THE RELATIONAL APPROACH TO THE MATHEMATICAL MODEL OF MEANING OF INFORMATION

A mathematical model of the meaning of the signal is proposed. The meaning is not the signal itself, but its effect on the recipient. Under the action of the signal, the state of the receiver changes, which is the meaning of the signal. The most general mathematical model is the description of the recipient’s state with the help of some mathematical object, and the meaning is modeled by the action of some operator on this object. Various concrete formalisms are considered: abstract automata, matrix representation, algorithms, Markov chains, parameter spaces. The article deals with finite, countable and continuous meanings, reversible and irreversible meanings, ambiguous meanings, decomposition into elementary meanings.

Avaliação de modelos matemáticos para estimativa da erosividade da chuva na região de São Mateus-ES

Revista Verde de Agroecologia e Desenvolvimento Sustentável ◽

10.18378/rvads.v11i3.4132 ◽

2016 ◽

Vol 11 (3) ◽

pp. 98

Author(s):

Dione Pereira Cardoso ◽

Fábio Ribeiro Pires ◽

Robson Bonomo

Keyword(s):

Mathematical Model ◽

Mathematical Models ◽

Holy Spirit ◽

Climatic Conditions ◽

The State ◽

Rainfall Erosivity ◽

Climatological Station ◽

Average Rainfall ◽

The Holy Spirit ◽

Objetivou-se estimar a erosividade da chuva, mediante seis modelos matemáticos, de regressão linear avaliando entre estes, qual é mais indicado para as condições climáticas da região de São Mateus-ES. Os dados pluviométricos foram obtidos junto à Agência Nacional das Águas-ANA, sendo de 1947 a 2014 para Itauninhas, de 1971 a 2014 para Barra Nova, de 1981 a 2014 para São João da Cachoeira Grande e de 1993 a 2014 para Boca da Vala. Para estimar a erosividade da chuva, a partir da precipitação anual e do coeficiente de chuva, foram utilizadas diferentes equações utilizadas em outros estados com aplicação ao estado do Espírito Santo ou ajustadas para o próprio estado. Para os modelos matemáticos (II) e (I), os valores médios foram de 6.541,2 MJ ha-1 mm h-1 ano-1 a 936,357 MJ ha-1 mm h-1 ano-1 (Itauninhas), de 6.995,855 MJ ha-1 mm h-1 ano-1 a 1.420,296 MJ ha-1 mm h-1 ano-1 (Barra Nova), de 6.297,272 MJ ha-1 mm h-1 ano-1 a 1.014,815 MJ ha-1 mm h-1 ano-1 (São João da Cachoeira Grande) e de 5.427,659 MJ ha-1 mm h-1 ano-1 a 1.626,489 MJ ha-1 mm h-1 ano-1 (Boca da Vala). Para os municípios de Barra Nova e Boca da Vala a erosividade da chuva foi estimada pela equação EI30 = 6,4492*pi – 391,63 com distribuição leptocúrtica. Para as outras duas localidades, a distribuição foi platicúrtica. A estação climatológica com o maior valor de erosividade média da chuva foi Barra Nova, enquanto Boca da Vala apresentou a menor erosividade, considerando apenas a estimativa da erosividade da chuva pelo modelo matemático II. Os maiores e menores valores de erosividade da chuva foram obtidos com os modelos matemáticos I e II. Para estimar a erosividade da chuva, nas condições climáticos da região de São Mateus-ES, o modelo matemático mais adequado é o II.Evaluation of mathematical models to estimate rainfall erosivity in the region of São Mateus-ESAbstract: This study aimed to estimate the rainfall erosivity by six mathematical models, linear regression, and evaluate these, which is more suitable for the climatic conditions of São Mateus-ES region. The rainfall data were obtained from the National Water Agency-ANA, and 1947-2014 for Itauninhas, 1971-2014 to Barra Nova, 1981-2014 for São João da Cachoeira Grande and 1993-2014 for Boca da Vala. To estimate the rainfall erosivity, from the annual precipitation and rainfall coefficient were used different equations used in other states with application to the state of the Holy Spirit or adjusted to the state itself. For mathematical models (II) and (I), the average values were 6541.2 MJ ha-1 mm h-1 year-1 to 936.357 MJ ha-1 mm h-1 year-1 (Itauninhas) of 6995.855 MJ mm ha-1 h-1 year-1 to 1420.296 MJ ha-1 mm h-1 year-1 (Barra nova), to 6297.272 MJ ha-1 mm h-1 year-1 and 1014.815 MJ mm ha-1 h-1 year-1 (São João da Cachoeira Grande) and 5427.659 MJ ha-1 mm h-1 year-1 to 1626.489 MJ ha-1 mm h-1 year-1 (Boca da Vala). For the municipalities of Barra Nova and Boca da Vala the rainfall erosivity was estimated by EI30 = 6.4492*pi - 391.63 with leptokurtic distribution. For the other two locations, the distribution was platykurtic. The climatological station with the highest amount of average rainfall erosivity was Barra Nova, while Boca da Vala had the lowest erosivity, considering only an estimated rainfall erosivity by the mathematical model II. The highest and lowest values erosivity of the rain were obtained with the mathematical models I and II. To estimate the rainfall erosivity in the climatic conditions of São Mateus-ES region, the most suitable mathematical model is II.

