Study Of Various Classes Research Articles

Numerical investigation of convergence of Fourier series, poly-nomials, and method of finite elements

Purpose. To compare the efficiency of using finite elements with variable and averaged mechanical and geometric parameters and to investigate the convergence of results obtained by the semi-analytical finite element method (SAFEM) using Fourier series and polynomials with the results obtained by the finite element method (FEM). The methods. The construction and development of an algorithm for studying the stress-strain state of spatial bodies with variable and averaged mechanical and geometric parameters were carried out based on SAFEM. Findings. Solvability indicators of SAFEM were obtained for calculating nodal reactions and stiffness matrix coefficients of finite elements with variable and averaged mechanical and geometric parameters. Numerical convergence studies of results obtained using SAFEM with Fourier series, polynomials, and the finite element method were conducted for a benchmark example, which was the Boussinesq problem for a half-space subjected to a concentrated force. The results indicate that the convergence of the investigated coordinate functions in the considered problem is of the first order. The originality. The obtained solvability indicators of SAFEM for calculating nodal reactions and stiffness matrix coefficients of finite elements with variable and averaged mechanical and geometric parameters allow for the study of various classes of problems. Numerical convergence studies using Fourier series, polynomials, and the finite element method were conducted for the benchmark example. Practical implementation. The practical significance lies in the development of a methodology for determining the stress-strain state of relevant spatial elements of structures with variable and averaged mechanical and geometric parameters subjected to arbitrarily distributed spatial loads.

Spectrum of bounded operators in Hilbert spaces

This paper sought to study the spectrum operators by emphasising on condition of commuting operators so as to expose classes of operators. Here study of various classes of bounded operators on a Hilbert space H is one of the most important topics in the preparation of the study of the Hilbert spaces. In case a abounded operator A commutes at least with its own adjoint A* it forms important classes of operators on H, eg normal, unitary, self – adjoint etc. The operators under the study are bounded operators operating in a complete space called Hilbert spaces.

Normal structure spaces of groups

Can we do a topological study of various classes of normal subgroups endowed with a hull-kernel-type topology? In this paper, we have provided an answer to this question. We have introduced as well a new class of normal subgroups called primitive subgroups. Separation axioms, compactness, connectedness, and continuities of these spaces have been studied . We have concluded with the question of determining spectral spaces among them.

Monotonicity Arguments for Variational–Hemivariational Inequalities in Hilbert Spaces

We consider a variational–hemivariational inequality in a real Hilbert space, which depends on two parameters. We prove that the inequality is governed by a maximal monotone operator, then we deduce various existence, uniqueness and equivalence results. The proofs are based on the theory of maximal monotone operators, fixed point arguments and the properties of the subdifferential, both in the sense of Clarke and in the sense of convex analysis. These results lay the background in the study of various classes of inequalities. We use them to prove existence, uniqueness and continuous dependence results for the solution of elliptic and history-dependent variational–hemivariational inequalities. We also present some iterative methods in solving these inequalities, together with various convergence results.

Inverse problems of the dynamics of observation interpretation systems

Based on the analysis and systematization of the inverse problems of dynamics, the study of the properties and features of the types of dynamic models under consideration, an approach is proposed for the development of appropriate methods of mathematical modeling based on the use and implementation of integral models in the form of Volterra equations of the I and II kind, their functional capabilities are determined in the study of various classes of problems, and also formulated the features that affect the choice of methods for their numerical solution. Methods for obtaining integral models are proposed, which are the basis for constructing algorithms for solving inverse problems of dynamics for a fairly wide class of dynamic objects. Integral methods for the identification of dynamic objects have been developed, which make it possible to obtain stable non-optimization algorithms for calculating the parameters of mathematical models. Recurrent methods of parametric identification of transfer functions of dynamic objects with an arbitrary input action are proposed (the obtained parameters of the transfer functions are also coefficients of the corresponding differential equations, which makes it possible to obtain equivalent mathematical models in the form of integral equations). The study of algorithms that implement the proposed identification methods allows us to conclude about their efficiency in terms of the amount of computation and ease of implementation, as well as the high accuracy of calculating the model parameters.

