Log in

Relevant bibliographies by topics / Polynomial calculus / Journal articles

To see the other types of publications on this topic, follow the link: Polynomial calculus.

Journal articles on the topic 'Polynomial calculus'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Polynomial calculus.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Bulmer, M., D. Fearnley-Sander, and T. Stokes. "Towards a calculus of algorithms." Bulletin of the Australian Mathematical Society 50, no. 1 (August 1994): 81–89. http://dx.doi.org/10.1017/s000497270000959x.

Full text

Abstract:

We develop a generalised polynomial formalism which captures the concept of an algebra of piece-wise denned polynomials. The formalism is based on the Boolean power construction of universal algebra. A generalisation of the theory of substitution homomorphisms is developed. The abstract operation of composition of generalised polynomials in one variable is denned and shown to correspond to function composition.

APA, Harvard, Vancouver, ISO, and other styles

2

FUKUHARA, SHINJI, YUKIO MATSUMOTO, and NORIKO YUI. "NON-COMMUTATIVE POLYNOMIAL RECIPROCITY FORMULAE." International Journal of Mathematics 12, no. 08 (November 2001): 973–86. http://dx.doi.org/10.1142/s0129167x01001088.

Full text

Abstract:

We prove non-commutative reciprocity formulae for certain polynomials using Fox's free differential calculus. The abelianizations of these reciprocity formulae rediscover the polynomial reciprocity formulae of Carlitz and Berndt–Dieter. Further, many other reciprocity formulae related to Dedekind sums are rederived from our polynomial reciprocity formulae; these include, for instance, generalizations of the classical Eisenstein reciprocity formula.

APA, Harvard, Vancouver, ISO, and other styles

3

Songhafouo Tsopméné, Paul Arnaud, and Donald Stanley. "Polynomial functors in manifold calculus." Topology and its Applications 248 (October 2018): 75–116. http://dx.doi.org/10.1016/j.topol.2018.08.012.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Filmus, Yuval, Massimo Lauria, Jakob Nordström, Noga Ron-Zewi, and Neil Thapen. "Space Complexity in Polynomial Calculus." SIAM Journal on Computing 44, no. 4 (January 2015): 1119–53. http://dx.doi.org/10.1137/120895950.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Buresh-Oppenheim, Joshua, Matthew Clegg, Russell Impagliazzo, and Toniann Pitassi. "Homogenization and the polynomial calculus." Computational Complexity 11, no. 3-4 (June 1, 2002): 91–108. http://dx.doi.org/10.1007/s00037-002-0171-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Stick, Marvin E. "Maclaurin Taylor Series for Transcendental Functions: A Graphing-Calculator View of Convergence." Mathematics Teacher 92, no. 9 (December 1999): 833–37. http://dx.doi.org/10.5951/mt.92.9.0833.

Full text

Abstract:

Most calculus students can perform the manipulation necessary for a polynomial approximation of a transcendental function. However, many do not understand the underlying concept. Graphing-calculator technology can be used to bridge this gap between the concept of an interval of convergence for a series and polynomial approximations. Calculus-reform textbooks usually treat this topic by displaying lower-order Maclaurin series approximations to selected transcendental functions to encourage discussions of intervals of convergence. Some textbooks display lower-order Taylor polynomials for ln x expanded about x = 1. This article presents a way to examine the topic in more depth.

APA, Harvard, Vancouver, ISO, and other styles

7

Gatto, Letterio, and Taíse Santiago. "Schubert Calculus on a Grassmann Algebra." Canadian Mathematical Bulletin 52, no. 2 (June 1, 2009): 200–212. http://dx.doi.org/10.4153/cmb-2009-023-x.

Full text

Abstract:

AbstractThe (classical, small quantum, equivariant) cohomology ring of the grassmannian G(k, n) is generated by certain derivations operating on an exterior algebra of a free module of rank n (Schubert calculus on a Grassmann algebra). Our main result gives, in a unified way, a presentation of all such cohomology rings in terms of generators and relations. Using results of Laksov and Thorup, it also provides a presentation of the universal factorization algebra of a monic polynomial of degree n into the product of two monic polynomials, one of degree k.

