Büşra Aydoğan, M. Olgun, F. Smarandache, Mehmet Ünver
In this study, we propose a new approach based on fuzzy TODIM (Portuguese acronym for interactive and multicriteria decision-making) for decision-making problems in uncertain environments. Our method incorporates group utility and individual regret, which are often ignored in traditional multicriteria decision-making (MCDM) methods. To enhance the analysis and application of fuzzy sets in decision-making processes, we introduce novel entropy and distance measures for q-rung picture fuzzy sets. These measures include an entropy measure based on the sine function and a distance measure derived from the Jensen-Shannon divergence. In our methodology, incorporating the sine function into the entropy measure stands out as a distinctive decision, grounded in a profound understanding of the inherent characteristics of fuzzy sets. Utilizing the sine function proves especially advantageous when handling fuzzy sets that exhibit cyclical variations or fluctuations in their membership degrees. We effectively weight the criteria for an improved evaluation by using this new entropy measure. The introduced distance measure finds application in the TODIM approach, allowing the execution of TODIM method steps within a fuzzy environment until the determination of one alternative’s dominance over another—an advancement beyond traditional approaches. We apply our enhanced fuzzy TODIM method to a real-life construction project management problem from the literature and compare the results with those in the literature and obtained from other MCDM methods. Our proposed measures are robust, as demonstrated by the sensitivity analysis that varied the weights of group utility and individual regret, with the results visualized in a 3D sensitivity plot. The findings demonstrate the superiority of our method in providing a more comprehensive evaluation of alternatives, making it a useful tool for decision-makers facing complex and uncertain decision-making problems.
{"title":"A Decision-Making Approach Incorporating TODIM Method and Sine Entropy in q-Rung Picture Fuzzy Set Setting","authors":"Büşra Aydoğan, M. Olgun, F. Smarandache, Mehmet Ünver","doi":"10.1155/2024/3798588","DOIUrl":"https://doi.org/10.1155/2024/3798588","url":null,"abstract":"In this study, we propose a new approach based on fuzzy TODIM (Portuguese acronym for interactive and multicriteria decision-making) for decision-making problems in uncertain environments. Our method incorporates group utility and individual regret, which are often ignored in traditional multicriteria decision-making (MCDM) methods. To enhance the analysis and application of fuzzy sets in decision-making processes, we introduce novel entropy and distance measures for q-rung picture fuzzy sets. These measures include an entropy measure based on the sine function and a distance measure derived from the Jensen-Shannon divergence. In our methodology, incorporating the sine function into the entropy measure stands out as a distinctive decision, grounded in a profound understanding of the inherent characteristics of fuzzy sets. Utilizing the sine function proves especially advantageous when handling fuzzy sets that exhibit cyclical variations or fluctuations in their membership degrees. We effectively weight the criteria for an improved evaluation by using this new entropy measure. The introduced distance measure finds application in the TODIM approach, allowing the execution of TODIM method steps within a fuzzy environment until the determination of one alternative’s dominance over another—an advancement beyond traditional approaches. We apply our enhanced fuzzy TODIM method to a real-life construction project management problem from the literature and compare the results with those in the literature and obtained from other MCDM methods. Our proposed measures are robust, as demonstrated by the sensitivity analysis that varied the weights of group utility and individual regret, with the results visualized in a 3D sensitivity plot. The findings demonstrate the superiority of our method in providing a more comprehensive evaluation of alternatives, making it a useful tool for decision-makers facing complex and uncertain decision-making problems.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139612997","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}
The streamline upwind Petrov-Galerkin (SUPG) finite element method was used in this study to investigate the thermal and surface roughness effects on an inclined slider bearing with an unsteady fluid film. One-dimensional transverse and longitudinal surface roughness models were considered with the supposition that roughness is stochastic and has a Gaussian random distribution. For simplicity of numerical computation, the irregularity caused by the texture of the surface is transformed into a regular domain. The bearing performance of the combined effect is lower than the thermal and surface roughness effects of the one-dimensional longitudinal surface roughness for all modified Reynolds numbers of nonparallel slider bearings; this means that for nonparallel (w=0.4) between the surface roughness effect and the combined effect condition, there is a decrease of 13% in load-carrying capacity performance and a minimal change in friction force, respectively. However, in the case of nonparallel one-dimensional transverse type slider bearings, the bearing performance of the thermal effect is lower than the combined and surface roughness effects for all modified Reynolds numbers, where between the combined effect and the thermal effect condition, there is a reduction of 19% in load-carrying capacity performance and 2% in friction force practically for all changed Reynolds values, respectively. Furthermore, the combined effects at various temperatures have been investigated. As a result, in both longitudinal and transverse models, in the case of the pad temperature being lower than the slider, the load-carrying capacity performance is higher than in other cases for nonparallel slider bearings, whereas when the slider temperature is lower than the pad temperature, the drag frictional force is the leading one in both models. In general, considering surface texture and inertial effects will increase the performance of a slider. The results obtained are displayed using figures and tables.
