为提高小麦条锈病的遥感监测精度,该研究利用分数阶微分能够突出光谱的细微信息以及描述光谱数据间微小差异的优势,在对条锈病胁迫下小麦冠层光谱数据进行分数阶微分处理的基础上,构建了两波段和三波段分数阶微分光谱指数,并将其应用于...为提高小麦条锈病的遥感监测精度,该研究利用分数阶微分能够突出光谱的细微信息以及描述光谱数据间微小差异的优势,在对条锈病胁迫下小麦冠层光谱数据进行分数阶微分处理的基础上,构建了两波段和三波段分数阶微分光谱指数,并将其应用于小麦条锈病的遥感探测。研究结果表明,1.2阶次微分光谱与小麦条锈病冠层病情严重度的相关性最高,较原始反射率光谱、一阶微分光谱和二阶微分光谱分别提高了20.9%、3.9%和20.5%;基于分数阶微分光谱指数的最优分数阶次及其对应波长构建的三波段分数阶微分光谱指数对小麦条锈病的探测能力优于两波段分数阶微分光谱指数,其中分数阶微分光化学指数与冠层病情严重度的相关系数达到0.875;以分数阶微分光谱指数为自变量构建的高斯过程回归(Gaussian Process Regression,GPR)模型对小麦条锈病冠层病情严重度的预测精度优于反射率光谱指数,其训练数据集及验证数据集病情指数(Disease Index,DI)预测值和实测值间的决定系数较反射率光谱指数分别提高了3.8%和19.1%。研究结果可为进一步实现作物健康状况大面积高精度遥感监测提供参考。展开更多
This paper introduces the main methods and steps of modeling principle by ordinary differential equations, and is used to explore the differential equation model to solve some practical problems, some features of the ...This paper introduces the main methods and steps of modeling principle by ordinary differential equations, and is used to explore the differential equation model to solve some practical problems, some features of the related problems. With the development of science and technology and production practice, differential equation is more closely connected with other subjects, and a mathematical model for some practical problems of good.展开更多
Autoimmune diseases are generated through irregular immune response of the human body. Psoriasis is one type of autoimmune chronic skin diseases that is differentiated by T-Cells mediated hyper-proliferation of epider...Autoimmune diseases are generated through irregular immune response of the human body. Psoriasis is one type of autoimmune chronic skin diseases that is differentiated by T-Cells mediated hyper-proliferation of epidermal Keratinocytes. Dendritic Cells and CD8＋ T-Cells have a significant role for the occurrence of this disease. In this paper, the authors have developed a mathematical model of Psoriasis involving CD4＋ T-Cells, Dendritic Ceils, CD8＋ T-Cells and Keratinocyte cell populations using the fractional differential equations with the effect of Cytokine release to observe the impact of memory on the cell-biological system. Using fractional calculus, the authors try to explore the suppressed memory, associated with the cell-biological system and to locate the position of Keratinocyte cell population as fractional derivative possess non-local property. Thus, the dynamics of Psoriasis can be predicted in a better way using fractional differential equations rather than its corresponding integer order model. Finally, the authors introduce drug into the system to obstruct the interaction between CD4＋ T-Cells and Keratinocytes to restrict the disease Psoriasis. The authors derive the Euler-Lagrange conditions for the optimality made through Matlab by developing iterative of the drug induced system. Numerical simulations are schemes.展开更多
Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated.In particular,we derive sufficient conditions for the permanence of species,existence of an attracting ...Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated.In particular,we derive sufficient conditions for the permanence of species,existence of an attracting periodic solution to the periodic system.The results of Wang Ke in 1994 and 1998 are improved and extended.展开更多
The problem of fragmentation(disintegration) process is theoretically studied with allowance for the initial particle volume. An exact analytical solution of integro-differential model governing the fragmentation phen...The problem of fragmentation(disintegration) process is theoretically studied with allowance for the initial particle volume. An exact analytical solution of integro-differential model governing the fragmentation phenomenon is obtained. The key role of a finite initial volume of particles leading to substantial changes of the particle-size distribution function is demonstrated.展开更多
In this paper, we extensively studied a mathematical model of biology. It helps us to understand the dynamical procedure of population changes in biological population model and provides valuable predictions. In this ...In this paper, we extensively studied a mathematical model of biology. It helps us to understand the dynamical procedure of population changes in biological population model and provides valuable predictions. In this model, we establish a variety of exact solutions. To study the exact solutions, we used a fractional complex transform to convert the particular partial differential equation of fractional order into corresponding partial differential equation and modified exp-function method is implemented to investigate the nonlinear equation. Graphical demonstrations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, unfailing, well-organized and pragmatic for fractional PDEs and could be protracted to further physical happenings.展开更多
A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability an...A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability analysis using geometric approach to stability, based on the higher-order generalization of Bendixson＇s criterion. The result is also supported numerically. An important epidemiological issue of eradicating hepatitis C virus has been addressed through the global stability analysis.展开更多
