The compressible Euler equations are an elementary model in mathematical fluid mechanics. In this article, we combine the Sideris and Makino-Ukai-Kawashima's classical functional techniques to study the new second inertia functional of reference:
for the blowup phenomena of $ C^{1} $ solutions $ (rho, vec{u}) $ with the support of $ left({ rho-bar{rho}}, vec{u}right) $, and with a positive constant $ { bar{rho}} $ for the adiabatic index $ gamma > 1 $. We find that if the total reference mass
with a positive constant $ K $ is sufficiently large, then the corresponding solution blows up on or before any finite time $ T > 0 $.
The compressible Euler equations are an elementary model in mathematical fluid mechanics. In this article, we combine the Sideris and Makino-Ukai-Kawashima's classical functional techniques to study the new second inertia functional of reference: begin{document}$ { H}_{ref}{ (t) = }frac{1}{2}int_{Omega(t)}left( { rho-bar{rho}}right) leftvert { vec{x} }rightvert ^{2}dV{{ , }} $end{document} for the blowup phenomena of $ C^{1} $ solutions $ (rho, vec{u}) $ with the support of $ left({ rho-bar{rho}}, vec{u}right) $, and with a positive constant $ { bar{rho}} $ for the adiabatic index $ gamma > 1 $. We find that if the total reference mass begin{document}$ M_{ref}(0) = { int_{{bf R}^{N}}} (rho_{0}({ vec{x}})-bar{rho})dVgeq0, $end{document} and the total reference energy begin{document}$ E_{ref}(0) = int_{{bf R}^{N}}left( frac{1}{2}rho_{0}({ vec {x}})leftvert vec{u}_{0}({ vec{x}})rightvert ^{2}+frac {K}{gamma-1}left( rho_{0}^{gamma}({ vec{x}})-bar{rho }^{gamma}right) right) dV, $end{document} with a positive constant $ K $ is sufficiently large, then the corresponding solution blows up on or before any finite time $ T > 0 $.
{"title":"Blowup for $ {{rm{C}}}^{1} $ solutions of Euler equations in $ {{rm{R}}}^{N} $ with the second inertia functional of reference","authors":"Manwai Yuen","doi":"10.3934/math.2023412","DOIUrl":"https://doi.org/10.3934/math.2023412","url":null,"abstract":"<abstract><p>The compressible Euler equations are an elementary model in mathematical fluid mechanics. In this article, we combine the Sideris and Makino-Ukai-Kawashima's classical functional techniques to study the new second inertia functional of reference:</p> <p><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ { H}_{ref}{ (t) = }frac{1}{2}int_{Omega(t)}left( { rho-bar{rho}}right) leftvert { vec{x} }rightvert ^{2}dV{{ , }} $end{document} </tex-math></disp-formula></p> <p>for the blowup phenomena of $ C^{1} $ solutions $ (rho, vec{u}) $ with the support of $ left({ rho-bar{rho}}, vec{u}right) $, and with a positive constant $ { bar{rho}} $ for the adiabatic index $ gamma > 1 $. We find that if the total reference mass</p> <p><disp-formula> <label/> <tex-math id=\"FE2\"> begin{document}$ M_{ref}(0) = { int_{{bf R}^{N}}} (rho_{0}({ vec{x}})-bar{rho})dVgeq0, $end{document} </tex-math></disp-formula></p> <p>and the total reference energy</p> <p><disp-formula> <label/> <tex-math id=\"FE3\"> begin{document}$ E_{ref}(0) = int_{{bf R}^{N}}left( frac{1}{2}rho_{0}({ vec {x}})leftvert vec{u}_{0}({ vec{x}})rightvert ^{2}+frac {K}{gamma-1}left( rho_{0}^{gamma}({ vec{x}})-bar{rho }^{gamma}right) right) dV, $end{document} </tex-math></disp-formula></p> <p>with a positive constant $ K $ is sufficiently large, then the corresponding solution blows up on or before any finite time $ T > 0 $.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70182449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work considers a discrete-time predator-prey system with a strong Allee effect. The existence and topological classification of the system's possible fixed points are investigated. Furthermore, the existence and direction of period-doubling and Neimark-Sacker bifurcations are explored at the interior fixed point using bifurcation theory and the center manifold theorem. A hybrid control method is used for controlling chaos and bifurcations. Some numerical examples are presented to verify our theoretical findings. Numerical simulations reveal that the discrete model has complex dynamics. Moreover, it is shown that the system with the Allee effect requires a much longer time to reach its interior fixed point.
