Unreferenced date December 2009 Policy Debate In policy debate , impact calculus is a type of argumentation which seeks to compare the impacts presented by both teams. Basic impact calculus There are three basic types of impact calculus that compare the impacts of the plan to the impacts of a disadvantage Probability one impact is more likely e.g. Economic collapse is more probable than an outbreak of grey goo , therefore the risk of economic collapse outweighs the risk of a grey goo disaster. Timeframe one impact will happen faster e.g. An asteroid impact will cause extinction before Global warming will, therefore an asteroid impact outweighs Global Warming. Magnitude one impact is bigger e.g. Nuclear war kills more people than car accidents. Other types of impact calculus Some other more sophisticated arguments are also considered impact calculus Impact inclusivity one impact is inclusive of the other e.g. Global war is inclusive of a Taiwan war, therefore global war outweighs Taiwan war. X creates Y one impact causes the other impact to happen e.g. War causes genocide, therefore war outweighs genocide Internal link shortcircuiting one impact prevents a positive impact from happening e.g. Nuclear war halts space colonization, therefore nuclear war outweighs space colonization Reversibility e.g. Civil liberties lost in the name of security during a time of crisis can be restored later, but deaths caused by a lack of security are irreversible. Framework arguments can also be considered impact calculus. Arguments as to why the judge policy debate judge should adopt a utilitarianism ... perspective may change the way they compare impacts. Impact calculus and new arguments Basic impact calculus arguments may be made at any time and are generally not considered new arguments, even ... forms of impact calculus should generally be brought up earlier in the debate and evidenced if possible. DEFAULTSORT Impact Calculus Category Policy debate ... more details
In mathematics , a functional calculus is a theory allowing one to apply mathematical function s to mathematical operator s. It is now a branch more accurately, several related areas of the field of functional analysis , connected with spectral theory . Historically, the term was also used synonymously with calculus of variations this usage is obsolete, but see functional derivative . Sometimes it is used in relation to types of functional equation , or in logic for systems of predicate calculus . If f is a function, say a numerical function of a real number , and M is an operator, there is no particular reason why the expression f M should make sense. If it does, then we are no longer using f on its original function domain . In the tradition of operational calculus , algebraic expressions in operators are handled irrespective of their meaning. This passes nearly unnoticed if we talk about squaring a matrix , though, which is the case of f x x sup 2 sup and M an n × n matrix mathematics matrix . The idea of a functional calculus is to create a principled approach to this kind of overloading of the notation. The most immediate case is to apply polynomial function s to a square matrix , extending what has just been discussed. In the finite dimensional case, the polynomial functional calculus yields quite a bit of information about the operator. For example, consider the family of polynomials which annihilates an operator T . This family is an ideal ring theory ideal in the ring ... calculus is not as informative in the infinite dimensional case. Consider the unilateral shift with the polynomials calculus the ideal defined above is now trivial. Thus one is interested in functional ... be. For technical accounts see holomorphic functional calculus continuous functional calculus Borel functional calculus . References Springer id F f042030 title Functional calculus DEFAULTSORT Functional Calculus Category Functional calculus de Funktionalkalk l nl Functionele calculus ... more details
Geometric calculus extends the geometric algebra to include differentiation and integration including differential geometry and differential forms. ref David Hestenes , Garrett Sobczyk Clifford Algebra to Geometric Calculus, a Unified Language for mathematics and Physics Dordrecht Boston G.Reidel Publ.Co., 1984, ISBN 90 277 2561 6 ref File Geometric Calculus Family Tree.png right 300px thumb Figure 1 from 32 A diagram of the history of Geometric Calculus Given a geometric algebra, the vector derivative is defined as the operator math 1 . Essentially, the vector derivative is defined so that the GA version of Green s theorem is true, math oint A dA nabla f oint dA dx f math and then one can write math nabla f nabla cdot f nabla wedge f math as a geometric product, effectively generalizing Stokes theorem including the differential forms version of it . In math 1D math when A is a curve with endpoints math a math and math b math , then math oint A dA nabla f oint dA dx f math reduces to math int a b dx nabla f int a b dx cdot nabla f int a b df f b f a math or the fundamental theorem of integral calculus. Also developed are the concept of vector manifold and geometric integration theory which generalizes Cartan s differential forms . References reflist differential geometry stub Category Calculus ... more details
