System Of Mathematical Equations Research Articles

Mathematical Modelling of the Thermosolutal Effect on Blood Flow through a Micro-Channel in the Presence of a Magnetic Field

Substances such as mass concentrations in the blood cause circulation challenges. Blood is a substance made up of 55% plasma and 45% hemoglobin, which flows through the blood vessels and is aided by the heart in pumping to all organs and other tissues and cells in the human body. Mathematical modelling plays an important role in understanding the blood circulation problem in the human body, and it helps transform the real-life cardiovascular problem into a system of mathematical equations. In this research, we transformed the real-life cardiovascular problem of the heat effect on mass concentration and blood flow through blood vessels into a system of partial differential equations representing blood momentum, energy, and mass concentration equations after modifying the Navier-Stoke equation. The models are scaled from dimensional to dimensionless using specific scaling parameters. The scaled dimensionless equations were further perturbed and reduced to a system of ordinary differential equations, and the system of ODEs was solved using the Laplace method, where mathematical models representing blood velocity profiles, temperature profiles, and mass concentration profiles were obtained. A numerical simulation was performed using Wolfram Mathematica, version 12, where the effect of the pertinent parameters on the flow profiles was investigated and the results were presented graphically. The variation of the pertinent parameters such as the Grashof number, solutal Grashof number, Prandtl number, Soret number, Schmidt number, Darcy number, and magnetic field affect the flow profile such that the increase in Grashof number and solutal Grashof number causes the blood velocity to increase substantially at the centre of the vessel before decreasing to zero as the wall boundary layer increases, while the increase in Prandtl number and Soret number increases the blood temperature and velocity.

CONSTRUCTIONS OF THE PROTECTIVE STRUCTURES UNDER THE CONDITIONS OF HIGH-SPEED IMPACT

The stability of the building is characterized by the depth of penetration of the punch into the body of the structures, as well as their local damage due to the impact load. There was accumulated experience of mathematical modeling of the impact processes of solid bodies on various targets. The range of deformations changes of the reinforced concrete elements ("slab"), which corresponds to the high-speed interaction at the moment of punching by a solid body ("impactor") with an initial impact speed of up to 1000 m/s, as well as the determination of their dynamic nature of deformation require comprehensive justification. The analytical solution of the mathematical system of equations describing the movement of the impactor, as well as the state of the impactor and the slab during their interaction can be applied in a limited range. Therefore, the assessment of the local effect of the impact can be carried out on the basis of the results of experimental studies using empirical formulas, as well as numerical methods of modeling the work of bodies taking into account their elastic-plastic characteristics. The ANSYS software package was used in the conducted research, which implements a system of mathematical equations that describe the movement and state of the "impactor-slab" during their interaction. Based on the results of the performed numerical modeling, it was established that the tested slabs with the use of combined reinforcement - mesh and dispersed metal fiber - are not penetrated by the impactor, part of the sample remains intact. At the same time, the final speed of the impactor in these slabs is up to 35.0% less than in the slabs with the mesh reinforcement. The penetration depth decreased up to 20.0%. The experience of dispersion strengthening of the concrete indicates the inhibition of cracking in the fiber concrete elements, which makes it expedient for usage in the combined reinforced constructions of the protective structures, capable of withstanding the dynamic impacts under conditions of high-speed impact. Further development of the of technological concretes studies is needed for their possible use in barrier structures of protective structures.

