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Applied Mathematics-A Journal of Chinese Universities Series B最新文献

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Modeling and Numerical Solution of a Cancer Therapy Optimal Control Problem 肿瘤治疗最优控制问题的建模与数值解
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2018-08-14 DOI: 10.4236/AM.2018.98067
Melina-Lorén Kienle Garrido, Tim Breitenbach, K. Chudej, A. Borzì
{"title":"Modeling and Numerical Solution of a Cancer Therapy Optimal Control Problem","authors":"Melina-Lorén Kienle Garrido, Tim Breitenbach, K. Chudej, A. Borzì","doi":"10.4236/AM.2018.98067","DOIUrl":"https://doi.org/10.4236/AM.2018.98067","url":null,"abstract":"A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the combination of two well established models, represents the differential constraint of a non-smooth optimal control problem that aims at reducing the volume of the tumor while keeping the radio- and anti-angiogenesis chemical dosage to a minimum. Existence of optimal solutions is proved and necessary conditions are formulated in terms of the Pontryagin maximum principle. Based on this principle, a so-called sequential quadratic Hamiltonian (SQH) method is discussed and benchmarked with an “interior point optimizer—a mathematical programming language” (IPOPT-AMPL) algorithm. Results of numerical experiments are presented that successfully validate the SQH solution scheme. Further, it is shown how to choose the optimisation weights in order to obtain treatment functions that successfully reduce the tumor volume to zero.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78469783","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}
引用次数: 5
Ordered Rate Constitutive Theories for Non-Classical Thermoviscoelastic Fluids with Internal Rotation Rates 具有内旋转速率的非经典热粘弹性流体的有序速率本构理论
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2018-08-14 DOI: 10.4236/AM.2018.98063
K. Surana, S. W. Long, J. Reddy
{"title":"Ordered Rate Constitutive Theories for Non-Classical Thermoviscoelastic Fluids with Internal Rotation Rates","authors":"K. Surana, S. W. Long, J. Reddy","doi":"10.4236/AM.2018.98063","DOIUrl":"https://doi.org/10.4236/AM.2018.98063","url":null,"abstract":"The paper presents constitutive theories for non-classical thermoviscoelastic \u0000fluids with dissipation and memory using a thermodynamic framework based \u0000on entirety of velocity gradient tensor. Thus, the conservation and the balance \u0000laws used in this work incorporate symmetric as well as antisymmetric part of \u0000the velocity gradient tensor. The constitutive theories derived here hold in coand \u0000contra-variant bases as well as in Jaumann rates and are derived using \u0000convected time derivatives of Green’s and Almansi strain tensors as well as \u0000the Cauchy stress tensor and its convected time derivatives in appropriate \u0000bases. The constitutive theories are presented in the absence as well as in the \u0000presence of the balance of moment of moments as balance law. It is shown \u0000that the dissipation mechanism and the fading memory in such fluids are due \u0000to stress rates as well as moment rates and their conjugates. The material \u0000coefficients are derived for the general forms of the constitutive theories \u0000based on integrity. Simplified linear (or quasi-linear) forms of the constitutive \u0000theories are also presented. Maxwell, Oldroyd-B and Giesekus constitutive \u0000models for non-classical thermoviscoelastic fluids are derived and are compared \u0000with those derived based on classical continuum mechanics. Both, \u0000compressible and incompressible thermoviscoelastic fluids are considered.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90479145","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}
引用次数: 5
Methodology for Constructing a Short-Term Event Risk Score in Heart Failure Patients 心力衰竭患者短期事件风险评分的构建方法
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2018-08-14 DOI: 10.4236/AM.2018.98065
K. Duarte, J. Monnez, É. Albuisson
{"title":"Methodology for Constructing a Short-Term Event Risk Score in Heart Failure Patients","authors":"K. Duarte, J. Monnez, É. Albuisson","doi":"10.4236/AM.2018.98065","DOIUrl":"https://doi.org/10.4236/AM.2018.98065","url":null,"abstract":"We present a methodology for constructing a short-term event risk score in heart failure patients from an ensemble predictor, using bootstrap samples, two different classification rules, logistic regression and linear discriminant analysis for mixed data, continuous or categorical, and random selection of explanatory variables to build individual predictors. We define a measure of the importance of each variable in the score and an event risk measure by an odds-ratio. Moreover, we establish a property of linear discriminant analysis for mixed data. This methodology is applied to EPHESUS trial patients on whom biological, clinical and medical history variables were measured.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82883190","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}