{"title":"Stability, bifurcation, and chaos control in a discrete predator-prey model with strong Allee effect","authors":"Ali Al Khabyah, Rizwan Ahmed, M. Akram, S. Akhtar","doi":"10.3934/math.2023408","DOIUrl":"https://doi.org/10.3934/math.2023408","url":null,"abstract":"This work considers a discrete-time predator-prey system with a strong Allee effect. The existence and topological classification of the system's possible fixed points are investigated. Furthermore, the existence and direction of period-doubling and Neimark-Sacker bifurcations are explored at the interior fixed point using bifurcation theory and the center manifold theorem. A hybrid control method is used for controlling chaos and bifurcations. Some numerical examples are presented to verify our theoretical findings. Numerical simulations reveal that the discrete model has complex dynamics. Moreover, it is shown that the system with the Allee effect requires a much longer time to reach its interior fixed point.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70182612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ahmad Bin Azim, Ahmad Aloqaily, Asad Ali, Sumbal Ali, Nabil Mlaiki, F. Hussain
This article's purpose is to investigate and generalize the concepts of rough set, in addition to the q-spherical fuzzy set, and to introduce a novel concept that is called q-spherical fuzzy rough set (q-SFRS). This novel approach avoids the complications of more recent ideas like the intuitionistic fuzzy rough set, Pythagorean fuzzy rough set, and q-rung orthopair fuzzy rough set. Since mathematical operations known as "aggregation operators" are used to bring together sets of data. Popular aggregation operations include the arithmetic mean and the weighted mean. The key distinction between the weighted mean and the arithmetic mean is that the latter allows us to weight the various values based on their importance. Various aggregation operators make different assumptions about the input (data kinds) and the kind of information that may be included in the model. Because of this, some new q-spherical fuzzy rough weighted arithmetic mean operator and q-spherical fuzzy rough weighted geometric mean operator have been introduced. The developed operators are more general. Because the picture fuzzy rough weighted arithmetic mean (PFRWAM) operator, picture fuzzy rough weighted geometric mean (PFRWGM) operator, spherical fuzzy rough weighted arithmetic mean (SFRWAM) operator and spherical fuzzy rough weighted geometric mean (SFRWGM) operator are all the special cases of the q-SFRWAM and q-SFRWGM operators. When parameter q = 1, the q-SFRWAM operator reduces the PFRWAM operator, and the q-SFRWGM operator reduces the PFRWGM operator. When parameter q = 2, the q-SFRWAM operator reduces the SFRWAM operator, and the q-SFRWGM operator reduces the SFRWGM operator. Besides, our approach is more flexible, and decision-makers can choose different values of parameter q according to the different risk attitudes. In addition, the basic properties of these newly presented operators have been analyzed in great depth and expounded upon. Additionally, a technique called multi-criteria decision-making (MCDM) has been established, and a detailed example has been supplied to back up the recently introduced work. An evaluation of the offered methodology is established at the article's conclusion. The results of this research show that, compared to the q-spherical fuzzy set, our method is better and more effective.
{"title":"q-Spherical fuzzy rough sets and their usage in multi-attribute decision-making problems","authors":"Ahmad Bin Azim, Ahmad Aloqaily, Asad Ali, Sumbal Ali, Nabil Mlaiki, F. Hussain","doi":"10.3934/math.2023415","DOIUrl":"https://doi.org/10.3934/math.2023415","url":null,"abstract":"This article's purpose is to investigate and generalize the concepts of rough set, in addition to the q-spherical fuzzy set, and to introduce a novel concept that is called q-spherical fuzzy rough set (q-SFRS). This novel approach avoids the complications of more recent ideas like the intuitionistic fuzzy rough set, Pythagorean fuzzy rough set, and q-rung orthopair fuzzy rough set. Since mathematical operations known as \"aggregation operators\" are used to bring together sets of data. Popular aggregation operations include the arithmetic mean and the weighted mean. The key distinction between the weighted mean and the arithmetic mean is that the latter allows us to weight the various values based on their importance. Various aggregation operators make different assumptions about the input (data kinds) and the kind of information that may be included in the model. Because of this, some new q-spherical fuzzy rough weighted arithmetic mean operator and q-spherical fuzzy rough weighted geometric mean operator have been introduced. The developed operators are more general. Because the picture fuzzy rough weighted arithmetic mean (PFRWAM) operator, picture fuzzy rough weighted geometric mean (PFRWGM) operator, spherical fuzzy rough weighted arithmetic mean (SFRWAM) operator and spherical fuzzy rough weighted geometric mean (SFRWGM) operator are all the special cases of the q-SFRWAM and q-SFRWGM operators. When parameter q = 1, the q-SFRWAM operator reduces the PFRWAM operator, and the q-SFRWGM operator reduces the PFRWGM operator. When parameter q = 2, the q-SFRWAM operator reduces the SFRWAM operator, and the q-SFRWGM operator reduces the SFRWGM operator. Besides, our approach is more flexible, and decision-makers can choose different values of parameter q according to the different risk attitudes. In addition, the basic properties of these newly presented operators have been analyzed in great depth and expounded upon. Additionally, a technique called multi-criteria decision-making (MCDM) has been established, and a detailed example has been supplied to back up the recently introduced work. An evaluation of the offered methodology is established at the article's conclusion. The results of this research show that, compared to the q-spherical fuzzy set, our method is better and more effective.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"378 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70183173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce F-b-metric space (function weighted b-metric space) as a generalization of the F-metric space (the function weighted metric space). We also propose and prove some topological properties of the F-b-metric space, the theorems of fixed point and the common fixed point for the generalized expansive mappings, and an application on dynamic programing.