{"title":"Performance Analysis of Thermal and Surface Roughness Effect of Slider Bearings with Unsteady Fluid Film Lubricant Using Finite Element Method","authors":"G. Tessema, G. A. Derese, A. A. Tiruneh","doi":"10.1155/2024/9993489","DOIUrl":"https://doi.org/10.1155/2024/9993489","url":null,"abstract":"The streamline upwind Petrov-Galerkin (SUPG) finite element method was used in this study to investigate the thermal and surface roughness effects on an inclined slider bearing with an unsteady fluid film. One-dimensional transverse and longitudinal surface roughness models were considered with the supposition that roughness is stochastic and has a Gaussian random distribution. For simplicity of numerical computation, the irregularity caused by the texture of the surface is transformed into a regular domain. The bearing performance of the combined effect is lower than the thermal and surface roughness effects of the one-dimensional longitudinal surface roughness for all modified Reynolds numbers of nonparallel slider bearings; this means that for nonparallel (w=0.4) between the surface roughness effect and the combined effect condition, there is a decrease of 13% in load-carrying capacity performance and a minimal change in friction force, respectively. However, in the case of nonparallel one-dimensional transverse type slider bearings, the bearing performance of the thermal effect is lower than the combined and surface roughness effects for all modified Reynolds numbers, where between the combined effect and the thermal effect condition, there is a reduction of 19% in load-carrying capacity performance and 2% in friction force practically for all changed Reynolds values, respectively. Furthermore, the combined effects at various temperatures have been investigated. As a result, in both longitudinal and transverse models, in the case of the pad temperature being lower than the slider, the load-carrying capacity performance is higher than in other cases for nonparallel slider bearings, whereas when the slider temperature is lower than the pad temperature, the drag frictional force is the leading one in both models. In general, considering surface texture and inertial effects will increase the performance of a slider. The results obtained are displayed using figures and tables.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139528006","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}
F. W. Tchuimmo, J. B. G. Tafo, A. Chamgoue, N. C. T. Mezamo, F. Kenmogne, L. Nana
The dynamical behaviour of traveling waves in a class of two-dimensional system whose amplitude obeys the two-dimensional complex cubic-quintic Ginzburg-Landau equation is deeply studied as a function of parameters near a subcritical bifurcation. Then, the bifurcation method is used to predict the nature of solutions of the considered wave equation. It is applied to reduce the two-dimensional complex cubic-quintic Ginzburg-Landau equation to the quintic nonlinear ordinary differential equation, easily solvable. Under some constraints of parameters, equilibrium points are obtained and phase portraits have been plotted. The particularity of these phase portraits obtained for new ordinary differential equation is the existence of homoclinic or heteroclinic orbits depending on the nature of equilibrium points. For some parameters, one has the orbits starting to one fixed point and passing through another fixed point before returning to the same fixed point, predicting then the existence of the combination of a pair of pulse-dark soliton. One has also for other parameters, the orbits linking three equilibrium points predicting the existence of a dark soliton pair. These results are very important and can predict the same solutions in many domains, particularly in wave phenomena, mechanical systems, or laterally heated fluid layers. Moreover, depending on the values of parameter systems, the analytical expression of the solutions predicted is found. The three-dimensional graphs of these solutions are plotted as well as their 2D plots in the propagation direction.