Research in the Field of Geometric Analysis at Volgograd State University

This article discusses the main directions of research in geometric analysis, which were conducted and are being carried out by the scientific mathematical school of Volgograd State University. The results of the founder of the scientific school, Doctor of Physics and Mathematics, Professor Vladimir Mikhailovich Miklyukov and his students are summarized. These results concern the solution of a number of problems in the field of quasiconformal flat mappings and mappings with bounded distortion of surfaces and Riemannian manifolds, the theory of minimal surfaces and surfaces of prescribed mean curvature, surfaces of zero mean curvature in Lorentz spaces, as well as problems associated with the study of the stability of such surfaces. In addition, the results of the study of various classes of triangulations — an object that appears at the junction of research in the field of geometric analysis and computational mathematics — are noted. Besides, this review discusses papers that use the Fourier decomposition method for solutions of the Laplace — Beltrami equations and the stationary Schr¨odinger equation with respect to the eigenfunctions of the corresponding boundary value problems. In particular, the authors give the results on finding capacitive characteristics that allowed for the first time to formulate and prove the criteria for the fulfillment of various theorems of Liouville type and the solvability of boundary value problems on model and quasimodel Riemannian manifolds. The role of the equivalent function method is also indicated in the study of such problems on manifolds of a fairly general form. In addition to this, the article gives an overview of the results concerning estimates of calculating error integral functionals and convergence of piecewise polynomial solutions of nonlinear variational type equations: minimal surface equations, equilibrium equations capillary surface and equations of biharmonic functions.

The Value of Multi-Stage Stochastic Programming in Risk-Averse Unit Commitment Under Uncertainty

Day-ahead scheduling of electricity generation or unit commitment is an important and challenging optimization problem in power systems. Variability in net load arising from the increasing penetration of renewable technologies has motivated study of various classes of stochastic unit commitment models. In two-stage models, the generation schedule for the entire day is fixed while the dispatch is adapted to the uncertainty, whereas in multi-stage models the generation schedule is also allowed to dynamically adapt to the uncertainty realization. Multi-stage models provide more flexibility in the generation schedule; however, they require significantly higher computational effort than two-stage models. To justify this additional computational effort, we provide theoretical and empirical analyses of the value of multi-stage solution for risk-averse multi-stage stochastic unit commitment models. The value of multi-stage solution measures the relative advantage of multi-stage solutions over their two-stage counterparts. Our results indicate that, for unit commitment models, the value of multi-stage solution increases with the level of uncertainty and number of periods, and decreases with the degree of risk aversion of the decision maker.

Numerical and Analytical Methods of Study of Stochastic Systems with Delay

This paper is a brief review of methods of qualitative and quantitative study of various classes of stochastic systems with aftereffect. We describe schemes of analysis of stochastic ordinary and partial differential and integrodifferential equations, which are also applicable for their deterministic analogs. These numerical and analytical schemes are implemented in the software package Mathematica and in the language Intel Fortran.

Current Status of Oxide Dielectric Materials for Terahertz Applications–An Overview

Terahertz electromagnetic radiation, its generation, detection and material interaction is an emerging field of study. Diverse range of researches is going on to explore and understand this frequency range and its potential applications. Situated between microwave and optical frequency domain, THz radiation is non-responding to the techniques commonly used for these two domains, thus insufficiency of supporting technology, high atmospheric absorption, lack of high power source have kept this spectrum away from technical and commercial interest for a long time. Advancements in Photonics like high power ultrafast lasing devices, high-power THz generation by means of nonlinear effects, band-engineered hetero-structures have greatly extended its potential. In order to explore all its merits and realize it as a full-fledged functional frontier, more high power sources, more sensitive sensors and efficient waveguides need to be developed. In order to achieve that, the main focus of the research world has moved towards the study of various classes of materials so that they can be categorized based on the applications they can be used for. In this overview article, recent studies on THz dielectric material interaction, their observations, outcomes and their prospect have been presented in a condensed manner so that the information can be used for further developments in this frequency regime.

Mechanical and Numerical Analysis Concerning Compressive Properties of Tin-Lead Open-Cell Foams

The design of new or innovative materials has to meet two essential criteria: increased mechanical performance and minimization of the mass. This dual requirement leads to interest in the study of various classes of metallic foams. The actual research is focused on open-cell Tin-Lead foams manufactured by replication process using NaCl preform. A mechanical press equipped with a load cell and a local extensometer with a controlled deformation rate is used. Experimental tests were carried out in order to study the influences of both the cell size and of the relative density on the mechanical behavior during a compression deformation and to analyze the obtained properties variation within a new framework. This study has three main sections which start with the manufacturing description and mechanical characterization of the proposed metallic foams followed by the understanding and modeling of their response to a compression load via a Gibson-Ashby model, a Feret law, a proposed simple Avrami model, and a generalized Avrami model. Finally, an exposition of a numerical simulation analyzing the compression of the Sn-Pb foams concerning the variation of the relative densities with respect to the plastic strain is proposed.

