Representation Of Mathematical Models Research Articles

Modeling the dynamic semantics of a computer program

In this paper, two approaches are used to construct the dynamic semantics of computer programs: the first is the representation of mathematical models of computational processes generated by a computer program in the form of a discrete transformer; the second is the representation of the mathematical model of a computer program in terms of functional grammars. The study focuses on the computational process generated by a computer program. Application of the discrete transducers concept to describe computational processes allows us to obtain a mathematical model or dynamic semantics of a program, which is a composition of two discrete systems B and C. In this case, component A is a control component (a model of the program block diagram), and component B is a model of the program memory. The decomposition of a program into two components B and B is convenient when studying the process of modelling a computational process. This is due to the fact that the prospects of searching for invariants in critical nodes of a programme for mathematical proof of correctness of a computer programme are opened. The comparative analysis of the two approaches leads to the theorem on the regularity of the representation of a function generated by a programme within the framework of functional grammar.

Differential-difference systems in the analysis of weak solvability of initial-boundary value problems with a spatial variable in a network-like domain

In the work, the approach and the corresponding methods, which make it possible to construct a priori estimates of weak solutions of a differential-difference system with a spatial variable varying in a multidimensional network-like domain are indicated. Such estimates in spaces of summable functions are used to find solvability conditions for boundary value problems of various types for differential-difference systems. In addition, a priori estimates are used to justify the application of the method of discretization with respect to the time variable (semi-discretization) to the analysis of the weak solvability of initial-boundary value problems and the subsequent construction of approximations of weak solutions. The rationale for the approach used is the fact that in a fairly wide class applied analysis of the problems of transporting continuous media networks-like carriers, the representation of mathematical models of the process using the formalisms of differential-difference systems is the only tool for effectively solving these problems. For example, the reduction of a differential system (initial-boundary value problem) to the corresponding differential-difference system makes it possible not only to significantly simplify the analysis of problems of optimal control of a differential system (since this analysis reduces to studying the problem of optimal control of a system of elliptic equations), but also, using classical methods of control theory for elliptic systems, algorithmize the original problem. The reduction used often facilitates establishing the conditions for the existence and uniqueness of optimal control of a differential system. These problems also include a fairly large range of studies of non-stationary network-like hydrodynamic processes and flow phenomena. As an illustration of the approach used and the results obtained, the analysis of the solvability of the linearized Navier–Stokes system is given and the ways of studying the nonlinear Navier–Stokes system are indicated.

On a Mathematical Model of Tumor‐Immune Interaction with a Piecewise Differential and Integral Operator

The representation of mathematical models via piecewise differential and integral operators for dynamic systems has this potential to capture cross‐over behaviors such as a passage from deterministic to randomness which can be exhibited by different systems. A 3D mathematical model, similar to the prey‐predator system, of tumor‐immune interaction with piecewise differential and integral operators is developed and analyzed. Three different scenarios, namely, cross‐overs from deterministic to randomness, the Mittag‐Leffler law to randomness, and a cross‐over behavior from fading memory to the power‐law and a random process, are considered. The existence, uniqueness, positivity, and boundedness of the solutions of the systems are proved via the linear growth and Lipschitz conditions. The numerical approximations by Toufik, Atangana, and Araz are used for approximation of solutions and simulation of the piecewise models in different scenarios. From the nondimensionalized version of the 3D model representation, it is shown that the parameter values have an impact on the growth of tumor cells, and activating the proliferation of the resting cells has negatively affected the development of tumor cells. Moreover, the dynamics of tumor‐immune interaction exhibited a cross‐over behavior, and this behavior is exposed by the piecewise modeling approach used for the representations.

