688 results
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2. Some properties and applications of odd-colorable [formula omitted]-hypergraphs.
- Author
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Yuan, Xiying, Qi, Liqun, Shao, Jiayu, and Ouyang, Chen
- Subjects
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HYPERGRAPHS , *MATHEMATICAL analysis , *GRAPH theory , *GRAPHIC methods , *MATHEMATICS - Abstract
Let r ≥ 2 and r be even. An r -hypergraph G on n vertices is called odd-colorable if there exists a map φ : [ n ] → [ r ] such that for any edge { j 1 , j 2 , … , j r } of G , we have φ ( j 1 ) + φ ( j 2 ) + ⋅ ⋯ ⋅ + φ ( j r ) ≡ r ∕ 2 ( mod r ) . In this paper, we first determine that, if r = 2 q ( 2 t + 1 ) and n ≥ 2 q ( 2 q − 1 ) r , then the maximum chromatic number in the class of the odd-colorable r -hypergraphs on n vertices is 2 q , which answers a question raised by V. Nikiforov recently in Nikiforov (2017). We also study some applications of the spectral symmetry of the odd-colorable r -hypergraphs given in the same paper by V. Nikiforov. We show that the Laplacian spectrum S p e c ( L ( G ) ) and the signless Laplacian spectrum S p e c ( Q ( G ) ) of an r -hypergraph G are equal if and only if r is even and G is odd-colorable. As an application of this result, we give an affirmative answer for the remaining unsolved case r ⁄ ≡ 0 ( m o d 4 ) of a question raised in Shao et al. (2015) about whether S p e c ( L ( G ) ) = S p e c ( Q ( G ) ) implies that L ( G ) and Q ( G ) have the same H-spectrum. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
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3. Global existence of weak solutions for [formula omitted] system of chromatography.
- Author
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Lu, Yun-Guang, Roa, Elder Villamizar, and Xie, Jian
- Subjects
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CHROMATOGRAPHIC analysis , *ENTROPY , *RIEMANN surfaces , *CAUCHY problem , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
In the paper James et al. (1995), the authors established a compact framework for general n × n system of chromatography (1.1) by using the kinetic formulation coupled with the compensated compactness method. However, how to construct suitable approximated solutions { u i l } of system (1.1) and then to prove the compactness of η ( u i l ) t + q ( u i l ) x in H l o c − 1 , for the entropy–entropy flux pairs ( η , q ) constructed by the kinetic formulation, with respect to the sequence { u i l } , is an open problem. In this paper, we construct the approximated solutions { u i ε } by using the parabolic viscosity method. By carefully calculating the Riemann invariants of system (1.1) , we obtained all necessary estimates in the compact framework of James et al. (1995), and gave a complete proof of the global existence of weak solutions for the Cauchy problem (1.1) with the bounded, nonnegative initial data (1.2) . As a direct by-product, when the total variation of the initial data is bounded, we obtained a simple proof of the existence of global weak solutions by applying the Div-Curl lemma in the compensated compactness theorem to some pairs of functions ( c , f ( u i ) ) , where c is a constant. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
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4. Groups which do not have four irreducible characters of degrees divisible by a prime p.
- Author
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Alizadeh, Fereydoon, Behravesh, Houshang, Ghaffarzadeh, Mehdi, and Ghasemi, Mohsen
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FINITE groups , *GROUP theory , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS - Abstract
Abstract Given a finite group G , we say that G has property P n if for every prime integer p , G has at most n − 1 irreducible characters whose degrees are multiples of p. In this paper, we classify all finite groups that have property P 4. We show that the groups satisfying property P 4 are exactly the finite groups with at most three nonlinear irreducible characters, one solvable group of order 168, SL 2 (3) , A 5 , S 5 , PSL 2 (7) and A 6. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
5. On the balanced condition for the Eguchi–Hanson metric.
- Author
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Cannas Aghedu, Francesco
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INTEGERS , *MANIFOLDS (Mathematics) , *MATHEMATICAL analysis , *MATHEMATICS , *RATIONAL numbers - Abstract
Abstract Let g E H be the Eguchi–Hanson metric on the blow-up of ℂ 2 at the origin. In this paper we show that m g E H is not balanced for any positive integer m. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
6. Investigating results and performance of search and construction algorithms for word-based LFSRs, [formula omitted]-LFSRs.
- Author
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Bishoi, Susil Kumar and Matyas, Vashek
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ALGORITHMS , *SEARCH algorithms , *POLYNOMIALS , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Linear feedback shift registers (LFSRs) play a significant role in communications security and we investigate design of a selected class of word-based LFSRs known as σ -LFSRs. Both the search algorithm and the construction algorithm generate efficient primitive σ -LFSRs. The search algorithm first constructs the σ -polynomial and then checks the primitiveness of the σ -polynomial, whereas the construction algorithm for the σ -LFSR, first finds a primitive polynomial f ( x ) and then constructs the primitive σ -LFSR from f ( x ) . In this paper, we present some novel results pertaining to the search algorithm for primitive σ -LFSR along with the exhaustive search space complexity of the search algorithm for σ -LFSRs. Then we investigate and compare the performance of the construction algorithm with the search algorithm for the primitive σ -LFSR. Finally, the number of σ -LFSRs similar to the σ -LFSRs generated by the construction algorithm is provided. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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7. Snarks from a Kászonyi perspective: A survey.
