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...     

Impenetrable barriers in phase-space.

Dynamical systems theory is used to construct a general phase-space version of transition state theory. Special multidimensional separatrices are found which act as impenetrable barriers in phase-space between reacting and nonreacting trajectories. The elusive momentum-dependent transition state between reactants and products is thereby characterized. A practical algorithm is presented and applied to a strongly coupled Hamiltonian.     

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.     

Spectrophotometric determination of cyclotrimethylenetrinitramine (RDX) in explosive mixtures and residues with the Berthelot reaction

On-site colorimetric methods are a valuable, cost-effective tool to assess the nature and extent of contamination in remediated sites and to enable on-site screening for police criminology laboratories. The existing colorimetric method for cyclotrimethylenetrinitramine (RDX) based on a Griess reaction suffers from the non-quantitative reduction to nitrite and from the unstable character of HNO₂ in acidic medium. Thus we propose a novel spectrophotometric RDX assay in explosive mixtures and residues, based on (Zn + HCl) reduction of RDX in a microwave oven, followed by neutralization of the reduction products to ammonia and low molecular-weight amines, and Berthelot reaction of these amine-compounds with phenol and hypochlorite in alkaline medium to give an intensely blue indophenol dye absorbing at 631 nm. The molar absorptivity and limit of detection (LOD) for RDX were (1.08 ± 0.04) × 10⁴ L mol⁻¹ cm⁻¹ and 0.18 mg L⁻¹, respectively. Application of the method to synthetic mixture solutions of RDX and trinitrotoluene (TNT) at varying proportions showed that there was minimal interference from TNT (which could be compensated for by dicyclohexylamine colorimetry), since the Berthelot reaction was essentially non-responsive to m-substituted anilines derived from TNT upon (Zn + HCl) reduction. The proposed method was successfully applied to military-purpose explosive mixtures of (RDX + inert matter) such as Comp A5, Comp C4, and Hexal P30, and to (RDX + TNT) mixtures such as Comp B. The molar absorptivity of RDX was much higher than that of either ammonium or nitrate; RDX could be effectively separated from ammonium and nitrate in soil mixtures, based on solubility differences. The Berthelot method for RDX was statistically validated using Comp B mixtures against standard HPLC equipped with a Hypersil C-18 column with (40% MeOH-60% H₂O) mobile phase, and against gas chromatography-thermal energy analysis (GC-TEA) system.     

Bifurcations as dissociation mechanism in bichromatically driven diatomic molecules

We discuss the influence of periodic orbits on the dissociation of a model diatomic molecule driven by a strong bichromatic laser fields. Through the stability of periodic orbits, we analyze the dissociation probability when parameters, such as the two amplitudes and the phase lag between the laser fields, are varied. We find that qualitative features of dissociation can be reproduced by considering a small set of short periodic orbits. The good agreement with direct simulations demonstrates the importance of bifurcations of short periodic orbits in the dissociation dynamics of diatomic molecules.