引用次数: 6
Numerical Solution of the Coupled Viscous Burgers’ Equation Using Differential Quadrature Method Based on Fourier Expansion Basis 基于傅里叶展开基的耦合粘性Burgers方程微分积分法数值解
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2018-07-30 DOI: 10.4236/AM.2018.97057
M. Jima, Alemayehu Shiferaw, Ali Tsegaye
{"title":"Numerical Solution of the Coupled Viscous Burgers’ Equation Using Differential Quadrature Method Based on Fourier Expansion Basis","authors":"M. Jima, Alemayehu Shiferaw, Ali Tsegaye","doi":"10.4236/AM.2018.97057","DOIUrl":"https://doi.org/10.4236/AM.2018.97057","url":null,"abstract":"The differential quadrature method based on Fourier expansion basis is applied in this work to solve coupled viscous Burgers’ equation with appropriate initial and boundary conditions. In the first step for the given problem we have discretized the interval and replaced the differential equation by the Differential quadrature method based on Fourier expansion basis to obtain a system of ordinary differential equation (ODE) then we implement the numerical scheme by computer programing and perform numerical solution. Finally the validation of the present scheme is demonstrated by numerical example and compared with some existing numerical methods in literature. The method is analyzed for stability and convergence. It is found that the proposed numerical scheme produces a good result as compared to other researcher’s result and even generates a value at the nodes or mesh points that the results have not seen yet.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73994385","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}
引用次数: 8
Optimal Investment-Reinsurance Strategies for Insurers with Mean-Reversion and Mispricing under Variance Premium Principle 方差保费原则下具有均值回归和错定价的保险公司最优投资再保险策略
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2018-07-25 DOI: 10.4236/AM.2018.97056
Yuzhen Wen
{"title":"Optimal Investment-Reinsurance Strategies for Insurers with Mean-Reversion and Mispricing under Variance Premium Principle","authors":"Yuzhen Wen","doi":"10.4236/AM.2018.97056","DOIUrl":"https://doi.org/10.4236/AM.2018.97056","url":null,"abstract":"This paper considers a robust optimal reinsurance-investment problem for an \u0000insurer with mispricing and model ambiguity. The surplus process is described \u0000by a classical Cramer-Lunderg model and the financial market contains \u0000a market index, a risk-free asset and a pair of mispriced stocks, where the \u0000expected return rate of the stocks and the mispricing follow mean reverting \u0000processes which take into account liquidity constraints. In particular, both the \u0000insurance and reinsurance premium are assumed to be calculated via the variance \u0000premium principle. By employing the dynamic programming approach, \u0000we derive the explicit optimal robust reinsurance-investment strategy \u0000and the optimal value function.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85354403","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}
引用次数: 1
Newton, Halley, Pell and the Optimal Iterative High-Order Rational Approximation of √N Newton, Halley, Pell和√N的最优迭代高阶有理逼近
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2018-07-12 DOI: 10.4236/am.2018.97059
I. Fried
{"title":"Newton, Halley, Pell and the Optimal Iterative High-Order Rational Approximation of √N","authors":"I. Fried","doi":"10.4236/am.2018.97059","DOIUrl":"https://doi.org/10.4236/am.2018.97059","url":null,"abstract":"In this paper we examine single-step iterative methods for the solution of the \u0000nonlinear algebraic equation f (x) = x2 - N = 0 , for some integer N, generating \u0000rational approximations p/q that are optimal in the sense of Pell’s equation p2 - Nq2 = k for some integer k, converging either alternatingly or \u0000oppositely.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72530581","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}
引用次数: 0
A Discrete Analogue of Energy Integral for a Difference Scheme for Quasilinear Hyperbolic Systems 拟线性双曲型系统差分格式能量积分的离散模拟
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2018-07-12 DOI: 10.4236/AM.2018.97055
R. Aloev, Z. Eshkuvatov, M. Khudayberganov, N. Long
{"title":"A Discrete Analogue of Energy Integral for a Difference Scheme for Quasilinear Hyperbolic Systems","authors":"R. Aloev, Z. Eshkuvatov, M. Khudayberganov, N. Long","doi":"10.4236/AM.2018.97055","DOIUrl":"https://doi.org/10.4236/AM.2018.97055","url":null,"abstract":"The class of three-dimensional quasilinear hyperbolic systems is studied. The \u0000initial boundary value problem for this class of quasilinear hyperbolic systems \u0000is given. By constructing the energy’s integral, a priori estimate for the solution \u0000of the initial boundary value problem is obtained. Difference scheme is \u0000constructed and an a priori estimate for its solution is obtained. Numerical \u0000example exhibits the efficiency and accuracy of the method.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76011276","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}
