Artículos de revistas: "Algebraic normal form"

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Vardasbi, Ali, Mahmoud Salmasizadeh y Javad Mohajeri. "Superpoly algebraic normal form monomial test on Trivium". IET Information Security 7, n.º 3 (1 de septiembre de 2013): 230–38. http://dx.doi.org/10.1049/iet-ifs.2012.0175.

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2

Trenn, Stephan. "A normal form for pure differential algebraic systems". Linear Algebra and its Applications 430, n.º 4 (febrero de 2009): 1070–84. http://dx.doi.org/10.1016/j.laa.2008.10.004.

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3

Gazor, Majid y Mahsa Kazemi. "Normal Form Analysis of ℤ2-Equivariant Singularities". International Journal of Bifurcation and Chaos 29, n.º 02 (febrero de 2019): 1950015. http://dx.doi.org/10.1142/s0218127419500159.

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Singular parametric systems usually experience bifurcations when their parameters slightly vary around certain critical values, that is, surprising changes occur in their dynamics. The bifurcation analysis is important due to their applications in real world problems. Here, we provide a brief review of the mathematical concepts in the extension of our developed Maple library, Singularity, for the study of [Formula: see text]-equivariant local bifurcations. We explain how the process of this analysis is involved with algebraic objects and tools from computational algebraic geometry. Our procedures for computing normal forms, universal unfoldings, local transition varieties and persistent bifurcation diagram classifications are presented. Finally, we consider several Chua circuit type systems to demonstrate the applicability of our Maple library. We show how Singularity can be used for local equilibrium bifurcation analysis of such systems and their possible small perturbations. A brief user interface of [Formula: see text]-equivariant extension of Singularity is also presented.

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4

Bakoev, Valentin. "Fast Bitwise Implementation of the Algebraic Normal Form Transform". Serdica Journal of Computing 11, n.º 1 (27 de noviembre de 2017): 45–57. http://dx.doi.org/10.55630/sjc.2017.11.45-57.

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The representation of Boolean functions by their algebraic normalforms (ANFs) is very important for cryptography, coding theory andother scientific areas. The ANFs are used in computing the algebraic degreeof S-boxes, some other cryptographic criteria and parameters of errorcorrectingcodes. Their applications require these criteria and parameters tobe computed by fast algorithms. Hence the corresponding ANFs should alsobe obtained by fast algorithms. Here we continue our previous work on fastcomputing of the ANFs of Boolean functions. We present and investigatethe full version of bitwise implementation of the ANF transform. The experimental results show that this implementation ismore than 25 times faster in comparison to the well-known byte-wise ANFtransform.ACM Computing Classification System (1998): F.2.1, F.2.2.

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5

Reissig, G. "Semi-implicit differential-algebraic equations constitute a normal form". IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 42, n.º 7 (julio de 1995): 399–402. http://dx.doi.org/10.1109/81.401157.

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6

Gilkey, Peter y Raina Ivanova. "The Jordan normal form of Osserman algebraic curvature tensors". Results in Mathematics 40, n.º 1-4 (octubre de 2001): 192–204. http://dx.doi.org/10.1007/bf03322705.

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7

Gauthier, Yvon. "On Cantor's normal form theorem and algebraic number theory". International Journal of Algebra 12, n.º 3 (2018): 133–40. http://dx.doi.org/10.12988/ija.2018.8413.

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8

Talwar, S., N. Sri Namachchivaya y P. G. Voulgaris. "Approximate Feedback Linearization: A Normal Form Approach". Journal of Dynamic Systems, Measurement, and Control 118, n.º 2 (1 de junio de 1996): 201–10. http://dx.doi.org/10.1115/1.2802305.

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The emerging field of nonlinear control theory has attempted to alleviate the problem associated with applying linear control theory to nonlinear problems. A segment of nonlinear control theory, called exact feedback linearization, has proven useful in a class of problems satisfying certain controllability and integrability constraints. Approximate feedback linearization has enlarged this class by weakening the integrability conditions, but application of both these techniques remains limited to problems in which a series of linear partial differential equations can easily be solved. By use of the idea of normal forms, from dynamical systems theory, an efficient method of obtaining the necessary coordinate transformation and nonlinear feedback rules is given. This method, which involves the solution of a set of linear algebraic equations, is valid for any dimensional system and any order nonlinearity provided it meets the approximate feedback linearization conditions.

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9

GAZOR, MAJID y PEI YU. "INFINITE ORDER PARAMETRIC NORMAL FORM OF HOPF SINGULARITY". International Journal of Bifurcation and Chaos 18, n.º 11 (noviembre de 2008): 3393–408. http://dx.doi.org/10.1142/s0218127408022445.

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In this paper, we introduce a suitable algebraic structure for efficient computation of the parametric normal form of Hopf singularity based on a notion of formal decompositions. Our parametric state and time spaces are respectively graded parametric Lie algebra and graded ring. As a consequence, the parametric state space is also a graded module. Parameter space is observed as an integral domain as well as a vector space, while the near-identity parameter map acts on the parametric state space. The method of multiple Lie bracket is used to obtain an infinite order parametric normal form of codimension-one Hopf singularity. Filtration topology is revisited and proved that state, parameter and time (near-identity) maps are continuous. Furthermore, parametric normal form is a convergent process with respect to filtration topology. All the results presented in this paper are verified by using Maple.

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Chand Gupta, Kishan y Palash Sarkar. "Computing Walsh Transform from the Algebraic Normal Form of a Boolean Function". Electronic Notes in Discrete Mathematics 15 (mayo de 2003): 92–96. http://dx.doi.org/10.1016/s1571-0653(04)00542-6.