- Author
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Bradley, Richard C.
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MATHEMATICAL analysis , *UNDERGRADUATES , *ORTHOGONAL codes , *PROBLEM solving , *MATHEMATICS - Abstract
This is a survey or exposition of a particular collection of results and open problems involving snarks — simple “cubic” (3-valent) graphs for which, for nontrivial reasons, the edges cannot be 3-colored. The results and problems here are rooted in a series of papers by László Kászonyi that were published in the early 1970s. The problems posed in this survey paper can be tackled without too much specialized mathematical preparation, and in particular seem well suited for interested undergraduate mathematics students to pursue as independent research projects. This survey paper is intended to facilitate research on these problems. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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8. Extended mixed-level supersaturated designs.
- Author
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Qin, Hong, Chatterjee, Kashinath, and Ghosh, Sutapa
- Subjects
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OPTIMAL designs (Statistics) , *MATHEMATICAL bounds , *FRACTIONAL calculus , *FACTORIAL experiment designs , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
This paper considers the study of the optimality of the extended design generated by adding few runs to an existing E ( χ 2 ) -optimal mixed-level supersaturated design. This paper covers the work of Gupta et al. (2010, 2012) on extended two-level and s -level supersaturated designs as two special cases. A lower bound to E ( χ 2 ) has been obtained for the proposed designs. A small example is presented here attaining the lower bound. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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9. The omega-rule interpretation of transfinite provability logic.
- Author
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Fernández-Duque, David and Joosten, Joost J.
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LOGIC , *ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis , *PROBABILITY theory , *MATHEMATICS - Abstract
Given a computable ordinal Λ, the transfinite provability logic GLP Λ has for each ξ < Λ a modality [ ξ ] intended to represent a provability predicate within a chain of increasing strength. One possibility is to read [ ξ ] ϕ as ϕ is provable in T using ω-rules of depth at most ξ, where T is a second-order theory extending ACA 0 . In this paper we will formalize such iterations of ω -rules in second-order arithmetic and show how it is a special case of what we call uniform provability predicates. Uniform provability predicates are similar to Ignatiev's strong provability predicates except that they can be iterated transfinitely. Finally, we show that GLP Λ is sound and complete for any uniform provability predicate. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
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10. On upper bounds for the independent transversal domination number.
- Author
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Brause, Christoph, Henning, Michael A., Ozeki, Kenta, Schiermeyer, Ingo, and Vumar, Elkin
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GRAPH theory , *MATHEMATICAL analysis , *GRAPHIC methods , *MATHEMATICS , *BIPARTITE graphs - Abstract
In this paper we continue studying the independent transversal domination number in a graph, i.e., the cardinality of a smallest dominating set which intersects each maximum independent set. As our main result, we prove two upper bounds on the independent transversal domination number in terms of the order and minimum degree of a graph. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
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11. First order sentences about random graphs: Small number of alternations.
- Author
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Matushkin, A.D. and Zhukovskii, M.E.
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RANDOM graphs , *GRAPH theory , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS - Abstract
The spectrum of a first order sentence is the set of all α such that G ( n , n − α ) does not obey zero–one law with respect to this sentence. In this paper, we prove that the minimal number of quantifier alternations of a first order sentence with infinite spectrum equals 3. We have also proved that the spectrum of a first-order sentence with quantifier depth 4 has no limit points except possibly the points 1 ∕ 2 and 3 ∕ 5 . [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
12. Scaling invariant regularity criteria for the Navier–Stokes–Maxwell system.
- Author
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Ma, Caochuan, Jiang, Zaihong, and Zhu, Mingxuan
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INVARIANTS (Mathematics) , *NUMERICAL solutions to Navier-Stokes equations , *MATHEMATICAL analysis , *MATHEMATICS , *ADIABATIC invariants - Abstract
In this paper, we establish some scaling invariant regularity criteria for the Navier–Stokes–Maxwell system. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
13. On the moment generating function for random vectors via inverse survival function.
- Author
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Song, Pingfan, Tan, Changchun, and Wang, Shaochen
- Subjects
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VECTORS (Calculus) , *MATHEMATICAL functions , *DIFFERENTIAL equations , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract In this paper, we propose one new alternative formula for moment generating function of random vectors via the inverse survival function. A recursive formula for moment generating function of random vector is obtained and as application, we derive the corresponding alternative formula for mixed moment. Several examples are also presented along with the theory. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
14. Left-looking version of AINV preconditioner with complete pivoting strategy.
- Author
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Rafiei, A.
