 ∂tu = − i ∂xj (ajk(x, t, u, ū,∇u,∇ū)∂xku) +~b1(x, t, u, ū,∇u,∇ū) · ∇u+~b2(x, t, u, ū,∇u,∇ū) · ∇ū + c1(x, t, u, ū)u+ c2(x, t, u, ū)ū+ f(x, t), where x ∈ R, t > 0, and A = (ajk(·))j,k=1,..,n is a real, symmetric matrix. Our aim is to study the existence, uniqueness and regularity of local solutions to the initial value problem (IVP) associated to the equation (1.1). In the case where A = (ajk(·...

In this paper, computational efficient technique is proposed to calculate the eigenvalues of a tridiagonal system matrix using Strum sequence and Gerschgorin theorem. The proposed technique is applicable in various control system and computer engineering applications. KeywordsEigenvalues, tridiagonal matrix, Strum sequence and Gerschgorin theorem. I.INTRODUCTION Solving tridiagonal linear syste...

Current nonnegative matrix factorization (NMF) deals with X = FG type. We provide a systematic analysis and extensions of NMF to the symmetric W = HH , and the weighted W = HSH . We show that (1) W = HH is equivalent to Kernel K-means clustering and the Laplacian-based spectral clustering. (2) X = FG is equivalent to simultaneous clustering of rows and columns of a bipartite graph. Algorithms a...

A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin–Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables x1, x2, . . .. This construction provides explicit expressions for the Hamiltonians in terms of the power sum symmetric functions pn = x n 1 + x n 2 + · · · and is ba...

Abstract This paper concerns test matrices for numerical linear algebra using an error-free transformation of floating-point arithmetic. For specified eigenvalues given by a user, we propose methods generating matrix whose are exactly known based on, example, Schur or Jordan normal form and block diagonal form. It is also possible to produce real with complex eigenvalues. Such useful algorithms...

In his survey paper [4], P. A. Griffiths conjectured (§9.2) the existence of a partial compactification for the arithmetic quotients of period matrix domains. In this paper we want to announce some results concerning the topological aspects of this conjecture for the case of the periods of 2-forms on a polarized Hodge manifold V. The period matrix domain D of all possible period matrices for th...

We study the system consisting of a linear matrix inequality (LMI) constraint and linear constraints of the form: A(x) := A0 + n ∑ i=1 xiAi 0, bj + a T j x ≥ 0 (j = 1, 2, . . . , q) where Ai are m×m symmetric matrices, aj and x ∈ IR , and bj ∈ IR. A(x) 0 means that A(x) is positive semidefinite. A constraint in the above system is redundant if eliminating it from the system does not change the ...

Inspired by recent work in the theory of central projections onto hyper-surfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert– Burch matrix that has a maximal symmetric subblock. We also prove that every Gorenstein perfect algebra of grade 1 can be presented, as a module, by a symmetric matrix. Both results are derived from the same elementary lemma about symme...

We study the asymmetric respectively symmetric conflict matrix of a multi-clause-set F , where the entry at position (i, j) is the number of literals, which appear positively in clause Ci of F and negatively in clause Cj (at the same time), respectively the number of clashes (at all) between Ci and Cj . A central problem is the determination of the symmetric/asymmetric conflict number of a (sym...

An $n$-by-$n$ matrix $A$ is called symmetric, skew-symmetric, and orthogonal if $A^T=A$, $A^T=-A$, $A^T=A^{-1}$, respectively. We give necessary sufficient conditions on a complex so that it sum of type ``"orthogonal $+$ symmetric" in terms the Jordan form $A-A^T$. also "orthogonal skew-symmetric" $A+A^T$.