APA, Harvard, Vancouver, ISO, and other styles

8

Pavlyuk, A. M. "HOMFLY Polynomial Invariants of Torus Knots and Bosonic (q, p)-Calculus." Ukrainian Journal of Physics 58, no. 12 (December 2013): 1178–81. http://dx.doi.org/10.15407/ujpe58.12.1178.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Grant, Melva R., William Crombie, Mary Enderson, and Nell Cobb. "Polynomial calculus: rethinking the role of calculus in high schools." International Journal of Mathematical Education in Science and Technology 47, no. 6 (January 12, 2016): 823–36. http://dx.doi.org/10.1080/0020739x.2015.1133851.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Galesi, Nicola, and Massimo Lauria. "On the Automatizability of Polynomial Calculus." Theory of Computing Systems 47, no. 2 (February 14, 2009): 491–506. http://dx.doi.org/10.1007/s00224-009-9195-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Razborov, A. A. "Lower bounds for the polynomial calculus." Computational Complexity 7, no. 4 (December 2, 1998): 291–324. http://dx.doi.org/10.1007/s000370050013.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Costabile, Francesco Aldo, Maria Italia Gualtieri, and Anna Napoli. "General Bivariate Appell Polynomials via Matrix Calculus and Related Interpolation Hints." Mathematics 9, no. 9 (April 25, 2021): 964. http://dx.doi.org/10.3390/math9090964.

Full text

Abstract:

An approach to general bivariate Appell polynomials based on matrix calculus is proposed. Known and new basic results are given, such as recurrence relations, determinant forms, differential equations and other properties. Some applications to linear functional and linear interpolation are sketched. New and known examples of bivariate Appell polynomial sequences are given.

APA, Harvard, Vancouver, ISO, and other styles

13

AGUDELO, JUAN C., and WALTER CARNIELLI. "POLYNOMIAL RING CALCULUS FOR MODAL LOGICS: A NEW SEMANTICS AND PROOF METHOD FOR MODALITIES." Review of Symbolic Logic 4, no. 1 (September 14, 2010): 150–70. http://dx.doi.org/10.1017/s1755020310000213.

Full text

Abstract:

A new (sound and complete) proof style adequate for modal logics is defined from the polynomial ring calculus (PRC). The new semantics not only expresses truth conditions of modal formulas by means of polynomials, but also permits to perform deductions through polynomial handling. This paper also investigates relationships among the PRC here defined, the algebraic semantics for modal logics, equational logics, the Dijkstra–Scholten equational-proof style, and rewriting systems. The method proposed is throughly exemplified for S5, and can be easily extended to other modal logics.

APA, Harvard, Vancouver, ISO, and other styles

14

Mahto, Sanjay Kumar, Atanu Manna, and P. D. Srivastava. "Bigeometric Cesàro difference sequence spaces and Hermite interpolation." Asian-European Journal of Mathematics 13, no. 04 (April 4, 2019): 2050084. http://dx.doi.org/10.1142/s1793557120500849.

Full text

Abstract:

In this paper, we introduce some difference sequence spaces in bigeometric calculus. We determine the [Formula: see text]-duals of these sequence spaces and study their matrix transformations. We also develop an interpolating polynomial in bigeometric calculus which is analogous to the classical Hermite interpolating polynomial.

APA, Harvard, Vancouver, ISO, and other styles

15

Friesen, Charles D. "Microcomputer-Assisted Mathematics: Using the Microcomputer to Find the Zeros of a Polynomial Function." Mathematics Teacher 79, no. 7 (October 1986): 554–58. http://dx.doi.org/10.5951/mt.79.7.0554.