Calculus medicine Calculus bovis ref Ingredients, AN KUNG NIU HUANG WAN Bezoar Chest Functioning Pills , Peking Tung Jen Tang, Peking, China. 1980. ref , niu huang or ox bezoar s are dried gallstone s of cattle used in Chinese herbology , where they are claimed to remove toxins from the body. In Asian countries calculus bovis are harvested when cattle Bos taurus domesticus Gmelin are slaughtered. Their gall bladder s are taken out, the bile is filtered, and the stones are cleaned and dried. In western countries they are usually discarded. Calculus bovis have a color varying from golden yellow to brownish yellow. The shape of a stone is variable and depends on how it was formed, becoming spherical, oval, triangular, tubular or irregular. Since natural calculus bovis are scarce they can be very expensive. There are artificial calculus bovis used as substitutes. These are manufactured from cholic acid derived from bovine bile ref http www.nzp.co.nz products.php?cid 1&pid 1 ref , but it is said that the effect may not be the same. References reflist Category Traditional Chinese medicine Category Article Feedback 5 pt C lculo biliar bovino zh ... more details
Quantum calculus , sometimes called calculus without limits , is equivalent to traditional infinitesimal calculus without the notion of Limit of a function limits . It defines q calculus and h calculus . h ostensibly stands for Planck s constant while q stands for quantum. The two parameters are related by the formula math q e i h e 2 pi i hbar , math where math scriptstyle hbar frac h 2 pi , math is the reduced Planck constant . Differentiation In the q calculus and h calculus, differential of a function differentials of functions are defined as math d q f x f qx f x , math and math d h f x f x h f x , math respectively. Derivative s of functions are then defined as fractions by the q derivative math D q f x frac d q f x d q x frac f qx f x q 1 x math and by math D h f x frac d h f x d h x frac f x h f x h math In the Limit of a function limit , as h goes to 0, or equivalently as q goes to 1, these expressions take on the form of the derivative of classical calculus. Integration q integral A function F x is a q antiderivative of f x if D sub q sub F x f x . The q antiderivative or q ... calculus is math nx n 1 math . The corresponding expressions in q calculus and h calculus are math ... calculus analogue of the simple power rule for positive integral powers. In this sense, the function math x n math is still nice in the q calculus, but rather ugly in the h calculus the h calculus ... cetera, and even arrive at q calculus analogues for all of the usual functions one would want to have ... . History The h calculus is just the calculus of finite differences , which had been studied ... mechanics . The q calculus, while dating in a sense back to Leonhard Euler and Carl Gustav Jacobi ... calculus Time scale calculus q analog References reflist this section is for references ... reading should go into further reading Victor Kac , Pokman Cheung , Quantum calculus , Universitext ... calculus mathanalysis stub pl Analiza kwantowa ... more details
Stochastic calculus is a branch of mathematics that operates on stochastic process es. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave randomly. The best known stochastic process to which stochastic calculus is applied is the Wiener process named in honor of Norbert Wiener , which is used for modeling Brownian motion as described by Louis Bachelier in 1900 and by Albert Einstein in 1905 and other physical diffusion processes in space of particles subject to random forces. Since the 1970s, the Wiener process has been widely applied in financial mathematics and economics to model the evolution in time of stock prices and bond interest rates. The main flavours of stochastic calculus are the It calculus and its variational relative the Malliavin calculus . For technical reasons the It integral is the most useful for general classes of processes but the related Stratonovich integral is frequently useful in problem formulation particularly in engineering disciplines. The Stratonovich integral can readily be expressed in terms of the It integral. The main benefit of the Stratonovich integral is that it obeys the usual chain rule and does therefore not require ... when developing stochastic calculus on manifolds other than R sup n sup . The dominated ... results without re expressing the integrals in It form. It integral main It calculus The It integral is central to the study of stochastic calculus. The integral math int H ,dX math is defined ... integral. Applications A very important application of stochastic calculus is in quantitative ... date August 2011 References Fima C Klebaner, 2012, Introduction to Stochastic Calculus with Application ... http arxiv.org PS cache arxiv pdf 0712 0712.3908v2.pdf Preprint Category Stochastic calculus Category Mathematical finance Category Integral calculus ar de Stochastische ... more details
The Malliavin calculus , named after Paul Malliavin , extends the calculus of variations from functions to stochastic processes . The Malliavin calculus is also called the stochastic calculus of variations ... s original proof was based on the theory of partial differential equation s. The calculus has been applied to stochastic partial differential equation s as well. The calculus allows integration by parts ... of derivative finance financial derivative s. The calculus has applications for example in stochastic filtering . Overview and history Paul Malliavin s stochastic calculus of variations extends the calculus ... of derivative s of random variable s. Malliavin invented his calculus to provide a stochastic ... on the theory of partial differential equation s. His calculus enabled Malliavin to prove regularity bounds for the solution s density. The calculus has been applied to stochastic partial differential ... Ocone theorem One of the most useful results from Malliavin calculus is the Clark Ocone theorem ... in the formal development of the Malliavin calculus involves extending this result to the largest ... integral to non adapted integrands. Applications The calculus allows integration by parts with random ... finance financial derivative s. The calculus has applications for example in stochastic control ... of Malliavin Calculus I , Stochastic Analysis, Proceedings Taniguchi International Symposium Katata and Kyoto 1982, pp 271 306 Kusuoka, S. and Stroock, D. 1985 Applications of Malliavin Calculus ... of Malliavin Calculus III , J. Faculty Sci. Univ. Tokyo Sect. 1A Math. , 34 pp 391 442 Malliavin, Paul and Thalmaier, Anton. Stochastic Calculus of Variations in Mathematical Finance , Springer 2005, ISBN 3 540 43431 3 cite book last Nualart first David title The Malliavin calculus and related .... 2007 The Malliavin Calculus , Dover. ISBN 0486449947 Schiller, Alex 2009 http www.alexschiller.com media Thesis.pdf Malliavin Calculus for Monte Carlo Simulation with Financial Applications . Thesis ... more details