A Study of Various classes of police officers in the traffic division of Ahmedabad and their Work Stress/Anxiety/Worry

The following study was conducted to study the work related stress and its effect on the police officers working in the traffic division of Ahmedabad city, Gujarat, India. For this the sample selected was Constables and Head Constables who held an experience of 1-5 years of duty (60 samples) and 10-15 years of duty (60 samples). The total samples in the population was 120 (N=120). The samples were selected from a variety of regions throughout the city of Ahmedabad. To measure the job related stress, the Job Stress Scale was used which was developed by A. K. Shrivastava and M. M. Sinha. The psychometric method used for statistical analysis was the ‘t’ test. The study showed that the second group (10-15 years experience) showed less work related stress than the first group (1-5 years experience); in both the classes of officers, that is, constables and head constables.

Ordered groups with a conucleus

Our work proposes a new paradigm for the study of various classes of cancellative residuated lattices by viewing these structures as lattice-ordered groups with a suitable operator (a conucleus). One consequence of our approach is the categorical equivalence between the variety of cancellative commutative residuated lattices and the category of abelian lattice-ordered groups endowed with a conucleus whose image generates the underlying group of the lattice-ordered group. In addition, we extend our methods to obtain a categorical equivalence between Π MTL -algebras and product algebras with a conucleus. Among the other results of the paper, we single out the introduction of a categorical framework for making precise the view that some of the most interesting algebras arising in algebraic logic are related to lattice-ordered groups. More specifically, we show that these algebras are subobjects and quotients of lattice-ordered groups in a “quantale like” category of algebras.

Canonical Extensions of Hermitian Operators

The concept of canonical extensions of Hermitian operators is introduced. Not only are such extensions of interest on their own merits, but they also have significant applications (Theorem 3 in particular) in constructing spaces of boundary values of Hermitian operators with various defect numbers. In recent years boundary-value spaces have found important applications in the study of various classes of extensions of Hermitian operators and in scattering theory.

Block-form control of linear time-invariant discrete-time systems defined over commutative rings

A new approach based on a block-input, block-output state model is developed for the study of linear time-invariant discrete-time systems whose coefficients belong to a commutative ring with 1. It is well known that such systems arise in the study of various classes of complex linear systems including systems depending on parameters and multidimentional systems. By time-compressing the block-input state representation, new results are obtained on the construction of a memoryless block-form state feedback control law that yields a type of assignability and/or deadbeat control. These results are then dualized to yield results on a new type of state observer based on a block of output measurements. The observer and state feedback controller are then combined to yield new results on input-output regulation and set-point tracking for systems defined over an arbitrary commutative ring. In the last part of the paper, the block-input form is utilized to study the stabilization of systems defined over a normed algebra.

ON TYPES OF DEGENERATE ELLIPTIC OPERATORS

A general method for studying various classes of degenerate operators connected with Newton polyhedra is presented. This method extends the approach of Vishik and Grushin, permits the study of various classes of operators to be more easily reduced to a few model classes, and allows new classes to be studied. Bibliography: 11 titles.

A unified theory of polynomial expansions and their applications involving Clebsch-Gordan type linearization relations and Neumann series

Motivated by their potential for applications in several diverse fields of physical, astrophysical, and engineering sciences, this paper aims at presenting a unified study of various classes of polynomial expansions and multiplication theorems associated with the general multivariable hypergeometric function (studied recently by A. W. Niukkanen and H. M. Srivastava), which provides an interesting and useful unifiation of numerous families of special functions in one and more variables, encoutered naturally (and rather frequently) in many physical, quantum chemical, and quantum mechanical situations. Several interesting applications of these general polynomial expansions are considered, not only in the derivations of various Clebsch-Gordan type linearization relations involving products of several Jacobi or Laguerre polynomials, but also to associated Neumann expansions in series of the Bessel functionsJ v (z) andI v (z) (and of their suitable products).

On permutations passable by the gamma network

The Gamma network is a multiprocessor interconnection network with redundant paths between source and destination terminals. The basic switching element in this network is a 3 × 3 crossbar, and the stages are linked by “power of two” and identity connections. The Gamma network is known to realize many classes of permutations useful in parallel processing, and in this paper a detailed study of various classes of permutations passable by the network with a simple control algorithm is presented. Conditions for passability of an arbitrary permutation with this algorithm have been formulated and used to show that several useful classes of permutations in parallel processing can be realized. Although the algorithm does not utilize the full connection capability of the network, it produces conflict-free routing for most of the useful classes of permutations the network is capable of passing.

