Modeling of dynamic processes on the market of goods and services

2019 ◽  
Vol 39 (2) ◽  
pp. 158-162
Author(s):  
N. A. Volkova ◽  
N. T. Katanaev
Keyword(s):  
Differential Equations ◽  
Mathematical Description ◽  
Market Research ◽  
Dynamic Processes ◽  
Goods And Services ◽  
Multidimensional Models ◽  
Market Volume

The work is aimed at solving problems related to dynamic market research with a limited number of participants and domestic factors, which are used in market volume, the release of the product and its price. Lists the mathematical description of "logistics functions" in the form of analyses and solutions of differential equations processes on the market of goods and services. Given the necessity of transition to multidimensional models of market.

Stress and Deformation

1996 ◽  
Author(s):  
Gerhard Oertel
Keyword(s):  
Differential Equations ◽  
Mathematical Description ◽  
Finite Strain ◽  
Stress Strain ◽  
Complex Problems ◽  
Vector Algebra ◽  
Stress And Deformation

Students of geology who may have only a modest background in mathematics need to become familiar with the theories of stress, strain, and other tensor quantities, so that they can follow, and apply to their own research, developments in modern, quantitative geology. This book, based on a course taught by the author at UCLA, can provide the proper introduction. Included throughout the eight chapters are 136 complex problems, advancing from vector algebra in standard and subscript notations, to the mathematical description of finite strain and its compounding and decomposition. Fully worked solutions to the problems make up the largest part of the book. With their help, students can monitor their progress, and geologists will be able to utilize subscript and matrix notations and formulate and solve tensor problems on their own. The book can be successfully used by anyone with some training in calculus and the rudiments of differential equations.

scholarly journals Laser Opto-Electronic Oscillator and the Modulation of a Laser Emission

2021 ◽  
Author(s):  
Alexander Bortsov
Keyword(s):  
Spectral Line ◽  
Differential Equations ◽  
Low Noise ◽  
Noise Generator ◽  
Dynamic Processes ◽  
Nonlinear Method ◽  
External Modulation ◽  
Mach Zehnder Modulator ◽  
Electronic Oscillator

The autonomous optoelectronic generator (OEO) is considered in the chapter as a source of low-noise oscillations. Differential equations are considered and methods with OEO modulation with direct and external modulation are analyzed. The complexity of both approaches is related to the non-standard way of description of the nonlinear method modulation for the internal (direct) structure and the utilization of the specific Mach-Zehnder modulator for the first stage on external modulation. The purpose of the presentation is to consider the main features of OEO as a low-noise generator. This includes consideration based on the study of differential equations, the study of transients in OEO, and the calculation of phase noise. It is shown that different types of fibers with low losses at small bending radii can be used as a FOLD in OEO. The important role of the choice of a coherent laser for OEO with a small spectral line width is shown. The prospects of using structured fibers with low losses at bends of less than 10 mm in OEO are described. The results of modeling dynamic processes in OEO with direct modulation are presented.

Modeling of the Process of Drying and Coalescing Nanodispersion Spreading

2021 ◽  
Vol 887 ◽  
pp. 557-563
Author(s):  
D.M. Mordasov ◽  
M.D. Mordasov
Keyword(s):  
Contact Angle ◽  
Differential Equations ◽  
Mathematical Description ◽  
Transition Function ◽  
System Of Differential Equations ◽  
Theoretical Justification ◽  
Spreading Process ◽  
Optimal Amount ◽  
First Order ◽  
Energy Processes

The spreading process of drying and coalescing nanodispersion was simulated using the method of analogies. A mathematical description of the energy processes in the proposed physical model was obtained in the form of a system of differential equations of the first order. A transition function that describes the dynamics of the change in the contact angle when the nanodispersion drop spreads was obtained as a result of solving the system of differential equations. The physical meaning of the transition function coefficients was established. Based on the analysis of the ratio of the transition function coefficients, a theoretical justification for the results of experiments on choosing the optimal amount of desiccant introduced into styrene-acrylic nanodispersion was given.

scholarly journals Robust Low-Rank Discovery of Data-Driven Partial Differential Equations

2020 ◽  
Vol 34 (01) ◽  
pp. 767-774
Author(s):  
Jun Li ◽  
Gan Sun ◽  
Guoshuai Zhao ◽  
Li-wei H. Lehman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Minimization Problem ◽  
Real World ◽  
Low Rank ◽  
Dynamic Processes ◽  
Complex Data ◽  
Sparse Regression ◽  
Partial Differential ◽  
Regression Methods

Partial differential equations (PDEs) are essential foundations to model dynamic processes in natural sciences. Discovering the underlying PDEs of complex data collected from real world is key to understanding the dynamic processes of natural laws or behaviors. However, both the collected data and their partial derivatives are often corrupted by noise, especially from sparse outlying entries, due to measurement/process noise in the real-world applications. Our work is motivated by the observation that the underlying data modeled by PDEs are in fact often low rank. We thus develop a robust low-rank discovery framework to recover both the low-rank data and the sparse outlying entries by integrating double low-rank and sparse recoveries with a (group) sparse regression method, which is implemented as a minimization problem using mixed nuclear norms with ℓ1 and ℓ0 norms. We propose a low-rank sequential (grouped) threshold ridge regression algorithm to solve the minimization problem. Results from several experiments on seven canonical models (i.e., four PDEs and three parametric PDEs) verify that our framework outperforms the state-of-art sparse and group sparse regression methods. Code is available at https://github.com/junli2019/Robust-Discovery-of-PDEs