{"title":"Analytic Solutions of 2D Cubic Quintic Complex Ginzburg-Landau Equation","authors":"F. W. Tchuimmo, J. B. G. Tafo, A. Chamgoue, N. C. T. Mezamo, F. Kenmogne, L. Nana","doi":"10.1155/2023/2549560","DOIUrl":"https://doi.org/10.1155/2023/2549560","url":null,"abstract":"The dynamical behaviour of traveling waves in a class of two-dimensional system whose amplitude obeys the two-dimensional complex cubic-quintic Ginzburg-Landau equation is deeply studied as a function of parameters near a subcritical bifurcation. Then, the bifurcation method is used to predict the nature of solutions of the considered wave equation. It is applied to reduce the two-dimensional complex cubic-quintic Ginzburg-Landau equation to the quintic nonlinear ordinary differential equation, easily solvable. Under some constraints of parameters, equilibrium points are obtained and phase portraits have been plotted. The particularity of these phase portraits obtained for new ordinary differential equation is the existence of homoclinic or heteroclinic orbits depending on the nature of equilibrium points. For some parameters, one has the orbits starting to one fixed point and passing through another fixed point before returning to the same fixed point, predicting then the existence of the combination of a pair of pulse-dark soliton. One has also for other parameters, the orbits linking three equilibrium points predicting the existence of a dark soliton pair. These results are very important and can predict the same solutions in many domains, particularly in wave phenomena, mechanical systems, or laterally heated fluid layers. Moreover, depending on the values of parameter systems, the analytical expression of the solutions predicted is found. The three-dimensional graphs of these solutions are plotted as well as their 2D plots in the propagation direction.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138959289","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}
Giardiasis is among the ignored zoonotic illnesses accorded by the World Health Organization that is caused by Giardia duodenalis. The disease is ignored regardless of the harm it causes to people and other creatures. In this paper, a mathematical model for giardiasis illness transmission is formed, which considers sickness carriers and control measures such as screening, treatment, and sanitation of the environment around people. In the assessment, the basic reproduction number, R 0 , which is used for analyzing the local stability of the equilibria is determined using the state-of-the-art next-generation matrix, while the Metzler constancy speculation is used to show the overall adequacy of the global stability of the equilibrium point free from the disease. In addition, a Lyapunov function has been used to study the stability of the endemic equilibrium point. The assessment of parameters is performed to explore the limits that significantly influence the transmission components of the disease disorders using the normalizing sensitivity index method. The result revealed that the recruitment rate is the most sensitive limit to the reproduction number. The environment-human interaction parameter is the second influential factor in the transmission of giardiasis in the community. In the same manner, the outcomes recommend that carriers assume an expected part in the rate of giardiasis subsequently; disregarding them could risk endeavors to control the pestilence. Besides, the mathematical recreation of the model shows that a mix of each of the three interventions fundamentally affects the control of giardiasis. In this way, we advise implementing the strategies simultaneously in endemic areas to effectively stop the spread of the giardiasis disease in humans.
贾第虫病是世界卫生组织认定的被忽视的人畜共患病之一，由十二指肠贾第虫引起。这种疾病对人类和其他生物造成的危害被忽视。本文建立了一个关于贾第虫病传播的数学模型，该模型考虑了疾病携带者和控制措施，如筛查、治疗和人周围环境的卫生。在评估中，利用最先进的新一代矩阵确定了用于分析平衡点局部稳定性的基本繁殖数 R 0，同时利用梅兹勒常数推测来说明无疾病平衡点的整体稳定性是否充分。此外，还使用了 Lyapunov 函数来研究地方病平衡点的稳定性。参数评估采用归一化敏感度指数法，以探索对疾病紊乱传播成分有重大影响的极限。结果显示，招募率是对繁殖数量最敏感的限制。环境与人的交互作用参数是社区中传播贾第虫病的第二大影响因素。同样，结果表明，带菌者在随后的贾第虫病发病率中发挥着预期作用；忽视带菌者可能会危及控制疫情的努力。此外，模型的数学再现表明，三种干预措施的混合使用会从根本上影响对贾第虫病的控制。因此，我们建议在流行地区同时实施这些策略，以有效阻止贾第虫病在人类中的传播。
{"title":"Mathematical Modeling of Giardiasis Transmission Dynamics with Control Strategies in the Presence of Carriers","authors":"Yustina A. Liana, F. M. Chuma","doi":"10.1155/2023/1562207","DOIUrl":"https://doi.org/10.1155/2023/1562207","url":null,"abstract":"Giardiasis is among the ignored zoonotic illnesses accorded by the World Health Organization that is caused by Giardia duodenalis. The disease is ignored regardless of the harm it causes to people and other creatures. In this paper, a mathematical model for giardiasis illness transmission is formed, which considers sickness carriers and control measures such as screening, treatment, and sanitation of the environment around people. In the assessment, the basic reproduction number, \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 \u0000 , which is used for analyzing the local stability of the equilibria is determined using the state-of-the-art next-generation matrix, while the Metzler constancy speculation is used to show the overall adequacy of the global stability of the equilibrium point free from the disease. In addition, a Lyapunov function has been used to study the stability of the endemic equilibrium point. The assessment of parameters is performed to explore the limits