scholarly journals INTEGRATED ESTIMATION OF ENTERPRISE’S DIVISIONS INFLUENCE ON MANUFACTURED PRODUCTS QUALITY BASED ON THE MATRIX ECONOMIC-AND-MATHEMATICAL MODEL

2019 ◽  
Vol 33 ◽  
pp. 243-246
Author(s):  
Zelikman Vladyslav ◽  
Sokolska Renata ◽  
Zelikman Anna
Keyword(s):  
Mathematical Model ◽  
Manufactured Products ◽  
The Matrix ◽  
Integrated Estimation

A NUMERICAL PROOF THAT CERTAIN CELLS FOLLOW THE TRAILS OF THE DIFFUSIONS OF SOME CHEMICALS IN THE EXTRACELLULAR MATRIX

2021 ◽  
pp. 2150027
Author(s):  
İREM ÇAY ◽  
SERDAL PAMUK
Keyword(s):  
Mathematical Model ◽  
Extracellular Matrix ◽  
Tumor Angiogenesis ◽  
Numerical Solutions ◽  
Extra Cellular Matrix ◽  
The Matrix ◽  
Good Agreement ◽  
Cellular Matrix

In this work, we obtain the numerical solutions of a 2D mathematical model of tumor angiogenesis originally presented in [Pamuk S, ÇAY İ, Sazci A, A 2D mathematical model for tumor angiogenesis: The roles of certain cells in the extra cellular matrix, Math Biosci 306:32–48, 2018] to numerically prove that the certain cells, the endothelials (EC), pericytes (PC) and macrophages (MC) follow the trails of the diffusions of some chemicals in the extracellular matrix (ECM) which is, in fact, inhomogeneous. This leads to branching, the sprouting of a new neovessel from an existing vessel. Therefore, anastomosis occurs between these sprouts. In our figures we do see these branching and anastomosis, which show the fact that the cells diffuse according to the structure of the ECM. As a result, one sees that our results are in good agreement with the biological facts about the movements of certain cells in the Matrix.

scholarly journals Mathematical model of methane driven by hydraulic fracturing in gassy coal seams

2020 ◽  
Vol 38 (3-4) ◽  
pp. 127-147
Author(s):  
Weiyong Lu ◽  
Bingxiang Huang
Keyword(s):  
Mathematical Model ◽  
Hydraulic Fracturing ◽  
Pore Pressure ◽  
Hydraulic Fracture ◽  
Water Saturation ◽  
Reduction Rate ◽  
Space Time ◽  
Matrix Block ◽  
The Matrix ◽  
Pore Pressure Gradient

During hydraulic fracturing in gassy coal, methane is driven by hydraulic fracturing. However, its mathematical model has not been established yet. Based on the theory of ‘dual-porosity and dual-permeability’ fluid seepage, a mathematical model is established, with the cleat structure, main hydraulic fracture and methane driven by hydraulic fracturing considered simultaneously. With the help of the COMSOL Multiphysics software, the numerical solution of the mathematical model is obtained. In addition, the space–time rules of water and methane saturation, pore pressure and its gradient are obtained. It is concluded that (1) along the direction of the methane driven by hydraulic fracturing, the pore pressure at the cleat demonstrates a trend of first decreasing and later increasing. The pore pressure gradient exhibits certain regional characteristics along the direction of the methane driven by hydraulic fracturing. (2) Along the direction of the methane driven by hydraulic fracturing, the water saturation exhibits a decreasing trend; however, near the cleat or hydraulic fracture, the water saturation first increases and later decreases. The water saturation in the central region of the coal matrix block is smaller than that of its surrounding region, while the saturation of water in the entire matrix block is greater than that in the cleat or hydraulic fracture surrounding the matrix block. The water saturation at the same space point increases gradually with the time progression. The space–time distribution rules of methane saturation are contrary to those of the water saturation. (3) The free methane driven by hydraulic fracturing includes the original free methane and the free methane desorbed from the adsorption methane. The reduction rate of the adsorption methane is larger than that of free methane.