We propose a fractional time scale to model the calcium ion channels model which is retarded with injection of calcium-chelator Ethylene Glycol Tetraacetic Acid （EGTA）. By using this nonlinear time scale and Modifie...We propose a fractional time scale to model the calcium ion channels model which is retarded with injection of calcium-chelator Ethylene Glycol Tetraacetic Acid （EGTA）. By using this nonlinear time scale and Modified Riemann-Liouville fractional derivative, we convert the integer-order calcium ion channels model into fractional-order differential equations. We also analyze the range of order of fractional-order differentiM equations to ensure the equilibria of it are asymptotically stable. The simulation results are given to demonstrate the solutions of this model coincide with the real experiment data.展开更多
文摘为提高小麦条锈病的遥感监测精度,该研究利用分数阶微分能够突出光谱的细微信息以及描述光谱数据间微小差异的优势,在对条锈病胁迫下小麦冠层光谱数据进行分数阶微分处理的基础上,构建了两波段和三波段分数阶微分光谱指数,并将其应用于小麦条锈病的遥感探测。研究结果表明,1.2阶次微分光谱与小麦条锈病冠层病情严重度的相关性最高,较原始反射率光谱、一阶微分光谱和二阶微分光谱分别提高了20.9%、3.9%和20.5%;基于分数阶微分光谱指数的最优分数阶次及其对应波长构建的三波段分数阶微分光谱指数对小麦条锈病的探测能力优于两波段分数阶微分光谱指数,其中分数阶微分光化学指数与冠层病情严重度的相关系数达到0.875;以分数阶微分光谱指数为自变量构建的高斯过程回归(Gaussian Process Regression,GPR)模型对小麦条锈病冠层病情严重度的预测精度优于反射率光谱指数,其训练数据集及验证数据集病情指数(Disease Index,DI)预测值和实测值间的决定系数较反射率光谱指数分别提高了3.8%和19.1%。研究结果可为进一步实现作物健康状况大面积高精度遥感监测提供参考。
文摘This paper introduces the main methods and steps of modeling principle by ordinary differential equations, and is used to explore the differential equation model to solve some practical problems, some features of the related problems. With the development of science and technology and production practice, differential equation is more closely connected with other subjects, and a mathematical model for some practical problems of good.
基金supported by the Council of Scientific and Industrial Research,Government of India under Grant No.38(1320)/12/EMR-II
文摘Autoimmune diseases are generated through irregular immune response of the human body. Psoriasis is one type of autoimmune chronic skin diseases that is differentiated by T-Cells mediated hyper-proliferation of epidermal Keratinocytes. Dendritic Cells and CD8＋ T-Cells have a significant role for the occurrence of this disease. In this paper, the authors have developed a mathematical model of Psoriasis involving CD4＋ T-Cells, Dendritic Ceils, CD8＋ T-Cells and Keratinocyte cell populations using the fractional differential equations with the effect of Cytokine release to observe the impact of memory on the cell-biological system. Using fractional calculus, the authors try to explore the suppressed memory, associated with the cell-biological system and to locate the position of Keratinocyte cell population as fractional derivative possess non-local property. Thus, the dynamics of Psoriasis can be predicted in a better way using fractional differential equations rather than its corresponding integer order model. Finally, the authors introduce drug into the system to obstruct the interaction between CD4＋ T-Cells and Keratinocytes to restrict the disease Psoriasis. The authors derive the Euler-Lagrange conditions for the optimality made through Matlab by developing iterative of the drug induced system. Numerical simulations are schemes.
基金This research is supported by the National Natural Science Foundation of China.
文摘Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated.In particular,we derive sufficient conditions for the permanence of species,existence of an attracting periodic solution to the periodic system.The results of Wang Ke in 1994 and 1998 are improved and extended.
基金Supported by the Russian Science Foundation under Grant No.16-11-10095
文摘The problem of fragmentation(disintegration) process is theoretically studied with allowance for the initial particle volume. An exact analytical solution of integro-differential model governing the fragmentation phenomenon is obtained. The key role of a finite initial volume of particles leading to substantial changes of the particle-size distribution function is demonstrated.
文摘In this paper, we extensively studied a mathematical model of biology. It helps us to understand the dynamical procedure of population changes in biological population model and provides valuable predictions. In this model, we establish a variety of exact solutions. To study the exact solutions, we used a fractional complex transform to convert the particular partial differential equation of fractional order into corresponding partial differential equation and modified exp-function method is implemented to investigate the nonlinear equation. Graphical demonstrations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, unfailing, well-organized and pragmatic for fractional PDEs and could be protracted to further physical happenings.
文摘A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability analysis using geometric approach to stability, based on the higher-order generalization of Bendixson＇s criterion. The result is also supported numerically. An important epidemiological issue of eradicating hepatitis C virus has been addressed through the global stability analysis.
基金Acknowledgments The research of this paper is supported by National Natural Science Foundation of China （Grant No. 11171238） and a project supported by Scientific Research Fund of Sichuan Provincial Education Department （Grant No. 13ZA0109）.
文摘We propose a fractional time scale to model the calcium ion channels model which is retarded with injection of calcium-chelator Ethylene Glycol Tetraacetic Acid （EGTA）. By using this nonlinear time scale and Modified Riemann-Liouville fractional derivative, we convert the integer-order calcium ion channels model into fractional-order differential equations. We also analyze the range of order of fractional-order differentiM equations to ensure the equilibria of it are asymptotically stable. The simulation results are given to demonstrate the solutions of this model coincide with the real experiment data.