On waiting times to populate an environment and a question of statistical inference

Journal of Applied Probability ◽

10.1239/jap/1032374246 ◽

1999 ◽

Vol 36 (1) ◽

pp. 261-267 ◽

Cited By ~ 8

Author(s):

F. Thomas Bruss ◽

M. Slavtchova-Bojkova

Keyword(s):

Mathematical Model ◽

Statistical Inference ◽

Waiting Time ◽

Branching Process ◽

Waiting Times ◽

The State ◽

Higher Moments ◽

Total Progeny ◽

Cycle Lengths ◽

The mathematical model we consider here is the classical Bienaymé–Galton–Watson branching process modified with immigration in the state zero.We study properties of the waiting time to explosion of the supercritical modified process, i.e. that time until all beginning cycles which die out have disappeared. We then derive the expected total progeny of a cycle and show how higher moments can be computed. With a view to applications the main goal is to show that any statistical inference from observed cycle lengths or estimates of total progeny on the fertility rate of the process must be treated with care. As an example we discuss population experiments with trout.

General Mathematical Model of Internal Meshing Spiral Bevel Gears for Nutation Drive

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.101-102.708 ◽

2011 ◽

Vol 101-102 ◽

pp. 708-712 ◽

Cited By ~ 4

Author(s):

Zheng Lin ◽

Li Gang Yao

Keyword(s):

Mathematical Model ◽

3D Modeling ◽

Gear Tooth ◽

Spiral Bevel Gears ◽

Bevel Gears ◽

Spiral Bevel ◽

The Mathematical Model ◽

Crown Gear ◽

Internal Meshing

The general mathematical model of internal meshing spiral bevel gears for nutation drive is studied. Based on conventional enveloping theory and transmission principle, the meshing of two spiral bevel gears in nutation drive was substituted by the meshing of an imaginary rotating crown gear engaging with the external and internal bevel gear respectively. The general mathematical model of crown gear was established. Then the general mathematical model of internal meshing spiral bevel gears is obtained by matrix transformation, which is suitable for a variety of gear tooth profiles. Finally, the mathematical model and 3D modeling of double circular-arc spiral bevel gears are developed.

Analysis of the state of the modified nanotitanium surface with the use of the mathematical model of a cyclic random process

Optoelectronics Instrumentation and Data Processing ◽

10.3103/s8756699015030073 ◽

2015 ◽

Vol 51 (3) ◽

pp. 254-263 ◽

Cited By ~ 7

Author(s):

I. V. Lytvynenko ◽

P. O. Maruschak

Keyword(s):

Mathematical Model ◽

Random Process ◽

The State ◽

Cyclic Random Process ◽

A Ball-Balancing System for Demonstration of Basic Concepts in the State-Space Control Theory

International Journal of Electrical Engineering Education ◽

10.1177/002072097401100415 ◽

1974 ◽

Vol 11 (4) ◽

pp. 367-376 ◽

Cited By ~ 7

Author(s):

V. Jørgensen

Keyword(s):

Mathematical Model ◽

Control Theory ◽

Physical Properties ◽

Graduate Education ◽

State Space ◽

The State ◽

Basic Concepts ◽

Conditions Of Stability ◽

The Ball-balancing Systems is intended to demonstrate the basic concepts in the state-space control theory in the graduate education. The physical properties of the system are stated and the mathematical model is evaluated. Conditions of stability are discussed.