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Gong, Xinxin, Bin Zhang, Wenling Wu y Dengguo Feng. "Computing Walsh coefficients from the algebraic normal form of a Boolean function". Cryptography and Communications 6, n.º 4 (27 de junio de 2014): 335–58. http://dx.doi.org/10.1007/s12095-014-0103-8.

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12

Iooss, Gérard y Klaus Kirchgässner. "Water waves for small surface tension: an approach via normal form". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 122, n.º 3-4 (1992): 267–99. http://dx.doi.org/10.1017/s0308210500021119.

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SynopsisIn this paper we determine the possible crest-forms of permanent waves of small amplitude which exist on the free surface of a two-dimensional fluid layer under the influence of gravity and surface tension when the Froude number is close to 1. The Bond number b, measuring surface tension, is assumed to satisfy b < ⅓. We find one-parameter families of periodic waves of two different types, quasiperiodic waves and solitary waves with oscillations at infinity. The existence of true solitary waves is established for a sequence of systems approximating the full Euler equations in every algebraic order of − 1.

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13

Kuzmina, T. A. "About the cubic part of the algebraic normal form of arbitrary bent functions". Prikladnaya diskretnaya matematika. Prilozhenie, n.º 12 (1 de septiembre de 2019): 53–55. http://dx.doi.org/10.17223/2226308x/12/15.

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14

Gupta, Kishan Chand y Palash Sarkar. "Computing Partial Walsh Transform From the Algebraic Normal Form of a Boolean Function". IEEE Transactions on Information Theory 55, n.º 3 (marzo de 2009): 1354–59. http://dx.doi.org/10.1109/tit.2008.2011439.

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15

YU, P. y Y. YUAN. "AN EFFICIENT METHOD FOR COMPUTING THE SIMPLEST NORMAL FORMS OF VECTOR FIELDS". International Journal of Bifurcation and Chaos 13, n.º 01 (enero de 2003): 19–46. http://dx.doi.org/10.1142/s0218127403006418.

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A computationally efficient method is proposed for computing the simplest normal forms of vector fields. A simple, explicit recursive formula is obtained for general differential equations. The most important feature of the approach is to obtain the "simplest" formula which reduces the computation demand to minimum. At each order of the normal form computation, the formula generates a set of algebraic equations for computing the normal form and nonlinear transformation. Moreover, the new recursive method is not required for solving large matrix equations, instead it solves linear algebraic equations one by one. Thus the new method is computationally efficient. In addition, unlike the conventional normal form theory which uses separate nonlinear transformations at each order, this approach uses a consistent nonlinear transformation through all order computations. This enables one to obtain a convenient, one step transformation between the original system and the simplest normal form. The new method can treat general differential equations which are not necessarily assumed in a conventional normal form. The method is applied to consider Hopf and Bogdanov–Takens singularities, with examples to show the computation efficiency. Maple programs have been developed to provide an "automatic" procedure for applications.

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de HOOG, FRANK R. y ROBERT S. ANDERSSEN. "ASYMPTOTIC FORMULAS FOR DISCRETE EIGENVALUE PROBLEMS IN LIOUVILLE NORMAL FORM". Mathematical Models and Methods in Applied Sciences 11, n.º 01 (febrero de 2001): 43–56. http://dx.doi.org/10.1142/s0218202501000738.

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In the analysis of both continuous and discrete eigenvalue problems, asymptotic formulas play a central and crucial role. For example, they have been fundamental in the derivation of results about the inversion of the free oscillation problem of the Earth and related inverse eigenvalue problems, the computation of uniformly valid eigenvalues approximations, the proof of results about the behavior of the eigenvalues of Sturm–Liouville problems with discontinuous coefficients, and the construction of a counterexample to the Backus–Gilbert conjecture. Useful formulas are available for continuous eigenvalue problems with general boundary conditions as well as for discrete eigenvalue problems with Dirichlet boundary condition. The purpose of this paper is the construction of asymptotic formulas for discrete eigenvalue problems with general boundary conditions. The motivation is the computation of uniformly valid eigenvalue approximations. It is now widely accepted that the algebraic correction procedure, first proposed by Paine et al.,13 is one of the simplest methods for computing uniformly valid approximations to a sequence of eigenvalues of a continuous eigenvalue problem in Liouville normal form.8 This relates to the fact that, for Liouville normal forms with Dirichlet boundary conditions, it is not too difficult to prove that such procedures yield, under quite weak regularity conditions, uniformly valid O(h2) approximations. For Liouville normal forms with general boundary conditions, the corresponding error analysis is technically more challenging. Now it is necessary to have, for such Liouville normal forms, higher order accurate asymptotic formulas for the eigenvalues and eigenfunctions of their continuous and discrete counterparts. Assuming that such asymptotic formulas are available, it has been shown1 how uniformly valid O(h2) results could be established for the application of the algebraic correction procedure to Liouville normal forms with general boundary conditions. Algorithmically, this methodology represents an efficient procedure for determining uniformly valid approximations to sequences of eigenvalues, even though it is more complex than for Liouville normal forms with Dirichlet boundary conditions. As well as giving a brief review of the subject for general (Robin) boundary conditions, this paper sketches proofs for the asymptotic formulas, for Robin boundary conditions, which are required in order to construct the mentioned O(h2) results.

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Sabzevari, Bijan. "The transformation of plasma equations to normal form in mode conversion theory". Journal of Plasma Physics 47, n.º 1 (febrero de 1992): 49–60. http://dx.doi.org/10.1017/s0022377800024077.