The fluent calculus is a formalism for expressing dynamical domains in first order logic . It is a variant of the situation calculus the main difference is that situations are considered representations of states. A binary function symbol math circ math is used to concatenate the terms that represent facts that hold in a situation. For example, that the box is on the table in the situation math s math is represented by the formula math exists t . s on box,table circ t math . The frame problem is solved by asserting that the situation after the execution of an action is identical to the one before but for the conditions changed by the action. For example, the action of moving the box from the table to the floor is formalized as math State Do move box,table,floor , s circ on box,table State s circ on box,floor math This formula states that the state after the move is added the term math on box,floor math and removed the term math on box,table math . Axioms specifying that math circ math is commutative and non idempotent are necessary for such axioms to work. See also Frame problem Situation calculus Event calculus References M. Thielscher 1998 . http www.ep.liu.se ej etai 1998 006 Introduction to the fluent calculus . Electronic Transactions on Artificial Intelligence , 2 3 4 179 192. M. Thielscher 2005 . Reasoning Robots The Art and Science of Programming Robotic Agents. Volume 33 of Applied Logic Series. Springer, Dordrecht. logic stub Category Logical calculi ... more details
In algebraic topology , a branch of mathematics , the calculus of functors or Goodwillie calculus is a technique for studying functors by approximating them by a sequence of simpler functors it generalizes the sheafification of a presheaf . This sequence of approximations is formally similar to the Taylor series of a smooth function , hence the term calculus of functors . Many objects of central interest in algebraic topology can be seen as functors, which are difficult to analyze directly, so the idea is to replace them with simpler functors which are sufficiently good approximations for certain purposes. The calculus of functors was developed by Thomas Goodwillie in a series of three papers in the 1990s and 2000s, ref T. Goodwillie, Calculus I The rst derivative of pseudoisotopy theory, K theory 4 1990 , 1 27. ref ref T. Goodwillie, Calculus II Analytic functors, K theory 5 1992 , 295 332. ref ref T. Goodwillie, Calculus III Taylor series, Geom. Topol. 7 2003 , 645 711. ref and has since ... N, whose first derivative in the sense of calculus of functors is the functor of Immersion mathematics ... 3 1999 , 103 118. ref Definition Here is an analogy with the Taylor series method from calculus ... accurate polynomial functions. In a similar way, with the calculus of functors method, you ... you can approximate using the calculus of functors method you want to know what sort of topological ... accurate approximations F sub 0 sub X , F sub 1 sub X , F sub 2 sub X , and so on. In the calculus ... branches of the calculus of functors, developed in the order manifold calculus, such as embeddings, homotopy calculus, and orthogonal calculus. Homotopy calculus has seen far wider application than ... theory, and can be seen as the linear form of the calculus of functors. The quadratic form can ... citation title Syllabus for Math 283 Calculus of Functors first Brian last Munson year 2005 ... staff display.php?key m.weiss Michael S. Weiss DEFAULTSORT Calculus Of Functors Category ... more details
Duration calculus DC is an interval logic for real time computing real time systems . It was originally developed by Zhou Chaochen with the help of Anders P. Ravn and C. A. R. Hoare on the European European Strategic Program on Research in Information Technology ESPRIT Basic Research Action BRA ProCoS project on Provably Correct Systems . ref Zhou Chaochen , C. A. R. Hoare and Anders P. Ravn , A Calculus of Durations, Information Processing Letters , 40 5 269 276, December 1991. ref ref Zhou Chaochen and Michael R. Hansen , Duration Calculus A Formal Approach to Real Time Systems . Springer Science Business Media Springer Verlag , Monographs in Theoretical Computer Science, An EATCS Series, 2003. ISBN 3 540 40823 1. ref DC is mainly useful at the requirements level of the software development process for real time systems. Some tools are available e.g., DCVALID, ref http www.tcs.tifr.res.in pandya dcvalid.html DCVALID A tool for model checking Duration Calculus formulae , TIFR , India. ref IDLVALID, ref http www.tcs.tifr.res.in pandya idlvalid.html IDLVALID Model checking dense time Duration Calculus formulae , TIFR, India. ref etc. . Subsets of Duration Calculus have been studied e.g., using discrete time rather than continuous time . DC is especially espoused by UNU IIST in Macau and the Tata Institute of Fundamental Research in Mumbai , which are major centres of excellence for the approach. See also Interval Temporal Logic ITL Temporal logic Temporal Logic of Actions TLA Modal logic References reflist External links http www.iist.unu.edu dc Duration Calculus Virtual Library entry formalmethods stub Category 1991 introductions Category Formal specification languages Category Temporal logic ... more details
