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Journal articles on the topic '080200 Computation Theory and Mathematics'

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Published: 10 December 2022

Last updated: 29 January 2023

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1

Simos, T. E. "On the Explicit Four-Step Methods with Vanished Phase-Lag and its First Derivative." Applied Mathematics & Information Sciences 8, no. 2 (March 1, 2014): 447–58. http://dx.doi.org/10.12785/amis/080201.

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2

Srdjevic, Bojan, Zorica Srdjevic, and Bosko Blagojevic. "First-Level Transitivity Rule Method for Filling in Incomplete Pair-Wise Comparison Matrices in the Analytic Hierarchy Process." Applied Mathematics & Information Sciences 8, no. 2 (March 1, 2014): 459–67. http://dx.doi.org/10.12785/amis/080202.

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3

Razborova, Polina, Bouthina Ahmed, and Anjan Biswas. "Solitons, Shock Waves and Conservation Laws of Rosenau-KdV-RLW Equation with Power Law Nonlinearity." Applied Mathematics & Information Sciences 8, no. 2 (March 1, 2014): 485–91. http://dx.doi.org/10.12785/amis/080205.

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4

Doerr, Benjamin, and Thomas Jansen. "Theory of Evolutionary Computation." Algorithmica 59, no. 3 (November 9, 2010): 299–300. http://dx.doi.org/10.1007/s00453-010-9472-3.

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5

Levesley, Jeremy. "Functions of matrices: Theory and computation." Bulletin of the London Mathematical Society 41, no. 6 (December 2009): 1145–46. http://dx.doi.org/10.1112/blms/bdp112.

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6

Maley, Carlo C. "DNA Computation: Theory, Practice, and Prospects." Evolutionary Computation 6, no. 3 (September 1998): 201–29. http://dx.doi.org/10.1162/evco.1998.6.3.201.

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L. M. Adleman launched the field of DNA computing with a demonstration in 1994 that strands of DNA could be used to solve the Hamiltonian path problem for a simple graph. He also identified three broad categories of open questions for the field. First, is DNA capable of universal computation? Second, what kinds of algorithms can DNA implement? Third, can the error rates in the manipulations of the DNA be controlled enough to allow for useful computation? In the two years that have followed, theoretical work has shown that DNA is in fact capable of universal computation. Furthermore, algorithms for solving interesting questions, like breaking the Data Encryption Standard, have been described using currently available technology and methods. Finally, a few algorithms have been proposed to handle some of the apparently crippling error rates in a few of the common processes used to manipulate DNA. It is thus unlikely that DNA computation is doomed to be only a passing curiosity. However, much work remains to be done on the containment and correction of errors. It is far from clear if the problems in the error rates can be solved sufficiently to ever allow for general-purpose computation that will challenge the more popular substrates for computation. Unfortunately, biological demonstrations of the theoretical results have been sadly lacking. To date, only the simplest of computations have been carried out in DNA. To make significant progress, the field will require both the assessment of the practicality of the different manipulations of DNA and the implementation of algorithms for realistic problems. Theoreticians, in collaboration with experimentalists, can contribute to this research program by settling on a small set of practical and efficient models for DNA computation.

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7

Kaddoum, G., Anthony J. Lawrance, P. Chargé, and D. Roviras. "Chaos Communication Performance: Theory and Computation." Circuits, Systems, and Signal Processing 30, no. 1 (October 14, 2010): 185–208. http://dx.doi.org/10.1007/s00034-010-9217-1.

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8

Yamada, Shinichi. "A mathematical theory of randomized computation, I." Proceedings of the Japan Academy, Series A, Mathematical Sciences 64, no. 4 (1988): 115–18. http://dx.doi.org/10.3792/pjaa.64.115.

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9

Yamada, Shinichi. "A mathematical theory of randomized computation, II." Proceedings of the Japan Academy, Series A, Mathematical Sciences 64, no. 5 (1988): 155–58. http://dx.doi.org/10.3792/pjaa.64.155.

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10

Yamada, Shinichi. "A mathematical theory of randomized computation, III." Proceedings of the Japan Academy, Series A, Mathematical Sciences 64, no. 6 (1988): 201–4. http://dx.doi.org/10.3792/pjaa.64.201.

