Mathematical Model Of Relation Research Articles

Linear Mathematical Model of Relation between Extraocular Muscles and Vestibular System

Linear Mathematical Model of Relation between Extraocular Muscles and Vestibular System

Methodology for Analyzing the Relationships Between Physical Parameters and Price Variables in Regional Demand for Wind Electricity (As Applied to the Latvian Aggregator)

The present paper presents the methodology for the complex analysis of correlation and regression dependences of the relationship between the electricity price and the wind power generation in an electricity market of Latvia. The methodology is based on the adaptation of classical mathematical models in relation to the analysis of dependencies using the examples of official statistical data: average hourly consumption and the price of one MWh of electricity for the period 2014-2019; average hourly consumption and price per MWh of wind power in 2019 and similar indicators for peak consumption hours in 2019. The calculated data showed that the polynomial regression models are not suitable for the purposes of the analysis. The use of the sinusoidal dependence of wind power indicators on the number of the month of the year as a basic model for a correlation study is substantiated. A method has been developed for modifying this model for the case when the maximum and minimum outliers of the studied data do not have the same average deviations from the total average. The quantitative analysis has been chosen for assessment of research results. The developed models are recommended to be used as a real-time analytical tool for understanding and evaluating the business model of a regional electricity aggregator in response to supply and demand. The development of the functionality of this aggregator will increase the efficiency of the use of Latvian wind power and increase the level of its energy security. In 2021, the European Commission proposed a strengthening of the EU Energy Efficiency Directive to reduce net greenhouse gas emissions by at least 55% compared to 1990. Russia’s invasion of Ukraine exposed the vulnerability in European energy system and accelerated the need to increase its resilience and independence from Russian fossil fuels.

On the Enhanced New Qualitative Results of Nonlinear Integro-Differential Equations

In this article, a class of scalar nonlinear integro-differential equations of first order with fading memory is investigated. For the considered fading memory problem, we discuss the effects of the memory over all the values of the parameter in the kernel of the equations. Using the Lyapunov–Krasovski functional method, we give various sufficient conditions of stability, asymptotic stability, uniform stability of zero solution, convergence and boundedness, and square integrability of nonzero solutions in relation to the considered scalar nonlinear integro-differential equations for various cases. As the novel contributions of this article, the new scalar nonlinear integro-differential equation with the fading memory is firstly investigated in the literature, and seven theorems, which have novel sufficient qualitative conditions, are provided on the qualitative behaviors of solutions called boundedness, convergence, stability, integrability, asymptotic stability and uniform stability of solutions. The novel outcomes and originality of this article are that the considered integro-differential equations are new mathematical models, they include former mathematical models in relation to the mathematical models of this paper as well as the given main seven qualitative results are also new. The outcomes of this paper enhance some present results and provide new contributions to the relevant literature. The results of the article have complementary properties for the symmetry of integro-differential equations.

Nonlinear mathematical model of relation of second-rank tensors for composite materials

Nonlinear mathematical model of relation of second-rank tensors for composite materials

A mathematical model of relation and origin of variation between CRI and CSR indexes

The aim of this work is both the mathematical relation and the value variation analysis between CRI and CSR indexes. For this aim the physical mathematical model is proposed on the basis of the ISO-test. The physical basis of the model is a material balance of a one piece of coke from the ISO sample. Results of calculating by the model are curves of CSR=f(CRI) which reproduces the regressions in analogy with CSR=a+b.CRI for most coke-producing countries. The model showed that a larger part of CSR=f(CRI) curve is linear and that a universal regression in analogy with CSR=a+b.CRI does not exist. As follows from the model, every piece of coke from the ISO sample has its own CSR=f(CRI) curve with a CRI and CSR point. Between pieces of coke, variations of CRI and CSR values can be explained by the open pore amount, the coke pores’ surface area, the statistical distribution of molecular oriented domains on the basis of Lc and the coke piece mass. In our results, pores with a geometrical orientation from the outside to the center of a coke piece and having a minimum length significantly influence on the coke quality according to CRI and CSR indexes.