File MandibularAnteriorCalculus.JPG thumb right Heavy staining and calculus deposits exhibited on the Commonly ... the gumline. Missing information Removal of Calculus After Formation date May 2011 In dentistry , calculus ... which calculus forms however, once formed, it is too hard and firmly attached to be removed with a toothbrush. Calculus buildup can be professionally removed with ultrasonic tools and periodontal ... many modern words, including calculate use stones for mathematical purposes , and calculus , which came ... calcify and become calculus. Citation needed date November 2008 Calculus is detrimental to gingival health because it serves as a trap for increased plaque formation and retention thus, calculus ... etiology of periodontitis . Calculus can form both along the gumline, where it is referred to as supragingival ... and the gingiva, where it is referred to as subgingival below the gum . Calculus formation can ... Fox first2 EC title Investigations into the mycology of dental calculus in town dwellers, agricultural ... and the gingival fibers that attach the teeth to the gums, leading to periodontitis . Calculus ... subgingival calculus deposits. These anaerobic bacteria have been linked to cardiovascular ... to prevent the build up of calculus is through twice daily toothbrushing and Dental floss flossing and regular cleaning visits based on a schedule recommended by the dental health care provider. Calculus .... There are also some external factors that facilitate the accumulation of calculus, including smoking ... pmid 7007451 ref Sub gingival calculus formation and chemical dissolution Ref improve section date May 2011 Importance section date May 2011 Sub gingival calculus tartar is composed almost entirely of two ... phosphate salts, and calcium phosphate salts that have joined the fossilized bacteria in calculus formations. The initial attachment mechanism and the development of mature calculus formations are based ... are detectable in calculus by X ray diffraction brushite , octacalcium phosphate , magnesium containing ... more details
Expert subject Computer science date November 2008 The calculus of constructions CoC is a formal language in which both computer programs and mathematical proof mathematics proof s can be expressed. This language ... calculus of inductive constructions . General traits The CoC is a higher order typed lambda calculus ... the richest calculus. The CoC is normalization property lambda calculus strongly normalizing ... later versions were built upon the calculus of inductive constructions , an extension of CoC with native ... as their polymorphic destructor function. The basics of the calculus of constructions The Calculus ... Howard isomorphism associates a term in the Typed lambda calculus simply typed lambda calculus with each natural deduction proof in intuitionistic logic intuitionistic propositional logic . The Calculus of Constructions extends this isomorphism to proofs in the full intuitionistic predicate calculus ... A term in the calculus of constructions is constructed using the following rules T is a term also called ... math math forall x A . B math The calculus of constructions has five kinds of objects proofs , which .... P is an example of a large type T itself, which is the type of large types. Judgments The calculus ... math , then term math t math has type math B math . The valid judgments for the calculus of constructions ... judgment, then so is math Gamma vdash C D math Inference rules for the calculus of constructions 1 . math ... qquad A beta B qquad qquad B K over Gamma vdash M B math Defining logical operators The calculus ... data types used in computer science can be defined within the Calculus of Constructions Booleans ... logic Intuitionistic type theory Lambda calculus Lambda cube System F Typed lambda calculus Theorists ... Huet The Calculus of Constructions. Information and Computation, Vol. 76, Issue 2 3, 1988. For a source freely accessible online, see Coquand and Huet http hal.inria.fr inria 00076024 en The calculus ... Calculus of Constructions . 2004. Category Dependently typed programming Category Lambda calculus ... more details
Calculus The Musical is a comic review of the concepts and history of Calculus . The musical was originally created by Matheatre, composed of Marc Gutman and Sadie Bowman. The musical used the story of the development of Calculus to tie together songs that Marc had created as mnemonics when he was a teacher. Gutman and Bowman launched the musical s tour at the Minnesota Fringe Festival in August 2006, and continued to tour the show to Fringe Festivals, High Schools, Colleges and Conferences until spring of 2008. In Autumn of 2008, Matheatre licensed the show to the Know Theatre of Cincinnati who continues the tour to this day. Current Cast Members Breona Conrad and Josh Murphy. External links http matheatre.com http calculusthemusical.com http www.knowtheatre.com References small http calculusthemusical.com about us http matheatre.com about.php http thefischbowl.blogspot.com 2008 02 calculus musical.html http www.knowtheatre.com about news 39 calculus the musical hits the road http www.unomaha.edu mavchannel bigpic 2009 0328.php http www.cinstages.com article.asp?CinstagenewsID 1938 http www.theconveyor.com node 117 http retrolowfi.com 2007 05 29 matheatre E2 80 93 calculus the musical self released 2007 small Category 2006 musicals ... more details
