Investigations of properties of programs by means of the extended algorithmic logic I

1977 ◽  
Vol 1 (1) ◽  
pp. 93-119
Author(s):  
Lech Banachowski
Keyword(s):  
Mathematical Model ◽  
Mathematical Tool ◽  
Methods Of Analysis ◽  
Semantic Correctness ◽  
Algorithmic Logic ◽  
Correctness Of Programs

The present paper contains investigations concerning the semantic correctness of programs. Presented methods of analysis of programs are appropriate for every domain of computation. Algorithmic logic extended by classical quantifiers is a fundamental mathematical tool used in the paper. Interrelations between properties of programs and properties of descriptions of programs are studied (a description of a program is a mathematical model of the notion of a documentation of a program).

Retrieval System and Dynamic Algorithm Looking for Axioms of Notions Defined by Programs

1993 ◽  
Vol 19 (3-4) ◽  
pp. 275-301
Author(s):  
Andrzej Biela
Keyword(s):  
Theorem Proving ◽  
Dynamic Process ◽  
Functional Equations ◽  
Automated Theorem Proving ◽  
Retrieval System ◽  
Formal System ◽  
Dynamic Algorithm ◽  
Algorithmic Logic ◽  
Correctness Of Programs

In this paper we shall introduce a formal system of algorithmic logic which enables us to formulate some problems connected with a retrieval system which provides a comprehensive tool in automated theorem proving of theorems consisting of programs, procedures and functions. The procedures and functions may occur in considered theorems while the program of the above mentioned system is being executed. We can get an answer whether some relations defined by programs hold and we can prove functional equations in a dynamic way by looking for a special set of axioms /assumptions/ during the execution of system. We formulate RS-algorithm which enables us to construct the set of axioms for proving some properties of functions and relations defined by programs. By RS-algorithm we get the dynamic process of proving functional equations and we can answer the question whether some relations defined by programs hold. It enables us to solve some problems concerning the correctness of programs. This system can be used for giving an expert appraisement. We shall provide the major structures and a sketch of an implementation of the above formal system.

scholarly journals Mathematical model of environmental waters purification

2019 ◽  
Vol 135 ◽  
pp. 01056
Author(s):  
Yuri Skolubovich ◽  
Alexey Skolubovich ◽  
Dmitry Volkov ◽  
Tamara Krasnova ◽  
Elena Gogina
Keyword(s):  
Mathematical Model ◽  
Mathematical Analysis ◽  
Stochastic Approach ◽  
Mathematical Tool ◽  
Environmental Waters ◽  
Mass Service ◽  
Coagulation Process ◽  
Service Theory

This article describes the use of the stochastic approach, in particular, mass service theory and the development of its methods, adapted directly to the coagulation process as a mathematical tool. The coagulation process will be concerned as a) supplying water to the mixer, b) processing it with reagents (coagulants), c) settling for the mathematical analysis of water clarification effectiveness.

scholarly journals Theoretical foundations of hypertrace-transform: scanning techniques, mathematical apparatus and experimental verification

2018 ◽  
Vol 42 (2) ◽  
pp. 273-282 ◽  
Author(s):  
N. G. Fedotov ◽  
A. A. Syemov ◽  
A. V. Moiseev
Keyword(s):  
Mathematical Model ◽  
Image Recognition ◽  
Experimental Verification ◽  
Automatic Generation ◽  
Analytic Structure ◽  
Mathematical Tool ◽  
Mathematical Apparatus ◽  
3D Image ◽  
3D Images ◽  
Scanning Technique