that significantly influence the transmission components of the disease disorders using the normalizing sensitivity index method. The result revealed that the recruitment rate is the most sensitive limit to the reproduction number. The environment-human interaction parameter is the second influential factor in the transmission of giardiasis in the community. In the same manner, the outcomes recommend that carriers assume an expected part in the rate of giardiasis subsequently; disregarding them could risk endeavors to control the pestilence. Besides, the mathematical recreation of the model shows that a mix of each of the three interventions fundamentally affects the control of giardiasis. In this way, we advise implementing the strategies simultaneously in endemic areas to effectively stop the spread of the giardiasis disease in humans.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139002861","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}
Automatic production system scheduling problem under a just-in-time environment is researched in this paper. The automatic production system is composed of many tanks and one robotic, the tank of the researched problem is responsible for processing the job, and the robotic moves the job from one tank to the other tank. The difference between the researched problem and the classic shop scheduling problem is that the former must consider job scheduling and the robotic move sequence, but the latter considers only job scheduling. For optimizing simultaneously job scheduling and robotic move sequence in the proposed problem and minimizing total earliness/tardiness, an improved NEH (Nawaz-Enscore-Ham) and variable search (INEH-VNS) algorithm are developed. In the proposed method, firstly, to obtain initial solution, an improved NEH is shown. Secondly, for computing value of the objective function, the double procedure method is constructed. Thirdly, according to the properties of the proposed problem, three neighborhood structures, adjacent exchange, random insertion, and job exchange, are investigated. To test the performance of the INEH-VNS, 100 instances are randomly generated. When the run time is the same, compared with CPLEX 12.5, the INEH-VNS algorithm can find high-quality approximate optimal solution, a special big scale. Compared with the G-VNS algorithm, the average improvement rate of the approximate optimal solution is 45.9%, and the average stability rate of the INEH-VNS algorithm enhances 75.04%. That is to say, the INEH-VNS algorithm is outstanding and more effective.
{"title":"INEH-VNS Algorithm Solved Automatic Production System Scheduling Problem under Just-in-Time Environment","authors":"Qingxiang Li, Xiaofei Zhao, He Yude, Shaojun Yin","doi":"10.1155/2023/6680897","DOIUrl":"https://doi.org/10.1155/2023/6680897","url":null,"abstract":"Automatic production system scheduling problem under a just-in-time environment is researched in this paper. The automatic production system is composed of many tanks and one robotic, the tank of the researched problem is responsible for processing the job, and the robotic moves the job from one tank to the other tank. The difference between the researched problem and the classic shop scheduling problem is that the former must consider job scheduling and the robotic move sequence, but the latter considers only job scheduling. For optimizing simultaneously job scheduling and robotic move sequence in the proposed problem and minimizing total earliness/tardiness, an improved NEH (Nawaz-Enscore-Ham) and variable search (INEH-VNS) algorithm are developed. In the proposed method, firstly, to obtain initial solution, an improved NEH is shown. Secondly, for computing value of the objective function, the double procedure method is constructed. Thirdly, according to the properties of the proposed problem, three neighborhood structures, adjacent exchange, random insertion, and job exchange, are investigated. To test the performance of the INEH-VNS, 100 instances are randomly generated. When the run time is the same, compared with CPLEX 12.5, the INEH-VNS algorithm can find high-quality approximate optimal solution, a special big scale. Compared with the G-VNS algorithm, the average improvement rate of the approximate optimal solution is 45.9%, and the average stability rate of the INEH-VNS algorithm enhances 75.04%. That is to say, the INEH-VNS algorithm is outstanding and more effective.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139263807","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}
I. Irakoze, Fulgence Nahayo, Dennis Ikpe, S. Gyamerah, F. Viens
This paper investigates the dynamics of systemic risk in banking networks by analyzing equilibrium points and stability conditions. The focus is on a model that incorporates interactions among distressed and undistressed banks. The equilibrium points are determined by solving a reduced system of equations, considering both homogeneous and heterogeneous scenarios. Local and global stability analyses reveal conditions under which equilibrium points are stable or unstable. Numerical simulations further illustrate the dynamics of systemic risk, while the theoretical findings offer insights into the behavior of distressed banks under varying conditions. Overall, the model enhances our understanding of systemic financial risk and offers valuable insights for risk management and policymaking in the banking sector.