citations needed date December 2007 Calculus of voting refers to any mathematical model which predicts voting behaviour by an electorate, including such features as participation rate. A calculus of voting represents an hypothesized decision making process. These models are used in political science in an attempt to capture the relative importance of various factors influencing an elector to vote or not vote in a particular way. Example One such model was proposed by Anthony Downs 1957 and is adapted by William H. Riker and Peter Ordeshook , in A Theory of the Calculus of Voting Riker and Ordeshook 1968 R pB &minus C D where R the reward gained from voting in a given election R, then, is a proxy for the probability that the voter will turn out p probability of vote mattering B utility benefit of voting differential benefit of one candidate winning over the other C costs of voting time effort spent D citizen duty, goodwill feeling, psychological and civic benefit of voting this term is not included in Downs s original model A political science model based on rational choice used to explain why citizens do or do not vote. References Downs, Anthony. 1957. An Economic Theory of Democracy. New York Harper & Row. Riker, William and Peter Ordeshook. 1968. A Theory of the Calculus of Voting. American Political Science Review 62 1 25 42. Category Voting theory Category Mathematical modeling ... more details
David Hilbert Hilbert s epsilon calculus is an extension of a formal language by the epsilon operator, where the epsilon operator substitutes for quantification quantifiers in that language as a method leading to a consistency proof proof of consistency for the extended formal language. The epsilon operator and epsilon substitution method are typically applied to a first order logic first order predicate calculus , followed by a showing of consistency. The epsilon extended calculus is further extended and generalized to cover those mathematical objects, classes, and categories for which there is a desire to show consistency, building on previously shown consistency at earlier levels. ref Stanford, overview paragraphs ref Epsilon operator Hilbert notation For any formal language L , extend L by adding the epsilon operator to redefine quantification math exists x A x equiv A epsilon x A math math forall x A x equiv A epsilon x neg A math The intended interpretation of x A is some x that satisfies A , if it exists. In other words, x A returns some term t such that A t is true, otherwise it returns some default or arbitrary term. If more than one term can satisfy A , then any one of these terms which make A true can be Axiom of Choice chosen , non deterministically. Equality is required to be defined under L , and the only rules required for L extended by the epsilon operator are modus ponens and the substitution of A t to replace A x for any term t . ref Stanford, the epsilon calculus paragraphs ref Bourbaki notation In tau square notation from Bourbaki N. Bourbaki s Theory ... extent, modern researchers find the epsilon calculus to provide alternatives for approaching proofs ... A theory to be checked for consistency is first embedded in an appropriate epsilon calculus. Second ... title The Epsilon Calculus Tutorial location Berlin publisher Springer Verlag oclc 108629234 Stanford Encyclopedia of Philosophy online . http plato.stanford.edu entries epsilon calculus The Epsilon Calculus ... more details
Quantity calculus is the formal method for describing the mathematical relations between abstract Physical quantity physical quantities . ref name deBoer citation title On the History of Quantity Calculus and the International System first J. last de Boer year 1995 journal Metrologia volume 31 issue 6 pages 405 429 doi 10.1088 0026 1394 31 6 001 bibcode 1995Metro..31..405D ref Here the term calculus should be understood in its broader sense of a system of computation, rather than in the sense of differential and integral calculus . The basic axiom of quantity calculus is James Clerk Maxwell Maxwell s description ref citation last Maxwell first J. C. authorlink James Clerk Maxwell title A Treatise on Electricity and Magnetism url http www.archive.org details electricandmagne01maxwrich location Oxford publisher Oxford University Press year 1873 ref of a physical quantity as the product mathematics product of a numerical value and a unit of measurement , although the roots can be traced to Joseph Fourier Fourier s concept of dimensional analysis 1822 ref citation last Fourier first Joseph authorlink Joseph Fourier title Th orie analytique de la chaleur year 1822 ref . De Boer summarizes the multiplication, division, addition and association rules of quantity calculus and proposes that a full axiomatization has yet to be completed. ref name deBoer Symbolically, measurements are expressed as products of a numeric value with a unit symbol, e.g. 12.7 m . Unlike algebra, the unit symbol represents an actual quantity such as a meter, not an Variable mathematics algebraic variable . A careful distinction needs to be made between abstract quantity abstract quantities and measured quantity measurable quantities . The multiplication and division rules of quantity calculus are applied ... Emerson citation doi 10.1088 0026 1394 45 2 002 title On quantity calculus and units of measurement .....45..134E ref Johansson proposes that there are logical flaws in the application of quantity calculus ... more details