Understanding hormonal crosstalk in Arabidopsis root development via emulation and history matching

Statistical Applications in Genetics and Molecular Biology ◽

10.1515/sagmb-2018-0053 ◽

2020 ◽

Vol 19 (2) ◽

Author(s):

Samuel E. Jackson ◽

Ian Vernon ◽

Junli Liu ◽

Keith Lindsey

Keyword(s):

Experimental Data ◽

Mathematical Model ◽

Parameter Space ◽

History Matching ◽

Parameter Spaces ◽

Arabidopsis Root ◽

Biologically Relevant ◽

Hormonal Crosstalk ◽

The Mathematical Model ◽

Insight Into

AbstractA major challenge in plant developmental biology is to understand how plant growth is coordinated by interacting hormones and genes. To meet this challenge, it is important to not only use experimental data, but also formulate a mathematical model. For the mathematical model to best describe the true biological system, it is necessary to understand the parameter space of the model, along with the links between the model, the parameter space and experimental observations. We develop sequential history matching methodology, using Bayesian emulation, to gain substantial insight into biological model parameter spaces. This is achieved by finding sets of acceptable parameters in accordance with successive sets of physical observations. These methods are then applied to a complex hormonal crosstalk model for Arabidopsis root growth. In this application, we demonstrate how an initial set of 22 observed trends reduce the volume of the set of acceptable inputs to a proportion of 6.1 × 10−7 of the original space. Additional sets of biologically relevant experimental data, each of size 5, reduce the size of this space by a further three and two orders of magnitude respectively. Hence, we provide insight into the constraints placed upon the model structure by, and the biological consequences of, measuring subsets of observations.

The Mathematical Model for Research of the UAV Longitudinal Moving

International Journal of Computer Network and Information Security ◽

10.5815/ijcnis.2021.05.03 ◽

2021 ◽

Vol 13 (5) ◽

pp. 29-39

Author(s):

Sergii Zhdanov ◽

◽

Natalia Kadet ◽

Valerii Silkov ◽

Mariia Zirka ◽

...

Keyword(s):

Mathematical Model ◽

Mathematical Models ◽

Frequency Response ◽

Unmanned Aerial Vehicles ◽

Control Systems ◽

Aerial Vehicles ◽

Logarithmic Frequency ◽

The Impact ◽

The paper presents one of the perspective directions of the development to modern aviation, which is connected with designing and producing unmanned aerial vehicles (UAV) of various functionalities for applying in both military and civilian spheres. The syntheses of UAV control systems, regardless of their type and purpose presumes creation of adequate mathematical models, first of all adequate aerodynamic mathematical models. In the paper results that forms and justify the aerodynamic mathematical model and as well as the results of building a general mathematical model of the longitudinal movement of the perspective UAV are presented. Also factors that forms the mathematical model on given aerodynamic, geometric, mass and inertial data for a hypothetical perspective altitude long-range UAV are submitted. Assessment of the impact of these data on the dynamic, temporal, and logarithmic frequency response UAV also has been given in this paper.

Dynamics of Working Processes in Automatic Direct-Acting Pressure Regulators of Pneumatic Spacecraft Systems

Proceedings of Higher Educational Institutions Маchine Building ◽

10.18698/0536-1044-2021-9-65-76 ◽

2021 ◽

pp. 65-76

Author(s):

A.V. Lebedev ◽

A.V. Chernyshev ◽

Y.V. Kyurdzhiev ◽

A.P. Mitrofanov ◽

O.S. Ilicheva ◽

...

