Some Classifications of Biharmonic Lorentzian Hypersurfaces in Minkowski 5-Space

Mediterranean Journal of Mathematics - In this paper, we study Lorentzian hypersurfaces in Minkowski 5-space with non-diagonalizable shape operator whose characteristic polynomial is (t − k...     

Space-Like Surfaces in the Minkowski Space with Pointwise 1-Type Gauss Maps

Ukrainian Mathematical Journal - We first classify space-like surfaces in the Minkowski space , de Sitter space , and hyperbolic space ?3 with harmonic Gauss maps. Then we characterize and...     

Expected Number of Real Roots for Random Linear Combinations of Orthogonal Polynomials Associated with Radial Weights

In this note, we obtain asymptotic expected number of real zeros for random polynomials of the form

$$f_{n}(z)=\sum\limits_{j=0}^{n}{a^{n}_{j}}{c^{n}_{j}}z^{j}$$

where \({a^{n}_{j}}\) are independent and identically distributed real random variables with bounded (2 + δ)th absolute moment and the deterministic numbers \({c^{n}_{j}}\) are normalizing constants for the monomials z ^j within a weighted L ²-space induced by a radial weight function satisfying suitable smoothness and growth conditions.

     

Synthesis and Characterization of Borax-Polyimide for Flame Retardant Applications

Polyamide-borax composites were prepared from solution of polyimide and the borax using N-methyl-2-pyrrolidone as a solvent. The Polyimide-borax composites films (PI-BX) characterized by FTIR, SEM and x-ray. The borax content significantly influences thermal behavior of the polymeric films, such as glass transition and decomposition temperatures of polyimide-borax composites. The glass transition temperatures of the composites were higher than that of the original polyimide. The flammability properties of them were demonstrated by cone calorimeter and indicate that the borax composites have significantly decreased in heat release rate, and mass loss rate. The PI-BX composites appears very good the flame retardant properties.     

A rational approximate solution for generalized pantograph‐delay differential equations

In this paper, a new rational approximation based on a rational interpolation and collocation method is proposed for the solutions of generalized pantograph equations. A comprehensive error analysis is provided. The first part of the error analysis gives an upper bound for the absolute error. The second part is based on residual error procedure that estimates the absolute error. Some numerical examples are given to illustrate the method. The theoretical results support the numerical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Toeplitz Operators on Arveson and Dirichlet Spaces

We define Toeplitz operators on all Dirichlet spaces on the unit ball of and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate some connections between Toeplitz and shift operators. The research of the second author is partially supported by a Fulbright grant.     

A Novel Method for the Synthesis of Newfangled Asymmetric Schiff Bases from α‐amino Acids under Ultrasonic Conditions and in Aqueous Medium

Chiral Schiff bases were obtained at high yields via a novel technique. Aryl aldehydes and chiral α‐amino acids were treated (1) in the presence of H₃PO₄ in ethanol at 80°C for 24 h, and (2) in the presence of K₂CO₃ under ultrasonic conditions in an aqueous ethanol medium within 5 min with yields reaching up to 96%. The results showed that the presented methodology under ultrasonic conditions was effective, practical, and eco‐friendly compared to that using an acidic medium. The corresponding asymmetric Schiff bases were synthesized for the first time, and were characterized by ¹H and ¹³C nuclear magnetic resonance and infrared spectroscopy and high‐resolution mass spectrometry.     

Bohr phenomena for Laplace-Beltrami operators

We investigate a Bohr phenomenon on the spaces of solutions of weighted Laplace-Beltrami operators associated with the hyperbolic metric of the unit ball in ?^N. These solutions do not satisfy the usual maximum principle, and the spaces have natural bases none of whose members is a constant function. We show that these bases exhibit a Bohr phenomenon, define a Bohr radius for them that extends the classical Bohr radius, and compute it exactly. We also compute the classical Bohr radius of the invariant harmonic functions on the real hyperbolic space.