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11

Chen, Naiwu (N N. Chan), and Jiankeng (Li Kimhung) Li. "Theory and computation of restricted linear models." Acta Mathematicae Applicatae Sinica 4, no. 4 (November 1988): 378–86. http://dx.doi.org/10.1007/bf02007242.

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12

N., S. P., and Richard C. Aiken. "Stiff Computation." Mathematics of Computation 47, no. 176 (October 1986): 755. http://dx.doi.org/10.2307/2008193.

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13

Lauder, Alan G. B. "Deformation theory and the computation of zeta functions." Proceedings of the London Mathematical Society 88, no. 03 (April 14, 2004): 565–602. http://dx.doi.org/10.1112/s0024611503014461.

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14

Al-Khaled, Kamel. "Theory and computation in singular boundary value problems." Chaos, Solitons & Fractals 33, no. 2 (July 2007): 678–84. http://dx.doi.org/10.1016/j.chaos.2006.01.047.

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15

Cooper, S. Barry, Benedikt Lowe, and Peter van Emde Boas. "Theory of Computation at CiE 2005." Theory of Computing Systems 41, no. 1 (July 2007): 1–2. http://dx.doi.org/10.1007/s00224-006-4101-x.

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16

KONDRAT’EVA, M. V., A. B. LEVIN, A. V. MIKHALEV, and E. V. PANKRAT’EV. "COMPUTATION OF DIMENSION POLYNOMIALS." International Journal of Algebra and Computation 02, no. 02 (June 1992): 117–37. http://dx.doi.org/10.1142/s0218196792000098.

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The consideration of differential versions of Hilbert dimension polynomials is due to A. Einstein [1] and E. Kolchin [2] (one can find the coverage of the theory of differential dimension polynomials in [6]). In this paper we introduce the notion of a dimension polynomial of a subset of ℕm associated with arbitrary partition of the set {1,…, m} into disjoint nonempty subsets (m∈ℕ, ℕ denoting the set of all nonnegative integers). The theory of such polynomials is developed. The importance of our considerations is connected with the fact that the computation of differential and difference dimen sion polynomials may be reduced to the computation of some dimension polynomials of subsets of ℕm where m∈ℕ (see [3, p. 115], [5]). We also give some methods and algorithms for computation of dimension polynomials.

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17

Demanet, Laurent, and Gabriel Peyré. "Compressive Wave Computation." Foundations of Computational Mathematics 11, no. 3 (February 24, 2011): 257–303. http://dx.doi.org/10.1007/s10208-011-9085-5.

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18

Agler, Jim, John Harland, and Benjamin J. Raphael. "Classical function theory, operator dilation theory, and machine computation on multiply-connected domains." Memoirs of the American Mathematical Society 191, no. 892 (2008): 0. http://dx.doi.org/10.1090/memo/0892.

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19

Yoosefzadeh, H. R., Hamed R. Tareghian, and M. H. Farahi. "Tri-directional Scheduling Scheme: Theory and Computation." Journal of Mathematical Modelling and Algorithms 9, no. 4 (May 22, 2010): 357–73. http://dx.doi.org/10.1007/s10852-010-9132-2.

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20

Cintioli, P., and R. Silvestri. "Helping by unambiguous computation and probabilistic computation." Theory of Computing Systems 30, no. 2 (April 1997): 165–80. http://dx.doi.org/10.1007/bf02679447.

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21

Cintioli, P. "Helping by Unambiguous Computation and Probabilistic Computation." Theory of Computing Systems 30, no. 2 (March 1, 1997): 165–80. http://dx.doi.org/10.1007/s002240000048.

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22

Karp, Richard M. "George Dantzig’s impact on the theory of computation." Discrete Optimization 5, no. 2 (May 2008): 174–85. http://dx.doi.org/10.1016/j.disopt.2006.12.004.

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23

I., E., K. Bowers, and J. Lund. "Computation and Control." Mathematics of Computation 57, no. 195 (July 1991): 448. http://dx.doi.org/10.2307/2938691.

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24

Ruhe, Axel, M. G. Cox, and S. Hammarling. "Reliable Numerical Computation." Mathematics of Computation 59, no. 199 (July 1992): 298. http://dx.doi.org/10.2307/2152999.

