scholarly journals GENERALIZED MATHEMATICAL MODEL OF THE CALIBRATION PROCESSAND THE DIRECT MEASUREMENT OF THE PARAMETERS MULTIPOLE

2018 ◽  
Vol 9 (1) ◽  
pp. 96-105
Author(s):  
A. V. Gusinsky
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Matrix Form ◽  
Measuring System ◽  
Microwave Range ◽  
Measuring Systems ◽  
Error Matrix ◽  
Direct Measurements ◽  
The Matrix ◽  
Measurement Object

The quality of measuring systems of the microwave range, including vector network analyzers, largely depends on the reliability of calibration procedures and direct measurements, which allow to take into account information about the reproducible errors of measuring systems for subsequent correction. The aim of the paper is mathematical modeling of the errors of the measuring system for the generalized case for 2-n pole device.The problems of increasing the accuracy of measuring microwave systems due to compensation of systematic errors determined during calibration are considered. Calibration of measuring systems and correction of the results of direct measurements based on calibration results require the use of appropriate mathematical models of errors. Mathematical models of errors are represented in the form of multipolar errors, included between the object of measurement and the measuring system, which is assumed to be ideal, free of errors. The article proposes a generalized mathematical model of errors, described by a network of errors containing n ports connected to the n-port measuring system, and n ports connected to the n port of the measurement object. To obtain in general form the calibration equation for the 2n-port model of the error multipolar network, its transmission wave matrix [T], recorded in a cellular form, was used, and then a relationship was found between the measurement result in a matrix form with the cellular wave matrix T. A solution for finding the error matrix of matrix equation that connects the matrices known from the results of the corresponding attestation for the standards with the results of measurements during calibration in the matrix form. When solving this equation, a matrix product of «sandwich» type appears due to the cellular wave matrix [T]. The solution is possible when using the Kronecker product of two matrix, the matrix translation operator, the RS operator of the matrix, and the Gaussian elimination method. An equation is obtained for reconstructing the actual values of the scattering matrix of the measurement object, starting from the results of direct measurements in the matrix form and the error matrix. When solving the reconstruction equation, it is advisable to use a matrix inverse to the transmission matrix [T].The developed generalized mathematical model can be used, for example, when it is necessary to measure the parameters of complex microwave devices made on boards (wafer), with probe transitions to measuring ports, where it is important to consider the presence of additional microwave power leaks between ports.

scholarly journals Full 16-parametric model of calibration processes and direct measurement of parameters of four-poles

2019 ◽  
Vol 55 (1) ◽  
pp. 69-76
Author(s):  
A. V. Gusinski ◽  
V. A. Bogush
Keyword(s):  
Mathematical Model ◽  
Direct Measurement ◽  
Scattering Matrix ◽  
Parametric Model ◽  
Matrix Form ◽  
Matrix Analysis ◽  
The Matrix ◽  
Measurement Object ◽  
Cellular Matrices ◽  
The Mathematical Model

A complete mathematical model for measuring the parameters of the scattering matrix for a measurement object [Sx] in the form of a four-port network is developed, in which the mathematical model of the eight-port error is described by 16 parameters of the scattering matrix [E]. In addition, in comparison with the 12-parameter model of the eight-port error network, four parameters are included, which allow taking into account leaks, parasitic transmissions of microwave modules under study (microwave microassemblies). Due to the use of matrix analysis methods, the equations in matrix form are obtained that connect the matrices of the measurement object [Sи] and the actual values of the matrix parameters [Sx], with the aim of enabling the solution of these equations instead of the scattering matrix [E] to use a transmition matrix [T] in the form of cellular matrices [Taa], [Tab], [Tba], [Tbb].

Modeling mitochondrial function

2006 ◽  
Vol 291 (6) ◽  
pp. C1107-C1113 ◽  
Author(s):  
Robert S. Balaban
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Mitochondrial Function ◽  
Metabolic Networks ◽  
Complex Biological System ◽  
Regulatory Data ◽  
The Matrix ◽  
Definition Of ◽  
The Individual