Full text

Abstract:

Mathematics teachers are finding more and more opportunities to use the microcomputer as a tool in their classes. The synthetic-division program listed in the Appendix has been used in advanced algebra, analysis, and calculus classes. This program can be used in a variety of settings. This article will deal with its use in searching for the zeros of polynomial functions. The program can also be used to evaluate polynomials, obtain quotients, and search for the upper and lower bounds of the zeros of a polynomial.

APA, Harvard, Vancouver, ISO, and other styles

16

Li, Hai-Xia, Sarfaraz Ahmad, and Iftikhar Ahmad. "Topology-Based Analysis of OTIS (Swapped) Networks OKn and OPn." Journal of Chemistry 2019 (November 7, 2019): 1–11. http://dx.doi.org/10.1155/2019/4291943.

Full text

Abstract:

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In this paper, M-polynomial OKn and OPn networks are computed. The M-polynomial is rich in information about degree-based topological indices. By applying the basic rules of calculus on M-polynomials, the first and second Zagreb indices, modified second Zagreb index, general Randić index, inverse Randić index, symmetric division index, harmonic index, inverse sum index, and augmented Zagreb index are recovered.

APA, Harvard, Vancouver, ISO, and other styles

17

Taylor, Ronald D., and Ryan Hansen. "Optimization of Cubic Polynomial Functions without Calculus." Mathematics Teacher 101, no. 6 (February 2008): 408–11. http://dx.doi.org/10.5951/mt.101.6.0408.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Gordon, Sheldon P. "INTRODUCING TAYLOR POLYNOMIAL APPROXIMATIONS IN INTRODUCTORY CALCULUS." PRIMUS 1, no. 3 (January 1991): 305–13. http://dx.doi.org/10.1080/10511979108965623.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Feinsilver, P., and R. Schott. "Operator calculus approach to orthogonal polynomial expansions." Journal of Computational and Applied Mathematics 66, no. 1-2 (January 1996): 185–99. http://dx.doi.org/10.1016/0377-0427(95)00161-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Chaurasia, V. B. L., and Vinod Gill. "New fractional calculus results involving Srivastava’s general class of multivariable polynomials and The H̅ - function." Journal of Applied Mathematics, Statistics and Informatics 11, no. 1 (May 1, 2015): 19–32. http://dx.doi.org/10.1515/jamsi-2015-0002.

Full text

Abstract:

Abstract A significantly large number of earlier works on the subjects of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis. In the present paper, we study and develop an important result involving a fractional differential operator for the product of general multivariable polynomials, general polynomial set and two -functions. The result discussed here can be used to investigate a wide class of new and known results, hitherto scattered in the literature. For the sake of illustration, six interesting special case have also been recorded here of our main findings.

APA, Harvard, Vancouver, ISO, and other styles

21

Alekhnovich, Michael, Sam Buss, Shlomo Moran, and Toniann Pitassi. "Minimum propositional proof length is NP-hard to linearly approximate." Journal of Symbolic Logic 66, no. 1 (March 2001): 171–91. http://dx.doi.org/10.2307/2694916.

Full text

Abstract:

AbstractWe prove that the problem of determining the minimum propositional proof length is NP-hard to approximate within a factor of . These results are very robust in that they hold for almost all natural proof systems, including: Frege systems, extended Frege systems, resolution. Horn resolution, the polynomial calculus, the sequent calculus, the cut-free sequent calculus, as well as the polynomial calculus. Our hardness of approximation results usually apply to proof length measured either by number of symbols or by number of inferences, for tree-like or dag-like proofs. We introduce the Monotone Minimum (Circuit) Satisfying Assignment problem and reduce it to the problems of approximation of the length of proofs.

APA, Harvard, Vancouver, ISO, and other styles

22

Adams, Caleb L. "Introducing Roots and Extrema in Calculus." Mathematics Teacher 112, no. 2 (October 2018): 132–35. http://dx.doi.org/10.5951/mathteacher.112.2.0132.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Yokoyama, Kazuhiro, Masaya Yasuda, Yasushi Takahashi, and Jun Kogure. "Complexity bounds on Semaev’s naive index calculus method for ECDLP." Journal of Mathematical Cryptology 14, no. 1 (October 30, 2020): 460–85. http://dx.doi.org/10.1515/jmc-2019-0029.