Secure Video Communication Using Multi-Equation Multi-Key Hybrid Cryptography

The safeguarding of intellectual property and maintaining privacy for video content are closely linked to the effectiveness of security protocols employed in internet streaming platforms. The inadequate implementation of security measures by content providers has resulted in security breaches within entertainment applications, hence causing a reduction in the client base. This research aimed to enhance the security measures employed for video content by implementing a multi-key approach for encryption and decryption processes. The aforementioned objective was successfully accomplished through the use of hybrid methodologies, the production of dynamic keys, and the implementation of user-attribute-based techniques. The main aim of the study was to improve the security measures associated with the process of generating video material. The proposed methodology integrates a system of mathematical equations and a pseudorandom key within its execution. This novel approach significantly augments the degree of security the encryption mechanism provides. The proposed methodology utilises a set of mathematical equations that are randomly employed to achieve encryption. Using a random selection procedure contributes to the overall enhancement of the system’s security. The suggested methodology entails the division of the video into smaller entities known as chunks. Following this, every segment is subjected to encryption using unique keys that are produced dynamically in real-time. The proposed methodology is executed via Android platforms. The transmitter application is tasked with the responsibility of facilitating the streaming of the video content, whereas the receiver application serves the purpose of presenting the video to the user. A careful study was conducted to compare and contrast the suggested method with other similar methods that were already in use. The results of the study strongly support the safety and dependability of the procedure that was made available.

What the future ocean has in common with an asthma attack

Ocean acidification and ocean deoxygenation are consequences of anthropogenic CO2 emissions that remain largely unknown to the general public. Mostly, because lay audiences are not familiar with the complex chain of physical and chemical processes that drive these phenomena. This demands that communicators find clear, simple and psychologically effective language to frame ocean health issues in familiar terms. From antiquity to the Renaissance, and independently across multiple cultures, premodern thinkers have conceptualized the Earth in terms of the human body. This is not surprising given that metaphor lies at the core of human understanding. Building on this premodern tradition, I found a system of mathematical equations that calculates the chemical composition of the human body or the ocean, when forced by human physiological or oceanographic parameters, respectively. Based on this result, I build an extended analogy that introduces the basic functioning of the oceanic CO2 and O2 cycles to the general public. The analogy incorporates ocean acidification and deoxygenation, that have parallels in the acidification and deoxygenation of the human body caused by an asthma attack, providing ocean health communicators with a tool that promotes interest in, and explains the origin of, declining ocean heath. Extending the analogy to the continental domain allows to see the Earth as a superorganism, a perspective that may help promote an environmentally healthier relationship between humanity and the Earth.

Theoretical Substantiation of the Main Parameters of Axial Devices for Threshing Grass Seeds

Introduction. The review of literature sources has shown that at the moment there are no reliable methods, which theoretically determine the main parameters of axial devices for threshing grass seeds and it is necessary to conduct researches to establish a mathematical relationship between these parameters and quality indicators. Aim of the Article. The article aim is theoretical substantiation of the dependence of the main parameters of axial devices for threshing grass seeds on the quality requirements to the technological process of threshing grass seeds. Materials and Methods. A set of priori information about the operation of axial rasp-bar threshers, the analysis of literary sources and own observations of the working process of the clover thresher K-0.3 allowed determining the basic prerequisites to develop an algorithm for solving the task. Results. As a result of theoretical consideration of the process of moving particles of the processed material in the working space of a drum-deck axial-rotor device for threshing grass seeds, a system of mathematical equations is obtained. The solution of the resulting system of equations makes it possible to determine the average axial velocity of the particles and a number of impacts inflicted by the rasps on them during movement. There is obtained an expression for linking the degree of seed threshing and main parameters of the device such as length, a number of rasps and the direction of their cleats, and the frequency of rotation of the drum. Discussion and Сonclusion. It was found that the degree of seed threshing significantly depends on both the length of the threshing device and a number of drum rasps and the direction of their cleats. The theoretical dependencies obtained as a result of the study make it possible to determine the main parameters of axial devices for threshing seeds, depending on the requirements imposed on the device.

