the tolerance rangeThe average of the lower and upper limiting values:2LSLUSL C +=Note: For characteristics with one-sided limits (only USL is specified), such as roughness (Rz), form and position (e.g. roundness, perpen-dicularity), it is not appropriate to assume 0=LSL and thus to set 2/USLC= (also refer to the first comment in Section 4.1.1.1).PopulationThe total of all units taken into considerationRandom sampleOne or more units taken from the population or from a sub-population (part of a population)Random sample size nThe number of units taken for the random sample Mean (arithmetic)The sum of theix measurements divided by the number of measurements n:∑=⋅=niixnx11Median of a sampleFor an odd number of samples put in order from the lowest to highest value, the value of the sample number (n+1)/2. For an even number of samples put in order from the lowest to highest value, normally the average of the two samples numbered n/2 and (n/2)+1. (also refer to [13])Example: For a sample of 5 parts put in order from the lowest to the highest value, the median is the middle value of the 5 values.Variance of a sampleThe sum of the squared deviations of the measurements from their arithmetic mean, divided by the number of samples minus 1:()∑=−⋅−=niixxns12211Standard deviation of a sampleThe square root of the variance:2ss=RangeThe largest individual value minus the smallest individual value:minmaxxxR−=2. PlanningPlanning according to the current edition of QSP 0402 “SPC”, which defines responsibilities. SPC control of a characteristic is one possibility for quality assurance during manufacturing and test engineering.2.1 Selection of Product CharacteristicsSpecification of SPC characteristics and their processes should be done as early as possible (e.g. by the simultaneous engineering team). They can also, for example, be an output of the FMEA.This should take• Function,• Reliability,• Safety,•Consequential costs of defects,•The degree of difficulty of the process,• Customer requests, and•Customer connection interfaces, etc.into account.The 7 W-questions can be helpful in specifying SPC characteristics (refer to “data collection” in “Elementary Quality Assurance Tools” [8]): Example of a simple procedure for inspection planning:Why do I need to know what, when, where and how exactly?How large is the risk if I don’t know this? Note: It may be necessary to add new SPC characteristics to a process already in operation. On the other hand, there can be reasons (e.g. change of a manufacturing method or intro-duction of 100% testing) for replacing existing SPC control with other actions.SPC characteristics can be product or process characteristics.Why?Which or what? Which number or how many?Where? Who?When?With what or how exactly?2.1.1 Test VariableDefinition of the “SPC characteristic”, direct or indirect test variable. Note: If a characteristic cannot be measured directly, then a substitute characteristic must be found that has a known relationship to it.2.1.2 ControllabilityThe process must be able to be influenced (controlled) with respect to the test variable. Normally manufacturing equipment can be directly controlled in a manner that changes the test variable in the desired way (small control loop). According to Section 1, “control” in the broadest sense can also be a change of tooling, machine repair or a quality meeting with a supplier to discuss quality assurance activities (large control loop).2.2 Measuring EquipmentDefinition and procurement or check of the measuring equipment for the test variable.Pay attention to:• Capability of measuring and test processes, • Objectiveness,• Display system (digital),• Handling. The suitability of a measurement process for the tested characteristic must be proven with a capability study per [12].In special cases, a measurement process with known uncertainty can be used (pay attention to [10] and [12]).Note: The units and reference value must correspond to the variables selected for the measurement process.2.3 MachineryBefore new or modified machinery is used, a machine capability study must be performed (refer to QSP0402 [1] and [11]). This also applies after major repairs.Short-term studies (e.g. machine capability studies) register and evaluate characteristics of products that were manufactured in one continuous production run. Long-term studies use product measurements from a longer period of time, representative of mass production. Note: The general definition of SPC (Section 1) does not presume capable machines. However, if the machines are not capable, then additional actions are necessary to ensure that the quality requirements for manufactured products are fulfilled.2.4 Types of Characteristics and Control Charts This booklet only deals with continuous anddiscrete characteristics. Refer to [6] for these andother types of characteristics.In measurement technology, physical variables are defined as continuous characteristics. Counted characteristics are special discrete characteristics. The value of the characteristic is called a “counted value”. For example, the number of “bad” parts (defective parts) resulting from testing with a limit gage is a counted value. The value of the characteristic (e.g. the number 17, if 17 defective parts were found) is called a “counted value”.SPC is performed with manually filled out form sheets (quality control charts) or on a computer.A control chart consists of a chart-like grid for entering numerical data from measured samples