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LINEAR systems , *MATRICES (Mathematics) , *GEOMETRIC dissections , *NUMERICAL analysis , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we apply a complete pivoting strategy to compute the left-looking version of AINV preconditioner for linear systems. As the preprocessing, the MultiLevel Nested Dissection reordering has also been applied. We have used this preconditioner as the right preconditioner for several linear systems where the coefficient matrices have been downloaded from the University of Florida Sparse Matrix Collection. Numerical experiments presented in this paper indicate the effectiveness of such a complete pivoting on the quality of left-looking version of AINV preconditioner. [Copyright &y& Elsevier]
- Published
- 2014
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15. Bases in semimodules over commutative semirings.
- Author
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Tan, Yi-Jia
- Subjects
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COMMUTATIVE rings , *MODULES (Algebra) , *SEMIRINGS (Mathematics) , *GENERALIZATION , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, the bases of a semimodule over a commutative semiring R are investigated. Some properties and characterizations of the bases are discussed and some equivalent conditions for a basis to be a free basis in a finitely generated free semimodule over R are given. The different possible cardinalities for a basis in a finitely generated free semimodule over R are considered and some equivalent descriptions are obtained for a commutative semiring R satisfying the property that any two bases for a finitely generated free R-semimodule have the same cardinality. Partial results obtained in the paper develop and generalize the corresponding results for commutative join-semirings and for commutative zerosumfree semirings. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
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16. Characterization for the general solution to a system of matrix equations with quadruple variables.
- Author
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Zhang, Xiang
- Subjects
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NUMERICAL solutions to differential equations , *MATRICES (Mathematics) , *MATHEMATICAL variables , *MAXIMA & minima , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we give some necessary and sufficient conditions for the solvability to the system of matrix equations and provide an expression of the general solution to (0.1). Furthermore, we obtain the maximal and minimal ranks of and in (0.1). The findings of this paper extend the known results in the literatures. [Copyright &y& Elsevier]
- Published
- 2014
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17. Homogeneously non-idling schedules of unit-time jobs on identical parallel machines.
- Author
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Quilliot, Alain and Chrétienne, Philippe
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PARALLEL algorithms , *SCHEDULING , *SET theory , *FEASIBILITY studies , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we study the basic homogeneous -machine scheduling problem where weakly dependent unit-time jobs have to be scheduled within the time windows between their release dates and due dates so that, for any subset of machines, the set of the time units at which at least one machine is busy, is in interval. We first introduce the notions of pyramidal structure, -hole, -matching, preschedule, -schedule and schedule for this problem. Then we provide a feasibility criteria for a preschedule. The key result of the paper is then to provide a structural necessary and sufficient condition for an instance of the problem to be feasible. We conclude by giving the directions of ongoing works and by bringing open questions related to different variants of the basic non-idling -machine scheduling problem. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
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18. Dynamics of the breathers, rogue waves and solitary waves in the (2+1)-dimensional Ito equation.
- Author
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Wang, Xiu-Bin, Tian, Shou-Fu, Qin, Chun-Yan, and Zhang, Tian-Tian
- Subjects
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OCEAN waves , *METEOTSUNAMIS , *MATHEMATICS , *MATHEMATICAL analysis , *DIMENSIONAL analysis - Abstract
In this paper, the homoclinic breather limit method is employed to find the breather wave and the rational rogue wave solutions of the ( 2 + 1 )-dimensional Ito equation. Moreover, based on its bilinear form, the solitary wave solutions of the equation are also presented with a detailed derivation. The dynamic behaviors of breather waves, rogue waves and solitary waves are analyzed with some graphics, respectively. The results imply that the extreme behavior of the breather solitary wave yields the rogue wave for the ( 2 + 1 )-dimensional Ito equation. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
19. Sperner type theorems with excluded subposets.
- Author
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Katona, Gyula O.H.
- Subjects
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SPERNER theory , *PARTIALLY ordered sets , *SET theory , *GENERALIZATION , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: Let be a family of subsets of an -element set. Sperner’s theorem says that if there is no inclusion among the members of then the largest family under this condition is the one containing all -element subsets. The present paper surveys certain generalizations of this theorem. The maximum size of is to be found under the condition that a certain configuration is excluded. The configuration here is always described by inclusions. More formally, let be a poset. The maximum size of a family which does not contain as a (not-necessarily induced) subposet is denoted by . The paper is based on a lecture of the author at the Jubilee Conference on Discrete Mathematics [Banasthali University, January 11–13, 2009], but it was somewhat updated in December 2010. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
20. Riemannian and Finslerian spheres with fractal cut loci.
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Itoh, Jin-ichi and Sabau, Sorin V.
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RIEMANNIAN manifolds , *FRACTAL analysis , *INTEGERS , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
The present paper shows that for a given integer k ≥ 2 it is possible to construct an at least k -differentiable Riemannian metric on the sphere of a certain dimension such that the cut locus of a point of it becomes a fractal. Moreover, we show that this construction can be extended to the case of Finslerian spheres as well. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
21. The classification of N-dimensional non-Lie Malcev algebras with (N-4)-dimensional annihilator.
- Author
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Hegazi, A.S., Abdelwahab, Hani, and Calderon Martin, A.J.