{"title":"Some results in function weighted b-metric spaces","authors":"B. Nurwahyu, N. Aris, Firman","doi":"10.3934/math.2023417","DOIUrl":"https://doi.org/10.3934/math.2023417","url":null,"abstract":"<abstract> <p>In this paper, we introduce <italic>F</italic>-<italic>b</italic>-metric space (function weighted <italic>b</italic>-metric space) as a generalization of the <italic>F</italic>-metric space (the function weighted metric space). We also propose and prove some topological properties of the <italic>F</italic>-<italic>b</italic>-metric space, the theorems of fixed point and the common fixed point for the generalized expansive mappings, and an application on dynamic programing.</p> </abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70183280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates the orbital stability of periodic standing waves for the following coupled Klein-Gordon-Zakharov equations begin{document} $ begin{equation*} left{ begin{aligned} &u_{tt}-u_{xx}+u+alpha uv+beta|u|^{2}u = 0, &v_{tt}-v_{xx} = (|u|^{2})_{xx}, end{aligned} right. end{equation*} $ end{document} where $alpha>0$ and $beta$ are two real numbers and $alpha>beta$. Under some suitable conditions, we show the existence of a smooth curve positive standing wave solutions of dnoidal type with a fixed fundamental period L for the above equations. Further, we obtain the stability of the dnoidal waves for the coupled Klein-Gordon-Zakharov equations by applying the abstract stability theory and combining the detailed spectral analysis given by using Lam'{e} equation and Floquet theory. When period $Lrightarrowinfty$, dnoidal type will turn into sech-type in the sense of limit. In such case, we can obtain stability of sech-type standing waves. In particular, $beta = 0$ is advisable, we still can show the the stability of the dnoidal type and sech-type standing waves for the classical Klein-Gordon-Zakharov equations.
This paper investigates the orbital stability of periodic standing waves for the following coupled Klein-Gordon-Zakharov equations begin{document}$begin{equation*}left{begin{aligned}&u_{tt}-u_{xx}+u+alpha uv+beta|u|^{2}u = 0, &v_{tt}-v_{xx} = (|u|^{2})_{xx}, end{aligned} right. end{equation*}$ end{document} where $alpha>0$ and $beta$ are two real numbers and $alpha>beta$. Under some suitable conditions, we show the existence of a smooth curve positive standing wave solutions of dnoidal type with a fixed fundamental period L for the above equations. Further, we obtain the stability of the dnoidal waves for the coupled Klein-Gordon-Zakharov equations by applying the abstract stability theory and combining the detailed spectral analysis given by using Lamé equation and Floquet theory. When period $Lrightarrowinfty$, dnoidal type will turn into sech-type in the sense of limit. In such case, we can obtain stability of sech-type standing waves. In particular, $beta = 0$ is advisable, we still can show the the stability of the dnoidal type and sech-type standing waves for the classical Klein-Gordon-Zakharov equations.
