Some aspects of polaritons and plasmons in materials

We have studied the interaction of optical phonons with photons. So, we have calculated the coupled modes of photons and transverse optical phonons and likewise, the dielectric function. We have found an alternative relation of the splitting between the frequencies of the longitudinal optical (LO) and transverse optical (TO) phonons in crystals. Likewise, we have studied the plasmon resonance frequency. We have determined the phonon–photon and the plasmon–photon coupling constant in ionic crystals and in metals, respectively, which is very close to the elastic force constant, and we have evaluated the bulk modulus. Further we have applied these results to tetrahedrally bonded III–V semiconductors.     

On some tests of growth curve model under Behrens-Fisher stituation

In this article, we have considered the problem of testing equality of several growth curves under Behrens-Fisher situation. In this context, the robustness of the existing test criteria have been studied. Also, some exact test procedures have been considered and the exact and asymptotic noncentral distribution problems have been studied.     

Force constants,generalised meansquare amplitudes of vibration,shrinkage constants and coriolis coupling coefficients of GeH3CCH and GeD3CCH

General Valence force constants have been evaluated for GeH₃CCH and GeD₃CCH. Generalised mean-square amplitudes of vibration have been obtained and the shrinkage constants have been calculated using the perpendicular mean-square amplitudes of vibration. Coriolis coupling constants have also been determined.     

Analyzing on stability of HIV-PI model with general incidence rate

In this article, we have constructed a PI model with general incidence rate and humoral immunity. We have analyzed about the equilibrium points in general case. Using appropriate Lyapunov functional and Lasalle’s invariance principle, the global stability of the newly constructed model have been discussed. Using patient data we have discussed about the model numerically.     

Rational tetrahedra with edges in arithmetic progression

This paper discusses tetrahedra with rational edges forming an arithmetic progression, focussing specifically on whether they can have rational volume or rational face areas. Several infinite families are found which have rational volume, a face can have rational area only if its edges are themselves in arithmetic progression, and a tetrahedron can have at most one such rational face area.     

A computational study on different penalty approaches for solving constrained global optimization problems with the electromagnetism-like method

In this article, the application of the electromagnetism-like method (EM) for solving constrained optimization problems is investigated. A number of penalty functions have been tested with EM in this investigation, and their merits and demerits have been discussed. We have also provided motivations for such an investigation. Finally, we have compared EM with two recent global optimization algorithms from the literature. We have shown that EM is a suitable alternative to these methods and that it has a role to play in solving constrained global optimization problems.     

On the foundations of game theory: The case of non-Archimedean utilities

Contrary to what appears to have become an accepted part of the folklore of game theory, a finite two-person zero-sum game with non-Archimedean utilities may have no equilibrium-point solution, and either one or both players may have no “minimax” strategy. Even when both players have “minimax” strategies, such a game may lack an equilibrium point.     

A multiple times scale solution for non-linear vibration of mass grounded system

In this paper, the vibration of a mass grounded system which includes two linear and non-linear springs in series has been considered. Since this system, depending on its parameters can oscillate symmetrically and asymmetrically, both cases have been solved using multiple times scales (MTS) method and some analytical relations have been obtained for natural frequency of oscillations. The results have been compared with previous work and good agreement has been obtained. Also forced vibrations of system in primary and secondary resonances have been studied for the first time and the effects of different parameters on the frequency-response have been investigated.     

Dissipative Nonlinear Evolution Equations and Chaos

In this article we have studied the nonlinear interaction between ellipticity and dissipation in a set of model equations (1.1) and established the relation between this interaction and chaos. In addition to theoretical investigations, extensive numerical simulations with these equations have been made, and different routes to chaos have been found. The numerical studies have revealed the chaotic nature of the solutions.     

Numerical evaluation of the flight mechanics and trajectory of a ski-jumper

The equations of motion governing the inrun and free-flight phases of a ski-jump have been set down. These equations have been used as the basis for a numerical scheme from which the in-flight trajectory and jump length have been calculated. The influence of such factors as the friction between the skis and snow, the jump technique at take-off, the angle of incidence of the airborne jumper and variations in air density have been investigated. Jump lengths consistent with those measured on the 90 m Sapporo ski-slope have been computed. Deductions are made concerning critical aspects of ski-jump technique.     