КОМПЬЮТЕРНОЕ МОДЕЛИРОВАНИЕ ОРБИТАЛЬНОЙ ТРОСОВОЙ СИСТЕМЫ

The article discusses the differential equations of motion of the orbital cable system.
 Systems of equations are solved by the Euler method and the Runge-Kutt method. Programs are written in Python in the graphic editor Blender with a visual representation of mathematical models

Maple app: specifies the vector derivative

This study aims to analysis the students’ representation ability of mathematics teacher candidate in using maple to determine vector derivative. This research uses quasi experimental method. Result of research indicate that student representation ability of teacher candidate can be classified into 3 based on indicator ability of mathematical representation that is: visual representation, representation of mathematical model and word representation. Three indicators on the ability of mathematical representation with words is a lower ability than other indicators. This study provides a mathematical representation profile of mathematics teacher candidates in vector-based analysis of maple analysis.

Model pathway diagrams for the representation of mathematical models

Mathematical models are the foundation of numerical simulation of optoelectronic devices. We present a concept for a machine-actionable as well as human-understandable representation of the mathematical knowledge they contain and the domain-specific knowledge they are based on. We propose to use theory graphs to formalize mathematical models and model pathway diagrams to visualize them. We illustrate our approach by application to the van Roosbroeck system describing the carrier transport in semiconductors by drift and diffusion. We introduce an approach for the block-based composition of models from simpler components.

Students’ Representation in Mathematical Word Problem-Solving: Exploring Students’ Self-efficacy

This descriptive qualitative research aims at investigating student represented in mathematical word problem solving based on self-efficacy. The research subjects are two eighth graders at a school in Surabaya with equal mathematical ability consisting of two female students with high and low self-efficacy. The subjects were chosen based on the results of test of mathematical ability, documentation of the result of middle test in even semester of 2016/2017 academic year, and results of questionnaire of mathematics word problem in terms of self-efficacy scale. The selected students were asked to do mathematical word problem solving and be interviewed. The result of this study shows that students with high self-efficacy tend to use multiple representations of sketches and mathematical models, whereas students with low self-efficacy tend to use single representation of sketches or mathematical models only in mathematical word problem-solving. This study emphasizes that teachers should pay attention of student’s representation as a consideration of designing innovative learning in order to increase the self-efficacy of each student to achieve maximum mathematical achievement although it still requires adjustment to the school situation and condition.

Решение задач теории автоматического управления в программном комплексе "МВТУ"

The software package "MVTU" (Modeling in Technical Devices; in Russian - Modelirovanie V Tehnicheskih Ustrojstvah) is intended for research and design of the systems described by the differential, algebraic and difference equations. Complex technical object is a controlled object, therefore in the package "MVTU", along with the methods of simulation, the methods of control theory are implemented. In terms of features this package is an alternative of package Simulink, which is a part of system of mathematical computations MATLAB. As well as in the package Simulink, in the package "MVTU" representation of mathematical model in the form of block diagram is accepted. Blocks of such diagram are described by the differential and difference equations, continuous and discrete transfer functions, algebraic relations and logical conditions. The package "MVTU" implements the following operating modes. The operating mode Simulation provides simulation of continuous, discrete and hybrid systems, including in real time in the presence of data exchange with external programs and devices. The mode Optimization allows us to find optimum parameters of the designed system. The modes Analysis and Synthesis provide the solution of problems of research and design of control systems with use of frequency and root methods. The paper describes the main features of the package "MVTU" according to the solution of problems of the analysis, synthesis, simulation and parametric optimization of automatic control systems. Examples of the solution of such problems are given. Experience of the solution of a large number of educational, scientific and applied problems showed that the package MVTU doesn't concede by the opportunities to the best foreign analogs.

Algorithm for repairing the damaged images of grain structures obtained from the cellular automata and measurement of grain size

Computational models are developed to create grain structures using mathematical algorithms based on the chaos theory such as cellular automaton, geometrical models, fractals, and stochastic methods. Because of the chaotic nature of grain structures, some of the most popular routines are based on the Monte Carlo method, statistical distributions, and random walk methods, which can be easily programmed and included in nested loops. Nevertheless, grain structures are not well defined as the results of computational errors and numerical inconsistencies on mathematical methods. Due to the finite definition of numbers or the numerical restrictions during the simulation of solidification, damaged images appear on the screen. These images must be repaired to obtain a good measurement of grain geometrical properties. Some mathematical algorithms were developed to repair, measure, and characterize grain structures obtained from cellular automata in the present work. An appropriate measurement of grain size and the corrected identification of interfaces and length are very important topics in materials science because they are the representation and validation of mathematical models with real samples. As a result, the developed algorithms are tested and proved to be appropriate and efficient to eliminate the errors and characterize the grain structures.