Full text

Abstract:

AbstractSince Semaev introduced summation polynomials in 2004, a number of studies have been devoted to improving the index calculus method for solving the elliptic curve discrete logarithm problem (ECDLP) with better complexity than generic methods such as Pollard’s rho method and the baby-step and giant-step method (BSGS). In this paper, we provide a deep analysis of Gröbner basis computation for solving polynomial systems appearing in the point decomposition problem (PDP) in Semaev’s naive index calculus method. Our analysis relies on linear algebra under simple statistical assumptions on summation polynomials. We show that the ideal derived from PDP has a special structure and Gröbner basis computation for the ideal is regarded as an extension of the extended Euclidean algorithm. This enables us to obtain a lower bound on the cost of Gröbner basis computation. With the lower bound, we prove that the naive index calculus method cannot be more efficient than generic methods.

APA, Harvard, Vancouver, ISO, and other styles

24

PAVLOVIĆ, DUšKO. "Categorical logic of names and abstraction in action calculi." Mathematical Structures in Computer Science 7, no. 6 (December 1997): 619–37. http://dx.doi.org/10.1017/s0960129597002296.

Full text

Abstract:

Milner's action calculus implements abstraction in monoidal categories, so that familiar λ-calculi can be subsumed together with the π-calculus and the Petri nets. Variables are generalised to names, which allow only a restricted form of substitution.In the present paper, the well-known categorical semantics of the λ-calculus is generalised to the action calculus. A suitable functional completeness theorem for symmetric monoidal categories is proved: we determine the conditions under which the abstraction is definable. Algebraically, the distinction between the variables and the names boils down to the distinction between the transcendental and the algebraic elements. The former lead to polynomial extensions, like, for example, the ring ℤ[x]; the latter lead to algebraic extensions like ℤ[√2] or ℤ[i].Building upon the work of P. Gardner, we introduce action categories, and show that they are related to the static action calculus in exactly the same way as cartesian closed categories are related to the λ-calculus. Natural examples of this structure arise from allegories and cartesian bicategories. On the other hand, the free algebras for any commutative Moggi monad form an action category. The general correspondence of action calculi and Moggi monads will be worked out in a sequel to this work.

APA, Harvard, Vancouver, ISO, and other styles

25

Voevoda, Aleksander, and Victor Shipagin. "Example of polynomial controller synthesis for a non-square object with one input and two outputs." Transaction of Scientific Papers of the Novosibirsk State Technical University, no. 4 (December 18, 2020): 7–20. http://dx.doi.org/10.17212/2307-6879-2020-4-7-20.

Full text

Abstract:

Polynomial methods for synthesizing controllers for automatic control systems with linear objects are becoming increasingly common. The synthesis of multichannel controllers is particularly difficult, which is caused by the need to use matrix polynomial calculus. However, this approach mainly considers objects with the number of inputs equal to the number of outputs. This is due to the convenience of solving a system of linear algebraic equations in matrix polynomial calculus. In this paper, we consider a polynomial method for synthesizing regulators for a non-square object, that is, one whose number of inputs is not equal to the number of outputs. The selected system contains not only a non-square object, but also a non-square controller.

APA, Harvard, Vancouver, ISO, and other styles

26

Rabin, Jeffrey M. "Tangent Lines without Calculus." Mathematics Teacher 101, no. 7 (March 2008): 499–503. http://dx.doi.org/10.5951/mt.101.7.0499.

Full text

Abstract:

A problem that can help high school students develop the concept of instantaneous velocity and connect it with the slope of a tangent line to the graph of position versus time. It also gives a method for determining the tangent line to the graph of a polynomial function at any point without using calculus. It encourages problem solving and multiple solutions.