Investigation on the Mathematical Relation Model of Structural Reliability and Structural Robustness

Structural reliability and structural robustness, from different research fields, are usually employed for the evaluative analysis of building and civil engineering structures. Structural reliability has been widely used for structural analysis and optimization design, while structural robustness is still in rapid development. Several dimensionless evaluation indexes have been defined for structural robustness so far, such as the structural reliability-based redundancy index. However, these different evaluation indexes are usually based on subjective definitions, and they are also difficult to put into engineering practice. The mathematical relational model between structural reliability and structural robustness has not been established yet. This paper is a quantitative study, focusing on the mathematical relation between structural reliability and structural robustness so as to further develop the theory of structural robustness. A strain energy evaluation index for structural robustness is introduced firstly by considering the energy principle. The mathematical relation model of structural reliability and structural robustness is then derived followed by a further comparative study on sensitivity, structural damage, and random variation factor. A cantilever beam and a truss beam are also presented as two case studies. In this study, a parabolic curve mathematical model between structural reliability and structural robustness is established. A significant variation trend for their sensitivities is also observed. The complex interaction mechanism of the joint effect of structural damage and random variation factor is also reflected. With consideration of the variation trend of the structural reliability index that is affected by different degrees of structural damage (mild impairment, moderate impairment, and severe impairment), a three-stage framework for structural life-cycle maintenance management is also proposed. This study can help us gain a better understanding of structural robustness and structural reliability. Some practical references are also provided for the better decision-making of maintenance and management departments.

Study on hydration reaction and structure evolution of cemented paste backfill in early-age based on resistivity and hydration heat

In order to reveal the hydration reaction of cemented paste backfill (CPB) more comprehensively, the non-contact electrical resistivity (NER) and microcalorimeter (TAM Air) were used to combine the hydration reaction with microstructure evolution of CPB in the early-age hydration process. The influence of tailings-cement ratio (TCR) on hydration reaction and microstructure evolution of CPB was studied, and the mathematical relationship model of resistivity and hydration heat of CPB was established; the kinetic parameters of CPB in the deceleration period were quantified by using the kinetic model; In combination with CPB’s unconfined compressive strength (UCS), the relationship between resistivity, hydration heat and UCS was established. The results show that the hydration process of resistivity and hydration heat characterization is highly consistent, which can be combined to characterize the hydration reaction and microstructure evolution of the CPB hydration process, and more comprehensively reveal the hydration reaction of CPB from a different perspective. Under different TCRs, the resistivity of CPB is affected by both tailings and cement. The content of tailings determines the overall value of its resistivity. As the content of tailings increases, the resistivity value increases, and the resistivity corresponds to the structural kinetic parameter Kc increases; the hydration heat of CPB is mainly affected by the cement content. The higher the cement content, the higher the hydration heat, and the larger the corresponding hydration kinetic parameter Km. In addition, the hydration reaction process characterized by resistivity and hydration heat is dominated by cement content, the specific manifestation is that as the cement content decreases, the induction period will be prolonged, the acceleration period and the deceleration period will be shortened, and the reaction constants D and D′ increase. The mathematical relation model of resistivity and accumulative heat release of CPB can realize the mutual characterization of resistivity and hydration heat.The resistivity and hydration heat of CPB under different TCR at 24, 36 and 48 h have good corresponding relationship with the UCS; the UCS of different TCRs at 28 days is negatively correlated with its resistivity at 48 h, and positively correlated with the hydration heat of 48 h. Studies have shown that the combination of resistivity and hydration heat can more fully reveal the hydration reaction and microstructure evolution of CPB, which is of great significance to the design of CPB.

Mathematical Model for Relation of Wheat and Barley Yield and Salinity in Thi-Qar Governorate Soils, Iraq

Mathematical Model for Relation of Wheat and Barley Yield and Salinity in Thi-Qar Governorate Soils, Iraq

Absolute quasi-static calibration method of piezoelectric high-pressure sensor based on force sensor.

In this paper, a strain-gauge-type force sensor which can be directly mounted on the existing drop-weight device and used to calibrate the piezoelectric high-pressure sensor is designed. The absolute quasistatic pressure calibration principle and the measurement principle of the strain-gauge-type force sensor are described. Based on the mathematical relation model between force and pressure, the influence factors of pressure calibration accuracy are discussed, and the empirical formula for correcting the peak pressure is obtained. To analyze the mechanical strength of the force sensor, the modal parameters of the force sensor in the impact direction, and the pressure loss in the transmission process, a finite element simulation based on ANSYS software is performed. In addition, the static characteristic of the force sensor and the dynamic characteristic of the new drop-weight system composed of the force sensor, the mounting frame, and weight stacks are analyzed. To verify the accuracy of the empirical formula, the absolute quasistatic pressure calibration experiment is performed based on the calibration device. The final experimental results show that the accuracy of pressure calibration can be effectively improved by means of empirical formula correction. Taking the peak pressure measured by the reference pressure sensors as the standard value, the maximum calculation difference can be reduced from 3.42% (obtained by the direct calculation method) to 0.70% by the empirical formula correction method.