Studies of the Use of Ultrasonic Equipment for the Removal of Asphalt-Resin Paraffin Deposits at Oil and Gas Transport and Storage Facilities

The article is devoted to the problem of cleaning oil transport and storage facilities from asphalt-resin-paraffin deposits. The issues of the use of ultrasound at oil transport and storage facilities for the removal of asphalt-tar and paraffin deposits are considered. The classification of methods for removing asphalt-tar and paraffin deposits in wells, pipelines and reservoirs is formulated. The review of scientific works on the use of ultrasound and ultrasonic installations for changing the basic physical and chemical characteristics of oil and tank cleaning is presented. Based on the analysis, a list of experimental studies is formulated that must be performed for the further formation of the scientific and technical base for the use of ultrasonic exposure for the removal of deposits. An overview of modern achievements in this field is presented, including scientific works on the use of ultrasound to accelerate the removal of deposits. An approach to the destruction of deposits directly during the operation of the tank due to the descent of the emitter to the surface of the boundary of the phases "oil-deposits" is considered. A system of mathematical equations has been developed that simulates the process of changing the temperature and melting of deposits, taking into account the operation of an ultrasonic emitter. As a result, the velocity of the movement of the melting front of deposits is determined depending on the duration of exposure. The recommended duration of exposure at each installation point is determined.

DeepISMNet: three-dimensional implicit structural modeling with convolutional neural network

Abstract. Implicit structural modeling using sparse and unevenly distributed data is essential for various scientific and societal purposes, ranging from natural source exploration to geological hazard forecasts. Most advanced implicit approaches formulate structural modeling as least squares minimization or spatial interpolation, using various mathematical methods to solve for a scalar field that optimally fits all the inputs under an assumption of smooth regularization. However, these approaches may not reasonably represent complex geometries and relationships of structures and may fail to fit a global structural trend when the known data are too sparse or unevenly distributed. Additionally, solving a large system of mathematical equations with iterative optimization solvers could be computationally expensive in 3-D. To deal with these issues, we propose an efficient deep learning method using a convolution neural network to create a full structural model from the sparse interpretations of stratigraphic interfaces and faults. The network is beneficial for the flexible incorporation of geological empirical knowledge when trained by numerous synthetic models with realistic structures that are automatically generated from a data simulation workflow. It also presents an impressive characteristic of integrating various types of geological constraints by optimally minimizing a hybrid loss function in training, thus opening new opportunities for further improving the structural modeling performance. Moreover, the deep neural network, after training, is highly efficient for the generation of structural models in many geological applications. The capacity of our approach for modeling complexly deformed structures is demonstrated by using both synthetic and field datasets in which the produced models can be geologically reasonable and structurally consistent with the inputs.

The General Dispersion Relation for the Vibration Modes of Helical Springs

A system of mathematical equations was developed for the calculation of the natural frequencies of helical springs, its predictions being compared with finite element simulation with ANSYS®. Authors derive the general equations governing the helical spring vibration relative to the Frenet trihedral representing the normal, binormal and tangent unit vectors to the spring medium line. The dispersion relation ω=f(k) has been obtained to model a wave traveling along the axis of the wire.

Effect of inclined magnetic field on flow of Williamson nanofluid over an exponentially stretching surface in Darcy‐Forchheimer model

AbstractThe present study elaborates magnetohydrodynamics (MHD) boundary layer flow with heat and mass transfer of pseudo‐plastic nanofluid over an exponentially stretching sheet embedded in a porous medium. Also, the effects of Brownian motion and thermophoresis on heat transfer and nanoparticle concentration are taken into account. With the help of suitable similarity transformations, the governing partial differential equations (PDEs) are transformed into a system of ordinary differential equations (ODEs). An inbuilt solver of MATLAB is being used to solve the system of mathematical equations. The effects of dimensionless parameters on the flow, heat transfer and nanoparticle concentration have been investigated. Graphs have been plotted and discussed to analyze the effects of various dimensionless parameters on velocity, temperature and concentration. As per the results, fluid velocity diminishes as the values of the aligned angle elongate, although temperature and concentration profiles reflect a switch pattern. Furthermore, as the values of Brownian motion, thermophoresis parameter and Lewis number rise, the temperature and concentration profiles rise as well. However, the concentration profiles for Brownian motion and Lewis number shows the reverse tendency.