ALGORITHMIC SUPPORT FOR SELECTING OPTIMAL TRAFFIC ROUTE OF MOTOR CONVOY OF RAPID REACTION BORDER COMMAND POST

2019 ◽  
pp. 25-35
Author(s):  
O. Borovyk ◽  
V. Kupelskiy
Keyword(s):  
Mathematical Model ◽  
Traffic Safety ◽  
The State ◽  
Optimal Route ◽  
The Road ◽  
Starting Point ◽  
Branching Points ◽  
The Matrix ◽  
The Status ◽  
Speed Function

The rapid response border commandant's office is a structural unit of the border detachment, designed to protect and strengthen the protection of a certain section of the state border, and must quickly redeploy its forces and assets. The success of the tasks assigned to the unit depends largely on the timeliness of arrival at the destination. Operational transportation of a significant amount of weapons, personnel and dissimilar cargoes on land is carried out using equipment. At the preparatory stage of the organization of transportation, the problem of forming the optimal composition of the convoy of equipment is solved. The existing road network provides a sufficiently large number of traffic routes between the starting and ending points. Moreover, this takes place even for insignificant distances between points of departure and destination. The specified conditions for multivariance in the selection. In addition, the choice of the route of movement depends on many auxiliary conditions: driver training, technical characteristics and reliability of vehicles, traffic safety, road and environmental conditions, distance and timing of transportation, and the like. Poor accounting of these factors in the aggregate may lead to the choice of an irrational route of movement, will not ensure the timely arrival of the unit at the destination, and may lead to the failure to fulfill certain tasks. Therefore, the task of choosing the optimal route of movement of the column of equipment is relevant. At the substantive level, the task looks like the justification of the mathematical model for choosing the optimal route for the column of equipment, if the criterion of optimality is minimizing the time it takes to move from the starting point to the destination. The authors formed a mathematical model of the given problem, proposed an algorithm for its solution for three cases: discrete-stochastic, discretely-determined and continuously-indefinite, and the corresponding software was developed. The choice of routes is carried out for three options, taking into account the fact that the change in the weights of the ribs can be carried out: at times when the column is at a certain vertex of the graph, and the update of the matrix of weights is carried out precisely at these moments. This is the case when a decision on the further route of movement is formed at the road branching points, taking into account the situation, the status of individual sections changes dynamically and data for which appears periodically; at times when the column is at a certain vertex of the graph, and for these moments, the matrix of weights that will occur when the column hits the vertex are known in advance. This is the case when a decision on the route of movement can be formed at the beginning of the movement, taking into account the known situation on the state of the roads, dynamically change, but data on which can be taken into account in advance; randomly depending on the speed of the column at a fixed point in time for which the column speed function is known.

scholarly journals MENENTUKAN DETERMINAN SUATU MATRIKS DENGAN METODE CHIO

2016 ◽  
Vol 6 (1:) ◽  
pp. 33-40
Author(s):  
Asep Saepudin
Keyword(s):  
Mathematical Model ◽  
Matrix Element ◽  
Matrix Theory ◽  
Human Life ◽  
Equation System ◽  
Inverse Matrix ◽  
Matrix Methods ◽  
Linear Equation System ◽  
The Matrix ◽  
Mathematical Sciences

Matrix theory is a branch of linear algebra that discussed in the mathematical sciences. Mathematical sciences play an important role in human life, it is necessary to solve problems that can not be solved directly. Thus, the problem can be transformed into the form of a mathematical model. One is the SPL (Linear Equation System). Various methods can be used to solve it. But for the SPL with a large variable can be solved by matrix methods, namely the inverse matrix. In the inverse matrix of the determinants involved. If the search value that ordo major determinant of the matrix (𝑛×𝑛), it would require an effective method. One is the method of Chio. Chio method can be applied to all square matrixas long as the element is 𝑎11 not equal to zero (𝑎11≠0). Chio method of calculating the determinant of the matrix by decomposing determinant will look into sub-determinant of degree two (2×2) using the matrix element row 1 and column 1 as pointof departure. The decomposition is performed using the following sized matrix:   Keywords: Matrix, Matrix Determinant, Chio method.

scholarly journals SIMULATION OF COMPACT POLARIZERS FOR SATELLITE TELECOMMUNICATION SYSTEMS WITH THE ACCOUNT OF THICKNESS OF IRISES

2021 ◽  
Author(s):  
Andrew V. Bulashenko ◽  
Stepan I. Piltyay ◽  
Ivan V. Demchenko
Keyword(s):  
Mathematical Model ◽  
Design Parameters ◽  
Matrix Elements ◽  
Satellite Telecommunication ◽  
Telecommunication Systems ◽  
Satellite Télécommunication ◽  
Scattering Wave ◽  
The Matrix ◽  
Electromagnetic Characteristics ◽  
Ku Band

