On the Big-R Notation for Describing Iterative and Recursive Behaviors

2011 ◽  
pp. 292-307
Author(s):  
Yingxu Wang
Keyword(s):  
Mathematical Model ◽  
Software Engineering ◽  
Mathematical Models ◽  
Programming Languages ◽  
Real Time ◽  
Mathematical Treatment ◽  
Time Process ◽  
Control Structures ◽  
Fundamental Properties ◽  
The Mathematical Model

Iterative and recursive control structures are the most fundamental mechanisms of computing that make programming more effective and expressive. However, these constructs are perhaps the most diverse and confusable instructions in programming languages at both syntactic and semantic levels. This article introduces the big-R notation that provides a unifying mathematical treatment of iterations and recursions in computing. Mathematical models of iterations and recursions are developed using logical inductions. Based on the mathematical model of the big-R notation, fundamental properties of iterative and recursive behaviors of software are comparatively analyzed. The big-R notation has been adopted and implemented in Real-Time Process Algebra (RTPA) and its supporting tools. Case studies demonstrate that a convenient notation may dramatically reduce the difficulty and complexity in expressing a frequently used and highly recurring concept and notion in computing and software engineering.

On the Cognitive Processes of Human Perception with Emotions, Motivations, and Attitudes

2009 ◽  
pp. 141-153
Author(s):  
Yingxu Wang
Keyword(s):  
Software Engineering ◽  
Mathematical Models ◽  
Real Time ◽  
Cognitive Processes ◽  
Reference Model ◽  
Human Perception ◽  
Comprehensive Model ◽  
Time Process ◽  
Rigorous Model ◽  
The Brain

An interactive motivation-attitude theory is developed based on the Layered Reference Model of the Brain (LRMB) and the object-attributerelation (OAR) model. This paper presents a rigorous model of human perceptual processes such as emotions, motivations, and attitudes. A set of mathematical models and formal cognitive processes of perception is developed. Interactions and relationships between motivation and attitude are formally described in real-time process algebra (RTPA). Applications of the mathematical models of motivations and attitudes in software engineering are demonstrated. This work is a part of the formalization of LRMB, which provides a comprehensive model for explaining the fundamental cognitive processes of the brain and their interactions. This work demonstrates that the complicated human emotional and perceptual phenomena can be rigorously modeled and formally treated based on cognitive informatics theories and denotational mathematics.

On the Cognitive Processes of Human Perception with Emotions, Motivations, and Attitudes

2009 ◽  
pp. 685-697
Author(s):  
Yingxu Wang
Keyword(s):  
Software Engineering ◽  
Mathematical Models ◽  
Real Time ◽  
Cognitive Processes ◽  
Reference Model ◽  
Human Perception ◽  
Comprehensive Model ◽  
Time Process ◽  
Rigorous Model ◽  
The Brain

An interactive motivation-attitude theory is developed based on the Layered Reference Model of the Brain (LRMB) and the object-attributerelation (OAR) model. This paper presents a rigorous model of human perceptual processes such as emotions, motivations, and attitudes. A set of mathematical models and formal cognitive processes of perception is developed. Interactions and relationships between motivation and attitude are formally described in real-time process algebra (RTPA). Applications of the mathematical models of motivations and attitudes in software engineering are demonstrated. This work is a part of the formalization of LRMB, which provides a comprehensive model for explaining the fundamental cognitive processes of the brain and their interactions. This work demonstrates that the complicated human emotional and perceptual phenomena can be rigorously modeled and formally treated based on cognitive informatics theories and denotational mathematics.

scholarly journals Mathematical model of tumour spheroid experiments with real-time cell cycle imaging

2020 ◽  
Author(s):  
Wang Jin ◽  
Loredana Spoerri ◽  
Nikolas K. Haass ◽  
Matthew J. Simpson
Keyword(s):  
Mathematical Model ◽  
Cell Cycle ◽  
Mathematical Models ◽  
Real Time ◽  
Living Cells ◽  
G1 Phase ◽  
Tumour Spheroid ◽  
Spheroid Growth ◽  
M Phase ◽  
The Mathematical Model