APA, Harvard, Vancouver, ISO, and other styles

27

Singh, Dharmendra Kumar, and Priyanka Umaro. "Fractional Calculus of Wright Function with Raizada Polynomial." Progress in Fractional Differentiation and Applications 4, no. 3 (July 1, 2018): 229–46. http://dx.doi.org/10.18576/pfda/040307.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Galesi, Nicola, and Massimo Lauria. "Optimality of size-degree tradeoffs for polynomial calculus." ACM Transactions on Computational Logic 12, no. 1 (October 2010): 1–22. http://dx.doi.org/10.1145/1838552.1838556.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Wiseman, Gus. "Set maps, umbral calculus, and the chromatic polynomial." Discrete Mathematics 308, no. 16 (August 2008): 3551–64. http://dx.doi.org/10.1016/j.disc.2007.07.009.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Ben-Sasson, Eli, and Russell Impagliazzo. "Random Cnf’s are Hard for the Polynomial Calculus." computational complexity 19, no. 4 (August 11, 2010): 501–19. http://dx.doi.org/10.1007/s00037-010-0293-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Bataineh, Ahmad. "Bernstein polynomials method and it’s error analysis for solving nonlinear problems in the calculus of variations: Convergence analysis via residual function." Filomat 32, no. 4 (2018): 1379–93. http://dx.doi.org/10.2298/fil1804379b.

Full text

Abstract:

In this paper, Bernstein polynomials method (BPM) and their operational matrices are adopted to obtain approximate analytical solutions of variational problems. The operational matrix of differentiation is introduced and utilized to reduce the calculus of variations problems to the solution of system of algebraic equations. The solutions are obtained in the form of rapidly convergent finite series with easily computable terms. Comparison between the present method and the homotopy perturbation method (HPM), the non-polynomial spline method and the B-spline collocation method are made to show the effectiveness and efficiency for obtaining approximate solutions of the calculus of variations problems. Moreover, convergence analysis based on residual function is investigated to verified the numerical results.

APA, Harvard, Vancouver, ISO, and other styles

32

Zawada, Robert. "Turning Points." Mathematics Teacher 108, no. 2 (September 2014): 152–55. http://dx.doi.org/10.5951/mathteacher.108.2.0152.

Full text

Abstract:

Traditionally in calculus, the maximum number of turning points in the graph of a onevariable polynomial function is presented as (n − 1), where n is the degree of the polynomial. However, by using Descartes' rule of signs and certain properties of polynomial functions, we can establish a better estimate than the (n − 1) rule provides.

APA, Harvard, Vancouver, ISO, and other styles

33

Bate, Andrew, Boris Motik, Bernardo Cuenca Grau, David Tena Cucala, František Simančík, and Ian Horrocks. "Consequence-Based Reasoning for Description Logics with Disjunctions and Number Restrictions." Journal of Artificial Intelligence Research 63 (November 29, 2018): 625–90. http://dx.doi.org/10.1613/jair.1.11257.

Full text

Abstract:

Classification of description logic (DL) ontologies is a key computational problem in modern data management applications, so considerable effort has been devoted to the development and optimisation of practical reasoning calculi. Consequence-based calculi combine ideas from hypertableau and resolution in a way that has proved very effective in practice. However, existing consequence-based calculi can handle either Horn DLs (which do not support disjunction) or DLs without number restrictions. In this paper, we overcome this important limitation and present the first consequence-based calculus for deciding concept subsumption in the DL ALCHIQ+. Our calculus runs in exponential time assuming unary coding of numbers, and on ELH ontologies it runs in polynomial time. The extension to disjunctions and number restrictions is technically involved: we capture the relevant consequences using first-order clauses, and our inference rules adapt paramodulation techniques from first-order theorem proving. By using a well-known preprocessing step, the calculus can also decide concept subsumptions in SRIQ---a rich DL that covers all features of OWL 2 DL apart from nominals and datatypes. We have implemented our calculus in a new reasoner called Sequoia. We present the architecture of our reasoner and discuss several novel and important implementation techniques such as clause indexing and redundancy elimination. Finally, we present the results of an extensive performance evaluation, which revealed Sequoia to be competitive with existing reasoners. Thus, the calculus and the techniques we present in this paper provide an important addition to the repertoire of practical implementation techniques for description logic reasoning.