and a diagram to visualize the statistical indices for the process location and variation calculated from the data.If a characteristic can be measured, then a control chart for continuous characteristics must be used. Normally the sx− chart with sample size 5=n is used.2.5 Random Sample SizeThe appropriate random sample size is a compromise between process performance, desired accuracy of the selected control chart (type I and type II errors, operation characteristic) and the need for an acceptable amount of testing. Normally 5=n is selected. Smaller random samples should only be selected if absolutely necessary.2.6 Defining the Interval for Taking Random SamplesWhen a control chart triggers action, i.e. when the control limits are exceeded, the root cause must be determined as described in Section 5.4, reaction to the disturbance initiated with suitable actions (refer to the action catalog) and a decision made on what to do with the parts produced since the last random sample was taken. In order to limit the financial “damage” caused by potentially necessary sorting or rework, the random sample interval – the time between taking two random samples – should not be too long.The sampling interval must be individually determined for each process and must be modified if the process performance has permanently changed.It is not possible to derive or justify the sampling interval from the percentage of defects. A defect level well below 1% cannot be detected on a practical basis with random samples. A 100% test would be necessary, but this is not the goal of SPC. SPC is used to detect process changes.The following text lists a few examples of SPC criteria to be followed.1. After setup, elimination of disturbances orafter tooling changes or readjustment, measure continuously (100% or with randomsamples) until the process is correctly centered (the average of several measure-ments/medians!). The last measurements canbe used as the first random sample for furtherprocess monitoring (and entered in the control chart). 2. Random sample intervals for ongoingprocess control can be defined in the following manner, selecting the shortest interval appropriate for the process.Definition corresponding to the expected average frequency of disturbances (as determined in the trial run or as is knownfrom previous process experience).Approximately 10 random samples within this time period.Definition depending on specified preventivetooling changes or readjustment intervals.Approximately 3 random samples within thistime period.Specification of tooling changes or readjust-ment depending on SPC random samples.Approximately 5 random samples within theaverage tooling life or readjustment interval.But at least once for the production quantitythat can still be contained (e.g. delivery lot,transfer to the next process, defined lots forconnected production lines)!3. Take a final random sample at the end of aseries, before switching to a different producttype, in order to confirm process capabilityuntil the end of the series.Note: The test interval is defined based on quantities (or time periods) in a manner that detects process changes before defects are produced. More frequent testing is necessary for unstable processes.3. Determining Statistical Process Parameters3.1 Trial RunDefinition of control limits requires knowledge or estimation of process parameters. This is determined with a trial run with sampling size and interval as specified in Sections 2.5 and 2.6. For an adequate number of parts for initial calculations, take a representative number of unsorted parts, at least 25=m samples (with n = 5, for example), yielding no fewer than 125 measured values. It is important to assess the graphs of the measured values themselves, the means and the standard deviations. Their curves can often deliver information on process performance characteristics (e.g. trends, cyclical variations).3.2 DisturbancesIf non-random influences (disturbances) occur frequently during the trial run, then the process is not stable (not in control). The causes of the disturbances must be determined and elimi-nated before process control is implemented (repeat the trial run).3.3 General Comments on Statistical Calculation MethodsComplicated mathematical procedures are no longer a problem due to currently available statistics software, and use of these programs is of course allowed and widespread (also refer to QSP0402 [1]).The following procedures were originally developed for use with pocket calculators. They are typically included in statistics programs.Note: Currently available software programs allow use of methods for preparing, using and evaluation control charts that are better adapted to process-specific circumstances (e.g. process models) than is possible with manual calculation methods. However, this unavoidably requires better knowledge of statistical methods and use of statistics software. Personnel and training requirements must take this into account.Each business division and each plant should have a comprehensively trained SPC specialist as a contact person.Parameter µ is estimated by:Example (Section 10): samplesof number valuesx the of total mxx mj j===∑=1ˆµ3622562862662.......x ˆ=+++==µor:samplesof number mediansthe of total mxx m j j===∑=1~~ˆµ46225626363....x ~ˆ=+++==µIf µˆ significantly deviates from the center point C for a characteristic with two-sided limits, then this deviation should be corrected by adjusting the machine.Parameter σ is estimated by:Example (Section 10):a) ∑=⋅=m j j s m 121ˆσ41125552450550222.......