On lie algebras with modular lattices of subalgebras

The aim of the article is to classify Lie algebras over an arbitrary field with modular lattices of subalgebras. The study of various classes of universal algebras, all subalgebras of which have a lattice satisfying the modular identity (M-algebras), has a long history. The first works which dealt the group case appeared at the end of the 1920s and the beginning of the 1930s (A. RottEnder, 0. Ore, R. Baer). There are a great number of papers devoted to the study of modular semi-groups, associative and nonassociative rings and algebras, quasigroups, modules over commutative rings, and other algebraic structures. However, a full classification of the universal algebras with a modular lattice of subalgebras for any class of the “classical” universal algebras does not exist. In the middle of the 1960s an attempt was made to describe Lie algebras with various restrictions imposed on the lattice of subalgebras and, in particular, to describe the Lie algebras with a modular lattice of subalgebras (Kolman Cl, 23, Goto [3], Barnes [4]). A few years later, the papers of Towers [S], Amayo [6], Amayo and Schwarz [7], Gein [S] appeared, in which they studied Lie algebras with modular lattices of subalgebras. Similar problems were considered in [9, 10, 111. The above papers classified the Lie algebras with modular lattices of subalgebras, when certain restrictions are imposed on the ring of operators, on 80 0021-8693186 53.00

Thermochemical study of polymer compounds

The paper presents the results of a thermochemical study of various classes of high molecular weight compounds. The experimental values of the enthalpies of combustion and the enthalpies of formation of a number of polymers have been obtained. A scheme is proposed for calculating the enthalpies of formation the possibility of using which is illustrated by the compounds studied.

The Effect of Mutual Solvents on Adsorption In Sandstone Acidizing

The role of mutual solvents in sandstone acidizing is investigated. An experimental technique for evaluating various solvents was used to examine various classes of solvents to relate chemical structure to mutual solvent properties. Glycol ethers were the most effective class of chemicals examined. Introduction Acid solutions containing hydrofluoric acid have been used extensively to stimulate sandstone reservoirs. Normally, these solutions are restricted to treating shallow clay damage due to the extremely fast spending rate of HF on clay. In acidizing sandstone formations, the acid is pumped below fracturing pressure, and the large surface area of the formation matrix is contacted and reacted upon by the acid. Stimulation fluids usually contain various surfactant additives in an effort to help control emulsions, asphaltenic sludge deposits, surface tension, and corrosion of steel. When acid solutions containing surfactants contact the rock surface, significant amounts of additives can be adsorbed onto the rock. These adsorbed additives are then no longer present in the fluids to perform their designed function. Consequently, conditions the surfactants were supposed to help control may occur during or after the treatment, resulting in less-than-satisfactory stimulation results. In 1971, Gidley reported on the use of the mutual solvent ethylene glycol monobutyl ether (EGMBE) in conjunction with sandstone acidizing treatments. Significant improvements were observed when the mutual solvent was present in either the acid solution or the oil after-flush. Gidley also pointed out the importance of proper treating technique. The mutual solvent was proper treating technique. The mutual solvent was shown to decrease the stability of acid/oil emulsions in the presence of formation fines. The compatibility of some acid additives with formation fluids and mineral surfaces was investigated by Sutton and Lasater. Their findings supported those of Gidley that EGMBE does improve the separation of acid solution/crude oil emulsions. Sutton and Lasater attributed this to decreased adsorption of surfactant on silica surfaces in the presence of EGMBE. They also found that acid corrosion inhibitors exhibited reduced adsorption on silica when EGMBE was present in the acid. The present investigation included two phases of work:a study of various classes of solvents to relate chemical structure to mutual solvent properties, anda further study of the influence of mutual solvents on surfactant adsorption. Experimental Procedure Adsorption effects were observed by measuring solution properties before and after flowing acid solutions properties before and after flowing acid solutions through columns packed with either silica sand or a mixture of silica sand and clay. The procedure for preparing the columns and performing the flow tests is preparing the columns and performing the flow tests is outlined in the Appendix. Solution properties measured were surface tension, emulsification, and corrosiveness. Surface tensions, reported in dynes per centimeter, were measured using the du Nouy ring method. Emulsion tests were conducted by mixing equal volumes of acid solutions and a crude oil from Southern Louisiana at 15,000 rpm for 1 minute with an Eberbach stirrer equipped with an homogenizer head. Separation of acid and oil was noted after 10 minutes and was reported as percent acid separated. JPT P. 1439