{"title":"Mathematical Modeling and Stability Analysis of Systemic Risk in the Banking Ecosystem","authors":"I. Irakoze, Fulgence Nahayo, Dennis Ikpe, S. Gyamerah, F. Viens","doi":"10.1155/2023/5628621","DOIUrl":"https://doi.org/10.1155/2023/5628621","url":null,"abstract":"This paper investigates the dynamics of systemic risk in banking networks by analyzing equilibrium points and stability conditions. The focus is on a model that incorporates interactions among distressed and undistressed banks. The equilibrium points are determined by solving a reduced system of equations, considering both homogeneous and heterogeneous scenarios. Local and global stability analyses reveal conditions under which equilibrium points are stable or unstable. Numerical simulations further illustrate the dynamics of systemic risk, while the theoretical findings offer insights into the behavior of distressed banks under varying conditions. Overall, the model enhances our understanding of systemic financial risk and offers valuable insights for risk management and policymaking in the banking sector.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139269173","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}
Graph theory (GT) is a mathematical field that involves the study of graphs or diagrams that contain points and lines to represent the representation of mathematical truth in a diagrammatic format. From simple graphs, complex network architectures can be built using graph operations. Topological indices (TI) are graph invariants that correlate the physicochemical and interesting properties of different graphs. TI deal with many properties of molecular structure as well. It is important to compute the TI of complex structures. The corona product (CP) of two graphs and gives us a new graph obtained by taking one copy of and copies of and joining the th vertex of to every vertex in the th copy of . In t
图论（GT）是一个数学领域，涉及对包含点和线的图或图的研究，以图解的形式表示数学真理。利用图运算，可以从简单的图建立复杂的网络架构。拓扑指数（TI）是与不同图形的物理化学和有趣特性相关联的图形不变式。拓扑指数也涉及分子结构的许多特性。计算复杂结构的 TI 非常重要。两个图 G 和 H 的日冕乘积（CP）给出了一个新图，该新图取 G 的一个副本和 H 的 V G 副本，并将 G 的第 i 个顶点与 H 的第 i 个副本中的每个顶点连接起来。本文基于由路径、循环和完整图组成的各种 CP 图，研究了几何指数（GA）和原子键连通性指数（ABC）。特别是讨论了电晕乘积 P s ⨀ P t、C t ⨀ C s、K t ⊙ K s、K t ⊙ P s 和 P s ⊙ K t 以及 GA 和 ABC 指数。此外，通过考虑相关的数学结论并辅以证明，还可以预测一些分子图谱和理化特征。
{"title":"Mapping Connectivity Patterns: Degree-Based Topological Indices of Corona Product Graphs","authors":"Nasir Ali, Zaeema Kousar, Maimoona Safdar, Fikadu Tesgera Tolasa, Enoch Suleiman","doi":"10.1155/2023/8975497","DOIUrl":"https://doi.org/10.1155/2023/8975497","url":null,"abstract":"<jats:p>Graph theory (GT) is a mathematical field that involves the study of graphs or diagrams that contain points and lines to represent the representation of mathematical truth in a diagrammatic format. From simple graphs, complex network architectures can be built using graph operations. Topological indices (TI) are graph invariants that correlate the physicochemical and interesting properties of different graphs. TI deal with many properties of molecular structure as well. It is important to compute the TI of complex structures. The corona product (CP) of two graphs <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"> <mi>G</mi> <mtext> </mtext> </math> </jats:inline-formula> and <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"> <mi>H</mi> </math> </jats:inline-formula> gives us a new graph obtained by taking one copy of <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\"> <mi>G</mi> </math> </jats:inline-formula> and <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\"> <mfenced open=\"|\" close=\"|\"> <mrow> <mi>V</mi> <mfenced open=\"(\" close=\")\"> <mrow> <mi>G</mi> </mrow> </mfenced> </mrow> </mfenced> </math> </jats:inline-formula> copies of <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\"> <mi>H</mi> </math> </jats:inline-formula> and joining the <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\"> <mi>i</mi> </math> </jats:inline-formula>th vertex of <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\"> <mi>G</mi> </math> </jats:inline-formula> to every vertex in the <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M8\"> <mi>i</mi> </math> </jats:inline-formula>th copy of <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M9\"> <mi>H</mi> </math> </jats:inline-formula>. In t","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139269725","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}