Solutions of ordinary differential equations as limits of pure jump markov processes

1970 ◽  
Vol 7 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Thomas G. Kurtz
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Population Growth ◽  
Ordinary Differential Equations ◽  
Markov Processes ◽  
Radioactive Decay ◽  
Dynamic Processes ◽  
Deterministic Models ◽  
Image Position ◽  
Jump Markov Processes

In a great variety of fields, e.g., biology, epidemic theory, physics, and chemistry, ordinary differential equations are used to give continuous deterministic models for dynamic processes which are actually discrete and random in their development. Perhaps the simplest example is the differential equation used to describe a number of processes including radioactive decay and population growth.

Mass Dynamics of U.S. Presidential Competitions, 1928–1936

1988 ◽  
Vol 82 (4) ◽  
pp. 1153-1181 ◽  
Author(s):  
Courtney Brown
Keyword(s):  
United States ◽  
Differential Equations ◽  
Republican Party ◽  
Democratic Party ◽  
Formal System ◽  
Electoral Politics ◽  
The United States ◽  
Dynamic Processes ◽  
Dominant Characteristic ◽  
Modeling Strategy

This analysis investigates the mass dynamics of competitive electoral politics with respect to the presidential vote during the 1928–36 realigning period for the United States. A formal system of three interdependent differential equations is employed to characterize the dynamic processes of the aggregate voter shifts between the Republican, Democratic, and nonvoter populations. The modeling strategy is used to locate substantial variations in the mass dynamics between large subgroups in the electorate as well as to identify both national and socially interactive components to the patterns of voter movements. The results show that the overall realignment period was quite complex. Vote switching from the Republican party to the Democratic party was the dominant characteristic of the 1932 election, whereas additional Democratic gains in 1936 came mostly from new voters.

scholarly journals THE NONLINEAR MODEL OF BEHAVIOR OF TWO COMPETITIVE FIRMS

2021 ◽  
Vol I (81) ◽  
pp. 115-128
Author(s):  
Bohdan Drin ◽  
◽  
Iryna Drin ◽  
Svitlana Drin ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Mathematical Description ◽  
Information Technologies ◽  
Dynamic Models ◽  
Nonlocal Problem ◽  
Variable Coefficients ◽  
Economic Behavior ◽  
Algebraic Equations ◽  
Mathematical Methods

The practical task of economics lies in applying the methods of substantiating its decisions. For economics, the main method is the modeling of economic phenomena and processes and, above all, mathematical modeling, which has been stipulated by the presence of stable MATHEMATICAL METHODS, MODELS AND INFORMATION TECHNOLOGIES IN ECONOMY Issue I (81), 2021 117 quantitative patterns and the possibility of a formalized description of many economic processes. The economic-mathematical model contains a system of equations of linear and nonlinear units that promote a mathematical description of economic processes and phenomena, consists of a set of variables and parameters and serves to study these processes and control them. Dynamic models of the economy describe it in development, as well as provide a detailed description of technological methods of production. Mathematical description of dynamic models is carried out with the use of a system of differential equations (in models with continuous time), difference equations (in models with discrete time), as well as systems of algebraic equations. It is important that the investigation of various economic issues has led to the development of the mathematical apparatus. In linear algebra, productive matrices are caused by the studies of intersectoral balance, whereas mathematical programming arose in the course of researching the optimal plan for the distribution of limited resources. In a similar way, there emerged the theory of economic indices and econometrics, the theory of production functions and the theory of consumption, the theory of general economic balance and social welfare, the theory of optimal economic growth. The paper under studies deals with the dynamic economic behavior of two competing objects, whose mathematical model is a nonlinear nonlocal problem for a system of ordinary differential equations with variable coefficients and argument deviation. The dynamic mathematical model is based on the assumption that the volume of output of both firms is determined by such factors on which output depends linearly. The model under discussion includes nonlinear factors, which describe the level of distrust of the competitors and depend on the time of observations and production volumes in previous moments, because the latter significantly affect the production activities of the firm. Such mathematical models are called time-delayed models.

scholarly journals The Dynamic Characteristics of Sensors of Primary Currents of Energy Sources to Secondary Voltages

2020 ◽  
Vol 9 (4) ◽  
pp. 2529-2534
Keyword(s):  
Cloud Computing ◽  
Dynamic Characteristics ◽  
Mathematical Description ◽  
Graph Model ◽  
Energy Sources ◽  
Dynamic Processes ◽  
Computing Technology ◽  
Distributed Parameters ◽  
Secondary Voltage

In this article representation of analytical equations, mathematical description of the dynamic processes and result of researches of sensors-transducers of multiphase primary currents to secondary voltage are given. The base of the researches of dynamic characteristics of sensors of multiphase primary currents to secondary voltages is graph model of sensors with distributed parameters and digital-based cloud computing technology, that are three services, SaaS, PaaS and IaaS.

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