The problem of finding mr(F,G) and describing Gk(F ) has recently attracted considerable attention, particularly for the case in which F = R (see [29, 17, 26, 25, 27, 13, 33, 5, 9, 22, 2, 11, 6, 7, 10, 18, 4]). The minimum rank problem over R is a sub-problem of a much more general problem, the inverse eigenvalue problem for symmetric matrices: given a family of real numbers, find every symmetr...

A result of Zyczkowski and Sommers [J. Phys. A 33, 2045–2057 (2000)] gives the eigenvalue probability density function for the top N ×N sub-block of a Haar distributed matrix from U(N + n). In the case n ≥ N , we rederive this result, starting from knowledge of the distribution of the sub-blocks, introducing the Schur decomposition, and integrating over all variables except the eigenvalues. The...

In this paper, we use a simple method to derive di¤erent recurrence relations on the Tribonacci numbers and their sums. By using the companion matrices and generating matrices, we get more identities on the Tribonacci numbers and their sums, which are more general than that given in literature [E. Kilic, Tribonacci Sequences with Certain Indices and Their Sum, Ars Combinatoria 86 (2008), 13-22....

One important class of hydrogels based on natural polymers is the Glycosaminoglycan (GAG)-based hydrogels. In hydrogels biomaterial science, the mathematical modeling and computer simulation plays a complementary interpretative role in deciphering the complex physical/chemical and biological properties of this class of substances. Aim: the molecular modeling studies presented here aimed the inf...

We present a scheme for reconstructing a 3D structure from optical flow observed by a camera with an unknown focal length in a statistically optimal way as well as evaluating the reliability of the computed shape. First, the flow fundamental matrices are optimally computed from the observed flow. They are then decomposed into the focal length, its rate of change, and the motion parameters. Next...

This is a critical review of what the Marxist scientific literature presents on forms countertendency to falling profit rates carried out during COVID-19 pandemic. The 33 articles included in this were studied using approach. following elements synthesized and criticized: analysis matrices, methodological aspects articles, contrary law tendency rate fall, cases their contexts analysis. reviewed...

[1] Several recent publications have indicated that cloud droplets belonging to a particular size range may tend to cluster by forming small random particle groups imbedded in an otherwise uniform cloud. To analyze radiative transfer in clouds with such small-scale inhomogeneities, we invoke the concepts of statistical electromagnetics. We show that as long as the assumptions of ergodicity and ...

0. Introduction and Preliminary 2 0.1. Existence and uniqueness theorem 2 0.2. Equation of a chain 7 1. Nonsingular matrices 9 1.1. A family of nonsingular matrices 9 1.2. Sufficient condition for Nonsingularity 12 1.3. Estimates 16 2. Local automorphism group of a real hypersurface 23 2.1. Polynomial Identities 23 2.2. Injectivity of a Linear Mapping 33 2.3. Beloshapka-Loboda Theorem 42 3. Com...

MOTIVATION Sequence similarity searches performed with BLAST, SSEARCH and FASTA achieve high sensitivity by using scoring matrices (e.g. BLOSUM62) that target low identity (<33%) alignments. Although such scoring matrices can effectively identify distant homologs, they can also produce local alignments that extend beyond the homologous regions. RESULTS We measured local alignment start/stop b...

Abstract Methods for experimental reconstruction of molecular frame (MF) photoionization dynamics, and related properties—specifically MF photoelectron angular distributions (PADs) continuum density matrices—are outlined discussed. General concepts are introduced the non-expert reader, theoretical techniques further in some depth. Particular focus is placed on a detailed example numerical matri...