Mathematical model of the process of ultrafiltration concentration of secondary milk raw materials in tubular membrane devices with filtering elements of BTU 05/2 type

For the qualitative application of ultrafiltration processes for the concentration and purification of food solutions, both experimental studies and a mathematical description of the processes of the membrane separation process of solutions from the standpoint of the development of computational mathematical models are required. In this work, by analytical solution of equations, that is, by the method of finite differences, mathematical equations are solved. To obtain the system, the flow continuity equations, convective diffusion equations, Navier-Stokes equations and flow equations with boundary conditions were solved in order to build a mathematical model of the process of ultrafiltration protein concentration in cheese whey in the production of rennet cheeses. As a result of the analytical solution of the equations, a system of mathematical equations was obtained that allows one to construct a profile of changes in the flow rates of the solution along the cross-section of the intermembrane channel and to determine the protein concentration in cheese whey along the length of the tubular ultrafiltration element BTU 05/2 of industrial type. The obtained mathematical model makes it possible to theoretically describe the process of ultrafiltration protein concentration in cheese whey along the entire length of the membrane channel of the tubular element under laminar and transient regimes of solution flow. The resulting system of mathematical equations makes it possible to find the numerical values of the mass flow rate of cheese whey, make it possible to calculate the specific output flow when the transmembrane pressure changes and to calculate the concentration of solutes in the secondary milk raw materials on the left and right ultrafiltration membrane of the intermembrane channel. The adequacy of the developed mathematical model was carried out by comparing the calculated and experimental data on the specific output flow when the transmembrane pressure in the intermembrane channel changes from 0.1 to 0.25 MPa with ultrafiltration concentration of cheese whey. The deviation of the calculated data found by the mathematical model from experimental studies obtained on a semi-industrial tubular ultrafiltration plant BTU 05/2 using semipermeable membranes, in which the active layer is made of fluoroplastic, hemisulphone and polyethersulfone, did not exceed 10%.

THERMAL PHYSICAL ASPECTS OF DETERMINATION OF LOAD CAPACITY MEDIUM VOLTAGE POWER CABLES WITH CROSS-POLYETHYLENE INSULATION IN STATIONARY OPERATING MODES

Currently, the development trends of global medium voltage cable networks are aimed at the introduction of cables with cross-linked polyethylene insulation. Such cables have a higher operating temperature, which allows to increase their throughput, and increased stability when working in conditions of overload and short circuits. It is possible to determine the allowable heat and electrical loads only if the heat balance is observed. Fundamentally important for solving the problems of heat balance is the significant dependence of thermal conductivity and heat capacity of polyethylene insulation on temperature. It is established that the capacity of the cable, determined by regulatory models and average environmental parameters, provides only preliminary information about its heating. For certain requirements and for innovative cable designs, a necessary condition for determining the load capacity in real stationary modes of operation is the use of the heat balance model. A system of mathematical equations is proposed, which due to the combination of structural and thermophysical parameters of the cable with the conditions of the external environment allows to determine the parameters of the stationary thermal regime of the cable at any load current.

The Problem of Accuracy of Economic Data

In his classic book On the Accuracy of Economic Observation Oskar Morgenstern deals with a common, yet widely neglected problem with which economic historians are faced, namely the quality of economic data. For the economic historian in the Austrian tradition, the quality of economic data is of utmost importance, since false data or belief in inaccurate data can lead the economic historian to faulty interpretations of the past.
 The quality of economic data is at least as important for economists who adhere to positivism in economics, since they use economic data to confirm or falsify their models.
 Likewise, Morgenstern’s insights are relevant for mathe-matical economists, as it makes sense to perform computations and solve a system of mathematical equations only if one has reliable data. 
 Morgenstern’s sample equations show the significance of a small error in the observation. Yet, in more complex equations with extensive mathematical operations the extent of error due to unreliable data may increase (or, depending on the equation, the errors may cancel out). It is indeed surprising to note how much the problem of accuracy in economic data has been neglected.
 This is not so in the physical sciences. There the error of observation is always explicitly mentioned. Yet in economics there is simply no error estimate. This means that we do not know the accuracy of the economic data presented to us. This is even more troubling when we consider that in social or economic data there are more possible sources of error than in the physical sciences. We therefore face the question of why the problem of accuracy of economic data is rarely mentioned or passed over in silence in economics, while in the physical sciences this problem is widely acknowledged.

