Convex bodies and multiplicities of ideals

We associate convex regions in ? ⁿ to m-primary graded sequences of subspaces, in particular m-primary graded sequences of ideals, in a large class of local algebras (including analytically irreducible local domains). These convex regions encode information about Samuel multiplicities. This is in the spirit of the theory of Gröbner bases and Newton polyhedra on the one hand, and the theory of Newton-Okounkov bodies for linear systems on the other hand. We use this to give a new proof as well as a generalization of a Brunn-Minkowski inequality for multiplicities due to Teissier and Rees-Sharp.     

PDA and Neural Network Investigation of Swirl Spray Interaction Phenomena

Experiments are performed to investigate the atomization characteristics of mixed‐interaction regions of sprays of two swirl injectors installed side by side. Both droplet size and velocity distributions on a plane perpendicular to the axes of the injectors are measured using a PDA system. As a result of the interaction phenomenon, a region of secondary atomization is identified that differs significantly from the hollow region spray of a single swirl injector. A neural network algorithm is used to reconstruct the entire spray field for both droplet size and velocity distribution in extrapolation regimes for injector spacing as well as three dimensional spatial coordinates. Excellent agreement between the predicted values and the measurements is obtained. It is observed that points on the extrapolation regime of the neural network can be predicted with an accuracy of 93 % using a training data set with less than 50 % of the number of data points to be predicted. The results indicate the capability of performing design‐ and optimization studies for pressure‐swirl injectors, with sufficient accuracy, by applying a modest amount of data in conjunction with an overall optimized value for the width of the probability.     

The study of thiazole adsorption upon BC2N nanotube: DFT/TD-DFT investigation

Structural Chemistry - Herein, we evaluated the adsorption of thiazole over the surface of BC2N nanotube using PBE and M06-2X functionals and 6-311G** standard basis set. We considered one and two...     

Algebraic Graph Theory for Sparse Flexibility Matrices

An efficient algorithm is presented for the formation of suboptimal cycle bases of graphs corresponding to sparse cycle adjacency matrices, leading to the formation of highly sparse flexibility matrices. The algorithm presented employs concepts from algebraic graph theory together with a Greedy-type algorithm to select cycles with small overlaps and uses a simple graph-theoretical method for controlling the independence of the selected cycles.     

Polystyrene-Supported,Al(OTf)3-Catalyzed Chemoselective Synthesis of Acylals from Aldehydes

Cross-linked polystyrene-supported aluminium triflate [Ps-Al(OTf)₃] has been shown to be a mild, efficient, and chemoselective heterogeneous Lewis acid catalyst for acetylation of aldehydes with acetic anhydride. The catalyst can be recovered simply and reused efficiently at least five times without any noticeable loss of catalytic activity.     

Extension of contractive maps in the Menger probabilistic metric space

In this article, the topological properties of the Menger probabilistic metric spaces and the mappings between these spaces are studied. In addition, contractive and k-contractive mappings are introduced. As an application, a new fixed point theorem in a chainable Menger probabilistic metric space is proved.     

Hopping spectroscopy in doped germanium near the metal-insulator transition

The density of states (DOS) in the vicinity of the Fermi level controls all transport phenomena at low temperatures near the metal-insulator transition (MIT). The well-known method for DOS-determination on the metallic side of the MIT, the so-called “tunneling spectroscopy”, is inapplicable on the insulating side because of the high sample resistance at low temperatures. In this work a new method for DOS-determination on the insulating side is presented. The method is based on the measurements of variable range hopping (VRH) resistance in magnetic fields. By analogy this method can be called “hopping spectroscopy”.     

Phonon-dislocation scattering and phonon equilibration in metals at low temperatures

It is shown that phonon-dislocation scattering does not contribute significantly to equilibrating the phonon system for potassium. The implications of this result are discussed for the phonon-drag contribution to the low-temperature electrical resistivity.     

Computation of some thermodynamic properties of nitrogen using a new intermolecular potential from molecular dynamics simulation

A new pair-potential energy function of nitrogen has been determined via the inversion of reduced viscosity collision integrals and fitted to obtain an analytical potential form. The pair-potential reproduces the second virial coefficient, viscosity, thermal conductivity, self-diffusion coefficient, and thermal diffusion factor of nitrogen in a good accordance with experimental data over wide ranges of temperatures and densities. We have also performed the molecular dynamics simulation to obtain pressure, internal energy, heat capacity at constant volume, and self-diffusion coefficient of nitrogen at different temperatures and densities using our calculated pair-potential and some other potentials. The molecular dynamics of the nitrogen molecules has been also used to determine nitrogen equation of state in two (low and high) pressure ranges. Our results are in a good agreement with experiment and literature values.