{"title":"Orbital stability of periodic standing waves of the coupled Klein-Gordon-Zakharov equations","authors":"Qiuying Li, Xiaoxiao Zheng, Zhenguo Wang","doi":"10.3934/math.2023430","DOIUrl":"https://doi.org/10.3934/math.2023430","url":null,"abstract":"This paper investigates the orbital stability of periodic standing waves for the following coupled Klein-Gordon-Zakharov equations begin{document} $ begin{equation*} left{ begin{aligned} &u_{tt}-u_{xx}+u+alpha uv+beta|u|^{2}u = 0, &v_{tt}-v_{xx} = (|u|^{2})_{xx}, end{aligned} right. end{equation*} $ end{document} where $alpha>0$ and $beta$ are two real numbers and $alpha>beta$. Under some suitable conditions, we show the existence of a smooth curve positive standing wave solutions of dnoidal type with a fixed fundamental period L for the above equations. Further, we obtain the stability of the dnoidal waves for the coupled Klein-Gordon-Zakharov equations by applying the abstract stability theory and combining the detailed spectral analysis given by using Lam'{e} equation and Floquet theory. When period $Lrightarrowinfty$, dnoidal type will turn into sech-type in the sense of limit. In such case, we can obtain stability of sech-type standing waves. In particular, $beta = 0$ is advisable, we still can show the the stability of the dnoidal type and sech-type standing waves for the classical Klein-Gordon-Zakharov equations.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70183834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper deals with a two-step explicit predictor-corrector approach so-called the two-step MacCormack formulation, for solving the one-dimensional nonlinear shallow water equations with source terms. The proposed two-step numerical scheme uses the fractional steps procedure to treat the friction slope and to upwind the convection term in order to control the numerical oscillations and stability. The developed scheme uses both forward and backward difference formulations in the predictor and corrector steps, respectively. The linear stability of the constructed technique is deeply analyzed using the Von Neumann stability approach whereas the convergence rate of the proposed method is numerically obtained in the $ L^{2} $-norm. A wide set of numerical examples confirm the theoretical results.
{"title":"Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms","authors":"R. T. Alqahtani, J. Ntonga, E. Ngondiep","doi":"10.3934/math.2023465","DOIUrl":"https://doi.org/10.3934/math.2023465","url":null,"abstract":"This paper deals with a two-step explicit predictor-corrector approach so-called the two-step MacCormack formulation, for solving the one-dimensional nonlinear shallow water equations with source terms. The proposed two-step numerical scheme uses the fractional steps procedure to treat the friction slope and to upwind the convection term in order to control the numerical oscillations and stability. The developed scheme uses both forward and backward difference formulations in the predictor and corrector steps, respectively. The linear stability of the constructed technique is deeply analyzed using the Von Neumann stability approach whereas the convergence rate of the proposed method is numerically obtained in the $ L^{2} $-norm. A wide set of numerical examples confirm the theoretical results.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A vertex set $ S $ of a graph $ G $ is called a double total dominating set if every vertex in $ G $ has at least two adjacent vertices in $ S $. The double total domination number $ gamma_{times 2, t}(G) $ of $ G $ is the minimum cardinality over all the double total dominating sets in $ G $. Let $ G square H $ denote the Cartesian product of graphs $ G $ and $ H $. In this paper, the double total domination number of Cartesian product of paths is discussed. We determine the values of $ gamma_{times 2, t}(P_isquare P_n) $ for $ i = 2, 3 $, and give lower and upper bounds of $ gamma_{times 2, t}(P_isquare P_n) $ for $ i geq 4 $.
如果$ G $中的每个顶点在$ S $中至少有两个相邻顶点，则图$ G $的顶点集$ S $称为双共支配集。$ G $的双总支配数$ gamma_{times 2, t}(G) $是$ G $中所有双总支配集的最小基数。设$ G square H $表示图$ G $和$ H $的笛卡尔积。本文讨论了路径笛卡尔积的双总支配数。我们确定了$ i = 2, 3 $的$ gamma_{times 2, t}(P_isquare P_n) $值，并给出了$ i geq 4 $的$ gamma_{times 2, t}(P_isquare P_n) $的下界和上界。
{"title":"Double total domination number of Cartesian product of paths","authors":"Linyu Li, Jun Yue, Xia Zhang","doi":"10.3934/math.2023479","DOIUrl":"https://doi.org/10.3934/math.2023479","url":null,"abstract":"A vertex set $ S $ of a graph $ G $ is called a double total dominating set if every vertex in $ G $ has at least two adjacent vertices in $ S $. The double total domination number $ gamma_{times 2, t}(G) $ of $ G $ is the minimum cardinality over all the double total dominating sets in $ G $. Let $ G square H $ denote the Cartesian product of graphs $ G $ and $ H $. In this paper, the double total domination number of Cartesian product of paths is discussed. We determine the values of $ gamma_{times 2, t}(P_isquare P_n) $ for $ i = 2, 3 $, and give lower and upper bounds of $ gamma_{times 2, t}(P_isquare P_n) $ for $ i geq 4 $.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The quadratic Riccati equations are first-order nonlinear differential equations with numerous applications in various applied science and engineering areas. Therefore, several numerical approaches have been derived to find their numerical solutions. This paper provided the approximate solution of the quadratic Riccati equation via the cubic b-spline method. The convergence analysis of the method is discussed. The efficiency and applicability of the proposed approach are verified through three numerical test problems. The obtained results are in good settlement with the exact solutions. Moreover, the numerical results indicate that the proposed cubic b-spline method attains a superior performance compared with some existing methods.