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Field variables in a slowly varying plasma are solutions of a system of differential and integral equations. To solve these equations, the fields are expanded in the eigenvectors of an algebraic plasma tensor, and the plasma equations can be transformed into a system of transport equations. The expansion becomes singular when eigenvalues coincide (for example in the case of mode conversion). It is shown how this problem can be resolved for an arbitrary system of Maxwell and/or fluid equations in arbitrary dimensions and for every kind of medium. The method is applied to horizontal stratified media as a simple example.

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Liu, Peng Xin y Yang Wang. "A Novel 3D Mesh Segmentation Method of Algebraic Models in Reverse Engineering". Key Engineering Materials 419-420 (octubre de 2009): 661–64. http://dx.doi.org/10.4028/www.scientific.net/kem.419-420.661.

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Conventional engineering parts usually composed by algebraic surfaces are important investigation objects of reverse engineering. In this paper a step segmentation method for algebraic models is proposed. The mesh normals and curvedness of every vertex are estimated as a shape descriptor. In the first segmentation fourteen directions are chosen initially, and a k-means algorithm according to the normal vectors is used, then the surface is divided to form patches by a region-growing scheme, as well as some sharp edges or flat areas are detected. In order to identify algebraic surface, curvedness of a patch is set as the criterion by which the surface merged into near constant curvedness region. Especially a novel mean shift algorithm is adopted in this method, that a powerful technique for clustering in image process, and is extended to normal filtering while preserving the features to increase robustness of the method. Experimental evaluations using scan data or noise data demonstrate the efficiency of the proposed method.

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19

Zhang, Xue y Qingling Zhang. "Hopf analysis of a differential-algebraic predator–prey model with Allee effect and time delay". International Journal of Biomathematics 08, n.º 03 (21 de abril de 2015): 1550041. http://dx.doi.org/10.1142/s1793524515500412.

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A differential-algebraic prey–predator model with time delay and Allee effect on the growth of the prey population is investigated. Using differential-algebraic system theory, we transform the prey–predator model into its normal form and study its dynamics in terms of local analysis and Hopf bifurcation. By analyzing the associated characteristic equation, it is observed that the model undergoes a Hopf bifurcation at some critical value of time delay. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions, and an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations. Finally, numerical simulations supporting the theoretical analysis are also included.

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Goranko, Valentin. "Transformations of Multi-Player Normal form Games by Preplay Offers between Players". Axioms 11, n.º 2 (12 de febrero de 2022): 73. http://dx.doi.org/10.3390/axioms11020073.

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The paper deals with multiplayer normal form games which are preceded by a ‘preplay negotiation phase’ consisting of exchange of preplay offers by players for payments of utility to other players conditional on them playing designated in the offers strategies. The game-theoretic effect of such preplay offers is a transformation of the payoff matrix of the game, obtained by transferring the offered payments between the payoffs of the respective players; thus, certain groups of game matrix transformations naturally emerge. The main result is an explicit and rather transparent algebraic characterization of the possible transformations of the payoff matrix of any given N-person normal form game induced by preplay offers for transfer of payments. That result can be used to describe the ‘bargaining space’ of the game and to determine the mutually optimal game transformations that rational players can achieve by exchange of preplay offers.

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21

YUAN, Y. y P. YU. "COMPUTATION OF SIMPLEST NORMAL FORMS OF DIFFERENTIAL EQUATIONS ASSOCIATED WITH A DOUBLE-ZERO EIGENVALUE". International Journal of Bifurcation and Chaos 11, n.º 05 (mayo de 2001): 1307–30. http://dx.doi.org/10.1142/s0218127401002742.

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In this paper a method is presented for computing the simplest normal form of differential equations associated with the singularity of a double zero eigenvalue. Based on a conventional normal form of the system, explicit formulae for both generic and nongeneric cases are derived, which can be used to compute the coefficients of the simplest normal form and the associated nonlinear transformation. The recursive algebraic formulae have been implemented on computer systems using Maple. The user-friendly programs can be executed without any interaction. Examples are given to demonstrate the computational efficiency of the method and computer programs.

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KULA, ANNA y ÉRIC RICARD. "ON A CONVOLUTION FOR q-NORMAL ELEMENTS". Infinite Dimensional Analysis, Quantum Probability and Related Topics 11, n.º 04 (diciembre de 2008): 565–88. http://dx.doi.org/10.1142/s0219025708003282.

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In 2000 Carnovale and Koornwinder defined a q-convolution and proved that for some classes of measures it is associative and commutative. We investigate its positivity preserving properties. One of them is the notion of q-positivity related to q-moments. In this paper we describe an algebraic interpretation of q-positivity which leads us to the definition of (p, q)-convolution. It has a form similar to the q-convolution of Carnovale and Koornwinder coming from a braided algebra. For the new convolution we find an appropriate analogue of Fourier transform and also present a central limit theorem.

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Balbuena, C., D. Ferrero, X. Marcote y I. Pelayo. "Algebraic properties of a digraph and its line digraph". Journal of Interconnection Networks 04, n.º 04 (diciembre de 2003): 377–93. http://dx.doi.org/10.1142/s0219265903000933.

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Let G be a digraph, LG its line digraph and A(G) and A(LG) their adjacency matrices. We present relations between the Jordan Normal Form of these two matrices. In addition, we study the spectra of those matrices and obtain a relationship between their characteristic polynomials that allows us to relate properties of G and LG, specifically the number of cycles of a given length.

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Testerman, Donna M. y Alexandre E. Zalesski. "Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with a single non-trivial Jordan block". Journal of Group Theory 21, n.º 1 (1 de enero de 2018): 1–20. http://dx.doi.org/10.1515/jgth-2017-0019.

