The question of a mathematical representation and theoretical overcoming by op-timised therapeutic strategies of drug-induced drug resistance in cancer cell populations is tackled here from the point of view of adaptive dynamics and optimal population growth control, using integro-differential equations. Combined impacts of external continuous-time functions, standing for drug actions, on targets in a plastic (i.e., able to quickly change its phenotype in deadly environmental conditions) cell population model, represent a therapeutical control to be optimised. A justification for the introduction of the adaptive dynamics setting, retaining such plasticity for cancer cell populations, is firstly presented in light of the evolution of multicellular species and disruptions in multicellularity coherence that are characteristics of cancer and of its progression. Finally, open general questions on cancer and evolution in the Darwinian sense are listed, that may open innovative tracks in modelling and treating cancer by circumventing drug resistance. This study sums up results that were presented at the international NUMACH workshop, Mulhouse, France, in July 2018.
{"title":"An Evolutionary Perspective on Cancer, with Applications to Anticancer Drug Resistance Modelling and Perspectives in Therapeutic Control","authors":"J. Clairambault","doi":"10.4208/jms.v52n4.19.06","DOIUrl":"https://doi.org/10.4208/jms.v52n4.19.06","url":null,"abstract":"The question of a mathematical representation and theoretical overcoming by op-timised therapeutic strategies of drug-induced drug resistance in cancer cell populations is tackled here from the point of view of adaptive dynamics and optimal population growth control, using integro-differential equations. Combined impacts of external continuous-time functions, standing for drug actions, on targets in a plastic (i.e., able to quickly change its phenotype in deadly environmental conditions) cell population model, represent a therapeutical control to be optimised. A justification for the introduction of the adaptive dynamics setting, retaining such plasticity for cancer cell populations, is firstly presented in light of the evolution of multicellular species and disruptions in multicellularity coherence that are characteristics of cancer and of its progression. Finally, open general questions on cancer and evolution in the Darwinian sense are listed, that may open innovative tracks in modelling and treating cancer by circumventing drug resistance. This study sums up results that were presented at the international NUMACH workshop, Mulhouse, France, in July 2018.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43862513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We investigate traveling fronts, including pulsating ones, of a forced curvature flow in a plane fibered medium. The main topic of this note is an uniqueness issue of such traveling fronts. In addition to line-shaped profiles, we also consider traveling fronts in the form of V-shaped parabolas.
{"title":"On the Uniqueness of Traveling Forced Curvature Fronts in a Fibered Medium","authors":"G. Namah","doi":"10.4208/JMS.V52N1.19.01","DOIUrl":"https://doi.org/10.4208/JMS.V52N1.19.01","url":null,"abstract":". We investigate traveling fronts, including pulsating ones, of a forced curvature flow in a plane fibered medium. The main topic of this note is an uniqueness issue of such traveling fronts. In addition to line-shaped profiles, we also consider traveling fronts in the form of V-shaped parabolas.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41383710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The motion of hydro-magnetic fluid can be described by Navier-StokesMaxwell system. In this paper, we prove global existence and uniqueness for the solutions of Navier-Stokes-Maxwell system in 3 dimensional space for small data. AMS subject classifications: 35Q30, 35Q35, 76D03, 76D05
{"title":"Global Existence of Solutions of the Navier-Stokes-Maxwell System in Besov Spaces","authors":"Haifeng Li","doi":"10.4208/JMS.V52N1.19.08","DOIUrl":"https://doi.org/10.4208/JMS.V52N1.19.08","url":null,"abstract":"The motion of hydro-magnetic fluid can be described by Navier-StokesMaxwell system. In this paper, we prove global existence and uniqueness for the solutions of Navier-Stokes-Maxwell system in 3 dimensional space for small data. AMS subject classifications: 35Q30, 35Q35, 76D03, 76D05","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49106974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 investigate the complete moment convergence and complete convergence for randomly weighted sums of negatively superadditive dependent (NSD, in short) random variables. The results obtained in the paper generalize the convergence theorem for constant weighted sums to randomly weighted sums of dependent random variables. In addition, strong law of large numbers for NSD sequence is obtained. AMS subject classifications: 60F15.