We consistently describe the theoretical basis of a new geometric method of analysis and recognition of three-dimensional (3D) images. The description of a scanning technique for forming a hypertrace transform and its mathematical model are given. This method, unlike the existing ones, enables 3D images to be analyzed directly from their 3D shape, without first simplifying them or constructing plane projections. We substantiate the selection of a particular scanning tool and the need to construct a reference spherical grid to address the problem of the rotational invariance of the 3D image recognition. A mathematical apparatus of the stochastic realization of the scanning technique based on stochastic geometry and functional analysis is developed. We introduce a new mathematical tool for 3D image analysis – a hypertrex matrix that allows spatial objects of complex shape and structure to be recognized by constructing a single mathematical model of the 3D image. We describe a new type of 3D image features that have an analytic structure – hypertryplet features, whose analytical structure makes possible an automatic generation of a large number of features with predetermined properties. Results of the experimental verification are presented, demonstrating the accurate calculation of features for 3D image recognition and proving the adequacy of the developed mathematical apparatus.

scholarly journals Numerical Study of the Process of Unsteady Filtration of a Fluid in Interacting Porous Pressure Layers

2021 ◽  
Keyword(s):  
Mathematical Model ◽  
Numerical Study ◽  
Management Decision ◽  
Permeability Barrier ◽  
Mathematical Tool ◽  
Gas Filtration ◽  
Groundwater Levels ◽  
Vertical Drainage ◽  
Unsteady Filtration ◽  
Drainage Wells

A review of the fundamental studies conducted in 2010 - 2020 is given in the article to develop a mathematical model related to the fluid and gas filtration processes in porous media. To conduct a comprehensive study of the process of unsteady filtration of fluid in multi-layer porous pressure media and to make a management decision, a mathematical model described by a system of partial differential equations with corresponding initial and boundary conditions and a conservative numerical algorithm were developed. On the basis of the developed software of the problem posed, computational experiments were conducted on a computer; the calculation results were presented in the form of tables and graphical objects. The schemes of location and capacity of vertical drainage wells to protect irrigated and non-irrigated areas from flooding were proposed on the basis of the developed software. Using the proposed mathematical tool, it is possible to obtain the prognostic groundwater levels for any area for the required period of time, considering a number of factors, for example, the formation heterogeneity in plan, the gradient of the permeability barrier, and other hydrogeological, hydro-technical, and natural conditions; to calculate the capacity and optimal drilling pattern of vertical drainage wells to protect the territory and to develop oil and gas fields.

A Mathematical Model for the Gilt-Edged Market

1977 ◽  
Vol 36 ◽  
pp. 85-160
Author(s):  
R. S. Clarkson
Keyword(s):  
Mathematical Model ◽  
Pension Fund ◽  
Yield Curve ◽  
British Government ◽  
Price Model ◽  
Methods Of Analysis ◽  
Switching Action ◽  
The Mathematical Model ◽  
Special Case

SynopsisThis paper investigates what general form of price model is required to represent a market that is in equilibrium under switching action and describes how a special case of this general price model can be applied to the gilt-edged market, with particular emphasis on long-dated stocks. Applications of the mathematical model are then developed in a form that could be used by a life office or pension fund for the management of a portfolio of long-dated British Government stocks. Finally, a comparison is made between conventional yield curve methods of analysis and methods based on this mathematical model.

Analysis of a single-phase capacitor induction motor operating at two power line frequencies

2012 ◽  
Vol 61 (2) ◽  
pp. 251-266 ◽  
Author(s):  
Aleksander Leicht ◽  
Krzysztof Makowski
Keyword(s):  
Mathematical Model ◽  
Induction Motor ◽  
Single Phase ◽  
Induction Motors ◽  
Power Line ◽  
Mathematical Tool ◽  
Simulation Results ◽  
Capacitor Capacitance ◽  
Load Conditions

Analysis of a single-phase capacitor induction motor operating at two power line frequenciesThe paper presents a modelling mathematical tool for prediction of dynamic and steady-states operation of the single-phase capacitor induction motor for different values of the capacitor capacitance and different frequency of voltage supply at no-load and rated load conditions. Developed mathematical model of the capacitor induction motor was implemented for calculation using Matlab/Simulink software. Presented simulation results may be utilized to achieve better starting quality of single-phase capacitor induction motors.