AbstractThree-dimensional (3D) in vitro tumour spheroid experiments are an important tool for studying cancer progression and potential drug therapies. Standard experiments involve growing and imaging spheroids to explore how different experimental conditions lead to different rates of spheroid growth. These kinds of experiments, however, do not reveal any information about the spatial distribution of the cell cycle within the expanding spheroid. Since 2008, a new experimental technology called fluorescent ubiquitination-based cell cycle indicator (FUCCI), has enabled real time in situ visualisation of the cell cycle progression. FUCCI labelling involves cells in G1 phase of the cell cycle fluorescing red, and cells in the S/G2/M phase of the cell cycle fluorescing green. Experimental observations of 3D tumour spheroids with FUCCI labelling reveal significant intratumoural structure, as the cell cycle status can vary with location. Although many mathematical models of tumour spheroid growth have been developed, none of the existing mathematical models are designed to interpret experimental observations with FUCCI labelling. In this work we extend the mathematical framework originally proposed by Ward and King (1997) to develop a new mathematical model of FUCCI-labelled tumour spheroid growth. The mathematical model treats the spheroid as being composed of three subpopulations: (i) living cells in G1 phase that fluoresce red; (ii) living cells in S/G2/M phase that fluoresce green; and, (iii) dead cells that do not fluoresce. We assume that the rates at which cells pass through different phases of the cell cycle, and the rate of cell death, depend upon the local oxygen concentration in the spheroid. Parameterising the new mathematical model using experimental measurements of cell cycle transition times, we show that the model can capture important experimental observations that cannot be addressed using previous mathematical models. Further, we show that the mathematical model can be used to quantitatively mimic the action of anti-mitotic drugs applied to the spheroid. All software required to solve the nonlinear moving boundary problem associated with the new mathematical model are available on GitHub.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

scholarly journals Analysis on Present Mathematical Model for Predicting the Crop Production

2020 ◽  
Vol 9 (12) ◽  
pp. 168-170
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Real World ◽  
Crop Production ◽  
Ghg Emissions ◽  
Data Set ◽  
Factors Affecting ◽  
The Government ◽  
The Mathematical Model ◽  
Government Website

India is a worldwide agriculture business powerhouse. Future of agriculture-based products depends on the crop production. A mathematical model might be characterized as a lot of equations that speak to the conduct of a framework. By using mathematical model in agriculture field, we can predict the production of crop in particular area. There are various factors affecting crops such as Rainfall, GHG Emissions, Temperature, Urbanization, climate, humidity etc. A mathematical model is a simplified representation of a real-world system. It forms the system using mathematical principles in the form of a condition or a set of conditions. Suppose we need to increase the crop production, at that time the mathematical model plays a major role and our work can be easier, more significant by using the mathematical model. Through the mathematical model we predict the crop production in upcoming years. .AI, ML, IOT play a major role to predict the future of agriculture, but without mathematical models it is not possible to predict crop production accurately. To solve the real-world agriculture problem, mathematical models play a major role for accurate results. Correlation Analysis, Multiple Regression analysis and fuzzy logic simulation standards have been utilized for building a grain production benefit depending model from crop production. Prediction of crop is beneficiary to the farmer to analyze the crop management. By using the present agriculture data set which is available on the government website, we can build a mathematical model.

A Modular Code for Real Time Dynamic Simulation of Gas Turbines in Simulink

2002 ◽  
Vol 128 (3) ◽  
pp. 506-517 ◽  
Author(s):  
S. M. Camporeale ◽  
B. Fortunato ◽  
M. Mastrovito
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Gas Turbine ◽  
Dynamic Behavior ◽  
Gas Turbines ◽  
Simulation Software ◽  
Computational Time ◽  
High Fidelity ◽  
Time Step ◽  
The Mathematical Model

A high-fidelity real-time simulation code based on a lumped, nonlinear representation of gas turbine components is presented. The code is a general-purpose simulation software environment useful for setting up and testing control equipments. The mathematical model and the numerical procedure are specially developed in order to efficiently solve the set of algebraic and ordinary differential equations that describe the dynamic behavior of gas turbine engines. For high-fidelity purposes, the mathematical model takes into account the actual composition of the working gases and the variation of the specific heats with the temperature, including a stage-by-stage model of the air-cooled expansion. The paper presents the model and the adopted solver procedure. The code, developed in Matlab-Simulink using an object-oriented approach, is flexible and can be easily adapted to any kind of plant configuration. Simulation tests of the transients after load rejection have been carried out for a single-shaft heavy-duty gas turbine and a double-shaft aero-derivative industrial engine. Time plots of the main variables that describe the gas turbine dynamic behavior are shown and the results regarding the computational time per time step are discussed.