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AbstractLetGbe a simply connected simple linear algebraic group of exceptional Lie type over an algebraically closed fieldFof characteristic{p\geq 0}, and let{u\in G}be a nonidentity unipotent element. Let ϕ be a non-trivial irreducible representation ofG. Then the Jordan normal form of{\phi(u)}contains at most one non-trivial block if and only ifGis of type{G_{2}},uis a regular unipotent element and{\dim\phi\leq 7}. Note that the irreducible representations of the simple classical algebraic groups in which a non-trivial unipotent element is represented by a matrix whose Jordan form has a single non-trivial block were determined by I. D. Suprunenko [21].

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Dudek, Jeffrey, Vu Phan y Moshe Vardi. "ADDMC: Weighted Model Counting with Algebraic Decision Diagrams". Proceedings of the AAAI Conference on Artificial Intelligence 34, n.º 02 (3 de abril de 2020): 1468–76. http://dx.doi.org/10.1609/aaai.v34i02.5505.

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We present an algorithm to compute exact literal-weighted model counts of Boolean formulas in Conjunctive Normal Form. Our algorithm employs dynamic programming and uses Algebraic Decision Diagrams as the main data structure. We implement this technique in ADDMC, a new model counter. We empirically evaluate various heuristics that can be used with ADDMC. We then compare ADDMC to four state-of-the-art weighted model counters (Cachet, c2d, d4, and miniC2D) on 1914 standard model counting benchmarks and show that ADDMC significantly improves the virtual best solver.

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Yasir, Kamal H. y Abbas M. Al_husenawe. "Two-Parameters Bifurcation in Quasilinear Dierential-Algebraic Equations". JOURNAL OF ADVANCES IN MATHEMATICS 12, n.º 1 (24 de febrero de 2016): 5786–96. http://dx.doi.org/10.24297/jam.v12i1.573.

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In this paper, bifurcation of solution of guasilinear dierential-algebraic equations (DAEs) is studied. Whereas basic principle that quasilinear DAE is eventually reducible to an ordinary dierential equation (ODEs) and that this reduction so we can apply the classical bifurcation theory of the (ODEs). The taylor expansion applied to the reduced DAEs to prove that is equivalent to an ODE which is a normal form under some non-degeneracy conditions theorems given in this work deal with the saddle node,transcritical and pitchfork bifurcation with two-parameters. Some illustrated examples are given to explain the idea of the paper.

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BUTCHER, ERIC A. y S. C. SINHA. "ON THE CONSTRUCTION OF TRANSFORMATIONS OF LINEAR HAMILTONIAN SYSTEMS TO REAL NORMAL FORMS". International Journal of Bifurcation and Chaos 10, n.º 09 (septiembre de 2000): 2177–91. http://dx.doi.org/10.1142/s0218127400001353.

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A technique for constructing the transformations to real Hamiltonian normal forms of linear Hamiltonian systems via permutation matrices is presented. In particular, a method is shown for obtaining the symplectomorphism between the symplectic basis of the real Jordan form to the standard symplectic basis in which the real Hamiltonian normal form resides. All possible degeneracies are accounted for since the algebraic and geometric multiplicities of nonsemisimple eigenvalues are not restricted, including the "difficult" cases of zero and imaginary eigenvalues. Since the normal forms are not unique, several possible arrangements of the suggested transformations are given which result in the various normal forms derived previously as well as in a few new ones for degenerate cases which have not appeared before.

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Alolaiyan, Hanan, Halimah A. Alshehri, Muhammad Haris Mateen, Dragan Pamucar y Muhammad Gulzar. "A Novel Algebraic Structure of (α,β)-Complex Fuzzy Subgroups". Entropy 23, n.º 8 (30 de julio de 2021): 992. http://dx.doi.org/10.3390/e23080992.

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A complex fuzzy set is a vigorous framework to characterize novel machine learning algorithms. This set is more suitable and flexible compared to fuzzy sets, intuitionistic fuzzy sets, and bipolar fuzzy sets. On the aspects of complex fuzzy sets, we initiate the abstraction of (α,β)-complex fuzzy sets and then define α,β-complex fuzzy subgroups. Furthermore, we prove that every complex fuzzy subgroup is an (α,β)-complex fuzzy subgroup and define (α,β)-complex fuzzy normal subgroups of given group. We extend this ideology to define (α,β)-complex fuzzy cosets and analyze some of their algebraic characteristics. Furthermore, we prove that (α,β)-complex fuzzy normal subgroup is constant in the conjugate classes of group. We present an alternative conceptualization of (α,β)-complex fuzzy normal subgroup in the sense of the commutator of groups. We establish the (α,β)-complex fuzzy subgroup of the classical quotient group and show that the set of all (α,β)-complex fuzzy cosets of this specific complex fuzzy normal subgroup form a group. Additionally, we expound the index of α,β-complex fuzzy subgroups and investigate the (α,β)-complex fuzzification of Lagrange’s theorem analog to Lagrange’ theorem of classical group theory.

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Gandhi, Ratnik y Samaresh Chatterji. "Applications of Algebra for Some Game Theoretic Problems". International Journal of Foundations of Computer Science 26, n.º 01 (enero de 2015): 51–78. http://dx.doi.org/10.1142/s0129054115500033.

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In this paper we present applications of polynomial algebra for the problem of computing Nash equilibria of a subclass of finite normal form games.We characterize Nash equilibria of a normal form game as solutions to a system of polynomial equations and define the subclass of games under consideration. We present an algebraic method for deciding membership decision to the subclass of games. A method based on group action to compute all Nash equilibria of the subclass of games is presented with examples to show working of the methods. We also present some related results and discuss properties of the subclass of games.

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Zhang, Hongyang y Chunrui Zhang. "Dynamic Properties of a Differential-Algebraic Biological Economic System". Journal of Applied Mathematics 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/205346.