{"title":"On Complete Moment Convergence for Randomly Weighted Sums of NSD Random Variables","authors":"xiangmin Sun","doi":"10.4208/JMS.V52N1.19.03","DOIUrl":"https://doi.org/10.4208/JMS.V52N1.19.03","url":null,"abstract":"In this paper, we investigate the complete moment convergence and complete convergence for randomly weighted sums of negatively superadditive dependent (NSD, in short) random variables. The results obtained in the paper generalize the convergence theorem for constant weighted sums to randomly weighted sums of dependent random variables. In addition, strong law of large numbers for NSD sequence is obtained. AMS subject classifications: 60F15.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45911547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Numerical Modeling and Simulation of Fully Coupled Processes of Reactive Multiphase Flow in Porous Media","authors":"E. Ahusborde","doi":"10.4208/jms.v52n4.19.01","DOIUrl":"https://doi.org/10.4208/jms.v52n4.19.01","url":null,"abstract":"","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44605622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We focus on the numerical solver of unilateral cracks by the Schwarz Method with Total Overlap. The aim is to isolate the treatment at the vicinity of the cracks from other regions of the computational domain. This avoids any direct interaction between specific approximations one may use around the singularities born at the tips of the cracks and more standard methods employed away from the cracks. We apply an iterative sub-structuring technique to capture the small structures by insulating the cracks into patches and making a zoom around each of them. The macro-problem is in turn set on the whole domain. As for the classical Schwarz method, the communication between the micro (local) and macro (global) levels is achieved iteratively through some suitable boundary conditions. The micro problem is fed by Dirichlet data along the (outer) boundary of the patches. The specificity of our approach is that the macro problem inherits transmission conditions. Although they are expressed across the cracks, the final algebraic system to invert is blind to the discontinuities of the solution. In fact, the stiffness matrix turns out to be the one related to a safe domain, as if cracks were closed or the unilateral singularities were switched off. Only the right hand side is affected by what happens at the vicinity of the cracks. This enables users to run one of many efficient algorithms found in the literature to solve the linear macro-problem. In the other hand side, in spite of the still bad conditioning and the non-linearity of the unilateral micro problems, they are reduced in size and may be inverted properly by convex optimization algorithms. A successful convergence analysis of this variant of the Schwarz Method is performed after adapting to the unilateral non-linearity the variational tools developed by P. L. Lions. AMS subject classifications: 35N86, 65N55 ∗Corresponding author. Email addresses: faker.ben-belgacem@utc.fr (F. Ben Belgacem), faten.jelassi@ utc.f (F. Jelassi), nmgmati@iau.edu.sa (N. Gmati) F. Ben. Belgacem, N. Gmati and F. Jelassi / J. Math. Study, 52 (2019), pp. 378-393 379
重点研究了具有全重叠的单边裂纹的Schwarz方法的数值求解。目的是将裂缝附近的处理与计算域的其他区域隔离开来。这避免了在裂缝尖端产生的奇点周围可能使用的特定近似与在裂缝之外使用的更标准的方法之间的任何直接相互作用。我们应用迭代子结构技术通过将裂缝绝缘成块并对每个裂缝进行缩放来捕获小结构。宏观问题反过来又涉及到整个领域。在经典的Schwarz方法中，微观(局部)和宏观(全局)之间的通信是通过一些合适的边界条件来迭代实现的。微问题由沿斑块(外)边界的狄利克雷数据馈送。我们方法的特殊性在于宏观问题继承了传导条件。尽管它们是在裂缝中表示的，但最终要反转的代数系统对解的不连续是视而不见的。事实上，刚度矩阵是与安全域相关的矩阵，就好像裂缝是闭合的或单边奇点被关闭了一样。只有右手边受到裂缝附近发生的情况的影响。这使用户能够运行文献中发现的许多有效算法之一来解决线性宏观问题。另一方面，尽管单侧微问题仍然具有较差的条件和非线性，但通过凸优化算法可以减小其规模，并可以适当地反转。在适应p.l. Lions开发的变分工具的单边非线性后，对这种施瓦茨方法的变体进行了成功的收敛分析。AMS学科分类:35N86, 65N55 *通讯作者。电子邮件地址:faker.ben-belgacem@utc.fr (F. Ben Belgacem)， faten。jelassi@ utc。f (f . Jelassi)， nmgmati@iau.edu.sa (N. Gmati) f . Ben。belgem, N. Gmati和F. Jelassi / J. Math。研究，52 (2019)，pp. 378-393 379
{"title":"Computational Zooming in Near Unilateral Cracks by Schwarz Method with Total Overlap","authors":"F. B. Belgacem","doi":"10.4208/jms.v52n4.19.02","DOIUrl":"https://doi.org/10.4208/jms.v52n4.19.02","url":null,"abstract":"We focus on the numerical solver of unilateral cracks by the Schwarz Method with Total Overlap. The aim is to isolate the treatment at the vicinity of the cracks from other regions of the computational domain. This avoids any direct interaction between specific approximations one may use around the singularities born at the tips of the cracks and more standard methods employed away from the cracks. We apply an iterative sub-structuring technique to capture the small structures by insulating the cracks into patches and making a zoom around each of them. The macro-problem is in turn set on the whole domain. As for the classical Schwarz method, the communication between the micro (local) and macro (global) levels is achieved iteratively through some suitable boundary conditions. The micro problem is fed by Dirichlet data along the (outer) boundary of the patches. The specificity of our approach is that the macro problem inherits transmission conditions. Although they are expressed across the cracks, the final algebraic system to invert is blind to the discontinuities of the solution. In fact, the stiffness matrix turns out to be the one related to a safe domain, as if cracks were closed or the unilateral singularities were switched off. Only the right hand side is affected by what happens at the vicinity of the cracks. This enables users to run one of many efficient algorithms found in the literature to solve the linear macro-problem. In the other hand side, in spite of the still bad conditioning and the non-linearity of the unilateral micro problems, they are reduced in size and may be inverted properly by convex optimization algorithms. A successful convergence analysis of this variant of the Schwarz Method is performed after adapting to the unilateral non-linearity the variational tools developed by P. L. Lions. AMS subject classifications: 35N86, 65N55 ∗Corresponding author. Email addresses: faker.ben-belgacem@utc.fr (F. Ben Belgacem), faten.jelassi@ utc.f (F. Jelassi), nmgmati@iau.edu.sa (N. Gmati) F. Ben. Belgacem, N. Gmati and F. Jelassi / J. Math. Study, 52 (2019), pp. 378-393 379","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46457246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Solvability of the Nonlocal Initial Value Problem and Application to Design of Controller for Heat-equation with Delay","authors":"Xiao Xu","doi":"10.4208/JMS.V52N2.19.02","DOIUrl":"https://doi.org/10.4208/JMS.V52N2.19.02","url":null,"abstract":"","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49491420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The concept of minimality is generalized in different ways, one of which is the definition of k-minimality. In this paper k-minimality is studied for minimal hypersurfaces of a Euclidean space under different conditions on the number of principal curvatures. We will also give a counterexample to Lk-conjecture. AMS subject classifications: 53D12, 53C40, 53C42.