THE IDEALIZED MODELS OF SOFTWARE SYSTEMS REENGINEERING

Content. Software systems are used in a variety of branches of life and human activities, but they are most widely used in industries where it is necessary to work with many routine operations – this applies to industry, production, transportation, training and info communications. Of course, in the process of exploiting these systems there is an evolutionary aging of the different types of security. This trend leads to a deterioration of high-speed, information-communication, graphic, time and other characteristics, up to the complete failure of the software system. The subject of the article is aimed to the design of ergative systems, project management and programs for re-designing or improving these systems. Reengineering allows the system to evolve, by making positive changes to its structure in order to improve operational characteristics and technical support. Objective. To form a representation of the estimation of resource cost parameters for the reengineering of software systems with the help of a mathematical tools for describing design models. Method. The idea of the article is based on the Boehm method and the principles of building an Archimedes spiral. Author’s research led to the idea of combining Boehm and Archimedes structures, adapting them to the software engineering methodology and transferring them to a cylindrical coordinate system. The basis of the obtained models is laid spiral principle of the organization of the reference. Results. The article deals with the process of creating and visualizing mathematical models in relation to the process of reengineering software systems. Transactions with these models can occur in projections of time and cost, in the isometric projection of software components, and in the logarithmic projection of lines of software code. Conclusions. For the first time, idealized models of reengineering have been formed, which will allow to increase the accuracy of cost estimation from the redesign of software systems. The model of cost visualization for reprogramming of software systems has been improved, which will increase the efficiency of forecasting the order of expenses. For the first time dependencies were obtained on the construction of the graphical cost model trajectory from the introduced reengineering automation coefficient and the similarity coefficient of the components that would make changes to the configuration of the model. The proposed idealized models for reengineering of software system security are evolutionary spirals, which are constructed in a cylindrical coordinate system. Reengineering, which will be accomplished with the help of developed idealized reengineering models, will not only reduce the cost of reprogramming software systems, but also increase the efficiency of technical support, increase the life cycle of software systems which are already in service and overcome the contradictions between the rapid pace of development of science, technology and processes of designing new software systems.

Mathematical model of short distance pistol shooting performance in experienced shooters of both gender

The aim of this paper is to determine the mathematical model of relation of accuracy and precision when shooting from a pistol Zastava CZ 99 in relation to gender and short target distance. The research included 49 participants (Men = 27, Women = 22). The testing was carried out using precision shooting from CZ 99 pistol on a Standard ISSF 25 m precision pistol target at a 6, 10 and 15 m distance (5 rounds per distance). The level of performance was evaluated in relation to accuracy and precision in the function of target distance. For the sample of men, the shooting accuracy was 76.98, 62.70 and 50.61%, while for the sample of women it was 60.32, 51.03 and 37.29% for the shooting distance of 6, 10 and 15 m respectively. The precision level was 8.52, 7.01 and 5.59 points (i.e. circles) for men and 6.63, 5.61 and 4.24 points for women respectively. The defined dependency models accuracy-distance and precision-distance have shown that for men the efficiency of shooting in relation to accuracy is decreasing 2.91%, i.e. 0.32 circles, while for women the accuracy decreases 2.57%, i.e. 0.27 circles, for every meter of increase in distance.

Relative motion relation in the external return spherical bearing pair of a balanced double-row axial piston pump

Based on the external compaction return mechanism of a balanced double-row axial piston pump and the vector coordinate transformation principle, a mathematical model of the relative motion relation within the external return spherical bearing pair was built. The influence of slant inclination of the external swash plate and of pump shaft rotating speed and eccentricity on the relative motion trail, movement speed and acceleration was analysed. The relative motion velocity and acceleration between external retainer plate and external spherical hinge, at top and bottom dead centres, were discussed. By increasing the slant inclination of the external swash plate, the relative motion trail increased correspondingly, leading to a larger size of the pump integral structure. The relative speed and acceleration increased with the pump shaft speed and the slant inclination of the external swash plate, leading to a larger fluctuation of the slipper pair oil film. The increase of eccentricity slightly influenced the relative velocity and acceleration along the x-axis, without significantly increasing the fluctuation of the slipper pair oil film. Increasing the pump shaft speed, the external swash plate slant inclination and the eccentricity all caused fluctuations in the relative velocity and acceleration along the y- and z-axes, deepening the grinding crack on the compaction surface of the external retainer plate. In case of eccentricity and a 0° rotation angle of the principal axis, the related acceleration of the radial friction surface of the retainer plate showed the largest fluctuation amplitude, and a scratch could easily occur.