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CLASSIFICATION , *DIMENSIONAL analysis , *ALGEBRA , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
In this paper we give a complete classification of all n -dimensional non-Lie Malcev algebras with ( n − 4 ) -dimensional annihilator over an algebraically closed field of characteristic 0. We also show that such algebras are special. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
22. Sufficient conditions for 2-rainbow connected graphs.
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Kemnitz, Arnfried and Schiermeyer, Ingo
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GRAPH connectivity , *GRAPH coloring , *NUMBER theory , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
An edge-coloured connected graph G is rainbow connected if each two vertices are connected by a path whose edges have distinct colours. If such a colouring uses k colours then G is called k -rainbow connected. The rainbow connection number of G , denoted by rc ( G ) , is the minimum k such that G is k -rainbow connected. Even the problem to decide whether rc ( G ) = 2 is NP-complete. It has been shown that if G is a connected graph of order n and size m with n − 2 2 + 2 ≤ m ≤ n − 1 2 , then 2 ≤ rc ( G ) ≤ 3 . In this paper we will present sufficient conditions for graphs G of this size to fulfil rc ( G ) = 2 depending on vertex degrees. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
23. Omega-limit sets for shift spaces and unimodal maps.
- Author
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Alvin, Lori and Ormes, Nicholas
- Subjects
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SET theory , *MATHEMATICAL mappings , *CANTOR sets , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
This paper investigates the structure of points u ∈ A N that are such that the omega-limit set ω ( u , σ ) is precisely X , where X ⊆ A N is an internally transitive shift space. We then use those results to study the possible structures of the omega-limit set of the turning point for a unimodal map. Examples are provided of unimodal maps f where no iterate of the turning point c is recurrent and ω ( c , f ) is either a minimal Cantor set or properly contains a minimal Cantor set. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
24. A search for the minimum value of Balaban index.
- Author
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Knor, M., Kranjc, J., Škrekovski, Riste, and Tepeh, Aleksandra
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GRAPH theory , *SET theory , *MATHEMATICAL analysis , *DUMBBELLS , *MATHEMATICS - Abstract
In this paper we consider graphs of order n with minimum Balaban index. Although the index was introduced 30 years ago, its minimum value and corresponding extremal graphs are still unknown, and it is unlikely that they can be precisely determined soon due to the mathematical intractability of the index. We show that this value is of order Θ ( n − 1 ) . For small values of n we determine the extremal graphs and we observe that they are similar to dumbbell graphs. We find out that in the class of balanced dumbbell graphs those with clique sizes π / 2 4 n + o ( n ) and the path length n − o ( n ) have asymptotically the smallest value. We study dumbbell-like graphs in more detail, and we propose several conjectures regarding the structure of the extremal graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
25. A Hölder continuity of minimizing symphonic maps
- Author
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Misawa, Masashi and Nakauchi, Nobumitsu
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MATHEMATICAL functions , *METRIC spaces , *MATHEMATICAL mappings , *MATHEMATICAL regularization , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: In the paper Nakauchi and Takenaka (2011) the second author introduced a stationary map for the functional of the -norm of the pullbacks of metrics. We call it a symphonic map. In this paper, using Morrey’s argument, we give a regularity of (locally) minimizing symphonic maps into the Euclidean space. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
26. Isotropic submanifolds of pseudo-Riemannian spaces
- Author
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Cabrerizo, J.L., Fernández, M., and Gómez, J.S.
- Subjects
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SUBMANIFOLDS , *RIEMANNIAN manifolds , *MATHEMATICS , *GEODESICS , *GEOMETRIC analysis , *MATHEMATICAL analysis - Abstract
Abstract: The family of all the submanifolds of a given Riemannian or pseudo-Riemannian manifold is large enough to classify them into some interesting subfamilies such as minimal (maximal), totally geodesic, Einstein, etc. Most of these have been extensively studied by many authors, but as far as we know, no paper has hitherto been published on the class of isotropic submanifolds. The purpose of this paper is therefore to gain a better understanding of this interesting class of submanifolds that arise naturally in mathematics and physics by studying their relationships with other closely distinguished families. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
27. A characterization of graphs with rank 5
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Chang, Gerard J., Huang, Liang-Hao, and Yeh, Hong-Gwa
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GRAPH theory , *MATRICES (Mathematics) , *GRAPH connectivity , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: The rank of a graph G is defined to be the rank of its adjacency matrix. In this paper, we consider the following problem: what is the structure of a connected graph G with rank 5? or equivalently, what is the structure of a connected n-vertex graph G whose adjacency matrix has nullity ? In this paper, we completely characterize connected graphs G whose adjacency matrix has rank 5. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
28. Some properties of James type constant
- Author
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Yang, Changsen and Wang, Yamin
- Subjects
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MATHEMATICAL constants , *MONOTONIC functions , *REAL variables , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: Recently Takahashi has introduced James type constant. In this paper, we will introduce some new properties of the constant such as monotonicity, uniform non-squareness characterized by James type constant, and so on. We also investigate some relations between James type constant and other constants. Our main results of the paper are three examples of the constant. These examples include , and space, where is the space with the norm . We calculate exact values of James type constant in these concrete spaces. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
29. On the Karush–Kuhn–Tucker reformulation of the bilevel optimization problem
- Author
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Dempe, S. and Zemkoho, A.B.
