Functions Of Dependent Variables Research Articles

Detecting multiple equilibria for continuous dependent variables

This article considers structural equations where continuous dependent variables are related to independent variables and unobservables through a nonparametric function. Multiple equilibria may arise when the structural equations admit multiple solutions. This article proposes a detecting criterion for the existence of multiple equilibria. The main finding is that multiple equilibria would reveal itself in the form of jump(s) in the density function of the dependent variables. When there is a unique equilibrium, the density function of dependent variables will be continuous, whereas when there are multiple equilibria, the density will have jump(s) under reasonable conditions.

Dynamical analysis of solitary waves, lumps and interaction phenomena of a (2+1)-dimensional high-order nonlinear evolution equation

A (2[Formula: see text]+[Formula: see text]1)-dimensional high-order nonlinear evolution (HNE) equation is considered in this paper. A Hirota bilinear form of the HNE equation is constructed by the dependent variable function. Solitary waves are derived by solving the Hirota bilinear form of the HNE equation. Lump waves of the HNE equation are obtained by introducing a positive quadratic function. By mixing an exponential function or two exponential functions with a quadratic function, interaction solutions between a lump and a one-soliton, and between a lump and a two-soliton are presented. For the interaction solution between a lump and a two-soliton, this kind of solution can be considered as a special rogue wave. The propagation phenomena of these explicit solutions are illustrated by some graphs.

Sub-Symmetries and Conservation Laws

The concept of sub-symmetry of a differential system was introduced in [ 40 ], where it was shown that a sub-symmetry is a considerably more powerful tool than a regular symmetry with regard to deformation of conservation laws. In this paper, we study the nature of a correspondence between sub-symmetries and conservation laws of a differential system. We show that for a large class of non-Lagrangian systems, there is a natural association between sub-symmetries and local conservation laws based on the Noether operator identity, and we prove an analogue of the first Noether theorem for sub-symmetries. We also demonstrate that a similar association can be established for infinite sub-symmetries of the system. We discuss the role of sub-symmetries in generation of infinite series of conservation laws for the constrained Maxwell system and the incompressible Euler equations of fluid dynamics. Despite the fact that infinite symmetries (with arbitrary functions of dependent variables) are not known for the Euler equations, we find infinite sub-symmetries for the two- and three-dimensional Euler equations with certain constraints. We show that these sub-symmetries generate known series of infinite conservation laws, and obtain new classes of infinite conservation laws.

THE EFFECT OF VIDEO GAMES ON THE LIFE STYLE OF ADOLESCENTS (OF ADOLESCENTS OF THE SECOND DISTRICT 5 TEHRAN)

The aim of this study was investigating effect of video games on change of life style of adolescence in the second grade of high schools in district 5 of Tehran. Methodology f this research is applied according to purpose and correlative-surveying according to method. Statistical population of this research is 28348 students in district 5 of Tehran high schools that sample volume was determined 384 by Cochran formula and sample was selected by simple random method and stratified sampling method. Results showed that the highest effect of life style among studied variables is first in apparent coverage (β=0.31), second in fashions (β=0.27), third spending leisure time (β= 0.16), and the fourth imitation and modeling (β=0.13). The results showed that the second term school district 5 Tehran lifestyle of adolescents' function of dependent variables, or cover appearance, fashion-oriented, leisure time activities and duplication of video games is modeling. Because the two variables influence social relationships and family relationships were eliminated from the equation of video games was not fixed.

Infinite conservation laws for differential systems

We study Lagrangian systems of partial differential equations admitting infinite-dimensional symmetry algebras parameterized by arbitrary functions of dependent variables. We show that these systems have infinite sets of essential conservation laws.

An infinite set of conservation laws for infinite symmetries

We consider partial differential equations of a variational problem admitting infinite-dimensional Lie symmetry algebras parameterized by arbitrary functions of dependent variables and their derivatives. We show that unlike differential systems with symmetry algebras parameterized by arbitrary functions of independent variables, these equations have infinite sets of essential conservation laws.

Essential Conservation Laws for Equations with Infinite Symmetries

We consider partial differential equations of variational problems with infinite symmetry groups. We study local conservation laws associated with arbitrary functions of one variable in the group generators. We show that only symmetries with arbitrary functions of dependent variables lead to an infinite number of conservation laws. We also calculate local conservation laws for the potential Zabolotskaya-Khokhlov equation for one of its infinite subgroups.

Dynamic Nuclear Power Plant Simulations Using Single-Board Peripheral Array Processors

The application of a host/ coprocessor system, consisting of an IBM PC/AT and a Marinco peripheral array proc essor, to the simulation of nuclear power plant transients is described. The simulation algorithm employs a multistep, multirate integration method. Rapidly varying transients were implemented on the array processor, while the slow components of the system dynamics were handled by the host computer. The generation of nonlinear functions of dependent variables using table lookup techniques was also implemented on the array processor. A simplified model of a pressurized water reactor was employed as a benchmark. Flow rate and power transients using a variety of integration formulas are presented along with data showing the speed up achieved through the use of the peripheral processor.

Analysis of control systems with complex nonlinearities and transportation lag

When a control system contains a hysteretic nonlinearity, or a dead time element (transportation lag), or a distributed lag, the system may be described by a characteristic equation with complex coefficients which are functions of dependent variables. The characteristic equation is partitioned and root locus methods are used to analyze stability, existence and characteristics of limit cycles, damping characteristics of stable systems, etc. Control systems with frequency dependent, hysteretic, nonlinearities and with adjustable parameters are analyzed using parameter plane and parameter space methods.

Slide Rule for Prediction of Physical Constants

In the previous paper (this journal, 14, 270 (1950)) the author suggested a simple slide rule based on the general temperature relation of vapor pressure of liquids obtained. In the present, several slide rules are proposed for prediction of such relations as viscosity and surface tension of liquids vs temperature, viscosity and thermal conductivity of gases vs temperature, and critical temperature and critical pressure from normal boiling point. This slide rule can be constructed when the correlation between a physical constant, y, and a related variable, x, is expressed by a general equation, f2(y)=f1(x)+C, in which f1 and f2 are functions of dependent variables, x and y, respectively, and C is a constant depending on substances. If a pair of corresponding values (x0, y0) are given, C is eliminated, and any other correspondings of x and y are obtained. That is, if an only one point is available for a physical constant of a substance, all other values for that substance are obtainable at a glance with an accuracy satisfactory for engineering purposes.