{"title":"Some Notes on k-minimality","authors":"A. E. Dehkordy","doi":"10.4208/JMS.V52N1.19.05","DOIUrl":"https://doi.org/10.4208/JMS.V52N1.19.05","url":null,"abstract":"The concept of minimality is generalized in different ways, one of which is the definition of k-minimality. In this paper k-minimality is studied for minimal hypersurfaces of a Euclidean space under different conditions on the number of principal curvatures. We will also give a counterexample to Lk-conjecture. AMS subject classifications: 53D12, 53C40, 53C42.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47560868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 study the global regularity issue of two dimensional incompressible magnetic Bénard equations with partial dissipation and magnetic diffusion. It remains open whether the smooth initial data produce solutions that are globally regular in time for all values of the parameters involved in the equations. We present conditional global regularity of the solutions. Moreover, we prove the global regularity for the slightly regularized system. AMS subject classifications: 35Q35, 35B35, 35B65, 76D03
{"title":"Regularity Criteria on the 2D Anisotropic Magnetic Bénard Equations","authors":"Dipendra Sharma","doi":"10.4208/JMS.V52N1.19.06","DOIUrl":"https://doi.org/10.4208/JMS.V52N1.19.06","url":null,"abstract":"In this paper, we study the global regularity issue of two dimensional incompressible magnetic Bénard equations with partial dissipation and magnetic diffusion. It remains open whether the smooth initial data produce solutions that are globally regular in time for all values of the parameters involved in the equations. We present conditional global regularity of the solutions. Moreover, we prove the global regularity for the slightly regularized system. AMS subject classifications: 35Q35, 35B35, 35B65, 76D03","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42090420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We are interested in the design of parallel numerical schemes for linear systems. We give an effective solution to this problem in the following case: the matrix A of the linear system is the product of p nonsingular matrices Am i with specific shape: Ai = I−hiX for a fixed matrix X and real numbers hi. Although having a special form, these matrices Ai arise frequently in the discretization of evolutionary Partial Differential Equations. For example, one step of the implicit Euler scheme for the evolution equation u′=Xu reads (I−hX)un+1 =un. Iterating m times such a scheme leads to a linear system Aun+m = un. The idea is to express A−1 as a linear combination of elementary matrices A−1 i (or more generally in term of matrices A −k i ). Hence the solution of the linear system with matrix A is a linear combination of the solutions of linear systems with matrices Ai (or Ak i ). These systems are then solved simultaneously on different processors. AMS subject classifications: 65M60, 65Y05, 35K45, 74S05, 74S20
{"title":"Partial Fraction Decomposition of Matrices and Parallel Computing","authors":"F. H. A. S. Kaber","doi":"10.4208/jms.v52n3.19.02","DOIUrl":"https://doi.org/10.4208/jms.v52n3.19.02","url":null,"abstract":"We are interested in the design of parallel numerical schemes for linear systems. We give an effective solution to this problem in the following case: the matrix A of the linear system is the product of p nonsingular matrices Am i with specific shape: Ai = I−hiX for a fixed matrix X and real numbers hi. Although having a special form, these matrices Ai arise frequently in the discretization of evolutionary Partial Differential Equations. For example, one step of the implicit Euler scheme for the evolution equation u′=Xu reads (I−hX)un+1 =un. Iterating m times such a scheme leads to a linear system Aun+m = un. The idea is to express A−1 as a linear combination of elementary matrices A−1 i (or more generally in term of matrices A −k i ). Hence the solution of the linear system with matrix A is a linear combination of the solutions of linear systems with matrices Ai (or Ak i ). These systems are then solved simultaneously on different processors. AMS subject classifications: 65M60, 65Y05, 35K45, 74S05, 74S20","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45652729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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