The mitochondrion represents a unique opportunity to apply mathematical modeling to a complex biological system. Understanding mitochondrial function and control is important since this organelle is critical in energy metabolism as well as playing key roles in biochemical synthesis, redox control/signaling, and apoptosis. A mathematical model, or hypothesis, provides several useful insights including a rigorous test of the consensus view of the operation of a biological process as well as providing methods of testing and creating new hypotheses. The advantages of the mitochondrial system for applying a mathematical model include the relative simplicity and understanding of the matrix reactions, the ability to study the mitochondria as a independent contained organelle, and, most importantly, one can dynamically measure many of the internal reaction intermediates, on line. The developing ability to internally monitor events within the metabolic network, rather than just the inflow and outflow, is extremely useful in creating critical bounds on complex mathematical models using the individual reaction mechanisms available. However, many serious problems remain in creating a working model of mitochondrial function including the incomplete definition of metabolic pathways, the uncertainty of using in vitro enzyme kinetics, as well as regulatory data in the intact system and the unknown chemical activities of relevant molecules in the matrix. Despite these formidable limitations, the advantages of the mitochondrial system make it one of the best defined mammalian metabolic networks that can be used as a model system for understanding the application and use of mathematical models to study biological systems.

A mathematical model and an algorithm for sampling sets of components on the Assembly enterprises of space technology

2018 ◽  
Vol 15 (1) ◽  
pp. 39-55
Author(s):  
V. B. Rudakov ◽  
V. M. Makarov ◽  
M. I. Makarov
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Space Technology ◽  
Economic Costs ◽  
Problem Statement ◽  
Optimal Plan ◽  
Product Mix ◽  
Technical Parameters ◽  
Complex Products ◽  
Assembly Plants

The article considers the problem of determining the rational plans of the input sampling reliability and technical parameters of components of space technology, the totality of which is supplied to the Assembly plants for the manufacture of complex products of space technology. Problem statement and mathematical model based on the minimization of the economic costs of control and losses related to the risks of taking wrong decisions, are given in the article. The properties of the mathematical models are investigated, the algorithm for its optimization is developed. The result is an optimal plan for the sampling of sets of components, which includes: an optimal product mix subject to mandatory control of the aggregate and optimum risks of first and second kind, when acceptance number of statistical plan is zero. The latter circumstance is due to the high requirements of reliability and technical parameters of products of space technology.

Homing Sensor System Design for a 2D Long Range Nanopositioning Moving Platform

2014 ◽  
Vol 615 ◽  
pp. 57-62 ◽  
Author(s):  
Raquel Acero Cacho ◽  
Jose Antonio Albajez ◽  
José Antonio Yagüe-Fabra ◽  
Marta Torralba ◽  
Margarita Valenzuela ◽  
...  
Keyword(s):  
Sensor System ◽  
Measuring System ◽  
Experimental Characterization ◽  
Measuring Systems ◽  
Precision Measuring ◽  
Atomic Force ◽  
Ultra Precision ◽  
Moving Platform ◽  
Sensor System Design

The nanotechnology field has been developing strongly in recent years and ultra-precision measuring systems are nowadays required. A new two-dimensional moving platform with 50x50 mm range of travel, nanometer resolution and sub micrometer accuracy is being designed by the authors in order to be integrated with an Atomic Force Microscope (AFM). In this work the definition, design and experimental characterization of a homing sensor system for this 2D moving platform is presented. The homing sensor system will allow the generation of an absolute 2D reference for the platform (X-Y axis and θz rotation), defining an initial cero for the measuring system, which is based on laser encoders.

Rapid determination of glomerular filtration rate by single-bolus inulin: a comparison of estimation analyses

1998 ◽  
Vol 84 (6) ◽  
pp. 2154-2162 ◽  
Author(s):  
Cord Sturgeon ◽  
Albert D. Sam ◽  
William R. Law
Keyword(s):  
Mathematical Model ◽  
Glomerular Filtration Rate ◽  
Mathematical Models ◽  
Glomerular Filtration ◽  
Filtration Rate ◽  
Rapid Determination ◽  
Constant Infusion ◽  
Sprague Dawley ◽  
Single Bolus ◽  
Sprague Dawley Rats