APA, Harvard, Vancouver, ISO, and other styles

34

Filmus, Yuval. "Another look at degree lower bounds for polynomial calculus." Theoretical Computer Science 796 (December 2019): 286–93. http://dx.doi.org/10.1016/j.tcs.2019.09.023.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Goldblatt, Robert. "A Calculus of Terms for Coalgebras of Polynomial Functors." Electronic Notes in Theoretical Computer Science 44, no. 1 (May 2001): 161–84. http://dx.doi.org/10.1016/s1571-0661(04)80907-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Carnielli, Walter, and Mariana Matulovic. "The method of polynomial ring calculus and its potentialities." Theoretical Computer Science 606 (November 2015): 42–56. http://dx.doi.org/10.1016/j.tcs.2015.05.015.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Miyakoda, Tsuyako. "Discretized Fractional Calculus with a Series of Chebyshev Polynomial." Electronic Notes in Theoretical Computer Science 225 (January 2009): 239–44. http://dx.doi.org/10.1016/j.entcs.2008.12.077.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Terui, Kazushige. "Light affine lambda calculus and polynomial time strong normalization." Archive for Mathematical Logic 46, no. 3-4 (February 21, 2007): 253–80. http://dx.doi.org/10.1007/s00153-007-0042-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Baillot, Patrick, and Kazushige Terui. "Light types for polynomial time computation in lambda calculus." Information and Computation 207, no. 1 (January 2009): 41–62. http://dx.doi.org/10.1016/j.ic.2008.08.005.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Lambek, J. "Least fixpoints of endofunctors of cartesian closed categories." Mathematical Structures in Computer Science 3, no. 2 (June 1993): 229–57. http://dx.doi.org/10.1017/s0960129500000190.

Full text

Abstract:

Least fixpoints are constructed for finite coproducts of definable endofunctors of Cartesian closed categories that have weak polynomial products and joint equalizers of arbitrary families of pairs of parallel arrows. Both conditions hold in PER, the category whose objects are partial equivalence relations on N, and whose arrows are partial recursive functions. Weak polynomial products exist in any cartesian closed category with a finite number of objects as well as in any model of second order polymorphic lambda calculus: that is, in the proof theory of any second order positive intuitionistic propositional calculus, but such a category need not have equalizers. However, any finite coproduct of definable endofunctors of a cartesian closed category with weak polynomial products will have a least fixpoint in a larger category with equalizers whose objects are right ideals (or sieves) of modulo certain congruence relations, and whose arrows are induced from .

APA, Harvard, Vancouver, ISO, and other styles

41

Perron, Steven. "Examining Fragments of the Quantified Propositional Calculus." Journal of Symbolic Logic 73, no. 3 (September 2008): 1051–80. http://dx.doi.org/10.2178/jsl/1230396765.

Full text

Abstract:

AbstractWhen restricted to proving formulas, the quantified propositional proof system is closely related to the theorems of Buss's theory . Namely, has polynomial-size proofs of the translations of theorems of , and proves that is sound. However, little is known about when proving more complex formulas. In this paper, we prove a witnessing theorem for similar in style to the KPT witnessing theorem for . This witnessing theorem is then used to show that proves is sound with respect to formulas. Note that unless the polynomial-time hierarchy collapses is the weakest theory in the S2 hierarchy for which this is true. The witnessing theorem is also used to show that is p-equivalent to a quantified version of extended-Frege for prenex formulas. This is followed by a proof that Gi, p-simulates with respect to all quantified propositional formulas. We finish by proving that S2 can be axiomatized by plus axioms stating that the cut-free version of is sound. All together this shows that the connection between and does not extend to more complex formulas.

