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Mathematical Modeling of Alcohol-Drug Concentration in the Bloodstream 血液中酒精-药物浓度的数学模型
Eurasian Journal of Mathematical and Computer Applications Pub Date : 2023-09-30 DOI: 10.47363/jmca/2023(2)119
KW Bunonyo
{"title":"Mathematical Modeling of Alcohol-Drug Concentration in the Bloodstream","authors":"KW Bunonyo","doi":"10.47363/jmca/2023(2)119","DOIUrl":"https://doi.org/10.47363/jmca/2023(2)119","url":null,"abstract":"This research involved the formulation of a system of mathematical models mimicking alcohol concentration in the human body and in the bloodstream, which are subjected to some initial conditions. The formulation starts with the an ideal presentation of the compartment diagram in Figure 1, the figure clearly indicates the two compartment in focus and the diffusion of alcohol from one compartment to the other with different rates including the elimination rate through urination and sweating that were not considered in this research. The aim of the research is to investigate the importance of the various rate constants on the alcohol concentration in the bloodstream, as well as investigating the drug dosage and volume of alcohol concentration impact in the bloodstream. The Laplace method (LM) was adopted to solve the model which represents, firstly, the alcohol concentration in the body where an exact solution was obtained, secondly, the exact solution was also obtained for the model depicting the alcohol concentration in the bloodstream with all pertinent parameters clearly spelt out. Lastly, numerical simulation was carried out using Wolfram Mathematica, version 12, where the pertinent parameters values were varied and the results presented graphically. The graphical results indicate that the various rate constants, dosage increase and the volumetric increase have impact and showed a corresponding effect on the drug concentration in the bloodstream. The novelty of this research is the fact that we’ve been able to mimic a real-life scenario, an alcohol concentration in the bloodstream, mathematically, and solved the system using Laplace methods and performed numerical simulation to show the importance of the pertinent parameters. This system can be recommended for scientists and engineers alike who could be interested in pharmacokinetics and Pharmacodynamics research.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136341417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
INITIATION OF A STREAMER IN A LIQUID FROM THE SURFACE OF A BUBBLE IN WHICH A PARTIAL DISCHARGE OCCURRED 在液体中从气泡表面产生的流线，其中发生了局部放电
Eurasian Journal of Mathematical and Computer Applications Pub Date : 2023-09-01 DOI: 10.32523/2306-6172-2023-11-3-63-75
Denis Karpov, Alexander Ridel, Roman Savenko, Sergey Korobeynikov
{"title":"INITIATION OF A STREAMER IN A LIQUID FROM THE SURFACE OF A BUBBLE IN WHICH A PARTIAL DISCHARGE OCCURRED","authors":"Denis Karpov, Alexander Ridel, Roman Savenko, Sergey Korobeynikov","doi":"10.32523/2306-6172-2023-11-3-63-75","DOIUrl":"https://doi.org/10.32523/2306-6172-2023-11-3-63-75","url":null,"abstract":"The analysis of experimental data on the initiation of streamers in a liquid di- electric from the surface of a free-floating up gas bubble after partial discharge is performed. Calculations of electric fields in a dielectric after partial discharge in bubbles corresponding to experimental conditions, with different degrees of deformation of the bubbles and their dif- ferent position relative to flat electrodes, have been carried out. The effect of image charges on the value of the maximum electric field on the surface of a spherical bubble is estimated. The probability of initiation of branching streamers from the bubble surface into the liquid is analyzed.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
AN STABILITY ESTIMATE IN 3D SOURCE PROBLEM FOR THE STATIONARY RADIATIVE TRANSFER EQUATION 稳态辐射传递方程三维源问题的稳定性估计
Eurasian Journal of Mathematical and Computer Applications Pub Date : 2023-09-01 DOI: 10.32523/2306-6172-2023-11-3-116-127
Vladimir Romanov
{"title":"AN STABILITY ESTIMATE IN 3D SOURCE PROBLEM FOR THE STATIONARY RADIATIVE TRANSFER EQUATION","authors":"Vladimir Romanov","doi":"10.32523/2306-6172-2023-11-3-116-127","DOIUrl":"https://doi.org/10.32523/2306-6172-2023-11-3-116-127","url":null,"abstract":"It is given a stability estimate of a solution of a source problem for the stationary radiative transfer equation. It is suppose that the source is an isotropic distribution. Earlier stability estimates for this problem were studied in several papers, the most part of those was related to a partial case of the emission tomography problem, when the scattering operator vanishes. For the complete transfer equation the stability estimate were given under additional conditions for the absorption coefficient and the scattering kernel, those are sufficiently difficult for checking. Moreover, it is still open the question about dependence a constant in the stability estimate on the coefficients of the transfer equation. In the present work, the stationary transfer equation is considered in an compact strongly convex domain of the tree-dimension space. In a forward problem it is assumed that incoming radiation is absent. In an inverse problem for recovering an unknown source some data for solutions of the forward problem are given. A new simple approach is suggested to obtain a stability estimate for the problem under the consideration. Using this way, an explicit constant in this estimate is given.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ASYMPTOTIC STABILITY OF POROUS THERMOELASTIC SYSTEM WITH INFINITE HISTORY, MICROTEMPERATURES EFFECTS AND VARYING DELAY 具有无限历史、微温度效应和变延迟的多孔热弹性系统的渐近稳定性