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MATHEMATICAL reformulation , *MATHEMATICAL optimization , *GENERALIZATION , *OPERATOR theory , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: This paper is mainly concerned with the classical KKT reformulation and the primal KKT reformulation (also known as an optimization problem with generalized equation constraint (OPEC)) of the optimistic bilevel optimization problem. A generalization of the MFCQ to an optimization problem with operator constraint is applied to each of these reformulations, hence leading to new constraint qualifications (CQs) for the bilevel optimization problem. - and -type stationarity conditions tailored for the problem are derived as well. Considering the close link between the aforementioned reformulations, similarities and relationships between the corresponding CQs and optimality conditions are highlighted. In this paper, a concept of partial calmness known for the optimal value reformulation is also introduced for the primal KKT reformulation and used to recover the -stationarity conditions. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
30. Graphs whose Szeged and Wiener numbers differ by 4 and 5
- Author
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Nadjafi-Arani, M.J., Khodashenas, H., and Ashrafi, A.R.
- Subjects
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GRAPH theory , *NUMBER theory , *GRAPH connectivity , *CATEGORIES (Mathematics) , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: Let be a connected graph and , where and stand for the Wiener and Szeged numbers of , respectively. A well-known result of Klavžar, Rajapakse and Gutman states that and by a result of Dobrynin and Gutman if and only if each block of is complete. In an earlier paper a classification of graphs with is presented. In this paper, we continue our earlier work to classify connected graphs which satisfy or . [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
31. Some new solitonary solutions of the modified Benjamin–Bona–Mahony equation
- Author
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Noor, Muhammad Aslam, Noor, Khalida Inayat, Waheed, Asif, and Al-Said, Eisa A.
- Subjects
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NONLINEAR evolution equations , *SOLITONS , *MATHEMATICAL physics , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS - Abstract
Abstract: In this paper, we use the exp-function method to construct some new soliton solutions of the Benjamin–Bona–Mahony and modified Benjamin–Bona–Mahony equations. These equations have important and fundamental applications in mathematical physics and engineering sciences. The exp-function method is used to find the soliton solution of a wide class of nonlinear evolution equations with symbolic computation. This method provides the concise and straightforward solution in a very easier way. The results obtained in this paper can be viewed as a refinement and improvement of the previously known results. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
32. A simple adaptive feedback control method for chaos and hyper-chaos control
- Author
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Chen, Guoxin
- Subjects
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FEEDBACK control systems , *CHAOS theory , *NUMERICAL analysis , *MATHEMATICS , *ALGEBRA , *MATHEMATICAL analysis - Abstract
Abstract: This paper investigates the problem of chaos and hyper-chaos control, and proposes a simple adaptive feedback control method for chaos control under a reasonable assumption. In comparison with previous methods, the present control technique is simple both in the form of the controller and its application. Several illustrative examples with numerical simulations are studied by using the results obtained in this paper. Study of examples shows that our control method works very well in chaos control. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
33. Additive results for the Drazin inverse of block matrices and applications
- Author
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Ljubisavljević, Jelena and Cvetković-Ilić, Dragana S.