APA, Harvard, Vancouver, ISO, and other styles

42

CARPENTIER, RUI PEDRO. "FROM PLANAR GRAPHS TO EMBEDDED GRAPHS - A NEW APPROACH TO KAUFFMAN AND VOGEL'S POLYNOMIAL." Journal of Knot Theory and Its Ramifications 09, no. 08 (December 2000): 975–86. http://dx.doi.org/10.1142/s0218216500000578.

Full text

Abstract:

In [4] Kauffman and Vogel constructed a rigid vertex regular isotopy invariant for unoriented four-valent graphs embedded in three dimensional space. It assigns to each embedded graph G a polynomial, denoted [G], in three variables, A, B and a, satisfying the skein relations: [Formula: see text] and is defined in terms of a state-sum and the Dubrovnik polynomial for links. Using the graphical calculus of [4] it is shown that the polynomial of a planar graph can be calculated recursively from that of planar graphs with less vertices, which also allows the polynomial of an embedded graph to be calculated without resorting to links. The same approach is used to give a direct proof of uniqueness of the (normalized) polynomial restricted to planar graphs. In the case B=A-1 and a=A, it is proved that for a planar graph G we have [G]=2c-1(-A-A-1)v, where c is the number of connected components of G and v is the number of vertices of G. As a corollary, a necessary, but not sufficient, condition is obtained for an embedded graph to be ambient isotopic to a planar graph. In an appendix it is shown that, given a polynomial for planar graphs satisfying the graphical calculus, and imposing the first skein relation above, the polynomial extends to a rigid vertex regular isotopy invariant for embedded graphs, satisfying the remaining skein relations. Thus, when existence of the planar polynomial is guaranteed, this provides a direct way, not depending on results for the Dubrovnik polynomial, to show consistency of the polynomial for embedded graphs.

APA, Harvard, Vancouver, ISO, and other styles

43

Zhukovsky, K. "Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators." Scientific World Journal 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/454865.

Full text

Abstract:

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

APA, Harvard, Vancouver, ISO, and other styles

44

Hamadou, Sardaouna, and John Mullins. "Calibrating the power of schedulers for probabilistic polynomial-time calculus." Journal of Computer Security 18, no. 2 (March 22, 2010): 265–316. http://dx.doi.org/10.3233/jcs-2010-0362.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Wailly, Olivier, Nicolas Héraud, and Eric Jean Roy Sambatra. "Evaluating sensor placement on extended system with polynomial symbolic calculus." IFAC Proceedings Volumes 46, no. 9 (2013): 1518–23. http://dx.doi.org/10.3182/20130619-3-ru-3018.00276.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Mitchell, J., A. Ramanathan, A. Scedrov, and V. Teague. "A Probabilistic Polynomial-time Calculus For Analysis of Cryptographic Protocols." Electronic Notes in Theoretical Computer Science 45 (November 2001): 280–310. http://dx.doi.org/10.1016/s1571-0661(04)80968-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Zhang, Qi, and Huaizhong Zhao. "SPDEs with polynomial growth coefficients and the Malliavin calculus method." Stochastic Processes and their Applications 123, no. 6 (June 2013): 2228–71. http://dx.doi.org/10.1016/j.spa.2013.02.004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Koeller, R. C. "Polynomial operators, stieltjes convolution, and fractional calculus in hereditary mechanics." Acta Mechanica 58, no. 3-4 (April 1986): 251–64. http://dx.doi.org/10.1007/bf01176603.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Baillot, Patrick, Erika De Benedetti, and Simona Ronchi Della Rocca. "Characterizing polynomial and exponential complexity classes in elementary lambda-calculus." Information and Computation 261 (August 2018): 55–77. http://dx.doi.org/10.1016/j.ic.2018.05.005.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

MATSUMOTO, SHO. "WEINGARTEN CALCULUS FOR MATRIX ENSEMBLES ASSOCIATED WITH COMPACT SYMMETRIC SPACES." Random Matrices: Theory and Applications 02, no. 02 (April 2013): 1350001. http://dx.doi.org/10.1142/s2010326313500019.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!