In computer science , the ambient calculus is a process calculus devised by Luca Cardelli and Andrew D. Gordon in 1998, and used to describe and theorise about concurrent systems that include mobility . Here mobility means both computation carried out on mobile devices i.e. networks that have a dynamic topology , and mobile computation i.e. executable code that is able to move around the network . The ambient calculus provides a unified framework for modeling both kinds of mobility. ref name cardelli1998 cite journal last Cardelli first L. coauthors A.D. Gordon authorlink Luca Cardelli title Mobile Ambients journal Proceedings of the First international Conference on Foundations of Software Science and Computation Structure March 28 April 4, 1998 . M. Nivat, Ed. Lecture Notes in Computer Science volume 1378 publisher Springer Verlag pages 140 155 ref It is used to model interactions in such concurrent systems as the Internet . Since its inception, the ambient calculus has grown into a family of closely related http xdguan.freezope.org wiki AmbientCalculiOnline ambient calculi . Informal description Ambients The fundamental primitive of the ambient calculus is the ambient . An ambient is informally defined as a bounded place in which computation can occur. The notion of boundaries is considered key to representing mobility, since a boundary defines a contained computational agent that can be moved in its entirety. ref name cardelli1998 Examples of ambients include a web page bounded by a file a virtual address space bounded by an addressing range a Unix file system bounded within ... case and data ports The key properties of ambients within the Ambient calculus are Ambients have ... level math copy m. math makes any number of copy of something math m math The Ambient calculus ... enough to simulate name passing channels in the Pi calculuscalculus . See also lambda calculus type theory API Calculus External links http lucacardelli.name Ambients.html Mobile Computational ... more details
DISPLAYTITLE calculus In theoretical computer science , the calculus or pi calculus is a process calculus originally developed by Robin Milner , http user.it.uu.se joachim Joachim Parrow and David Walker computer scientist David Walker as a continuation of work on the process calculus CCS Calculus of Communicating Systems . The calculus allows channel names to be communicated along the channels ... may change during the computation. The calculus is elegantly simple yet very expressive. Functional programs can be encoded into the calculus, and the encoding emphasises the dialogue nature of computation, drawing connections with game semantics . Extensions of the calculus, such as the spi calculus and applied , have been successful in reasoning about cryptographic protocols. Beside the original use in describing concurrent systems, the calculus has also been used to reason about business processes and molecular biology. Informal definition The calculus belongs to the family ... computation. In fact, the calculus, like the lambda calculuscalculus , is so minimal that it does ... Central to the calculus is the notion of name . The simplicity of the calculus lies in the dual role that names play as communication channels and variables . The process constructs available in the calculus ... P math . The constants of nowrap calculus are defined by their names only and are always communication ... calculus prevents us from writing programs in the normal sense, it is easy to extend the calculus. In particular ..., extensions of the nowrap calculus have been proposed which take into account distribution or public key cryptography. The applied nowrap calculus due to Abadi and Fournet http citeseer.ist.psu.edu ... put these various extensions on a formal footing by extending the nowrap calculus with arbitrary ... called names . The abstract syntax for the calculus is built from the following BNF grammar where x and y are any names from ref http www.lfcs.inf.ed.ac.uk reports 89 ECS LFCS 89 85 A Calculus ... more details
In mathematics , the Kirby calculus in geometric topology , named after Robion Kirby , is a method for modifying framed link s in the 3 sphere using a finite set of moves, the Kirby moves . Using four dimensional Cerf theory , he proved that if M and N are 3 manifold s, resulting from Dehn surgery on framed links L and J respectively, then they are homeomorphic if and only if L and J are related by a sequence of Kirby moves. According to the Lickorish Wallace theorem any closed orientable 3 manifold is obtained by such surgery on some link in the 3 sphere. Some ambiguity exists in the literature on the precise use of the term Kirby moves . Different presentations of Kirby calculus have a different set of moves and these are sometimes called Kirby moves. Kirby s original formulation involved two kinds of move, the blow up and the handle slide Roger Fenn and Colin Rourke exhibited an equivalent construction in terms of a single move, the Fenn Rourke move , that appears in many expositions and extensions of the Kirby calculus. Dale Rolfsen s book, Knots and Links , from which many topologists have learned the Kirby calculus, describes a set of two moves 1 delete or add a component with surgery coefficient infinity 2 twist along an unknotted component and modify surgery coefficients appropriately this is called the Rolfsen twist . This allows an extension of the Kirby calculus to rational surgeries. There are also various tricks to modify surgery diagrams. One such useful move is the slam dunk . An extended set of diagrams and moves are used for describing 4 manifold s. A framed link in the 3 sphere encodes instructions for attaching 2 handles to the 4 ball. The 3 dimensional ... Exotic R4 Exotic R sup 4 sup References Rob Kirby, A Calculus for Framed Links in S sup 3 sup . Inventiones Mathematicae, vol. 45 1978 , pp. 35&ndash 56. R. P. Fenn and C. P. Rourke, On Kirby s calculus ... Calculus , 1999 Volume 20 in Graduate Studies in Mathematics , American Mathematical Society ... more details