Estimation for Discrete-time Semi-Markov Reward Processes: Analysis and Inference

In this paper, the moments of a class of reward processes defined on a discrete-time semi-Markov process and the asymptotic behaviors of the corresponding empirical estimators have been investigated. Some known results concerning the asymptotic distribution and properties of semi-Markov kernel have been obtained by a different approach. By using the empirical estimator of the semi-Markov kernel and the mentioned approach, the estimators for the moments of the reward process have been introduced and their asymptotic properties have been established. As a consequence of the strong consistency and asymptotic normality, the confidence intervals have also been obtained. A numerical example illustrates the results.     

时滞矩阵微分方程的等度稳定性

在矩阵值范数定义的广义赋范空间上利用矩阵Liapunov泛函研究了时滞矩阵微分方程的等度稳定性,得出了若干新结果.     

On Functions with a Unique Identification Minor

We shed some new light to the problem of characterizing those functions of several arguments that have a unique identification minor. The 2-set-transitive functions are known to have this property. We describe another class of functions that have a unique identification minor, namely functions determined by the order of first occurrence. We also present some examples of other kinds of functions with a unique identification minor. These examples have a relatively small arity.     

Multi-level scheduling decisions in a class of FMS using simulation based metamodels

This paper pertains to a detailed simulation study conducted on a typical Flexible Manufacturing System (FMS). Initially, the configurations of the FMS under study have been established. Two types of FMSs have been evolved: one is failure free and the other is failure prone. For each of these cases, simulation models have been developed using SLAMSYSTEM. Orders arriving randomly at the FMS are subjected to three levels of scheduling decisions namely, launching of parts into the system, routing of parts through machines and sequencing of parts on AGVs at a central buffer. The simulation results have been used to develop metamodels for the two types of FMSs. These metamodels have been subjected to statistical analysis to ascertain their adequacy to represent the simulation models. These metamodels have been found to be useful for simulating the FMSs under study so as to evaluate various multi-level scheduling decisions in the FMS.     

The impact of energy function structure on solving generalized assignment problem using Hopfield neural network

In the last 20 years, neural networks researchers have exploited different penalty based energy functions structures for solving combinatorial optimization problems (COPs) and have established solutions that are stable and convergent. These solutions, however, have in general suffered from lack of feasibility and integrality. On the other hand, operational researchers have exploited different methods for converting a constrained optimization problem into an unconstrained optimization problem. In this paper we have investigated these methods for solving generalized assignment problems (GAPs). Our results concretely establishes that the augmented Lagrangean method can produce superior results with respect to feasibility and integrality, which are currently the main concerns in solving neural based COPs.     

Absolute summability of orthogonal series by Euler’s method

We have obtained a sufficient condition for the absolute summability of an orthogonal series by the (E, 1) method. We have proved that if the coefficients of the orthogonal series decrease monotonically in absolute value, then the condition we have found is exact. We have shown that for coefficients decreasing not necessarily monotonically the condition given is not exact. Translated from Matematicheskie Zametki, Vol. 21, No. 1, pp. 51–56, January, 1977.     

一类生态系统的周期解的全局渐近稳定性

本文研究了有三个种群相互作用的数学模式: 我们分别建立了系统(*)和(**)存在唯一的大范围渐近稳定的正周期解的充分条件.     

自然数幂和公式的另一种计算机实现方法

自然数幂和问题,许多文献给出不同算法,借助M ATLAB系统,利用自然数幂和的矩阵算法,给出可计算所有小于任意指定自然数m的自然数幂和公式的计算机实现方法.     

On the existence of multiple steady-state solutions in the theory of electrodiffusion. Part I: the nonelectroneutral case. Part II: a constructive method for the electroneutral case

We give a constructive method for giving examples of doping functions and geometry of the device for which the nonelectroneutral voltage driven equations have multiple solutions. We show in particular, by performing a singular perturbation analysis of the current driven equations that if the electroneutral voltage driven equations have multiple solutions then the nonelectroneutral voltage driven equations have multiple solutions for sufficiently small normed Debye length. We then give a constructive method for giving examples of data for which the electroneutral voltage driven equations have multiple solutions.

     

Eigenvalue approach to study the effect of rotation and relaxation time in generalized magneto-thermo-viscoelastic medium in one dimension

The fundamental equations of the problems of generalized thermoelasticity with one relaxation parameter including heat sources in infinite rotating magneto-thermo-viscoelastic media have been derived in the form of a vector matrix differential equation in the Laplace transform domain for a one dimensional problem. These equations have been solved by the eigenvalue approach to determine deformations, stress, and temperature. The results have been compared to those available in the existing literature. The graphs have been drawn to show the effect of rotation in the medium.