- Subjects
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MATRIX inversion , *ADDITION (Mathematics) , *MATHEMATICAL formulas , *MATRICES (Mathematics) , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we consider the Drazin inverse of a sum of two matrices and derive additive formulas under conditions weaker than those used in some recent papers on the subject. As a corollary we get the main results from the paper of Yang and Liu [H. Yang, X. Liu, The Drazin inverse of the sum of two matrices and its applications, J. Comput. Appl. Math. 235 (2011) 1412–1417]. As an application we give some new representations for the Drazin inverse of a block matrix. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
34. Existence and global attractivity of positive periodic solution for a Volterra model with mutual interference and Beddington–DeAngelis functional response
- Author
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Guo, Haijun and Chen, Xiaoxing
- Subjects
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VOLTERRA equations , *EXISTENCE theorems , *MATHEMATICAL analysis , *FUNCTIONAL analysis , *MATHEMATICS , *FUNCTIONAL equations , *PERIODIC functions - Abstract
Abstract: In this paper, a Volterra model with mutual interference and Beddington–DeAngelis functional response is investigated, some sufficient conditions which guarantee the existence and global attractivity of positive periodic solution for the system are obtained. Furthermore, our results improve the main results of paper . [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
35. Pseudo-isochronicity in a class of septic differential systems
- Author
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Wu, Yusen and Li, Peiluan
- Subjects
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SET theory , *DIFFERENTIAL equations , *MATHEMATICAL transformations , *MATHEMATICAL analysis , *MATHEMATICS , *CALCULUS - Abstract
Abstract: This paper deals with the pseudo-isochronicity for a class of septic differential systems. In this paper, we transform infinity into the origin so that the properties of infinity can be investigated with the methods developed for finite critical points. By calculating the singular point quantities and period constants of the origin, the problem of infinity being a pseudo-isochronous center has been solved in this case. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
36. Fundamentals of simple games from a viewpoint of blockability relations
- Author
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Ishikawa, Keitarou
- Subjects
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GAME theory , *BLOCKING sets , *GROUP decision making , *MATHEMATICAL analysis , *MATHEMATICS , *FINITE geometries - Abstract
Abstract: This paper shows some elementary facts on simple games with respect to blockability relations. It is verified in this paper that fundamental concepts on simple games as null players, dictators, veto players, and so on can be expressed in terms of blockability relations. More, some new concepts as “conflict-free” and so on, are introduced from the viewpoint of blockability relations into the framework of simple games. [Copyright &y& Elsevier]
- Published
- 2009
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37. On 2-factors with cycles containing specified edges in a bipartite graph
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Yan, Jin and Liu, Guizhen
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FACTORS (Algebra) , *BIPARTITE graphs , *QUADRILATERALS , *MATHEMATICAL analysis , *GRAPH theory , *MATHEMATICS - Abstract
Abstract: Let be an integer and a bipartite graph with such that . In this paper it has been proved that if for each pair of nonadjacent vertices and , , then for any independent edges of , has a 2-factor with cycles such that and for each . We shall also show that the conditions in this paper are sharp. [Copyright &y& Elsevier]
- Published
- 2009
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38. Relaxed very asymmetric coloring games
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Yang, Daqing
- Subjects
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GRAPH coloring , *GRAPH theory , *MATHEMATICAL analysis , *MATHEMATICS , *COMBINATORICS , *ALGEBRA - Abstract
Abstract: This paper investigates a competitive version of the coloring game on a finite graph . An asymmetric variant of the -relaxed coloring game is called the -relaxed -coloring game. In this game, two players, Alice and Bob, take turns coloring the vertices of a graph , using colors from a set , with . On each turn Alice colors vertices and Bob colors vertices. A color is legal for an uncolored vertex if by coloring with color , the subgraph induced by all the vertices colored with has maximum degree at most . Each player is required to color an uncolored vertex legally on each move. The game ends when there are no remaining uncolored vertices. Alice wins the game if all vertices of the graph are legally colored, Bob wins if at a certain stage there exists an uncolored vertex without a legal color. The -relaxed -game chromatic number, denoted by , of is the least for which Alice has a winning strategy in the -relaxed -coloring game. The -relaxed -coloring game has been well studied and there are many interesting results. For the -relaxed -coloring game, this paper proves that if a graph has an orientation with maximum outdegree and , then for all ; If , then - for all . [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
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39. The crossing numbers of generalized Petersen graphs with small order
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Lin, Xiaohui, Yang, Yuansheng, Zheng, Wenping, Shi, Lei, and Lu, Weiming
- Subjects
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PETERSEN graphs , *GRAPH theory , *EMBEDDINGS (Mathematics) , *NUMBER theory , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: The generalized Petersen graph is an undirected graph on vertices with and . Fiorini claimed to have determined the crossing numbers of and showed all the values of for up to 14, except 12 unknown values. Lovrečič Saražin proved . Richter and Salazar found a gap in Fiorini’s paper, which invalidated his principal results about , and gave the correct proof for . In this paper, we show the crossing numbers of all for up to 16. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
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40. Stochastic controllability and minimum energy control of systems with multiple delays in control
- Author
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Klamka, Jerzy
- Subjects
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LINEAR control systems , *STOCHASTIC processes , *AUTOMATIC control systems , *LINEAR systems , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: In the paper finite-dimensional stationary dynamical control systems described by linear stochastic ordinary differential state equations with multiple point delays in the control are considered. Using notations, theorems and methods taken directly from deterministic controllability problems for linear dynamical systems with delays in control, necessary and sufficient conditions for different kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that under suitable assumptions relative controllability of a deterministic linear associated dynamical system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamical system. As a special case relative stochastic controllability of dynamical systems with single point delay is also considered. Some remarks and comments on the existing results for stochastic controllability of linear dynamical systems are also presented. In the second part of the paper minimum energy control problem is considered. Under the assumption that system is stochastically relatively exactly controllable analytical formula for minimum energy control is given. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
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41. Rank equalities related to the generalized inverse with applications
- Author
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Wang, Qing-Wen, Song, Guang-Jing, and Lin, Chun-Yan
- Subjects
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MATHEMATICAL formulas , *MATRICES (Mathematics) , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: A variety of rank formulas of some matrix expressions and certain partitioned matrices with respect to the generalized inverse are established. Some necessary and sufficient conditions are given by using the rank formulas presented in this paper for two, three and four ordered matrices to be independent in the generalized inverse . As special cases, necessary and sufficient conditions are derived for two, three and four ordered matrices to be independent in the weighted Moore–Penrose inverse and the Drazin inverse. Some known results can be regarded as the special cases of the results in this paper. [Copyright &y& Elsevier]
- Published
- 2008
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42. Using Monte Carlo method for ranking interval data
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Jahanshahloo, G.R., Lotfi, F. Hosseinzadeh, Balf, F. Rezai, and Rezai, H. Zhiani
- Subjects
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MONTE Carlo method , *MATHEMATICAL analysis , *MATHEMATICAL models , *MATHEMATICS - Abstract
Abstract: Some methods have been presented for ranking efficient decision making units (DMUs) in data envelopment analysis (DEA). This paper addresses the ranking of interval data by using Monte Carlo method. This method is based on a paper [G.R. Jahanshahloo, F. Hosseinzadeh Lotfi, H. Zhiani Rezai, F. Rezai Balf, Using Monte Carlo method for ranking efficient DMUs, Applied Mathematics and Computation 162 (2005) 371–379]. The worthwhile this method is its ability in ranking of extreme and non-extreme efficient DMUs. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
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43. On approximation by a class of new Bernstein type operators
- Author
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Deo, Naokant, Noor, Muhammad Aslam, and Siddiqui, M.A.