ˆ=+++=σsamplesof number variancesthe of total =σˆNote: s =σˆ is calculated directly from 25 individual measurements taken from sequential random samples (pocket calculator).or b) na s=σˆ, where27125552450550.......s =+++=samplesof number deviationsdard tan s the of total ms s mj j==∑=1351940271...a s ˆn ===σnn a3 0.89 5 0.94 See Section 8, Table 1 7 0.96 for additional valuesor c) ndR =σˆ, with96225611....R =+++= samplesof number rangesthe of total mR R mj j==∑=1271332962...d R ˆn ===σn n d3 1.69 5 2.33 See Section 8, Table 1 7 2.70 for additional values Note: The use of table values n a and n d pre-supposes a normal distribution!Some of these calculation methods were originally developed to enable manual calculation using a pocket calculator. Formula a) is normally used in currently available statistics software.4. Calculation of Control Limits4.1 Process-Related Control LimitsThe control limits (lower control limit LCL andupper control limit UCL) are set such that 99% of all the values lie within the control limits in the case of a process which is only affected by random influences (random causes).If the control limits are exceeded, it must there-fore be assumed that systematic, non-random influences (non-random causes) are affecting the process.These effects must be corrected or eliminated by taking suitable action (e.g. adjustment).Relation between the variance (standard deviation x σ) of the single values (original values, individuals) and the variance (standard deviation x σ) of the mean values: nxx σσ=.4.1.1 Natural Control Limits for Stable Processes4.1.1.1 Control Limits for Location Control Charts (Shewhart Charts)For two-sided tolerances, the limits for controlling the mean must always be based on the center point C. Note: C is replaced by the process mean x =µˆ for processes where the center point C cannot be achieved or for characteristics with one-sided limits.* Do not use for moving calculation of indices!Note: Use of the median-R chart is onlyappropriate when charts are manually filled out, without computer support.n*A E C n c'E EE E3 1.68 1.02 1.16 2.93 1.73 5 1.230.59 1.20 3.09 1.337 1.020.44 1.21 3.19 1.18Estimated values µˆ and σˆ are calculated per Sections 3.4 and 3.5.Refer to Section 8 Table 2 for additional values.Comments on the average chart: For characteristics with one-sided limits (or in general for skewed distributions) and small n , the random sample averages are not necessarily normally distributed. It could be appropriate to use a Pearson chart in this case. This chart has the advantage compared to the Shewhart chart that the control limits are somewhat wider apart. However, it has the disadvantage that calculation of the control limits is more complicated, in actual practice only possible on the computer.Control charts with moving averagesThe x chart with a moving average is a special case of the x chart. For this chart, only single random samples are taken.n sample measurements are formally grouped as a random sample and the average of these n measurements is calculated as the mean.For each new measurement from a single random sample that is added to the group, the first measurement of the last group is deleted, yielding a new group of size n , for which the new average is calculated.Of course, moving averages calculated in this manner are not mutually independent. That is why this chart has a delayed reaction to sudden process changes. The control limits correspond to those for “normal” average charts:σˆn .C LCL ⋅−=582 σˆn.C UCL ⋅+=582Calculate σˆ according to Section 3.5 a)Control limits for )3(1=n :σˆ.C LCL ⋅−=51 σˆ.C UCL ⋅+=51Example for )3(1=n :3 74 741.x = 3 7 4 9 762.x = 3 7 4 9 2 053.x = 3 7 4 9 2 8 364.x =This approach for moving sample measurements can also be applied to the variation, so that an s x − chart with a moving average and moving standard deviation can be used.After intervention in the process or process changes, previously obtained measurements may no longer be used to calculate moving indices.4.1.1.2 Control Limits for Variation Control ChartsThe control limits to monitor the variation (depending on n ) relate to σˆ and s and like-wise R (= “Central line”).s charta) generally applicable formula(also for the moving s x − chart)Example (Section 10):σˆB UCL 'Eob⋅= 62351931...UCL =⋅=σˆB LCL 'Eun ⋅= 30351230...LCL =⋅=b) for standard s x − chartNote: Formula a) must be used in the case ofmoving s calculation. Calculation of σˆ per Section 3.5 a).s B UCL *Eob ⋅= 62271052...UCL =⋅=s B LCL *Eun ⋅=30271240...LCL =⋅=R chartR D UCL Eob ⋅=2696212...UCL =⋅=R D LCL Eun ⋅=70962240...LCL =⋅=Tablen 'Eun B 'Eob B *Eun B *Eob B Eun D Eob D3 5 70.07 0.23 0.34 2.30 1.93 1.76 0.08 0.24 0.35 2.60 2.05 1.88 0.08 0.24 0.34 2.61 2.10 1.91See Section 8, Table 2 for further values4.1.2 Calculating Control Limits for Processes with Systematic Changes in the AverageIf changes of the mean need to be considered as a process-specific feature (trend, lot steps, etc.) and it is not economical to prevent such changes of the mean, then it is necessary to extend the “natural control limits”. The procedure for calculating an average chart with extended control limits is shown below.The overall variation consists of both the “inner” variation (refer to Section 3.5) of the random samples and of the “outer” variation between the random samples.Calculation procedure Control limits for the mean。