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25

Labahn, George, and Richard Zippel. "Effective Polynomial Computation." Mathematics of Computation 64, no. 211 (July 1995): 1353. http://dx.doi.org/10.2307/2153509.

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26

Ransford, Thomas, and Jérémie Rostand. "Computation of capacity." Mathematics of Computation 76, no. 259 (January 24, 2007): 1499–521. http://dx.doi.org/10.1090/s0025-5718-07-01941-2.

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27

Baldoni, V., N. Berline, M. Köppe, and M. Vergne. "INTERMEDIATE SUMS ON POLYHEDRA: COMPUTATION AND REAL EHRHART THEORY." Mathematika 59, no. 1 (September 5, 2012): 1–22. http://dx.doi.org/10.1112/s0025579312000101.

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28

Green, Frederic. "Review of Mathematics and Computation by Avi Wigderson." ACM SIGACT News 52, no. 3 (October 17, 2021): 6–10. http://dx.doi.org/10.1145/3494656.3494659.

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Mathematics and computation are inextricably entangled3. We couldn't do one without the other. The need to calculate can be traced to early human history, and mathematics developed in large part to enable computation. And computation is necessary to propel mathematics. One often loses sight of the fact that the great mathematicians of the past were also prodigious computers: For example, Gauss, Kummer and the other great pioneers of number theory did vast amounts of computation to arrive at or reinforce many of their insights.

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29

Harsha, Prahladh, Yuval Ishai, Joe Kilian, Kobbi Nissim, and S. Venkatesh. "Communication vs. Computation." computational complexity 16, no. 1 (May 2007): 1–33. http://dx.doi.org/10.1007/s00037-007-0224-y.

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30

Lickteig, Thomas, and Marie-Françoise Roy. "Cauchy index computation." Calcolo 33, no. 3-4 (September 1996): 337–51. http://dx.doi.org/10.1007/bf02576008.

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31

Blaine, Larry. "Theory vs. Computation in Some Very Simple Dynamical Systems." College Mathematics Journal 22, no. 1 (January 1991): 42. http://dx.doi.org/10.2307/2686737.

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32

Liebling, Thomas M., Denis Naddef, and Laurence A. Wolsey. "Combinatorial Optimization: Theory and Computation The Aussois Workshop 2004." Mathematical Programming 105, no. 2-3 (November 10, 2005): 157–60. http://dx.doi.org/10.1007/s10107-005-0646-8.

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33

Bailey, David H., Jonathan M. Borwein, and Richard E. Crandall. "Computation and theory of extended Mordell-Tornheim-Witten sums." Mathematics of Computation 83, no. 288 (January 23, 2014): 1795–821. http://dx.doi.org/10.1090/s0025-5718-2014-02768-3.

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34

Vejdemo-Johansson, Mikael. "Blackbox computation of A ∞-algebras." gmj 17, no. 2 (June 2010): 391–404. http://dx.doi.org/10.1515/gmj.2010.005.

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Abstract Kadeishvili's proof of theminimality theorem [T. Kadeishvili, On the homology theory of fiber spaces, Russ. Math. Surv. 35:3 (1980), 231–238] induces an algorithm for the inductive computation of an A ∞-algebra structure on the homology of a dg-algebra. In this paper, we prove that for one class of dg-algebras, the resulting computation will generate a complete A ∞-algebra structure after a finite amount of computational work.

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35

Junde, Wu. "Special Issue “Quantum computation complexity theory and quantum network theory” (Preface)." International Journal of Theoretical Physics 60, no. 7 (June 2, 2021): 2345. http://dx.doi.org/10.1007/s10773-021-04846-5.

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36

Conceição, Ana C., and Jéssica C. Pires. "Symbolic Computation Applied to Cauchy Type Singular Integrals." Mathematical and Computational Applications 27, no. 1 (December 31, 2021): 3. http://dx.doi.org/10.3390/mca27010003.