- Subjects
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MATHEMATICAL optimization , *MATHEMATICAL analysis , *MATHEMATICAL models , *MATHEMATICS - Abstract
Abstract: This paper is concerned with a new type of the classical Bernstein operators where the function is evaluated at intervals . We also make extensive study simultaneous approximation by the linear combination of these new Bernstein type operators . At the end of this paper we have given an other modification of these operators. [Copyright &y& Elsevier]
- Published
- 2008
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44. Optimisation of a fuzzy physical habitat model for spawning European grayling (Thymallus thymallus L.) in the Aare river (Thun, Switzerland)
- Author
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Mouton, Ans M., Schneider, Matthias, Peter, Armin, Holzer, Georg, Müller, Rudolf, Goethals, Peter L.M., and De Pauw, Niels
- Subjects
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MATHEMATICAL optimization , *MATHEMATICAL analysis , *MATHEMATICS , *MAXIMA & minima - Abstract
Abstract: Ecological expert knowledge is often based on qualitative rules consisting of linguistic terms such as ‘low’, ‘moderate’ or ‘high’. Since fuzzy systems transform these rules and terms into a mathematical framework, they allow implementing this expert knowledge in ecological models. However, the development of a reliable knowledge base is complex and time consuming. Recent research has shown that complementing fuzzy systems by data-driven techniques can solve this knowledge acquisition bottleneck. In this paper, a heuristic nearest ascent hill-climbing algorithm for rule base optimisation is applied to construct a fuzzy rule-based habitat suitability model for spawning European grayling (Thymallus thymallus L.) in the Aare river (Bern, Switzerland). Optimisation of the fuzzy rule-based model was based on two different training criteria, the weighted correctly classified instances and Cohen''s Kappa. The ecological relevance of the results was assessed by comparing the optimised rule bases with a rule base derived from ecological expert knowledge. Optimisation based on Kappa appeared to generate acceptable results (CCI=0.70; Kappa=0.32) and was more practical than optimisation based on since the latter required fine tuning of a weight parameter, which accounted for the species prevalence. The optimal rules showed 74% similarity with the rules derived from expert knowledge, while 84% of all model errors was due to false positive predictions of the model. These errors might be due to the impact of variables, which were not included in this study on grayling presence and thus are not necessarily a model error. The habitat suitability model optimised in this paper is able to predict the effect of different impacts on the river system and to select the optimal restoration option. Hence, it could be a valuable decision support tool for river managers and ease the discussion between stakeholders. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
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45. Quantization of generalized Virasoro-like algebras
- Author
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Song, Guang’ai, Su, Yucai, and Wu, Yuezhu
- Subjects
- *
ALGEBRA , *MATHEMATICAL analysis , *MATHEMATICS , *VECTOR analysis - Abstract
Abstract: In a recent paper by the authors, Lie bialgebras structures of generalized Virasoro-like type were considered. In this paper, the explicit formula of the quantization of generalized Virasoro-like algebras is presented. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
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46. Qualitative analysis of second-order models of tumor–immune system competition
- Author
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Cattani, C. and Ciancio, A.