Frequency-spatial representation of mathematical models of energy loss during radiowave propagation

Frequency-spatial representation of mathematical models of energy loss during radiowave propagation

The algorithms of the organized search for identification of parameters of models of nonlinear dynamic system

The numerical methods for an estimation of parameters based on use of function f mins of the software package MATLAB 5.2 and on use of Bayes interpretation are stated. The parametrical mathematical model of dynamic system represented by system of the ordinary nonlinear differential equations depends on parameters. For dynamic system in discrete time the functions from the current state vectors are observed. The stated methods do not require calculation of gradients and are applicable, if into representation of mathematical model enter not differentiated function.

Framework for change notification and view synchronization in distributed model management systems

Large-scale model management systems are increasingly in demand to support groups of users in collaborative work environment. Users of such systems share common models but approach them with different views depending on individual needs and skills. Since models change along with the reality that is captured in them, so should their dependent models and views. This calls for a mechanism to manage and synchronize such changes in the models and views so that the integrity of the modelling environment can be maintained. In this paper we propose a framework for change notification and view synchronization in distributed model management systems that (1) manages the dependency relationships between the shared models and the dependent user views and (2) coordinates the changes by way of controlling and communicating the propagation activities. The framework identifies the change requirements based on the locus of changes in shared models and the effects of such changes in the dependents. It further defines change management constructs and processes to establish a view synchronization mechanism. In the framework, structured modeling was adopted for the representation of mathematical models, the generic model concept for constructing and dealing with mathematical models and the object-oriented database management system (ODBMS) to combine them in a single formalism. We present a prototype distributed model management system that has been developed to substantiate the efficacy of the proposed framework. The prototype was implemented on Windows NT using C++ and a commercial ODBMS called ObjectStore.

Vibration Signal Expert System for Fault Detection of Power Equipment Rolling Bearings

In this paper an approach of expert system construction for fault detection of rolling bearings is presented. The approach includes representation of mathematical models of rolling bearing vibration signals with application of linear random process theory. Some aspects of the expert system's construction and operation are discussed. Peculiarities of diagnosis parameters detection, training aggregates constructions and diagnostic rules' constructions are presented.

Fuzzy-Neural Model for Nonlinear Systems Identification

A state space representation of both continuous and discrete time mathematical models of Recurrent Neural Networks (RNN) are given in two layer Jordan canonical architecture, and a new improved Back-Propagation (BP) type learning method, is proposed. Some topology improvements, are suggested. The proposed RTNN model is linear in small and nonlinear in large, which permits to apply all well known state- and output linear systems design methods. The obtained RTNN model is incorporated in a rule-based fuzzy system, giving the possibility to approximate and to identify a complex nonlinear plants. Simulation results of nonlinear systems identification by the proposed fuzzy-neural system, using RNN BP learning, are given.

SQLMP: A Data Sublanguage for Representation and Formulation of Linear Mathematical Models

We show how algebraic linear optimization models can be mapped to the relational model of data. We then introduce SQLMP, a new language for model description and manipulation. SQLMP (SQL for Mathematical Programming) is the result of endowing the Structured Query Language (SQL) with additional constructs for the definition of the objective functions and the constraints of optimization models. Features of SQLMP enable 1) smooth integration of mathematical models with SQL-based databases, 2) model manipulation, and 3) attainment of a high degree of model independence. Formal syntax of the SQLMP is given. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Vibration Control in Industrial Plant: A Methodological Approach

The present paper is a report on the construction of nomograms to ascertain the domain of elastic-inertial-damping characteristics required in vibrating machine-foundation systems, in order to ensure that ergonomic and other technical constraints are complied with. Nomograms, which are the graphic representation of mathematical models in nondimensional form, prove to be an effective instrument for orientation in the design stage.