scholarly journals Tykhonov triples and convergence results for hemivariational inequalities

2021 ◽  
Vol 26 (2) ◽  
pp. 271-292
Author(s):  
Rong Hu ◽  
Mircea Sofonea ◽  
Yi-Bin Xiao
Keyword(s):  
Mathematical Model ◽  
Banach Space ◽  
Elastic Body ◽  
Metric Space ◽  
Reflexive Banach Space ◽  
Convergence Result ◽  
Hemivariational Inequalities ◽  
Mathematical Tool ◽  
Abstract Problem ◽  
Convergence Results

Consider an abstract Problem P in a metric space (X; d) assumed to have a unique solution u. The aim of this paper is to compare two convergence results u'n → u and u''n → u, both in X, and to construct a relevant example of convergence result un → u such that the two convergences above represent particular cases of this third convergence. To this end, we use the concept of Tykhonov triple. We illustrate the use of this new and nonstandard mathematical tool in the particular case of hemivariational inequalities in reflexive Banach space. This allows us to obtain and to compare various convergence results for such inequalities. We also specify these convergences in the study of a mathematical model, which describes the contact of an elastic body with a foundation and provide the corresponding mechanical interpretations.

scholarly journals DETERMINATION OF SUSTAINABLE LEVELS OF DESIGN ALTERNATIVES SELECTION IN THE WORKFLOW CAP SYSTEM

2021 ◽  
pp. 48-56
Author(s):  
S. G. Mitin ◽  
◽  
P. Yu. Bochkarev ◽  
V. V. Shalunov ◽  
I. A. Razmanov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Fast Response ◽  
Design Solution ◽  
Design Activity ◽  
Mathematical Tool ◽  
Process Implementation ◽  
Design Alternatives ◽  
Level Of Selection ◽  
The Mathematical Model ◽  
Production Situation

The development of the mechanical treatment workflow CAP system is aimed at the solution of a crucial task of reduction of terms and the improvement of quality of multiproduct machining manufactures work preparation, as the existing workflow CAP systems have not got the possibility of fast response to changes in a production situation often arising within the multiproduct manufacture. The authors of this paper developed the workflow CAP system, which contains the requirements of the design activity full automation, design solution multivariance, and the feedback with the engineering process implementation subsystem. The paper deals with the development of a mathematical model and the technique of searching for sustainable levels of selecting design alternatives depending on the production situation for the whole design procedures of the workflow CAP system. The authors prove the application of a mathematical tool of genetic algorithms; describe the mathematical model using its terms. As a gene, the level of selection in a separate project procedure is specified. A chromosome is a set of genes according to the project procedures. The objective function determines the minimum total time of processing of the specified nomenclature of parts based on the ranges of gene aggregates resulting from crossing and mutation operations. The result of the work is the mathematical model and the technique for identifying the sustainable levels of selection in each project procedure ensuring the possibility of self-adjustment of the workflow CAP system depending on the production situation.

scholarly journals The Mathematical Support of Machine Surfacing for the Railway Track

2020 ◽  
Vol 13 (3) ◽  
pp. 246-267
Author(s):  
Dmytro Kurhan ◽  
Maksym Havrylov
Keyword(s):  
Mathematical Model ◽  
Software Package ◽  
Geometric Shape ◽  
Railway Track ◽  
Mathematical Tool ◽  
Information Base ◽  
Automation Systems ◽  
Maintenance Personnel ◽  
The Mathematical Model

The condition of a railway track is characterized by many indices, including its geometric shape, both in the horizontal and vertical planes. The purpose of this paper is to create a mathematical tool to ensure the operation of track machines for surfacing, tamping, and alignment, which are equipped with automation systems. The developed mathematical model will be integrated into the AS "Strela" software package which is currently installed on machines. Scientific approaches used in the mathematical model allowed to reduce the operation of machines in "window", to simplify the work of maintenance personnel, to create an information base of track parameters, to establish rational parameters of curves during surfacing.

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