In order to consider the influence of liquid phase and soil anisotropy, the soil around the pile is considered a transversely isotropic saturated porous medium, and a horizontal dynamic model of transversely isotropic saturated soil-pile is established. Based on Beor’s saturated porous medium theory and the constitutive equation of transversely isotropic media, the horizontal dynamic control equation of transversely isotropic saturated soil is obtained without considering the vertical displacement. The horizontal vibration of transversely isotropic soil layers was solved using the potential function and separation of the variable method, and the horizontal and radial displacements of the solid soil skeleton of transversely isotropic saturated soil were obtained. The horizontal force of transversely isotropic saturated soil on a single pile was also obtained. On this basis, the horizontal dynamic equation of a single pile in transversely isotropic saturated soil was established, and the horizontal vibration of the pile foundation was solved using the initial parameter method, and the horizontal dynamic impedance of a single pile in transversely isotropic saturated soil is obtained. The influence of soil anisotropy parameter, liquid-solid coupling coefficient, diameter-length ratio, and modulus ratio on the horizontal dynamic impedance of a single pile in transversely isotropic saturated soil was analyzed through numerical examples. The analysis results show that the anisotropy parameters δ 1 , diameter-length ratio r 0 / H , and modulus ratio E p / C 66 have a significant impact on the horizontal dynamic impedance of pile foundation in transversely isotropic saturated soil, and the influence of anisotropy on the horizontal vibration of pile foundation should not be ignored. The influence of the liquid-solid coupling coefficient on the horizontal dynamic impedance factor is related to frequency to a certain extent.
为了考虑液相和土体各向异性的影响，将桩周围的土体视为横向各向同性饱和多孔介质，并建立了横向各向同性饱和土-桩的水平动力模型。基于 Beor 饱和多孔介质理论和横向各向同性介质的构成方程，在不考虑竖向位移的情况下，得到了横向各向同性饱和土的水平动力控制方程。利用势函数和变量分离法求解了横向各向同性土层的水平振动，得到了横向各向同性饱和土固体土骨架的水平位移和径向位移。同时还得到了横向各向同性饱和土对单根桩的水平力。在此基础上，建立了横向各向同性饱和土中单桩的水平动力方程，并利用初始参数法求解了桩基的水平振动，得到了横向各向同性饱和土中单桩的水平动力阻抗。通过数值实例分析了土体各向异性参数、液固耦合系数、径长比和模量比对横向各向同性饱和土中单桩水平动阻抗的影响。分析结果表明，各向异性参数 δ 1、径长比 r 0 / H 和模量比 E p / C 66 对横向各向同性饱和土中桩基的水平动阻抗有显著影响，各向异性对桩基水平振动的影响不容忽视。液固耦合系数对水平动阻抗系数的影响在一定程度上与频率有关。
{"title":"Horizontal Vibration of Pile in Transversely Isotropic Saturated Soil Based on Saturated Porous Medium Theory","authors":"Linchao Liu, Qifang Yan","doi":"10.1155/2023/8103614","DOIUrl":"https://doi.org/10.1155/2023/8103614","url":null,"abstract":"In order to consider the influence of liquid phase and soil anisotropy, the soil around the pile is considered a transversely isotropic saturated porous medium, and a horizontal dynamic model of transversely isotropic saturated soil-pile is established. Based on Beor’s saturated porous medium theory and the constitutive equation of transversely isotropic media, the horizontal dynamic control equation of transversely isotropic saturated soil is obtained without considering the vertical displacement. The horizontal vibration of transversely isotropic soil layers was solved using the potential function and separation of the variable method, and the horizontal and radial displacements of the solid soil skeleton of transversely isotropic saturated soil were obtained. The horizontal force of transversely isotropic saturated soil on a single pile was also obtained. On this basis, the horizontal dynamic equation of a single pile in transversely isotropic saturated soil was established, and the horizontal vibration of the pile foundation was solved using the initial parameter method, and the horizontal dynamic impedance of a single pile in transversely isotropic saturated soil is obtained. The influence of soil anisotropy parameter, liquid-solid coupling coefficient, diameter-length ratio, and modulus ratio on the horizontal dynamic impedance of a single pile in transversely isotropic saturated soil was analyzed through numerical examples. The analysis results show that the anisotropy parameters δ 1 , diameter-length ratio r 0 / H , and modulus ratio E p / C 66 have a significant impact on the horizontal dynamic impedance of pile foundation in transversely isotropic saturated soil, and the influence of anisotropy on the horizontal vibration of pile foundation should not be ignored. The influence of the liquid-solid coupling coefficient on the horizontal dynamic impedance factor is related to frequency to a certain extent.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139274551","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}