Unreferenced date January 2009 In mathematical logic , a proof calculus corresponds to a family of formal system s that use a common style of formal inference for its inference rules . The specific inference rules of a member of such a family characterize the theory mathematical logic theory of a logic. Usually a given proof calculus encompasses more than a single particular formal system, since many proof calculi are under determining and can be used for radically different logics. For example, a paradigmatic case is the sequent calculus, which can be used to express the consequence relation s of both intuitionistic logic and relevance logic . Thus, loosely speaking, a proof calculus is a template or design pattern , characterized by a certain style of formal inference, that may be specialized to produce specific formal systems, namely by specifying the actual inference rules for such a system. There is no consensus among logicians on how best to define the term. Examples of proof calculi The most widely known proof calculi are those classical calculi that are still in widespread use The class of Hilbert system s, of which the most famous example is the 1928 Hilbert Ackermann system of first order logic Gerhard Gentzen s calculus of natural deduction , which is the first formalism of structural proof theory , and which is the cornerstone of the formulae as types correspondence relating logic to functional programming Gentzen s sequent calculus , which is the most studied formalism of structural proof theory. Many other proof calculi were, or might have been, seminal, but are not widely used today. Aristotle s syllogistic calculus, presented in the Organon , readily admits formalisation. There is still some modern interest in syllogistic, carried out under the aegis of term logic . Gottlob Frege s two dimensional notation of the Begriffsschrift is usually regarded as introducing ... proposed calculi with deep inference , for instance display logic , hypersequents , the calculus ... more details
Utilitarianism Wiktionary The felicific calculus is an algorithm formulated by utilitarianism utilitarian philosopher Jeremy Bentham for calculating the degree or amount of pleasure that a specific action is likely to cause. Bentham, an ethics ethical hedonist , believed the moral rightness or wrongness of an action to be a function of the amount of pleasure or pain that it produced. The felicific calculus could, in principle at least, determine the moral status of any considered act. The algorithm is also known as the utility calculus , the hedonistic calculus and the hedonic calculus . Variable math Variable s, or vector space vector s, of the pleasures and pains included in this calculation, which Bentham called elements or dimensions , were Clarify date March 2008 Intensity Do NOT link this to Intensity How strong is the pleasure? Time Duration How long will the pleasure last? Certainty or uncertainty How likely or unlikely is it that the pleasure will occur? Propinquity or remoteness How soon will the pleasure occur? Fecundity The probability that the action will be followed by sensations of the same kind. wiktionary Purity Purity The probability that it will not be followed by sensations of the opposite kind. wikt extent Extent How many people will be affected? Bentham s instructions Begin with any one person of those whose interests seem most immediately to be affected by it and take an account, Of the value of each distinguishable pleasure which appears to be produced by it in the first instance. Of the value of each pain which appears to be produced by it in the first ... calculus may be termed hedons and dolors . ref http ethics.sandiego.edu Glossary.html San Diego ... to the utilitarian posends and negends. See also Ethical calculus Science of morality References reflist DEFAULTSORT Felicific Calculus Category Utilitarianism Category Hedonism Category Pleasure de Hedonistisches Kalk l es Felicific calculus pl Felicific calculus ... more details
Operational calculus , also known as operational analysis , is a technique by which problems in analysis , in particular differential equation s, are transformed into algebraic problems, usually the problem of solving a polynomial equation . History The idea of representing the processes of calculus, derivation and integration, as operators has a long history that goes back to Gottfried Leibniz . The mathematician Louis Fran ois Antoine Arbogast was one of the first to manipulate these symbols independently of the function to which they were applied. This approach was further developed by Servois ... by mathematicians. Operational calculus first found applications in electrical engineering problems ... operational calculus with Laplace transform ation methods see the books by Jeffreys, by Carslaw or by MacLachlan ... transform ation as done by Norbert Wiener . A different approach to operational calculus was developed ... element of the operational calculus is to consider differentiation as an Operator mathematics ... example of application of the operational calculus is to solve math py H t math , which gives math ... of math p math , thus establishing a connection between operational calculus and fractional calculus ... calculus is also applicable to finite difference equation s and to electrical engineering problems ... books?id f1ADAAAAQAAJ&dq Carmichael&as brr 1 A treatise on the calculus of operations Longman ... test.cgi?barcode 3371 Electric Circuit Theory and the Operational Calculus Mc Graw Hill, 1926 ... allmetainfor test.cgi?barcode 3371 Heaviside s Operational Calculus McGrawHill, 1929 . V Bush ... 42240 Modern operational calculus Macmillan, 1941 . HS Carslaw http www.new.dli.ernet.in cgi bin ... Press, 1941 . B van der Pol, H Bremmer Operational calculus Cambridge University Press, 1950 RV Churchill Operational Mathematics McGraw Hill, 1958 . J Mikusinski Operational Calculus Elsevier ... 2007 12 07 heavisides operator calculus Heaviside s Operator Calculus Category Calculus Category Mathematical ... more details