The analysis of olympiad student’s metacognition skills in solving the national sciences olympiad problem on two-variables linear equation system material

This research aimed to describing the metacognition skills of mathematical olympiad students’ in solving the national sciences olympiad problem on two-variables linear equation system material. The participants were four mathematical olympiad students at Banyuglugur–Situbondo. This research used qualitative descriptive research. Test and interview were used as data collection methods. The research findings show that all of the students had strengths and weaknesses in solving the problem. Three students among of them were able to write down and explain what was known and asked by the problem given. All of the students have re-evaluated all of the results before stating that the completion has been completed. The first student was showed not only the metacognition skills but also the creative-innovative thinking skills. The student has found the other method/technique to solve the problem by utilizing the other source. An interesting finding of this research was that one of the students presents a different technique than usual. This student cannot explain in detail and clearly, the techniques used, but he presents the appropriate result. The student has used “trying to guess” the possible answers and used them in the mathematical equation system formed.

Оцінка метрологічних характеристик методу спектрального аналізу для визначення морфології еритроцитів

Spectral photometry is currently widely used for quantitative and qualitative analysis of biological molecules in medical biology. The method is based on the ability of molecules to absorb electromagnetic radiation. Modern clinical laboratory diagnostics extensively uses optical methods of analysis that rely on these physical properties of semitransparent objects, such as blood components. Knowing the absorption spectra of blood and its components, it is possible to quantify the concentration of all the components by solving the mathematical system of equations corresponding to these spectra. However, the existing methods of optical analysis of erythrocytes do not allow quantifying their geometric parameters, which may also indicate certain diagnostic signs and be used to analyze the clinical condition of the patient's body. The aim of this work is to evaluate the metrological characteristics of the newly developed method of determining the geometric parameters of erythrocytes, which combines spectral analysis and double annealing. The input data for the 3D imaging of erythrocytes were taken from the images of the sample both made in natural light and illuminated by a coherent light source with different wavelengths. The latter, after some additional image correlation, increases the reliability of the result. The calculation results on the errors and the measuring channel resolution of the digital interference microscope indicate an acceptable accuracy of the method. The accuracy of the three-dimensional image obtained by the proposed method is more than 20% higher than that of other known methods. This allows determining the informative geometric parameters of the structure of erythrocytes more accurately and using them to obtain additional clinical diagnostic characteristics of the patient's body.

Exploring a novel fusion-scheme based on mathematical equation system for encryption-image algorithm

Exploring the conception of robust encryption techniques for the security of digital images is a permanent necessity due to the existence of the Internet where sending and receiving information to establish communication is a high priority activity. Encryption process is carried out by data transformation, i.e. shuffled or scrambled, so that the information can not be read by an unauthorized receiver and it can exclusively be decrypted using valid-keys. In this paper, a novel fusion-scheme based on mathematical equation system for encryption-image algorithm is explored. In order to do that, numerical pixels are introduced in a system of equations for fusing images with three different private-keys. In addition, classical tests between original and encrypted images such as correlation coefficient, number of changing pixel rate (NPCR), unified average changed intensity (UACI) and entropy have been carried out to support the effectiveness of image fusion for image encryption.

Rigidity of a Triaxial Parallel Machine Tool

A mathematical model is proposed for the rigidity of a triaxial parallel machine tool. The structure of the machine tool is resolved into components. A simulation algorithm is outlined, as well as a general system of mathematical equations for calculating the axial rigidity of a triaxial parallel machine tool.