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We analyze a differential-algebraic biological economic system with time delay. The model has two different Holling functional responses. By considering time delay as bifurcation parameter, we find that there exists stability switches when delay varies, and the Hopf bifurcation occurs when delay passes through a sequence of critical values. Furthermore, we also consider the stability and direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, using Matlab software, we do some numerical simulations to illustrate the effectiveness of our results.

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Dong, H. y J. Zeng. "Normal form method for large/small amplitude instability criterion with application to wheelset lateral stability". International Journal of Structural Stability and Dynamics 14, n.º 03 (16 de febrero de 2014): 1350073. http://dx.doi.org/10.1142/s0219455413500739.

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Subcritical and supercritical bifurcations are two typical behaviors that exist in high speed railway vehicles. In the presence of instability, the former and the latter behaviors may lead to large amplitude oscillation and small amplitude swaying, respectively. The normal form (NF) method of Hopf bifurcation provides a way to study the supercritical and subcritical bifurcation. The wheelset is a key component in the vehicle system and it plays an important role in vehicle lateral stability. To study the lateral stability problems, three wheelset models are considered, which involve the NF theory. This method is an algebraic approach as opposed to the integration approach. Like the sign of Re (λ) that determines the stability of linear system, the sign of Re c1(0) determines the two bifurcation modes, meaning that Re c1(0) > 0 for supercritical bifurcation and Re c1(0) < 0 for subcritical bifurcation. Furthermore, if the ordinary differential equation (ODE) is local linear near the equilibrium position, it leads to the condition of Re c1(0) = 0, resulting in the jumping phenomenon. Besides, the expression of the 1/2-order approximation of limit cycle can be further obtained.

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Farahmand, K. "On Zeros of Self-Reciprocal Random Algebraic Polynomials". Journal of Applied Mathematics and Stochastic Analysis 2007 (28 de enero de 2007): 1–7. http://dx.doi.org/10.1155/2007/43091.

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This paper provides an asymptotic estimate for the expected number of level crossings of a trigonometric polynomial TN(θ)=∑j=0N−1{αN−jcos(j+1/2)θ+βN−jsin(j+1/2)θ}, where αj and βj, j=0,1,2,…, N−1, are sequences of independent identically distributed normal standard random variables. This type of random polynomial is produced in the study of random algebraic polynomials with complex variables and complex random coefficients, with a self-reciprocal property. We establish the relation between this type of random algebraic polynomials and the above random trigonometric polynomials, and we show that the required level crossings have the functionality form of cos(N+θ/2). We also discuss the relationship which exists and can be explored further between our random polynomials and random matrix theory.

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Zhou, Xiaojian, Xin Chen y Yongzhong Song. "Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay". Journal of Applied Mathematics 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/768364.

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We investigate the dynamics of a differential-algebraic bioeconomic model with two time delays. Regarding time delay as a bifurcation parameter, we show that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Using the theories of normal form and center manifold, we also give the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical tests are provided to verify our theoretical analysis.

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Zhang, Xue, Qing-ling Zhang y Zhongyi Xiang. "Bifurcation Analysis of a Singular Bioeconomic Model with Allee Effect and Two Time Delays". Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/745296.

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A singular prey-predator model with time delays is formulated and analyzed. Allee effect is considered on the growth of the prey population. The singular prey-predator model is transformed into its normal form by using differential-algebraic system theory. We study its dynamics in terms of local analysis and Hopf bifurcation. The existence of periodic solutions via Hopf bifurcation with respect to two delays is established. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions by applying the normal form theory and the center manifold argument. Finally, numerical simulations are included supporting the theoretical analysis and displaying the complex dynamical behavior of the model outside the domain of stability.

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Skuratovskii, Ruslan y Volodymyr Osadchyy. "Elliptic and Edwards Curves Order Counting Method". International Journal of Mathematical Models and Methods in Applied Sciences 15 (5 de abril de 2021): 52–62. http://dx.doi.org/10.46300/9101.2021.15.8.

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We consider the algebraic affine and projective curves of Edwards over the finite field Fpn. It is well known that many modern cryptosystems can be naturally transformed into elliptic curves. In this paper, we extend our previous research into those Edwards algebraic curves over a finite field. We propose a novel effective method of point counting for both Edwards and elliptic curves. In addition to finding a specific set of coefficients with corresponding field characteristics for which these curves are supersingular, we also find a general formula by which one can determine whether or not a curve Ed[Fp] is supersingular over this field. The method proposed has complexity O ( p log2 2 p ) . This is an improvement over both Schoof’s basic algorithm and the variant which makes use of fast arithmetic (suitable for only the Elkis or Atkin primes numbers) with complexities O(log8 2 pn) and O(log4 2 pn) respectively. The embedding degree of the supersingular curve of Edwards over Fpn in a finite field is additionally investigated. Due existing the birational isomorphism between twisted Edwards curve and elliptic curve in Weierstrass normal form the result about order of curve over finite field is extended on cubic in Weierstrass normal form.

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36

Artés, Joan C., Regilene D. S. Oliveira y Alex C. Rezende. "Topological Classification of Quadratic Polynomial Differential Systems with a Finite Semi-Elemental Triple Saddle". International Journal of Bifurcation and Chaos 26, n.º 11 (octubre de 2016): 1650188. http://dx.doi.org/10.1142/s0218127416501881.

