Related papers: The Star of David Rule
Strange stars ought to exist in the universe according to the strange quark matter hypothesis, which states that matter made of roughly equal numbers of up, down, and strange quarks could be the true ground state of baryonic matter rather…
Recent work on the use of dimensional reduction for the regularisation of non--supersymmetric theories is reviewed. It is then shown that there exists a class of theories for which a universal form of the soft supersymmetry breaking terms…
Matrix inequalities that extend certain scalar ones have been at the center of numerous researchers' attention. In this article, we explore the celebrated subadditive inequality for matrices via concave functions and present a reversed…
We compare previously found finite-dimensional matrix and integral operator realizations of the Bailey lemma employing univariate elliptic hypergeometric functions. With the help of residue calculus we explicitly show how the integral…
A g-circulant matrix of order n is defined as a matrix of order n where each row is a right cyclic shift in g-places to the preceding row. Using number theory, certain nonnegative g-circulant real matrices are constructed. In particular, it…
Two new matrix classes are introduced; inverse cyclic matrices and bi-diagonal south-west matrices. An interesting relation is established between these classes. Applications to two classes of inverse $Z$-matrices are provided.
The famous \emph{circular law} asserts that if $M_n$ is an $n \times n$ matrix with iid complex entries of mean zero and unit variance, then the empirical spectral distribution (ESD) of the normalized matrix $\frac{1}{\sqrt{n}} M_n$…
Square matrices of the form $\widetilde{\mathbf{A}} =\mathbf{A} + \mathbf{e}D \mathbf{f}^*$ are considered. An explicit expression for the inverse is given, provided $\widetilde{\mathbf{A}}$ and $D$ are invertible with…
Pairwise comparison matrices often exhibit inconsistency, therefore many indices have been suggested to measure their deviation from a consistent matrix. A set of axioms has been proposed recently that is required to be satisfied by any…
The sign patterns of inverse doubly-nonnegative matrices are examined. A necessary and sufficient condition is developed for a sign matrix to correspond to an inverse doubly-nonnegative matrix. In addition, for a doubly-nonnegative matrix…
Rotation curves of spiral galaxies are known with reasonable precision for a large number of galaxies with similar morphologies. The data implies that non-Keplerian fall--off is seen. This implies that (i) large amounts of dark matter must…
Based on work presented in [4], we define $S^2$-Upper Triangular Matrices and $S^2$-Lower Triangular Matrices, two special types of $d\times d(2d-1)$ matrices generalizing Upper and Lower Triangular Matrices, respectively. Then, we show…
The Circle Pattern Theorem characterizes the existence and rigidity of circle patterns with prescribed intersection angles on simplicial triangulations of closed surfaces. In this paper we extend the theorem to quasi-simplicial…
An elementary proof of the two-sidedness of the matrix-inverse is given using only linear independence and the reduced row-echelon form of a matrix. In addition, it is shown that a matrix is invertible if and only if it is row-equivalent to…
This paper deals with a kind of design of a ruled surface. It combines concepts from the fields of computer aided geometric design and kinematics. A dual unit spherical B\'ezier-like curve on the dual unit sphere (DUS) is obtained with…
There has recently been renewed recognition of the need to understand the consistency properties that must be preserved when a generalized matrix inverse is required. The most widely known generalized inverse, the Moore-Penrose…
The antiprism triangulation provides a natural way to subdivide a simplicial complex $\Delta$, similar to barycentric subdivision, which appeared independently in combinatorial algebraic topology and computer science. It can be defined as…
We consider a nonstandard odd reduction of supermatrices (as compared with the standard even one) which arises in connection with possible extension of manifold structure group reductions. The study was initiated by consideration of the…
Recent studies have drawn attention to the untapped potential of the "star operation" (element-wise multiplication) in network design. While intuitive explanations abound, the foundational rationale behind its application remains largely…
We consider the problem of determining the limiting spectral distribution for random matrices whose row distributions are permitted to have limited dependence. We assume mild moment conditions and give an extension of the…