Wilhemina Adoma Pels, Atinuke O. Adebanji, Sampson Twumasi-Ankrah, Richard Minkah
The generalized Pareto distribution is one of the most important distributions in statistics of extremes as it has wide applications in fields such as finance, insurance, and hydrology. This study proposes two new methods for estimating the shape parameter of the generalized Pareto distribution (GPD). The proposed methods use the shrinkage principle to adapt the existing empirical Bayesian with data-based prior and the likelihood moment method to obtain two estimators. The performance of the proposed estimators is compared with the existing estimators (i.e., maximum likelihood, likelihood moment estimators, etc.) for the shape parameter of the generalized Pareto distribution in a simulation study. The results show that the proposed estimators perform better for small to moderate number of exceedances in estimating shape parameter of the light-tailed distributions and competitive when estimating heavy-tailed distributions. The proposed estimators are illustrated with practical datasets from climate and insurance studies.
{"title":"Shrinkage Methods for Estimating the Shape Parameter of the Generalized Pareto Distribution","authors":"Wilhemina Adoma Pels, Atinuke O. Adebanji, Sampson Twumasi-Ankrah, Richard Minkah","doi":"10.1155/2023/9750638","DOIUrl":"https://doi.org/10.1155/2023/9750638","url":null,"abstract":"The generalized Pareto distribution is one of the most important distributions in statistics of extremes as it has wide applications in fields such as finance, insurance, and hydrology. This study proposes two new methods for estimating the shape parameter of the generalized Pareto distribution (GPD). The proposed methods use the shrinkage principle to adapt the existing empirical Bayesian with data-based prior and the likelihood moment method to obtain two estimators. The performance of the proposed estimators is compared with the existing estimators (i.e., maximum likelihood, likelihood moment estimators, etc.) for the shape parameter of the generalized Pareto distribution in a simulation study. The results show that the proposed estimators perform better for small to moderate number of exceedances in estimating shape parameter of the light-tailed distributions and competitive when estimating heavy-tailed distributions. The proposed estimators are illustrated with practical datasets from climate and insurance studies.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136282348","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}
The main objective of this paper is to study the global behavior and oscillation of the following third-order rational difference equation , where the initial conditions are nonzero real numbers and are positive constants such that . Visual examples supporting solutions are given at the end of the study. The figures are found with the help of MATLAB.
本文的主要目的是研究全球行为和振荡的三阶有理差分方程x n + 1 =αx n n−1 x n−2 /βx n−1 2 +γx n−2 2,初始条件x−2,x−1,x非零实数和α,β,γ是积极的常量,α≤β+γ。在研究的最后给出了支持解决方案的可视化示例。图形是借助MATLAB软件进行绘制的。
{"title":"On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation","authors":"M. E. Erdogan","doi":"10.1155/2023/5726617","DOIUrl":"https://doi.org/10.1155/2023/5726617","url":null,"abstract":"The main objective of this paper is to study the global behavior and oscillation of the following third-order rational difference equation <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mi>α</mi> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mi>n</mi> <mo>−</mo> <mn>2</mn> </mrow> </msub> <mo>/</mo> <mi>β</mi> <msubsup> <mrow> <mi>x</mi> </mrow> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>γ</mi> <msubsup> <mrow> <mi>x</mi> </mrow> <mrow> <mi>n</mi> <mo>−</mo> <mn>2</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </math> , where the initial conditions <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </math> are nonzero real numbers and <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\"> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>,</mo> <mi>γ</mi> </math> are positive constants such that <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\"> <mi>α</mi> <mo>≤</mo> <mi>β</mi> <mo>+</mo> <mi>γ</mi> </math> . Visual examples supporting solutions are given at the end of the study. The figures are found with the help of MATLAB.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135043180","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}
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