primarysources date May 2008 Calculus of predispositions is a basic part of predispositioning theory and belongs to the indeterministic procedures. Introduction The key component of any indeterministic procedure is the evaluation of a position. Since it is impossible to devise a deterministic chain linking the inter mediate state with the outcome of the game, the most complex component of any indeterministic method is assessing these intermediate stages. It is precisely the function of predispositions to assess the impact of an intermediate state upon the future course of development. ref Katsenelinboigen, Aron. The Concept of Indeterminism and Its Applications Economics, Social Systems, Ethics, Artificial Intelligence, and Aesthetics Praeger Westport, Connecticut, 1997, p.33 ref According to Aron Katsenelinboigen , calculus of predispositions is another method of computing probability . Both methods may lead to the same results and, thus, can be interchangeable. However, it is not always possible to interchange them since computing via frequencies requires availability of statistics, possibility to gather the data as well as having the knowledge of the extent to which one can interlink the system s constituent elements. Also, no statistics can be obtained on unique events and, naturally, in such cases the calculus of predispositions becomes the only option. The procedure of calculating predispositions is linked to two steps dissection of the system on its constituent elements and integration of the analyzed parts in a new whole. According to Katsenelinboigen, the system is structured ... the skeleton of the system. Relationships between them form positional parameters. The calculus ... of a position we need new techniques, which I have grouped under the heading of calculus of predispositions. This calculus is based on a weight function, which represents a variation on the well ... to the Calculus of Predispositions , Proceedings 5th IEEE International Symposium on Intelligent ... more details
Infobox website name Electoral Calculus logo logocaption screenshot collapsible collapsetext caption url URL electoralcalculus.co.uk slogan commercial No type registration No language English content license owner Martin Baxter author launch date alexa revenue current status Online footnotes Electoral Calculus is a psephological web site which attempts to predict future United Kingdom general election results. It was developed by Martin Baxter and employs scientific techniques on data about Britain s electoral geography. ref name intute cite web url http www.intute.ac.uk cgi bin fullrecord.pl?handle 20100408 11403823 title Electoral Calculus publisher Intute accessdate 17 October 2011 quote An independent UK election prediction site maintained by Martin Baxter. He attempts to apply scientific techniques to the electoral geography of Britain to predict the future general election results. ref It has been cited by journalists Andrew Rawnsley and Michael White journalist Michael White in The Guardian , with reference to the 2010 United Kingdom general election . ref name guardian doubly hung cite news url http www.guardian.co.uk commentisfree 2009 nov 22 andrew rawnsley general election hung parliament title Why it s very likely the next parliament will be doubly hung work The Guardian date 22 November 2009 accessdate 17 October 2011 last Rawnsley first Andrew authorlink Andrew Rawnsley location London quote The different formulas used by Electoral Calculus and Swingo both translate a six point Tory poll lead into a Commons in which the Conservatives are short of a majority. ref ref name guardian too late for labour cite news url http www.guardian.co.uk politics blog 2010 apr ... measure about 1 to 1.5 up on 2005 source Electoral Calculus ? ref Main features The site ... newmodel.html title Transition Model publisher Electoral Calculus date 8 July 2004 ... Model publisher Electoral Calculus date 28 October 2007 accessdate 17 October 2011 last Baxter first ... more details
In general relativity , Regge calculus is a formalism for producing Simplicial manifold simplicial approximations of spacetimes that are solutions to the Einstein field equation . The calculus was introduced by the Italian theoretician Tullio Regge in the early 1960s. The starting point for Regge s work is the fact that every Lorentzian manifold admits a Triangulation geometry triangulation into simplices . Furthermore, the spacetime curvature can be expressed in terms of Defect geometry deficit angles associated with 2 faces where arrangements of 4 simplices meet. These 2 faces play the same role as the vertex geometry vertices where arrangements of triangles meet in a triangulation of a 2 manifold , which is easier to visualize. Here a vertex with a positive angular deficit represents a concentration of positive Gaussian curvature , whereas a vertex with a negative angular deficit represents a concentration of negative Gaussian curvature . The deficit angles can be computed directly from the various edge geometry edge lengths in the triangulation, which is equivalent to saying that the Riemann curvature tensor can be computed from the metric tensor of a Lorentzian manifold. Regge showed that the vacuum field equations can be reformulated as a restriction on these deficit angles ... Regge calculus has motivated the construction of further generalizations of this idea. In particular, Regge calculus has been adapted to study quantum gravity . See also Causal dynamical triangulation Mathematics of general relativity Ricci calculus References cite journal author Adrian P. Gentle title Regge calculus a unique tool for numerical relativity journal Gen. Rel. Grav. year 2002 volume ... . See section 3 . cite journal author Ruth M. Williams, Philip A. Tuckey title Regge calculus ... author J. W. Barrett title The geometry of classical Regge calculus journal Class. Quant. Grav ... physics ReggeCalculus.html Regge calculus on ScienceWorld Category Mathematical methods in general ... more details
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