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The study of planar quadratic differential systems is very important not only because they appear in many areas of applied mathematics but due to their richness in structure, stability and questions concerning limit cycles, for example. Even though many papers have been written on this class of systems, a complete understanding of this family is still missing. Classical problems, and in particular Hilbert’s 16th problem [Hilbert, 1900, 1902], are still open for this family. In this article, we make a global study of the family [Formula: see text] of all real quadratic polynomial differential systems which have a finite semi-elemental triple saddle (triple saddle with exactly one zero eigenvalue). This family modulo the action of the affine group and time homotheties is three-dimensional and we give its bifurcation diagram with respect to a normal form, in the three-dimensional real space of the parameters of this normal form. This bifurcation diagram yields 27 phase portraits for systems in [Formula: see text] counting phase portraits with and without limit cycles. Algebraic invariants are used to construct the bifurcation set and we present the phase portraits on the Poincaré disk. The bifurcation set is not just algebraic due to the presence of a surface found numerically, whose points correspond to connections of separatrices.

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37

Yong, Zhou y M. T. Hanson. "A Circular Crack System in an Infinite Elastic Medium Under Arbitrary Normal Loads". Journal of Applied Mechanics 61, n.º 3 (1 de septiembre de 1994): 582–88. http://dx.doi.org/10.1115/1.2901499.

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This analysis considers a circular crack system containing a penny-shaped crack and a concentric, coplanar external circular crack under arbitrary normal loading in a transversely isotropic body. The solution is obtained by transforming the governing two-dimensional integral equation to a set of algebraic equations which are easily solved numerically due to the special coefficient matrix. The normal stress component coplanar with the crack system is determined in power series form. The equations are solved and solutions for the stress intensity factors around the crack fronts are given for several different loading conditions. Including the rigid-body displacements at infinity allows the contact problem of an annular flat punch on an elastic half-space to be solved simultaneously.

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38

Fang, Xing, Hongxin Zhang, Danzhi Wang, Hao Yan, Fan Fan y Lei Shu. "Algebraic Persistent Fault Analysis of SKINNY_64 Based on S_Box Decomposition". Entropy 24, n.º 11 (22 de octubre de 2022): 1508. http://dx.doi.org/10.3390/e24111508.

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Algebraic persistent fault analysis (APFA), which combines algebraic analysis with persistent fault attacks, brings new challenges to the security of lightweight block ciphers and has received widespread attention since its introduction. Threshold Implementation (TI) is one of the most widely used countermeasures for side channel attacks. Inspired by this method, the SKINNY block cipher adopts the S_box decomposition to reduce the number of variables in the set of algebraic equations and the number of Conjunctive Normal Form (CNF) equations in this paper, thus speeding up the algebraic persistent fault analysis and reducing the number of fault ciphertexts. In our study, we firstly establish algebraic equations for full-round faulty encryption,and then analyze the relationship between the number of fault ciphertexts required and the solving time in different scenarios (decomposed S_boxes and original S_box). By comparing the two sets of experimental results, the success rate and the efficiency of the attack are greatly improved by using S_box decomposition. In this paper, We can recover the master key in a minimum of 2000s using 11 pairs of plaintext and fault ciphertext, while the key recovery cannot be done in effective time using the original S_box expression equations. At the same time, we apply S_box decomposition to another kind of algebraic persistent fault analysis, and the experimental results show that using S_box decomposition can effectively reduce the solving time and solving success rate under the same conditions.

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39

Skuratovskii, Ruslan y Volodymyr Osadchyy. "Criterions of Supersinguliarity and Groups of Montgomery and Edwards Curves in Cryptography". WSEAS TRANSACTIONS ON MATHEMATICS 19 (1 de marzo de 2021): 709–22. http://dx.doi.org/10.37394/23206.2020.19.77.

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We consider the algebraic affine and projective curves of Edwards over the finite field Fpn. It is well known that many modern cryptosystems can be naturally transformed into elliptic curves. The criterions of the supersingularity of Montgomery and Edwards curves are found. In this paper, we extend our previous research into those Edwards algebraic curves over a finite field and we construct birational isomorphism of them with cubic in Weierstrass normal form. One class of twisted Edwards is researched too. We propose a novel effective method of point counting for both Edwards and elliptic curves. In addition to finding a specific set of coefficients with corresponding field characteristics for which these curves are supersingular, we also find a general formula by which one can determine whether or not a curve Ed[Fp] is supersingular over this field. The method proposed has complexity O( p log2 2 p ) . This is an improvement over both Schoof’s basic algorithm and the variant which makes use of fast arithmetic (suitable for only the Elkis or Atkin primes numbers) with complexities O(log8 2 pn) and O(log4 2 pn) respectively. The embedding degree of the supersingular curve of Edwards over Fpn in a finite field is additionally investigated. Singular points of twisted Edwards curve are completely described. Due existing the birational isomorphism between twisted Edwards curve and elliptic curve in Weierstrass normal form the result about order of this curve over finite field is extended on cubic in Weierstrass normal form. Also it is considered minimum degree of an isogeny (distance) between curves of this two classes when such isogeny exists. We extend the existing isogenous of elliptic curves.

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40

Markakis, Michail P. y Panagiotis S. Douris. "On the Computation of Degenerate Hopf Bifurcations forn-Dimensional Multiparameter Vector Fields". International Journal of Mathematics and Mathematical Sciences 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/7658364.

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The restriction of ann-dimensional nonlinear parametric system on the center manifold is treated via a new proper symbolic form and analytical expressions of the involved quantities are obtained as functions of the parameters by lengthy algebraic manipulations combined with computer assisted calculations. Normal forms regarding degenerate Hopf bifurcations up to codimension 3, as well as the corresponding Lyapunov coefficients and bifurcation portraits, can be easily computed for any system under consideration.

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41

Liu, Wei y Yaolin Jiang. "Flip bifurcation and Neimark–Sacker bifurcation in a discrete predator–prey model with harvesting". International Journal of Biomathematics 13, n.º 01 (23 de diciembre de 2019): 1950093. http://dx.doi.org/10.1142/s1793524519500931.

