Property (A) of third-order advanced differential equations

In the paper we offer criteria for property (A) of the third-order nonlinear functional differential equation with advanced argument $(a(t)(x'(t))^\gamma )'' + p(t)f(x(\sigma (t))) = 0,$ , where $\mathop \smallint \limits^\infty a^{ - 1/\gamma } (s)ds = \infty $ . We establish new comparison theorems for deducing property (A) of advanced differential equations from that of ordinary differential equations without deviating argument. The presented comparison principle fill the gap in the oscillation theory.     

An indefinite variant of LOBPCG for definite matrix pencils

In this paper, we propose a novel preconditioned solver for generalized Hermitian eigenvalue problems. More specifically, we address the case of a definite matrix pencil \(A-\lambda B\) , that is, A, B are Hermitian and there is a shift \(\lambda _{0}\) such that \(A-\lambda _{0} B\) is definite. Our new method can be seen as a variant of the popular LOBPCG method operating in an indefinite inner product. It also turns out to be a generalization of the recently proposed LOBP4DCG method by Bai and Li for solving product eigenvalue problems. Several numerical experiments demonstrate the effectiveness of our method for addressing certain product and quadratic eigenvalue problems.     

On the guaranteed convergence of new two-point root-finding methods for polynomial zeros

We presented new two-point methods for the simultaneous approximation of all n simple (real or complex) zeros of a polynomial of degree n. We proved that the R-order of convergence of the total-step version is three. Moreover, computationally verifiable initial conditions that guarantee the convergence of one of the proposed methods are stated. These conditions are stated in the spirit of Smale’s point estimation theory; they depend only on available data, the polynomial coefficients, polynomial degree n and initial approximations \(x_{1}^{(0)},\ldots ,x_{n}^{(0)}\) , which is of practical importance. Using the Gauss-Seidel approach we state the corresponding single-step version and consequently its prove that the lower bound of its R-order of convergence is at least 2 + y _n > 3, where y _n ∈ (1, 2) is the unique positive root of the equation y ⁿ ? y ? 2 = 0. Two numerical examples are given to demonstrate the convergence behavior of the considered methods, including global convergence.     

An integer linear formulation for the file transfer scheduling problem

In this paper, we propose a new integer linear programming (ILP) formulation for solving a file transfer scheduling problem (FTSP), which is to minimize the overall time needed to transfer all files to their destinations for a given collection of various sized files in a computer network. Each computer in this network has a limited number of communication ports. The described problem is proved to be NP-hard in a general case. Our formulation enables solving the problem by standard ILP solvers like CPLEX or Gurobi. To prove the validity of the proposed ILP formulation, two new reformulations of FTSP are presented. The results obtained by CPLEX and Gurobi solvers, based on this formulation, are presented and discussed.     

Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces

In this paper, the boundedness of a large class of sublinear commutator operators T _b generated by a Calderón-Zygmund type operator on a generalized weighted Morrey spaces \({M_{p,\varphi }}(w)\) with the weight function w belonging to Muckenhoupt’s class A _p is studied. When 1 < p < ∞ and b ∈ BMO, sufficient conditions on the pair (φ ₁, φ ₂) which ensure the boundedness of the operator T _b from \({M_{p,\varphi 1}}(w)\) to \({M_{p,\varphi 2}}(w)\) are found. In all cases the conditions for the boundedness of T _b are given in terms of Zygmund-type integral inequalities on (φ ₁, φ ₂), which do not require any assumption on monotonicity of φ ₁(x, r), φ ₂(x, r) in r. Then these results are applied to several particular operators such as the pseudo-differential operators, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.     

On stretching the interval simplex-permutohedron

A family of polytopes introduced by E.M. Feichtner, A. Postnikov, and B. Sturmfels, which were named nestohedra, consists in each dimension of an interval of polytopes starting with a simplex and ending with a permutohedron. This paper investigates a problem of changing and extending the boundaries of these intervals. An iterative application of Feichtner–Kozlov procedure of forming complexes of nested sets is a solution of this problem. By using a simple algebraic presentation of members of nested sets it is possible to avoid the problem of increasing the complexity of the structure of nested curly braces in elements of the produced simplicial complexes.     

Schur‐convexity and quadrature formulae

This paper aims to contribute to the exploration of quadrature formulae by proving that the error of a quadrature formula has the Schur‐convexity property. The emphasis is on the quadrature formulae with the maximum degree of precision. The Schur‐convexity of the error has an interesting implication – the monotonicity of the error. Namely, it turns out that the absolute value of the error is always smaller on a smaller interval (of the two which share the same midpoint).     

Ca3N2 as a flux for crystallization of GaN

In this work Ca₃N₂ was investigated as a potential flux for crystallization of GaN. Melting temperature of the potential flux at high N₂ pressure evaluated by thermal analysis as 1380 °C is in good agreement with the theoretical prediction. It is shown that Ca₃N₂ present in the liquid gallium in small amount (1 at%) dramatically accelerates synthesis of GaN from its constituents. On the other hand, it does not influence significantly the rate of GaN crystallization from solution in gallium in temperature gradient for both unseeded and seeded configurations. However the habit and color of the spontaneously grown GaN crystals change drastically. For 10 mol% Ca₃N₂ content in the liquid Ga it was found that the GaN thick layer and GaN crystals (identified by micro-Raman scattering measurements) were grown on the substrate. For growth from molten Ca₃N₂ (100%) with GaN source, the most important observations were (i) GaN source material was completely dissolved in the molten Ca₃N₂ flux and (ii) after experiment, GaN crystals were found on the sapphire substrate.     

Chloro-Bridged Dimeric Cadmium(II)-Isothiocyanate Complex with a Tridentate NNN Type Ligand: Synthesis,X-ray Structure,Thermal Analysis

Abstract  

The dinuclear cadmium(II) complex with 2,6-bis(3,4,5-trimethyl-N-pyrazolyl)pyridine (btmpp) has been synthesized, and characterized by single crystal X-ray diffraction, IR, UV–Vis and TGA–DTA methods. Cd atoms are located in a distorted octahedral environment in the complex. The complex crystalizes in monoclinic space group C 2/c, with unit cell dimensions a = 20.5636(12) Å, b = 14.0167(13) Å, c = 15.6598(11) Å, β = 113.425(5)o, V = 4141.7(5) Å³. There are two intermolecular and a intramolecular hydrogen bonds interactions in crystal.     

Quantitative Structure—Retention Relationships Study of the Retention Data of 5,5-Disubstituted Hydantoins

JPC – Journal of Planar Chromatography – Modern TLC - The behavior of 5,5-disubstituted hydantoin derivatives has been studied using four chromatographic systems, two normal-phase...