Save the pine forests of wilt disease using a fractional optimal control strategy

Abstract There is no doubt that the pine trees contribute greatly to the strengthening of the economy and the domestic wealth in many countries, where they produce dense grain, maintain the soil, especially in the sand slopes, uses wood in fuel and is one of the most important sources of recreation. However, over the past few years, pine forests have been plagued by many diseases, notably the Pine Wilt Disease (PWD), which poses a major threat to these forests. So, in this article, we investigate the best strategy to reduce and eliminate this disease using fractional optimal control strategy. Here, we introduce a mathematical system of equations contains the fractional order derivative with respect to time which describes the transmission dynamics of PWD. We calculate the general basic reproduction number R 0 and discuss the stability of a disease-free and endemic equilibrium in the proposed model. Furthermore, a Fractional Optimal Control Problem (FOCP) with three proposed controls is formulated, and the fractional order necessary conditions of optimality by using the Ponntryagin maximum principle are derived. We apply both analytical and numerical techniques on the FOCP with suggested controls to demonstrate the effective control strategies to prevent the transmission of the PWD. The numerical simulation of the suggested FOCP is presented and these results are expected to be helpful in the early treatment of PWD-infected trees.

Diagnostic Differentiation of Crimean Congo Hemorrhagic Fever, Influenza and Bacterial Meningitis by Classic and Fuzzy Mathematics

Background: A correct diagnosis of a disease among several diseases with the same clinical symptoms is very important and is a difficult task in medical science. Misdiagnosis of these diseases in the short term causes very high and serious damage to the health of patients and usually results in loss of golden time. Objectives: In this paper, our purpose is to achieve the best conclusion, which contributes to the diagnosis of the critical illness without losing the golden opportunity based on clinical data and using mathematical models, especially fuzzy mathematics. Methods: The data regarding patient’s signs and symptoms were collected in the hospitals. We attained the best choice of diseases among the considered options of diseases by using basic fuzzy rules, fuzzy control techniques, fuzzy mathematics and fuzzy systems. To write the basic fuzzy rules, the information that we used was adopted by experts in infectious diseases or data records of patients who reached a definite diagnosis of disease by various tests. Then, by using these rules, the system of mathematical equations was formed. By solving this system, coefficients of a linear equation were estimated witch its values according to the clinical signs of a patient indicates the probability that the patient will be infected with that disease. In this process, the number of patients studied is n not effective. But the more patients are studied, the more accurately the coefficients of the diagnosis equation are obtained. Results: The symptoms of some patients whose disease have been definitely diagnosed were used as inputs of the system of our equations and it was observed that the system’s outputs approximately coincide the exact diagnosis of the disease, which indicates that the equations obtained for the diagnosis of diseases are acceptable. Conclusions: The findings of this study can help to correctly diagnose the disease without losing golden opportunities. We hope that using the results of this research, the error in the initial diagnosis of diseases is significantly reduced.

Numerical approach regarding functional and design optimization for a residential building daily hot water system composed by heat pump and auxiliary source

In this paper is presented the physical model and mathematical approach which describe the equation system used in system calibration and design optimization. The system proposed for study is built from heat pump, for energy demand delivery, together with auxiliary heating source to face in all low temperature days, when heat pump work at maximum load but the required demand for daily hot water by the building inhabitants is higher. The paper present few of the common used systems in market for which the mathematical equation system will be proposed to come in help designers for in simulation and cost optimization. Simulation of proposed design is realized and results are delivered. The system construction, is optimized by comparison study of design and simulation data for each system type proposed. The comparison study is used for cost estimation of system and energy balance.

Numerical approach regarding functional and design optimization for a residential building heating system composed by heat pump and auxiliary

In this paper is presented the physical model and mathematical approach which describe the equation system used in system calibration and design optimization. The system proposed for study is built from heat pump, for energy demand delivery, together with auxiliary heating source to face in all low temperature days, when heat pump work at maximum load but the required demand by the building is higher. The paper present few of the common used systems in market for which the mathematical equation system will be proposed to come in help designers for in simulation and cost optimization. Simulation of proposed design is realized and results are delivered. The system construction, is optimized by comparison study of design and simulation data for each system type proposed. The comparison study is used for cost estimation of system and energy balance.