{"title":"Cubic B-Spline method for the solution of the quadratic Riccati differential equation","authors":"O. Ala'yed, B. Batiha, Diala Alghazo, F. Ghanim","doi":"10.3934/math.2023483","DOIUrl":"https://doi.org/10.3934/math.2023483","url":null,"abstract":"The quadratic Riccati equations are first-order nonlinear differential equations with numerous applications in various applied science and engineering areas. Therefore, several numerical approaches have been derived to find their numerical solutions. This paper provided the approximate solution of the quadratic Riccati equation via the cubic b-spline method. The convergence analysis of the method is discussed. The efficiency and applicability of the proposed approach are verified through three numerical test problems. The obtained results are in good settlement with the exact solutions. Moreover, the numerical results indicate that the proposed cubic b-spline method attains a superior performance compared with some existing methods.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70187140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Merino, Juergen Doellner, Javier Martínez, F. Guzmán, R. Guzmán, Juan De Dios Lara
Mobile devices provide us with an important source of data that capture spatial movements of individuals and allow us to derive general mobility patterns for a population over time. In this article, we present a mathematical foundation that allows us to harmonize mobile geolocation data using differential geometry and graph theory to identify spatial behavior patterns. In particular, we focus on models programmed using Computer Algebra Systems and based on a space-time model that allows for describing the patterns of contagion through spatial movement patterns. In addition, we show how the approach can be used to develop algorithms for finding "patient zero" or, respectively, for identifying the selection of candidates that are most likely to be contagious. The approach can be applied by information systems to evaluate data on complex population movements, such as those captured by mobile geolocation data, in a way that analytically identifies, e.g., critical spatial areas, critical temporal segments, and potentially vulnerable individuals with respect to contact events.
{"title":"A space-time model for analyzing contagious people based on geolocation data using inverse graphs","authors":"S. Merino, Juergen Doellner, Javier Martínez, F. Guzmán, R. Guzmán, Juan De Dios Lara","doi":"10.3934/math.2023516","DOIUrl":"https://doi.org/10.3934/math.2023516","url":null,"abstract":"Mobile devices provide us with an important source of data that capture spatial movements of individuals and allow us to derive general mobility patterns for a population over time. In this article, we present a mathematical foundation that allows us to harmonize mobile geolocation data using differential geometry and graph theory to identify spatial behavior patterns. In particular, we focus on models programmed using Computer Algebra Systems and based on a space-time model that allows for describing the patterns of contagion through spatial movement patterns. In addition, we show how the approach can be used to develop algorithms for finding \"patient zero\" or, respectively, for identifying the selection of candidates that are most likely to be contagious. The approach can be applied by information systems to evaluate data on complex population movements, such as those captured by mobile geolocation data, in a way that analytically identifies, e.g., critical spatial areas, critical temporal segments, and potentially vulnerable individuals with respect to contact events.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70188826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Via the survival discretization method, this research revealed a novel discrete one-parameter distribution known as the discrete Erlang-2 distribution (DE2). The new distribution has numerous surprising improvements over many conventional discrete distributions, particularly when analyzing excessively dispersed count data. Moments and moments-generating functions, a few descriptive measures (central tendency and dispersion), monotonicity of the probability mass function, and the hazard rate function are just a few of the statistical aspects of the postulated distribution that have been developed. The single parameter of the DE2 distribution was estimated via the maximum likelihood technique. Real-world datasets, leukemia and COVID-19, were applied to analyze the effectiveness of the recommended distribution.
{"title":"Discrete Erlang-2 distribution and its application to leukemia and COVID-19","authors":"Mohamed Ahmed Mosilhy","doi":"10.3934/math.2023520","DOIUrl":"https://doi.org/10.3934/math.2023520","url":null,"abstract":"Via the survival discretization method, this research revealed a novel discrete one-parameter distribution known as the discrete Erlang-2 distribution (DE2). The new distribution has numerous surprising improvements over many conventional discrete distributions, particularly when analyzing excessively dispersed count data. Moments and moments-generating functions, a few descriptive measures (central tendency and dispersion), monotonicity of the probability mass function, and the hazard rate function are just a few of the statistical aspects of the postulated distribution that have been developed. The single parameter of the DE2 distribution was estimated via the maximum likelihood technique. Real-world datasets, leukemia and COVID-19, were applied to analyze the effectiveness of the recommended distribution.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70188894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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