Modeling Vehicle Collision Angle in Traffic Crashes Based on Three-Dimensional Laser Scanning Data.

In road traffic accidents, the analysis of a vehicle’s collision angle plays a key role in identifying a traffic accident’s form and cause. However, because accurate estimation of vehicle collision angle involves many factors, it is difficult to accurately determine it in cases in which less physical evidence is available and there is a lack of monitoring. This paper establishes the mathematical relation model between collision angle, deformation, and normal vector in the collision region according to the equations of particle deformation and force in Hooke’s law of classical mechanics. At the same time, the surface reconstruction method suitable for a normal vector solution is studied. Finally, the estimation model of vehicle collision angle is presented. In order to verify the correctness of the model, verification of multi-angle collision experiments and sensitivity analysis of laser scanning precision for the angle have been carried out using three-dimensional (3D) data obtained by a 3D laser scanner in the collision deformation zone. Under the conditions with which the model has been defined, validation results show that the collision angle is a result of the weighted synthesis of the normal vector of the collision point and the weight value is the deformation of the collision point corresponding to normal vectors. These conclusions prove the applicability of the model. The collision angle model proposed in this paper can be used as the theoretical basis for traffic accident identification and cause analysis. It can also be used as a theoretical reference for the study of the impact deformation of elastic materials.

Establishment of Mathematical Relation Model between Dislocation Motion and Machining Deformation of Titanium Alloy Monolithic Component

According to dislocation dynamics, a distribution equation of mobile dislocations during the deformation of monolithic component was established. Slip deformation was solved through dislocation density and Burgers vector, and then the mathematical relationship between slippage and plastic deformation was established. Thus the mathematical relation model between dislocations and the machining distortion of monolithic component was established by plastic deformation as intermediate variable. It is shown that the machining distortion of monolithic component is upward embossment, and its maximum deformation occurs near the middle of the beam. The amount of machining distortion is directly proportional to the stress field at different depths of the surface layer, proliferation strength of dislocation and the length of the work piece, and inversely proportional to the thickness of the work piece.

Research on Service Life Prediction Model of Thrust Needle Bearing

Needle roller thrust bear is small in size and of high ability in load bearing, therefore it is widely used in fields of aviation and automobile etc. But the relation between their service life and pre-tightening torque is not very clear, so the using design of the bear depends mainly on experience of engineer, because of lack of references. In the paper, the theoretical analysis on relation between torque and load is done, special wearing test instrument is developed and wearing test of thrust needle bear is conducted. Based on the results of the test, mathematical model of relation between the losing amount of pre-tightening torque and the pre-tightening torque is built, based on which use of the bear in engineering will be more reasonable, and their pre-tightening torque will be given more accurately. DOI: http://dx.doi.org/10.11591/telkomnika.v10i7.1553 Full Text: PDF

Mathematical Model of Relation between Microstructure and the Yield Strength of High Carbon Steel Wire Rods

Ferrite content and the plate distance of pearlite of high carbon steel wire rod are analyzed by Optical Microscope and SEM, using quantitative microstructure analysis technology. The relation between microstructure and yield strength of high carbon steel wire rods was investigated. And the mathematical model of the relation was established as: σs(Pa)=104.52×106+161.70(1－fα 1/3)S－1(m). It was validated by experiment data that the mathematical model agrees well with the experimental results.

1111 ニューラルネットワークを用いた概念設計支援に関する基礎的検討

In conceptual design phase, if designers are much more conscious of design objectives, they won't come up with various ideas about new product. On the other hand, using brainstorming allow to get various ideas, but to get a lot of unavailable ideas together. In this study, we propose the method that supports generating various and effective ideas in conceptual design. In the last our study, we have proposed conceptual design support method using Data Envelopment Analysis. The last method's approach is using several evaluation values to fill the gap of palate frontier. But it was too difficult for subjects to use this approach in the experiment. Proposed method in this paper supplies key words. These key words are made of calculated component values using made nonlinear mathematical model of relation between component and evaluation of idea with Neural Network. We confirm that the method is useful in terms of simplicity of generating various and effective ideas.

Synthesis-progress and challenges in work on tree, root systems and their mycorrhizas

There has been considerable progress in many areas of study on tree root systems and their mycorrhizas but some important subjects and approaches, with respect to both orchard and forest tree roots are very inadequately researched. These include anchorage, root growth and emergence of new roots after transplanting, factors controlling nutrient uptake by different parts of mature tree root systems and seasonal variations in nutrient uptake and the use of mathematical models in relation to mycorrhizal infection and its effects on plant growth.