Rapid measurement of glomerular filtration rate (GFR) by an inulin single-bolus technique would be useful, but its accuracy has been questioned. We hypothesized that reported inaccuracies reflect the use of inappropriate mathematical models. GFR was measured in 14 intact and 5 unilaterally nephrectomized conscious male Sprague-Dawley rats (mean weight 368 ± 12 g) by both single-bolus (25 mg/kg) and constant-infusion techniques (0.693 mg ⋅ kg−1 ⋅ min−1). The temporal decline in plasma inulin concentration was analyzed through biexponential curve fitting, which accounted for renal inulin loss before complete vascular and interstitial mixing. We compared our mathematical model based on empirical rationale with those of other investigators whose studies suggest inaccuracy of single-bolus methods. Our mathematical model yielded GFR values by single bolus that agreed with those obtained by constant infusion [slope = 0.94 ± 0.16 (SE); y intercept = 0.23 ± 0.64; r = 0.82]. In comparison to the data obtained by constant inulin infusion, this method yielded a very small bias of −0.0041 ± 0.19 ml/min. Two previously reported models yielded unsatisfactory values (slope = 1.46 ± 0.34, y intercept = 0.47 ± 1.5, r = 0.72; and slope = 0.17 ± 1.26, y intercept = 17.15 ± 5.14, r = 0.03). The biases obtained by using these methods were −2.21 ± 0.42 and −13.90 ± 1.44 ml/min, respectively. The data indicate that when appropriate mathematical models are used, inulin clearance after single-bolus delivery can be used to measure GFR equivalent to that obtained by constant infusion of inulin. Attempts to use methods of analysis for simplicity or expediency can result in unacceptable measurements relative to the clinical range of values seen.

Twin Models

1970 ◽  
Vol 19 (1-2) ◽  
pp. 141-141
Author(s):  
L. Gedda ◽  
G. Brenci ◽  
M. T. Lun
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Genetic Parameters ◽  
Simultaneous Recording ◽  
Theoretical Relationship ◽  
Twin Models

The theoretical relationship between the distribution of a given trait in a population of twin pairs and several genetic parameters has been examined. In particular, a series of mathematical models has been worked out, that, when applied to a twin population, nonselected for the occurrence of a given trait and nondiagnosed as to zygosity, leads to an estimate of:1) The MZ: DZ ratio in the population;2) The frequency of the genotype responsible for a given trait;3) The probability of manifestation of the trait;4) The value of epistatic factors.A further mathematical model affords the estimate of linkage in the hypothesis of simultaneous recording of more than one trait.

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.

The measuring system for monitoring the microarc heating process during surface hardening of steel products

2021 ◽  
pp. 33-39
Author(s):  
Makar S. Stepanov ◽  
rina G. Koshlyakova
Keyword(s):  
Heat Treatment ◽  
Mathematical Model ◽  
Electric Current ◽  
Measurement Method ◽  
Sample Surface ◽  
Steel Sample ◽  
Measuring System ◽  
Heating Process ◽  
Carbon Powder ◽  
Measured Temperature

The accelerated heat treatment during steel products hardening technology has been investigated. The possibility of measuring the temperature of steel products by thermoelectric platinum-platinum-rhodium thermocouple under microarc heating conditions is analyzed. During the experiments, working junctions of two S-type thermocouples: working and standard, were coined into the sample surface at the same level. The free thermocouples ends were connected to a digital multimeter and a personal computer. It was determined that 5 factors affect the measurement results: the electric current strength in the circuit, carbon powder, calibration, number of repeated measurement cycles, and a thermocouple copy. When planning the experiment, the concept of conducting a step-by-step nested experiment was used. Variance analysis method was used to process the experimental results. The measurement method precision parameters were calculated: repeatability and reproducibility. A linear mathematical model linking the measurement method reproducibility index with the measured temperature value has been obtained. A linear mathematical model is obtained that relates the reproducibility index of the measurement method to the measured temperature value. A measuring system for the experimental determination of the temperature of a steel sample is proposed and its application is justified for different electric current densities on the sample surface and varying duration of microarc heating. The possibilities of selecting and controlling the microarc heating modes depending on the required temperature of the heat treatment of the steel product are determined.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

Mathematical modelling.

2021 ◽  
Author(s):  
Ed Rutgers Durner
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Growth And Development ◽  
Fertilizer Recommendations ◽  
Mathematical Equations

Abstract Plants are studied to understand their growth and development so that their quality and productivity can be optimised. Models are developed that can be simple and descriptive, or quite complex with numerous mathematical equations; their level of complexity is linked to their purpose. This summary serves as an introduction to mathematical models in horticulture. It is not a manual for modelling itself, but rather an overview of how important mathematical models are in horticultural production. Mathematical models are used extensively in horticulture both extrinsically, i.e. when calculating chilling hour accumulations and intrinsically, i.e. when applying fertilizer to a crop. In chilling calculations, developed models are used directly. Fertilizer recommendations were probably developed using a mathematical model. The first part of this article discusses models in general and reviews general characteristics of mathematical models. The second part outlines the major uses of mathematical modelling in modern horticultural production. Presentations of specific models are limited in order to present a general discussion of models with examples that will interest most horticulturists.

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