引用次数: 11
A Knowledge Measure with Parameter of Intuitionistic Fuzzy Sets 一种带有直觉模糊集参数的知识度量
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2018-07-12 DOI: 10.4236/AM.2018.97060
Zhenhua Zhang, Shenguo Yuan, Jing Zhang, Chao Ma, Jinhui Xu, Xiaolong Lin
{"title":"A Knowledge Measure with Parameter of Intuitionistic Fuzzy Sets","authors":"Zhenhua Zhang, Shenguo Yuan, Jing Zhang, Chao Ma, Jinhui Xu, Xiaolong Lin","doi":"10.4236/AM.2018.97060","DOIUrl":"https://doi.org/10.4236/AM.2018.97060","url":null,"abstract":"A new knowledge measure with parameter of intuitionistic fuzzy sets (IFSs) is presented based on the membership degree and the non-membership degree of IFSs, which complies with the extended form of Szmidt-Kacprzyk axioms for intuitionistic fuzzy entropy. And a sufficient and necessary condition of order property in the Szmidt-Kacprzyk axioms is discussed. Additionally, some numerical examples are given to illustrate the applications of the proposed knowledge measure and some conventional entropies and knowledge measures of IFSs. The experimental results show that the results of the parametric model proposed in this paper are more accurate than those of most of the classic models.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82698251","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}
引用次数: 2
Different Rationales of Coalition Formation and Incentives for Strategic Voting 联盟形成的不同原理与战略投票的激励
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2018-07-12 DOI: 10.4236/am.2018.97058
Eric Linhart, Johannes Raabe
{"title":"Different Rationales of Coalition Formation and Incentives for Strategic Voting","authors":"Eric Linhart, Johannes Raabe","doi":"10.4236/am.2018.97058","DOIUrl":"https://doi.org/10.4236/am.2018.97058","url":null,"abstract":"Research on strategic voting has mainly focused on electoral system effects but \u0000largely neglected the impact of different rationales of coalition formation. Based \u0000on a formal model of rational party choice and a simulation study, we systematically \u0000investigate this impact and explore the implications. We show that the \u0000logic of the underlying coalition formation procedure clearly affects the degree \u0000to which the electorate is exposed to strategic incentives regarding the vote \u0000choice. The key implications are that sincere voting is more often in the voter’s \u0000best interest if parties are policy-seeking and if there is increased uncertainty \u0000during the stage of coalition formation. Furthermore, we explore how \u0000different types of coalition formation affect strategic incentives across the policy \u0000space.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81050853","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}
引用次数: 0
Mathematical Models and Numerical Simulation for Dynamic Evolutions of Cancer and Immune Cells 癌症和免疫细胞动态进化的数学模型和数值模拟
IF 1 4区 数学
Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2018-06-06 DOI: 10.4236/AM.2018.96040
B. O. Oyelami
{"title":"Mathematical Models and Numerical Simulation for Dynamic Evolutions of Cancer and Immune Cells","authors":"B. O. Oyelami","doi":"10.4236/AM.2018.96040","DOIUrl":"https://doi.org/10.4236/AM.2018.96040","url":null,"abstract":"Cancer is a major public health problem worldwide and finding a total cure or eradication of the disease has been the expectations of medical researchers and medical practitioners in the recent times. In this paper, invasion of normal cells by carcinogens is considered. The purpose of the research is to study the dynamic evolutions of cancer and immune cells with the view finding most effective strategic way to control or eradicate cancer growth in human beings. We proposed five growths and mitigate models for benign and malignant cancer which are coupled ordinary differential equations and partial differential equations and Numerical simulations are made for the models. Analytic and Numerical solutions and sensitivity analysis of the models to parameters are obtained. It is found that the benign and malignant cancer cells displayed out of control growth and hence unstable in nature and the immune cells depreciated to the point of immune collapse. By the use of energy function it is established that staving of cancer cells of oxygen or use of drugs are strategic ways of combating cancer disease. Moreover, if the cancer cells are starved of basic nutrients or some basic enzymes inhibited it is expected that similar effect can also be achieved. The starvation of cancer cells should focus on oxygen, nutrients and vital enzymes. However, it is hoped that drugs developers and bioengineers will come up with means to achieve the starvation strategies to combat cancer disease.","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91179365","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}
引用次数: 2
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