广义Nekrasov矩阵的细分迭代判别法

利用细分矩阵下标集合的思想,构造递进系数和特殊的正对角矩阵,结合不等式的放缩,给出广义Nekrasov矩阵的迭代判别法,推广和改进了已有相关结果,并用数值实例说明了所得结果的优越性.     

Numerical technique based on generalized Laguerre and shifted Chebyshev polynomials

In this study, we present a numerical scheme for solving a class of fractional partial differential equations. First, we introduce psi -Laguerre polynomials like psi-shifted Chebyshev polynomials and employ these newly introduced polynomials for the solution of space-time fractional differential equations. In our approach, we project these polynomials to develop operational matrices of fractional integration. The use of these orthogonal polynomials converts the problem under consideration into a system of algebraic equations. The solution of this system provide us the desired results. The convergence of the proposed method is analyzed. Finally, some illustrative examples are included to observe the validity and applicability of the proposed method.     

Combinatorial identities related to 2 × 2 submatrices of recursive matrices

Recursive matrices are ubiquitous in combinatorics, which have been extensively studied. We focus on the study of the sums of 2 × 2 minors of certain recursive matrices, the alternating sums of their 2 × 2 minors, and the sums of their 2 × 2 permanents. We obtain some combinatorial identities related to these sums, which generalized the work of Sun and Ma (2014) [23,24]. With the help of the computer algebra package HolonomicFunctions, we further get some new identities involving Narayana polynomials.     

Classification of multivariate skew polynomial rings over finite fields via affine transformations of variables

In this work, free multivariate skew polynomial rings are considered, together with their quotients over ideals of skew polynomials that vanish at every point (which includes minimal multivariate skew polynomial rings). We provide a full classification of such multivariate skew polynomial rings (free or not) over finite fields. To that end, we first show that all ring morphisms from the field to the ring of square matrices are diagonalizable, and that the corresponding derivations are all inner derivations. Secondly, we show that all such multivariate skew polynomial rings over finite fields are isomorphic as algebras to a multivariate skew polynomial ring whose ring morphism from the field to the ring of square matrices is diagonal, and whose derivation is the zero derivation. Furthermore, we prove that two such representations only differ in a permutation on the field automorphisms appearing in the corresponding diagonal. The algebra isomorphisms are given by affine transformations of variables and preserve evaluations and degrees. In addition, ours proofs show that the simplified form of multivariate skew polynomial rings can be found computationally and explicitly.     

Total positivity of Narayana matrices

We prove the total positivity of the Narayana triangles of type $A$ and type $B$, and thus affirmatively confirm a conjecture of Chen, Liang and Wang and a conjecture of Pan and Zeng. We also prove the strict total positivity of the Narayana squares of type $A$ and type $B$.     

Global bifurcation of solutions of the mean curvature spacelike equation in certain Friedmann–Lemaître–Robertson–Walker spacetimes

We study the existence of spacelike graphs for the prescribed mean curvature equation in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. By using a conformal change of variable, this problem is translated into an equivalent problem in the Lorentz–Minkowski spacetime. Then, by using Rabinowitz's global bifurcation method, we obtain the existence and multiplicity of positive solutions for this equation with 0-Dirichlet boundary condition on a ball. Moreover, the global structure of the positive solution set is studied.     

On the classification of Hadamard matrices of order 32

All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of Hadamard matrices. We find all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that there are exactly 13, 680, 757 Hadamard matrices of one type and 26, 369 such matrices of another type. Based on experience with the classification of Hadamard matrices of smaller order, it is expected that the number of the remaining two types of these matrices, relative to the total number of Hadamard matrices of order 32, to be insignificant. © 2009 Wiley Periodicals, Inc. J Combin Designs 18:328–336, 2010     

Motion transformation in a higher order dimensional space

The objective of the work presented in this paper is an attempt at solving and transforming of the known from the classical mechanics two dimensional-plane single mass mechanical and mathematical vibration models in a higher order dimensional space with any virtual sectional curvature-positive or negative, constant or variable. A characterization of the Riemannian manifolds is performed by means of curvature operators. The computer codes Mathematica and MATLAB are used in the numerical simulation. The objects of the investigation are a sphere – with a positive constant sectional curvature, a cylinder-with a zero constant sectional curvature, helicoid-with a negative variable sectional curvature, a torus-with a variable (±) sectional curvature, any virtual surface of second order-with a variable (±) sectional curvature, pseudo-sphere – with a negative constant sectional curvature and a saddle-with a negative variable sectional curvature. The system motion is investigated in a qualitative aspect in time and frequency domain on the cited surfaces. The common algorithm derived in the paper can transform any motion from 3D space to curved manifold. We can derive the trajectory in an explicit form on the curved manifold. We can change the trajectory by a suitable variation of the curved manifold.     

Existence of positive solutions of superlinear second-order Neumann boundary value problem

In this paper, we consider the Neumann boundary value problem

     

An always convergent algorithm for the largest eigenvalue of an irreducible nonnegative tensor

In this paper we propose an iterative method to calculate the largest eigenvalue of a nonnegative tensor. We prove this method converges for any irreducible nonnegative tensor. We also apply this method to study the positive definiteness of a multivariate form.