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In this paper, a difference-algebraic predator–prey model is proposed, and its complex dynamical behaviors are analyzed. The model is a discrete singular system, which is obtained by using Euler scheme to discretize a differential-algebraic predator–prey model with harvesting that we establish. Firstly, the local stability of the interior equilibrium point of proposed model is investigated on the basis of discrete dynamical system theory. Further, by applying the new normal form of difference-algebraic equations, center manifold theory and bifurcation theory, the Flip bifurcation and Neimark–Sacker bifurcation around the interior equilibrium point are studied, where the step size is treated as the variable bifurcation parameter. Lastly, with the help of Matlab software, some numerical simulations are performed not only to validate our theoretical results, but also to show the abundant dynamical behaviors, such as period-doubling bifurcations, period 2, 4, 8, and 16 orbits, invariant closed curve, and chaotic sets. In particular, the corresponding maximum Lyapunov exponents are numerically calculated to corroborate the bifurcation and chaotic behaviors.

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42

DAHL, MATIAS F. "A RESTATEMENT OF THE ALGEBRAIC CLASSIFICATION OF AREA METRICS ON 4-MANIFOLDS". International Journal of Geometric Methods in Modern Physics 09, n.º 05 (3 de julio de 2012): 1250046. http://dx.doi.org/10.1142/s0219887812500466.

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An area metric is a [Formula: see text]-tensor with certain symmetries on a 4-manifold that represents a non-dissipative linear electromagnetic medium. A recent result by Schuller, Witte and Wohlfarth gives a pointwise algebraic classification for such area metrics. This result is similar to the Jordan normal form theorem for [Formula: see text]-tensors, and the result shows that pointwise area metrics divide into 23 metaclasses and each metaclass requires two coordinate representations. For the first 7 metaclasses, we show that only one coordinate representation is needed. For the remaining 16 metaclasses we find an additional third coordinate representation.

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43

CARCASSÈS, J. P. y H. KAWAKAMI. "EXISTENCE OF A CUSP POINT ON A FOLD BIFURCATION CURVE AND STABILITY OF THE ASSOCIATED FIXED POINT: CASE OF AN n-DIMENSIONAL MAP". International Journal of Bifurcation and Chaos 09, n.º 05 (mayo de 1999): 875–94. http://dx.doi.org/10.1142/s0218127499000626.

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Considering an n–dimensional map T, a necessary and sufficient condition for the existence of a cusp point on a fold bifurcation curve in a parameter plane of T is proposed. In the case of a nondegenerated cusp point, a necessary and sufficient condition for the stability of the associated nonhyperbolic fixed point is established. These conditions, obtained using the classical methods (center manifold, normal form), are expressed in an explicit algebraic well adapted for numerical computing.

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44

Trudonoshin, V. A., V. A. Ovchinnikov y V. G. Fedoruk. "Modal Analysis Problem Solution for a Mathematical Model Formed by the Extended Nodal Method". Mathematics and Mathematical Modeling, n.º 2 (30 de mayo de 2021): 33. http://dx.doi.org/10.24108/mathm.0221.0000257.

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The article proposes an option for transforming a mathematical model of the object, formed by the extended nodal method in the time-domain solution for modal analysis. Since finding the eigenvalues and eigenvectors for systems of ordinary equations given in the Cauchy normal form is possible, calculations are presented that allow us to obtain a system of equations in the Cauchy normal form from a mathematical model in a differential-algebraic form through linearization. The extended nodal method contains derivatives of state variables in the vector of unknown, and the Jacobi matrix obtained at each Newton iteration of each step of numerical integration can be used to obtain a linearized mathematical model, but the equilibrium equations, as a rule, contain several derivatives with respect to time. By introducing additional variables, it is possible to reduce the linearized mathematical model to the Cauchy normal form, while the Jacobi matrix structure remains essentially unchanged.The proposed solution is implemented in the mathematical core of the PRADIS Gen2 PA-8 software package, which made it possible to expand its functionality by an operator of modal analysis.The presented calculations of test schemes have shown the correctness of the method proposed.

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45

Conidis, Chris J. y Richard A. Shore. "The complexity of ascendant sequences in locally nilpotent groups". International Journal of Algebra and Computation 24, n.º 02 (marzo de 2014): 189–205. http://dx.doi.org/10.1142/s0218196714500118.

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We analyze the complexity of ascendant sequences in locally nilpotent groups, showing that if G is a computable locally nilpotent group and x0, x1, …, xN ∈ G, N ∈ ℕ, then one can always find a uniformly computably enumerable (i.e. uniformly [Formula: see text]) ascendant sequence of order type ω + 1 of subgroups in G beginning with 〈x0, x1, …, xN〉G, the subgroup generated by x0, x1, …, xN in G. This complexity is surprisingly low in light of the fact that the usual definition of ascendant sequence involves arbitrarily large ordinals that index sequences of subgroups defined via a transfinite recursion in which each step is incomputable. We produce this surprisingly low complexity sequence via the effective algebraic commutator collection process of P. Hall, and a related purely algebraic Normal Form Theorem of M. Hall for nilpotent groups.

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46

Artés, Joan C., Alex C. Rezende y Regilene D. S. Oliveira. "The Geometry of Quadratic Polynomial Differential Systems with a Finite and an Infinite Saddle-Node (A, B)". International Journal of Bifurcation and Chaos 24, n.º 04 (abril de 2014): 1450044. http://dx.doi.org/10.1142/s0218127414500448.