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The development of operator theory is stimulated by the need to solve problems emerging from several fields in mathematics and physics. At the present time, this theory has wide applications in the study of non-linear differential equations, in linear transport theory, in the theory of diffraction of acoustic and electromagnetic waves, in the theory of scattering and of inverse scattering, among others. In our work, we use the computer algebra system Mathematica to implement, for the first time on a computer, analytical algorithms developed by us and others within operator theory. The main goal of this paper is to present new operator theory algorithms related to Cauchy type singular integrals, defined in the unit circle. The design of these algorithms was focused on the possibility of implementing on a computer all the extensive symbolic and numeric calculations present in the algorithms. Several nontrivial examples computed with the algorithms are presented. The corresponding source code of the algorithms has been made available as a supplement to the online edition of this article.

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37

Marcolli, Matilde, and John Napp. "Quantum Computation and Real Multiplication." Mathematics in Computer Science 9, no. 1 (April 24, 2014): 63–84. http://dx.doi.org/10.1007/s11786-014-0179-8.

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38

Eberbach, Eugene. "Toward a theory of evolutionary computation." Biosystems 82, no. 1 (October 2005): 1–19. http://dx.doi.org/10.1016/j.biosystems.2005.05.006.

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39

Xu, Ce. "Computation and theory of Euler sums of generalized hyperharmonic numbers." Comptes Rendus Mathematique 356, no. 3 (March 2018): 243–52. http://dx.doi.org/10.1016/j.crma.2018.01.004.

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40

W., L. B., and Seymour V. Parter. "Large Scale Scientific Computation." Mathematics of Computation 46, no. 174 (April 1986): 766. http://dx.doi.org/10.2307/2008019.

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41

O., F. W. J., and Jet Wimp. "Computation with Recurrence Relations." Mathematics of Computation 47, no. 175 (July 1986): 371. http://dx.doi.org/10.2307/2008104.

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42

Küçak, Huseyin. "Natural Minimal Surfaces: Via Theory and Computation With David Hoffman." SIAM Review 34, no. 4 (December 1992): 691–92. http://dx.doi.org/10.1137/1034152.

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43

Hauenstein, Jonathan D., Jose Israel Rodriguez, and Frank Sottile. "Numerical Computation of Galois Groups." Foundations of Computational Mathematics 18, no. 4 (June 14, 2017): 867–90. http://dx.doi.org/10.1007/s10208-017-9356-x.

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44

Harvey, David. "Efficient Computation of p-Adic Heights." LMS Journal of Computation and Mathematics 11 (2008): 40–59. http://dx.doi.org/10.1112/s1461157000000528.

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AbstractWe analyse and drastically improve the running time of the algorithm of Mazur, Stein and Tate for computing the canonical cyclotomic p-adic height of a point on an elliptic curve E/Q, where E has good ordinary reduction at p ≥ 5.

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45

Pikkarainen, Hanna K., and Josef Schicho. "A Bayesian Model for Root Computation." Mathematics in Computer Science 2, no. 4 (September 9, 2009): 567–86. http://dx.doi.org/10.1007/s11786-009-0071-0.

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46

Blažek, Jiří, and Pavel Pech. "Locus Computation in Dynamic Geometry Environment." Mathematics in Computer Science 13, no. 1-2 (July 3, 2018): 31–40. http://dx.doi.org/10.1007/s11786-018-0355-3.

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47

van Bommel, Raymond, David Holmes, and J. Steffen Müller. "Explicit arithmetic intersection theory and computation of Néron-Tate heights." Mathematics of Computation 89, no. 321 (May 17, 2019): 395–410. http://dx.doi.org/10.1090/mcom/3441.

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48

Hughes, D. I. "Symbolic computation with fermions." Journal of Symbolic Computation 10, no. 6 (December 1990): 657–64. http://dx.doi.org/10.1016/s0747-7171(08)80164-2.

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49

Gutierrez, Jaime, and David Sevilla. "Computation of unirational fields." Journal of Symbolic Computation 41, no. 11 (November 2006): 1222–44. http://dx.doi.org/10.1016/j.jsc.2005.05.009.

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50

Bayer, Dave, and Mike Stillman. "Computation of Hilbert functions." Journal of Symbolic Computation 14, no. 1 (July 1992): 31–50. http://dx.doi.org/10.1016/0747-7171(92)90024-x.

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