Eurasian Journal of Mathematical and Computer Applications Pub Date : 2023-09-01 DOI: 10.32523/2306-6172-2023-11-3-22-47
Fatima Djeradi, Fares Yazid, Nadhir Chougui
{"title":"ASYMPTOTIC STABILITY OF POROUS THERMOELASTIC SYSTEM WITH INFINITE HISTORY, MICROTEMPERATURES EFFECTS AND VARYING DELAY","authors":"Fatima Djeradi, Fares Yazid, Nadhir Chougui","doi":"10.32523/2306-6172-2023-11-3-22-47","DOIUrl":"https://doi.org/10.32523/2306-6172-2023-11-3-22-47","url":null,"abstract":"This work is concerned with a one-dimensional porous thermoelastic system with microtemperatures effects, past history term acting only on the porous equation, and a time- varying delay term in the internal feedbacks. We first give the well-posedness of the system by using the semigroup method. Then, we establish the global existence as well as energy decay results of solutions, under appropriate conditions on the parameters of the problem.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ELECTROMAGNETOELASTIC WAVES IN EARTH’S SUBSURFACE 地下的电磁弹性波
Eurasian Journal of Mathematical and Computer Applications Pub Date : 2023-09-01 DOI: 10.32523/2306-6172-2023-11-3-98-115
David da Costa de Pinho, Viatcheslav Priimenko
{"title":"ELECTROMAGNETOELASTIC WAVES IN EARTH’S SUBSURFACE","authors":"David da Costa de Pinho, Viatcheslav Priimenko","doi":"10.32523/2306-6172-2023-11-3-98-115","DOIUrl":"https://doi.org/10.32523/2306-6172-2023-11-3-98-115","url":null,"abstract":"The propagation of coupled mechanical and electromagnetic waves in a conducting elastic medium when the entire system is in an external magnetic field is considered. We use the mathematical model introduced by Dunkin and Eringen in 1963. The influence of an external magnetic field and medium parameters on the dispersion and attenuation of coupled electromagnetic and elastic waves is analyzed. We also simulated the propagation of coupled mechanical and electromagnetic waves in layered media using the Ursin method with a weak/strong external magnetic field. The results confirmed the effectiveness of using Ursin’s method in modeling magnetoelastic oscillations and can be used to analyze electrodynamic phenomena accompanying disturbances of the geomagnetic field during the movement of the conducting layers of the Earth.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
FORECASTING THE TIME OF COAL DEGASSING WHEN USING THE DATA OF THE INITIAL STAGE OF ITS DEGASSING PROCESS 利用煤脱气过程初始阶段的数据，预测煤脱气时间
Eurasian Journal of Mathematical and Computer Applications Pub Date : 2023-09-01 DOI: 10.32523/2306-6172-2023-11-3-48-62
A Karchevsky
{"title":"FORECASTING THE TIME OF COAL DEGASSING WHEN USING THE DATA OF THE INITIAL STAGE OF ITS DEGASSING PROCESS","authors":"A Karchevsky","doi":"10.32523/2306-6172-2023-11-3-48-62","DOIUrl":"https://doi.org/10.32523/2306-6172-2023-11-3-48-62","url":null,"abstract":"The paper proposes a method for predicting the degassing time based on pressure measurements in the coal seam at the initial stage of the process. The proposed method of forecasting is substantiated with the help of mathematical modeling. To carry out mathemat- ical modeling, it was necessary to solve a two-dimensional parabolic equation in a perforated domain. A numerical method for solving this problem is proposed.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
DEEP PROCESS-DATA MINING FOR BUILDING OF ANALYTICAL MODELS: 1. MEDIUM-TERM FORECAST OF SPRING FLOOD EXTREMES FOR MOUNTAIN RIVERS 基于深度过程数据挖掘的分析模型构建;山区河流春季极端洪水中期预报
Eurasian Journal of Mathematical and Computer Applications Pub Date : 2023-09-01 DOI: 10.32523/2306-6172-2023-11-3-76-97
Yuri Kirsta, Irina Troshkova