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Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this family. In this paper, we study the bifurcation diagram of the family QsnSN which is the set of all quadratic systems which have at least one finite semi-elemental saddle-node and one infinite semi-elemental saddle-node formed by the collision of two infinite singular points. We study this family with respect to a specific normal form which puts the finite saddle-node at the origin and fixes its eigenvectors on the axes. Our aim is to make a global study of the family [Formula: see text] which is the closure of the set of representatives of QsnSN in the parameter space of that specific normal form. This family can be divided into three different subfamilies according to the position of the infinite saddle-node, namely: (A) with the infinite saddle-node in the horizontal axis, (B) with the infinite saddle-node in the vertical axis and (C) with the infinite saddle-node in the bisector of the first and third quadrants. These three subfamilies modulo the action of the affine group and times homotheties are four-dimensional. Here, we provide the complete study of the geometry with respect to a normal form of the first two families, (A) and (B). The bifurcation diagram for the subfamily (A) yields 38 phase portraits for systems in [Formula: see text] (29 in QsnSN(A)) out of which only three have limit cycles and 13 possess graphics. The bifurcation diagram for the subfamily (B) yields 25 phase portraits for systems in [Formula: see text] (16 in QsnSN(B)) out of which 11 possess graphics. None of the 25 portraits has limit cycles. Case (C) will yield many more phase portraits and will be written separately in a forthcoming new paper. Algebraic invariants are used to construct the bifurcation set. The phase portraits are represented on the Poincaré disk. The bifurcation set of [Formula: see text] is the union of algebraic surfaces and one surface whose presence was detected numerically. All points in this surface correspond to connections of separatrices. The bifurcation set of [Formula: see text] is formed only by algebraic surfaces.

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47

Messias, Marcelo y Alisson C. Reinol. "Integrability and Dynamics of Quadratic Three-Dimensional Differential Systems Having an Invariant Paraboloid". International Journal of Bifurcation and Chaos 26, n.º 08 (julio de 2016): 1650134. http://dx.doi.org/10.1142/s0218127416501340.

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Invariant algebraic surfaces are commonly observed in differential systems arising in mathematical modeling of natural phenomena. In this paper, we study the integrability and dynamics of quadratic polynomial differential systems defined in [Formula: see text] having an elliptic paraboloid as an invariant algebraic surface. We obtain the normal form for these kind of systems and, by using the invariant paraboloid, we prove the existence of first integrals, exponential factors, Darboux invariants and inverse Jacobi multipliers, for suitable choices of parameter values. We characterize all the possible configurations of invariant parallels and invariant meridians on the invariant paraboloid and give necessary conditions for the invariant parallel to be a limit cycle and for the invariant meridian to have two orbits heteroclinic to a point at infinity. We also study the dynamics of a particular class of the quadratic polynomial differential systems having an invariant paraboloid, giving information about localization and local stability of finite singular points and, by using the Poincaré compactification, we study their dynamics on the Poincaré sphere (at infinity). Finally, we study the well-known Rabinovich system in the case of invariant paraboloids, performing a detailed study of its dynamics restricted to these invariant algebraic surfaces.

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48

Denier, J. P. y R. H. J. Grimshaw. "Nonlinear interaction of positive and negative energy modes in Hamiltonian systems". Journal of the Australian Mathematical Society. Series B. Applied Mathematics 31, n.º 4 (abril de 1990): 397–424. http://dx.doi.org/10.1017/s0334270000006755.

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AbstractWe consider the nonlinear evolution of a Hamiltonian system as the system passes through a linear resonance (as the system parameters vary). Two cases are considered. In the first case the linearized problem (at resonance) possess a full complement of normal mode solutions. This case is presented in the context of the interaction between modes which may have oppositely signed energy. The second case considered has an additional degeneracy in that the linearized problem (at resonance) has a single normal mode solution.Both cases are analysed using normal form theory and in both cases the systems governing the transition through resonance are shown to be completely integrable in the classical sense. Possible bifurcations as the resonance is traversed are discussed. Conditions for the existence of algebraic singularities at some finite positive time are also presented.

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49

Al Tahan, M., B. Davvaz, M. Parimala y S. Al-Kaseasbeh. "Linear Diophantine fuzzy subsets of polygroups". Carpathian Mathematical Publications 14, n.º 2 (30 de diciembre de 2022): 564–81. http://dx.doi.org/10.15330/cmp.14.2.564-581.

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Linear Diophantine fuzzy sets were recently introduced as a generalized form of fuzzy sets. The aim of this paper is to shed the light on the relationship between algebraic hyperstructures and linear Diophantine fuzzy sets through polygroups. More precisely, we introduce the concepts of linear Diophantine fuzzy subpolygroups of a polygroup, linear Diophantine fuzzy normal subpolygroups of a polygroup, and linear Diophantine anti-fuzzy subpolygroups of a polygroup. Furthermore, we study some of their properties and characterize them in relation to level and ceiling sets.

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50

FAGNOLA, FRANCO y ROLANDO REBOLLEDO. "ALGEBRAIC CONDITIONS FOR CONVERGENCE OF A QUANTUM MARKOV SEMIGROUP TO A STEADY STATE". Infinite Dimensional Analysis, Quantum Probability and Related Topics 11, n.º 03 (septiembre de 2008): 467–74. http://dx.doi.org/10.1142/s0219025708003142.

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Let [Formula: see text] be a uniformly continuous quantum Markov semigroup on [Formula: see text] with generator represented in a standard GKSL form [Formula: see text] and a faithful normal invariant state ρ. In this note we give new algebraic conditions for proving that [Formula: see text] converges towards a steady state, possibly different from ρ. Indeed, we show that this happens whenever the commutator of [Formula: see text] (i.e. its fixed point algebra) coincides with the commutator of [Formula: see text] (where δH(X) = [H, X]) for some n ≥ 1. As an application we discuss the convergence to the unique invariant state of a spin chain model.

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