BASIC MATHEMATICAL MODELS AND AN APPROXIMATE METHOD OF FILTRATION THEORY

2021 ◽  
pp. 25-31
Author(s):  
Alla A. Mussina
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Mathematical Models ◽  
Heterogeneous Porous Media ◽  
Effective Management ◽  
Filtration Theory ◽  
New Device ◽  
Scientific Papers ◽  
The Mathematical Model ◽  
Inhomogeneous Liquids

The article defines the basic concepts of filtration theory and provides an overview of the existing mathematical models of inhomogeneous liquids in porous media. The paper considers the Stefan problem. The number of scientific papers devoted to the study of porous structures has recently increased. This is primarily due to the fact that the prob-lems of oil and uranium production have been identified, and the solution of environmental problems is overdue. Therefore, a new device is needed to develop models of liquid filtration. With the advent and development of computer technology, it has become easier to solve problems that require numerical methods for their solution. Understanding the movement of fluids and the mechanism of dissolution of rocks under the action of acids in heterogeneous porous media is of great importance for the extraction and production of oil and the effective management of these processes. The article examines the mathematical model of the theory of isothermal filtration. Possible variants of the solva-bility of the model are shown. The research scheme consists of the output of a mathematical model, the formulation of the problem, one variant of the solution of the problem, the algorithm of the numerical method of solving the problem.

scholarly journals An Improved Capacitive Sensor for Detecting the Micro-Clearance of Spherical Joints

Sensors ◽  
2019 ◽  
Vol 19 (12) ◽  
pp. 2694 ◽  
Author(s):  
Wen Wang ◽  
Wenjun Qiu ◽  
He Yang ◽  
Haimei Wu ◽  
Guang Shi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Measurement Accuracy ◽  
Detection Method ◽  
Capacitive Sensor ◽  
Parallel Manipulators ◽  
Differential Capacitance ◽  
Industrial Robots ◽  
The Mathematical Model ◽  
Fringe Effect

Due to the flexible and compact structures, spherical joints are widely used in parallel manipulators and industrial robots. Real-time detection of the clearance between the ball and the socket in spherical joints is beneficial to compensate motion errors of mechanical systems and improve their transmission accuracy. This work proposes an improved capacitive sensor for detecting the micro-clearance of spherical joints. First, the structure of the capacitive sensor is proposed. Then, the mathematical model for the differential capacitance of the sensor and the eccentric micro-displacement of the ball is deduced. Finally, the capacitance values of the capacitive sensor are simulated with Ansoft Maxwell. The simulated values of the differential capacitances at different eccentric displacements agree well with the theoretical ones, indicating the feasibility of the proposed detection method. In addition, the simulated results show that the proposed capacitive sensor could effectively reduce the capacitive fringe effect, improving the measurement accuracy.

Formal Modeling and Specification of Design Patterns Using RTPA

2011 ◽  
pp. 239-253
Author(s):  
Yingxu Wang ◽  
Jian Huang
Keyword(s):  
Mathematical Model ◽  
Programming Languages ◽  
Software Design ◽  
Design Patterns ◽  
Expert Knowledge ◽  
Formal Model ◽  
Dynamic Structure ◽  
Generic Model ◽  
Time Process ◽  
Software Patterns

Software patterns are recognized as an ideal documentation of expert knowledge in software design and development. However, its formal model and semantics have not been generalized and matured. The traditional UML specifications and related formalization efforts cannot capture the essence of generic patterns precisely, understandably, and essentially. A generic mathematical model of patterns is presented in this article using real-time process algebra (RTPA). The formal model of patterns are more readable and highly generic, which can be used as the meta model to denote any design patterns deductively, and can be translated into code in programming languages by supporting tools. This work reveals that a pattern is a highly complicated and dynamic structure for software design encapsulation, because of its complex and flexible internal associations between multiple abstract classes and instantiations. The generic model of patterns is not only applicable to existing patterns’ description and comprehension, but also useful for future patterns’ identification and formalization.

scholarly journals Diagnostics of supercapacitors

2018 ◽  
Vol 182 ◽  
pp. 01009 ◽  
Author(s):  
Valeriy Martynyuk ◽  
Oleksander Eromenko ◽  
Juliy Boiko ◽  
Tomasz Kałaczyński
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Methodological Approach ◽  
Frequency Dispersion ◽  
Technical Condition ◽  
Transient Processes ◽  
Nonlinear Frequency ◽  
Diagnostic Reliability ◽  
General Reliability ◽  
The Mathematical Model

The paper represents the mathematical model for diagnostics of supercapacitors. The research objectives are the problem of determining a supercapacitor technical condition during its operation. The general reliability of diagnostics is described as the methodological and instrumental reliabilities of diagnostics. The instrumental diagnostic reliability of supercapacitor includes the probabilities of errors of the first and second kind, α and β respectively. The methodological approach to increasing the reliability of supercapacitor diagnostic has been proposed, in terms of multi-parameter supercapacitor diagnostic by applying nonlinear, frequency dependent mathematical models of supercapacitors that take into account nonlinearity, frequency dispersion of parameters and the effect of transient processes in supercapacitors. The more frequencies, operating voltages and currents are applied in the supercapacitor diagnostics, the more methodological reliability of diagnostics will increase in relation to the methodological reliability of supercapacitor diagnostics when only one frequency, voltage and current are applied.

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