{"title":"DEEP PROCESS-DATA MINING FOR BUILDING OF ANALYTICAL MODELS: 1. MEDIUM-TERM FORECAST OF SPRING FLOOD EXTREMES FOR MOUNTAIN RIVERS","authors":"Yuri Kirsta, Irina Troshkova","doi":"10.32523/2306-6172-2023-11-3-76-97","DOIUrl":"https://doi.org/10.32523/2306-6172-2023-11-3-76-97","url":null,"abstract":"A standard methodology of deep process-data mining for building high-performance process-driven (analytical) models of complex natural systems was proposed. The method- ology (called as system-analytical modeling) is based on a system-hierarchical approach and deep mining of large datasets providing both extraction of the information hidden in such datasets and quantitative characterization of real processes occurring in natural systems. With its help, deep process-data mining of data (1951–2020) on spring flood discharge peaks and troughs (with ice motion) on 34 mountain rivers of the Altai-Sayan mountain country was performed. An analytical hydrological model of high performance (Nash-Sutcliffe criterion NSE = 0.78) was developed for the annual medium-term forecasting of discharge peaks and troughs in April using the data on meteorological conditions of the recent autumn and current winter periods. Flood peaks depend on autumn-winter precipitation (which determines 29% of the peak variance), landscape structure of river basins (14%), and winter air temperatures (0.8%). Spring floods on mountain rivers often threaten the life of local population that makes the developed model topical.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
MODELING AND NUMERICAL SIMULATION OF THE PENALTY METHOD FOR UNILATERAL CONTACT PROBLEM WITH TRESCA’S FRICTION IN THERMO-ELECTRO-VISCO-ELASTICITY 热电粘弹性中含treca摩擦的单边接触问题罚法的建模与数值模拟
Eurasian Journal of Mathematical and Computer Applications Pub Date : 2023-09-01 DOI: 10.32523/2306-6172-2023-11-3-4-21
M Bouallala, EL-H. Essoufi, A Zafrar, M. Alaoui
{"title":"MODELING AND NUMERICAL SIMULATION OF THE PENALTY METHOD FOR UNILATERAL CONTACT PROBLEM WITH TRESCA’S FRICTION IN THERMO-ELECTRO-VISCO-ELASTICITY","authors":"M Bouallala, EL-H. Essoufi, A Zafrar, M. Alaoui","doi":"10.32523/2306-6172-2023-11-3-4-21","DOIUrl":"https://doi.org/10.32523/2306-6172-2023-11-3-4-21","url":null,"abstract":"In this work, we consider the penalty method applied to contact problem in thermo-electro-visco-elasticity with Signorini’s condition and Tresca’s friction law. Mathe- matical properties, such as the existence of a solution to the penalty problem and its conver- gence to the solution of the original problem, are reported. Then, we present some numerical results in the study of a two-dimensional test problem and we establish its convergence.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inverse coefficient problem for the time-fractional diffusion equation 时间分数扩散方程的反系数问题
IF 0.5
Eurasian Journal of Mathematical and Computer Applications Pub Date : 2023-06-30 DOI: 10.32523/2306-6172-2021-9-1-44-54
D. Durdiev
{"title":"Inverse coefficient problem for the time-fractional diffusion equation","authors":"D. Durdiev","doi":"10.32523/2306-6172-2021-9-1-44-54","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-1-44-54","url":null,"abstract":"We study the inverse problem of determining the time depending reaction diffu- sion coefficient in the Cauchy problem for the time-fractional diffusion equation by a single observation at the point x = 0 of the diffusion process. To represent the solution of the direct problem, the fundamental solution of the time-fractional diffusion equation is used and properties of this solution are investigated. The fundamental solution contains the Fox’s H− functions widely used in fractional calculus. In particular, using estimates of the fundamental solution and its derivatives, an estimate for the solution of the direct problem is obtained in terms of the norm of the unknown coefficient which will be used in study inverse problem. The inverse problem is reduced to the equivalent integral equation. For solving this equation the contracted mapping principle is applied. The local existence and global uniqueness results are proven. Also the stability estimate is obtained.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47080068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
ON DETERMINATION OF THE COEFFICIENT AND KERNEL IN AN INTEGRO -DIFFERENTIAL EQUATION OF PARABOLIC TYPE 抛物型积分-微分方程系数和核的确定
IF 0.5
Eurasian Journal of Mathematical and Computer Applications Pub Date : 2023-03-01 DOI: 10.32523/2306-6172-2023-11-1-49-65
{"title":"ON DETERMINATION OF THE COEFFICIENT AND KERNEL IN AN INTEGRO -DIFFERENTIAL EQUATION OF PARABOLIC TYPE","authors":"","doi":"10.32523/2306-6172-2023-11-1-49-65","DOIUrl":"https://doi.org/10.32523/2306-6172-2023-11-1-49-65","url":null,"abstract":"The inverse problem of determination of x-dependent coefficient a(x) at u and the kernel k(t) functions in the one-dimensional integro–differential parabolic equation is investigated. The direct problem is the initial-boundary problem for this equation. Firstly, we studied the solvability of the direct problem, by used to the Fourier method and approximation series methods. As additional information for solving inverse problem, the solution of the direct problem by over determining condition is given. The problem is reduced to an equivalent closed system of Volterra-type integral equations with respect to unknown functions. Applying the method of contraction mappings to this system in the continuous class of functions, we prove the main result of the article, which is a local existence and uniqueness theorem of inverse problem solution.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47881794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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