- Subjects
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MATHEMATICAL analysis , *MATHEMATICS , *ALGEBRA , *LINEAR algebra - Abstract
Abstract: This paper deals with the qualitative analysis, existence of equilibria and asymptotic behavior of some second-order models of the competition between tumor and immune cells. The background model belongs to d’Onofrio [A. d’Onofrio, A general framework for modeling tumor–immune system competition and immunotherapy: Mathematical analysis and biomedical inferences, Physica D 208 (2005) 220–235; A. d’Onofrio, Tumor–immune system interaction: Modelig the tumor-stimulated proliferation of effectors and immunotherapy, Math. Models Methods Appl. Sci. 16 (2006) 1375–1401]. Various developments proposed in this paper are focussed on the hiding–learning dynamics, followed by the qualitative analysis. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
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47. A typed lambda calculus with intersection types
- Author
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Bono, Viviana, Venneri, Betti, and Bettini, Lorenzo
- Subjects
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MATHEMATICAL analysis , *MATHEMATICAL functions , *SET theory , *MATHEMATICS - Abstract
Abstract: Intersection types are well known to type theorists mainly for two reasons. Firstly, they type all and only the strongly normalizable lambda terms. Secondly, the intersection type operator is a meta-level operator, that is, there is no direct logical counterpart in the Curry–Howard isomorphism sense. In particular, its meta-level nature implies that it does not correspond to the intuitionistic conjunction. The intersection type system is naturally a type inference system (system à la Curry), but the meta-level nature of the intersection operator does not allow to easily design an equivalent typed system (system à la Church). There are many proposals in the literature to design such systems, but none of them gives an entirely satisfactory answer to the problem. In this paper, we will review the main results in the literature both on the logical interpretation of intersection types and on proposed typed lambda calculi. The core of this paper is a new proposal for a true intersection typed lambda calculus, without any meta-level notion. Namely, any typable term (in the intersection type inference) has a corresponding typed term (which is the same as the untyped term by erasing the type decorations and the typed term constructors) with the same type, and vice versa. The main idea is to introduce a relevant parallel term constructor which corresponds to the intersection type constructor, in such a way that terms in parallel share the same resources, that is, the same context of free typed variables. Three rules allow us to generate all typed terms. The first two rules, Application and Lambda-abstraction, are performed on all the components of a parallel term in a synchronized way. Finally, via the third rule of Local Renaming, once a free typed variable is bounded by lambda-abstraction, each of the terms in parallel can do its local renaming, with type refinement, of that particular resource. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
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48. A multiresolution finite volume scheme for two-dimensional hyperbolic conservation laws
- Author
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Tang, Lingyan and Song, Songhe
- Subjects
- *
FINITE volume method , *NUMERICAL analysis , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, high-resolution finite volume schemes are combined with an adaptive mesh technique inspired by multiresolution analysis to improve the computational efficiency for two-dimensional hyperbolic conservation laws. The method is conservative. Moreover, it is stable which is proven numerically in this paper. The computational grid is dynamically adapted so that higher spatial resolution is automatically allocated to regions where strong gradients are observed. Using this proposed scheme, we compute several two-dimensional model problems and a compressive rate ranging from about 5–10 is observed in all simulations. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
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49. Security risks and probabilistic risk assessment of glazing subject to explosive blast loading
- Author
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Stewart, Mark G. and Netherton, Michael D.
- Subjects
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BLAST effect , *PROBABILITY theory , *MATHEMATICAL analysis , *AERODYNAMIC load , *RELIABILITY in engineering , *INDUSTRIAL engineering , *MATHEMATICS - Abstract
Abstract: A probabilistic risk assessment (PRA) procedure is developed which can predict risks of explosive blast damage to built infrastructure. The present paper focuses on window glazing since this is a load-capacity system which, when subject to blast loading, has caused significant damage and injury to building occupants. Structural reliability techniques are used to derive fragility and blast reliability curves (BRCs) for annealed and toughened glazing subjected to explosive blast, for a variety of threat scenarios. The probabilistic analyses include the uncertainties associated with blast modelling, glazing response and glazing failure criteria. Damage risks are calculated for an individual window and for windows in the facade of a multi-storey commercial building. If threat probabilities can be estimated then the paper shows illustrative examples of how this information, when combined with risk-based decision-making criteria, can be used to optimise risk mitigation strategies. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
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50. The model evolution calculus as a first-order DPLL method
- Author
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Baumgartner, Peter and Tinelli, Cesare
- Subjects
- *
MATHEMATICAL analysis , *MATHEMATICS , *CALCULUS , *MATHEMATICAL functions - Abstract
Abstract: The DPLL procedure is the basis of some of the most successful propositional satisfiability solvers to date. Although originally devised as a proof-procedure for first-order logic, it has been used almost exclusively for propositional logic so far because of its highly inefficient treatment of quantifiers, based on instantiation into ground formulas. The FDPLL calculus by Baumgartner was the first successful attempt to lift the procedure to the first-order level without resorting to ground instantiations. FDPLL lifts to the first-order case the core of the DPLL procedure, the splitting rule, but ignores other aspects of the procedure that, although not necessary for completeness, are crucial for its effectiveness in practice. In this paper, we present a new calculus loosely based on FDPLL that lifts these aspects as well. In addition to being a more faithful lifting of the DPLL procedure, the new calculus contains a more systematic treatment of universal literals, which are crucial to achieve efficiency in practice. The new calculus has been implemented successfully in the Darwin system, described elsewhere. The main results of this paper are theoretical, showing the soundness and completeness of the new calculus. In addition, the paper provides a high-level description of a proof procedure for the calculus, as well as a comparison with other calculi. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
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