Keyword(s):

Mathematical Model ◽

Software Package ◽

Block Diagram ◽

Working Fluid ◽

Pressure Regulator ◽

Conservation Of Energy ◽

Direct Acting ◽

The Mathematical Model ◽

Working Processes

The purpose of the study was by means of modern software to explore working processes taking place in automatic direct-acting pressure regulators of pneumatic spacecraft systems. As a result, we developed a general mathematical model of the pressure regulator. The design of the regulator is shown in the form of a block diagram, composed of a set of channels, cavities, and stages. The elements of the block diagram are interconnected by the basic laws of conservation of energy and mass. The mathematical model was evaluated in the Amesim software package. Findings of the full-scale and computational experiments led to the conclusions about the effect the heat exchange between the working fluid and the environment produces on the parameters of the pressure regulator, and about the use of the Amesim software package for further research of working processes in the valve units of pneumatic systems.

Estimation of State Variables in the Ćuk Converter Mathematical Model with Partially Unknown Parameters

Mekhatronika Avtomatizatsiya Upravlenie ◽

10.17587/mau.22.451-458 ◽

2021 ◽

Vol 22 (9) ◽

pp. 451-458

Author(s):

A. A. Bobtsov ◽

R. Ortega ◽

N. A. Nikolaev ◽

O. V. Slita ◽

O. A. Kozachek ◽

...

Keyword(s):

Mathematical Model ◽

Finite Time ◽

Control Algorithm ◽

Power Converter ◽

The State ◽

Model Parameters ◽

State Variables ◽

Unknown Parameters ◽

Proportional Integral ◽

In this paper the solution was proposed for the state variables estimation problem in the mathematical model of the DC switch-mode power converter built according to the Ćuk scheme. Pulse converters are one of the main components of most modern electrical devices and the circuit proposed by Slobodan Ćuk in the 70s of the 20th century is still relevant and demanded. Traditionally, PI (proportional-integral) controllers or proportional-integral adaptive control algorithm (PI-PBC), based on passification methods and superior to standard PI controllers in accuracy, are used as the control algorithm for power converters. However, you need to know the entire vector of the state variables of the converter to build a PI-PBC controller, and moreover, all its parameters must be accurately known. Unfortunately, in practice, such assumptions are not fulfilled, since parametric drifting is possible, and measurements of the converter’s state require additional sensors, which in some cases does not justify itself. Thus, there is a need to develop additional observers or estimators that allow obtaining data on all variables of the converter, as well as its parameters. The solution is based on the GPEBO method (generalized parameter estimation-based observers). The problem was solved under assumption that only the output signal (the output voltage of the converter) is measurable and some of the mathematical model parameters are unknown. An important aspect of the observer design is the development of an algorithm for unknown parameters and the state vector of a mathematical model estimation that ensures convergence in a finite time. Finite-time convergence is extremely important when designing observers since transients in pulse converters occur very quickly.

Study of the Drug Diffusion Through Polymeric Membranes

Revista de Chimie ◽

10.37358/rc.18.4.6200 ◽

2018 ◽

Vol 69 (4) ◽

pp. 783-789

Author(s):

Elena Grosu ◽

Ancuta Trifoi ◽

Maria Rapa ◽

Timea Gherman ◽

Andreea Turcanu ◽

...

Keyword(s):

Experimental Data ◽

Mathematical Model ◽

Effective Diffusion ◽

Ethylene Vinyl Acetate ◽

Polymeric Membranes ◽

Experimental Drug ◽

The Mathematical Model ◽

Active Substances ◽

Acetate Copolymer

We present the studies carried out on the transport properties of some membranes obtained from synthetic polymers: polyurethane and ethylene-vinyl acetate copolymer, for use in the development of transdermal therapeutic systems with limiting membranes of speed. The properties of drug active substances transport through membranes were highlighted by performing studies with a diffusion cell. Experimental drug active substances were paracetamol and tetracycline. The experimental data obtained was processed using a general mathematical model for drug release from non-porous, non-swellable transdermal devices, which starts from Fick�s second law and has terms that also take into account the possibility of retaining the drug in the membrane polymer. Even though the mathematical model does not take into account neither the swelling phenomenon nor the possibility of membrane erosion, a good agreement between model and experimental data was obtained. The values of effective diffusion coefficients of drug in the polymeric membranes were also determined.