Background. One of the main problems in modern satellite telecommunication systems is to increase the volume of information transmission with simultaneous preservation of its quality. Key element of such systems is antenna systems with polarization processing, which is carried out using polarizers. Therefore, development of new polarizers and simple techniques for their analysis and optimization are important problems. The most simple, effective, technological and actual for analysis are polarizers based on waveguides with irises. Objective. The purpose of the paper is to create a mathematical model of the polarizer based on a square waveguide with irises, which allows analyzing the influence of polarizer’s design parameters on its electromagnetic characteristics. Methods. A mathematical model of the waveguide polarizer with irises is created by decomposition technique using transfer and scattering wave matrices. To take into account the irises’ thickness their equivalent T- and Π-shaped circuits were used. Results. We have developed mathematical model of the waveguide polarizer with irises, which takes into account their thickness and is based on the complete scattering wave matrix of the waveguide polarizer. The matrix has been obtained using the microwave circuit theory. The main characteristics of the waveguide polarizer were defined using matrix elements. The optimization of characteristics of a polarizer was carried out in the operating Ku-band 10.7–12.8 GHz. Conclusions. Suggested mathematical model of a waveguide polarizer with irises provides the account of heights of irises, distances between them and their thickness. The results obtained show that this model is simpler and faster for the calculation of electromagnetic characteristics compared to finite elements method, which is often used for analysis of microwave devices for various applications.

scholarly journals SOLUTION OF PRODUCTION LOCATION PROBLEM WITH UNHOMOGENEOUS TRANSPORTATION COSTS

2021 ◽  
pp. 131-136
Author(s):  
F.K. Sharshembieva
Keyword(s):  
Mathematical Model ◽  
Location Problem ◽  
Sufficient Conditions ◽  
Transportation Costs ◽  
Transport Costs ◽  
Optimal Plan ◽  
Production Location ◽  
Manufactured Products ◽  
The Cost

In the work, an economic and mathematical model is formed for the problem of determining the optimal plan for production, transportation and processing of products according to the criterion of the minimum total costs. The functions that determine the dependence of the cost of manufactured products on the volume of production and the costs of processing products are linear, and the function that determines the dependence of transport costs on the volume of transported products is discontinuous at zero. Sufficient conditions for the applicability of the method of sequential calculations to the formulated problem are proved.

An Analytical Model Predicting Fixed Index Assembly Machine Performance

1972 ◽  
Vol 94 (2) ◽  
pp. 419-424
Author(s):  
W. B. Heginbotham ◽  
G. E. Rippon
Keyword(s):  
Mathematical Model ◽  
Analytical Model ◽  
Digital Computer ◽  
Matrix Operator ◽  
Operator Technique ◽  
Machine Performance ◽  
Simplified Method ◽  
The Matrix ◽  
Operating Methods

A simplified method of analyzing the performance of fixed index assembly machines using the matrix operator technique is described. This method can be used widely for exploring the effects of operating methods for assembly machines, and an example is quoted where each workhead has a different reliability. By using a digital computer, an exact mathematical model can be built which will enable studies to be made about machine performance when all the head parameters and method of operation are different for each individual head.

Development of a revolute-type kinematic model for human upper limb using a matrix approach

Robotica ◽  
2021 ◽  
pp. 1-22
Author(s):  
Anil Kumar Gillawat
Keyword(s):  
Mathematical Model ◽  
Upper Limb ◽  
Wrist Joint ◽  
Kinematic Model ◽  
Matrix Approach ◽  
Joint Torques ◽  
The Matrix ◽  
Distal Interphalangeal ◽  
Forward Kinematic ◽  
Human Upper Limb

Abstract A mathematical model is proposed for a revolute joint mechanism with an n-degree of freedom (DOF). The matrix approach is used for finding the relation between two consecutive links to determine desired link parameters such as position, velocity and acceleration using the forward kinematic approach. The matrix approach was confirmed for a proposed 10 DOF revolute type (R-type) human upper limb model with servo motors at each joint. Two DOFs are considered each at shoulder, elbow and wrist joint, followed by four DOF for the fingers. Two DOFs were considered for metacarpophalangeal (mcp) and one DOF each for proximal interphalangeal (pip) and distal interphalangeal (dip) joints. MATLAB script function was used to evaluate the mathematical model for determining kinematic parameters for all the proposed human upper limb model joints. The simplified method for kinematic analysis proposed in this paper will further simplify the dynamic modeling of any mechanism for determining joint torques and hence, easy to design control system for joint movements.

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