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Inverse time-dependent source problem for the heat equation with a nonlocal Wentzell-Neumann boundary condition 具有非局部温兹尔-诺伊曼边界条件的热方程的逆时源问题
4区 数学 Q2 Mathematics Pub Date : 2023-01-01 DOI: 10.3934/nhm.2023076
Fermín S. V. Bazán, Luciano Bedin, Mansur I. Ismailov, Leonardo S. Borges

In this work, we consider the problem of recovering the heat source term for the heat equation with a nonlocal Wentzell-Neumann boundary condition subject to an integral overdetermination condition. Conditions for the existence and uniqueness of the classical solution of the inverse problem are revisited, and a numerical method for practical source reconstruction is introduced. Unlike all of the source reconstruction methods found in literature, the method introduced in this work computes regularized solutions from a triangular linear system arising from a semi-discretization in the space of the continuous model. Regularization is introduced by applying the generalized singular value decomposition of a proper matrix pair along with truncation. Numerical results illustrate the effectiveness of the method.

在这项工作中,我们考虑了在积分超定条件下具有非局部Wentzell-Neumann边界条件的热方程的热源项的恢复问题。重新讨论了反问题经典解的存在唯一性条件,并介绍了一种实际源重构的数值方法。与文献中发现的所有源重构方法不同,本文介绍的方法从连续模型空间中的半离散化产生的三角形线性系统中计算正则解。利用适当矩阵对的广义奇异值分解和截断引入正则化。数值结果表明了该方法的有效性。</ </abstract>
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引用次数: 0
Two high-order compact difference schemes with temporal graded meshes for time-fractional Black-Scholes equation 时间分数阶Black-Scholes方程的两种高阶紧致差分格式
4区 数学 Q2 Mathematics Pub Date : 2023-01-01 DOI: 10.3934/nhm.2023074
Jie Gu, Lijuan Nong, Qian Yi, An Chen

In this paper, two high-order compact difference schemes with graded meshes are proposed for solving the time-fractional Black-Scholes equation. We first eliminate the convection term in the equivalent form of the considered equation by using exponential transformation, then combine the sixth-order/eighth-order compact difference method with a temporal graded meshes-based trapezoidal formulation for the temporal integral term to obtain the fully discrete high-order compact difference schemes. The stability and convergence analysis of the two proposed schemes are studied by applying Fourier analysis. Finally, the effectiveness of the proposed schemes and the correctness of the theoretical results are verified by two numerical examples.

本文提出了求解时间分数阶Black-Scholes方程的两种高阶紧致差分格式。首先利用指数变换消除方程等价形式中的对流项,然后将时间积分项的六阶/八阶紧致差分法与基于时间梯度网格的梯形公式相结合,得到完全离散的高阶紧致差分格式。利用傅里叶分析研究了两种方案的稳定性和收敛性分析。最后,通过两个数值算例验证了所提方案的有效性和理论结果的正确性。
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引用次数: 0
A new distributional approach: estimation, Monte Carlo simulation and applications to the biomedical data sets 一种新的分布方法:估计、蒙特卡罗模拟及其在生物医学数据集上的应用
IF 1 4区 数学 Q2 Mathematics Pub Date : 2023-01-01 DOI: 10.3934/nhm.2023069
M. Kamal, M. Alsolmi, Nayabuddin, Aned Al Mutairi, Eslam Hussam, M. Mustafa, S. G. Nassr
This paper introduces the generalized exponential-$ U $ family of distributions as a novel methodological approach to enhance the distributional flexibility of existing classical and modified distributions. The new family is derived by combining the T-$ X $ family method with the exponential model. The paper presents the generalized exponential-Weibull model, an updated version of the Weibull model. Estimators and heavy-tailed characteristics of the proposed method are derived. The new model is applied to three healthcare data sets, including COVID-19 patient survival times and mortality rate data set from Mexico and Holland. The proposed model outperforms other models in terms of analyzing healthcare data sets by evaluating the best model selection measures. The findings suggest that the proposed model holds promise for broader utilization in the area of predicting and modeling healthcare phenomena.
本文介绍了广义指数-$ U $分布族,作为一种新的方法来提高现有经典分布和修正分布的分布灵活性。将T-$ X $族方法与指数模型相结合,得到了新的族。本文提出了广义指数威布尔模型,这是威布尔模型的更新版本。推导了该方法的估计量和重尾特性。新模型应用于三个医疗保健数据集,包括墨西哥和荷兰的COVID-19患者生存时间和死亡率数据集。通过评估最佳模型选择度量,所提出的模型在分析医疗数据集方面优于其他模型。研究结果表明,该模型有望在医疗保健现象的预测和建模领域得到更广泛的应用。
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引用次数: 0
Algorithms for two-agent unbounded serial-batch scheduling with makespan and maximum lateness objectives 具有最大完工时间和最大延迟目标的双智能体无界串行批调度算法
4区 数学 Q2 Mathematics Pub Date : 2023-01-01 DOI: 10.3934/nhm.2023073
Shuguang Li, Mingsong Li, Muhammad Ijaz Khan

We study the problem of non-preemptively scheduling jobs from two agents on an unbounded serial-batch machine. Agents $ A $ and $ B $ have $ n_A $ and $ n_B $ jobs. The machine can process any number of jobs sequentially as a batch, and the processing time of the batch is equal to the total processing time of the jobs in it. Each batch requires a setup time before it is processed. Compatibility means that the jobs from different agents can be processed in a common batch; Otherwise, the jobs from different agents are incompatible. Both the compatible and incompatible models are considered, under both the batch availability and item availability assumptions. Batch availability means that any job in a batch is not available until all the jobs in this batch are completed. Item availability means that a job in a batch becomes available immediately after it is completed processing. The completion time of a job is defined to be the moment when it is available. The goal is to minimize the makespan of agent $ A $ and the maximum lateness of agent $ B $ simultaneously. For the compatible model with batch availability, an $ O(n_A+n_B^2log n_B) $-time algorithm is presented which improves the existing $ O(n_A+n_B^4log n_B) $-time algorithm. A slight modification of the algorithm solves the incompatible model with batch availability in $ O(n_A+n_B^2log n_B) $ time, which has the same time complexity as the existing algorithm. For the compatible model with item availability, the analysis shows that it is easy and admits an $ O(n_A+n_Blog n_B) $-time algorithm. For the incompatible model with item availability, an $ O(n_A+n_Blog n_B) $-time algorithm is also obtained which improves the existing $ O(n_A+n_B^2) $-time algorithm. The algorithms can generate all Pareto optimal points and find a corresponding Pareto optimal schedule for each Pareto optimal point.

研究了无界串行批处理机器上两个智能体的非抢占调度问题。代理$ A $和$ B $有$ n_A $和$ n_B $的任务。机器可以按顺序分批处理任意数量的作业,批作业的处理时间等于其中作业的总处理时间。每个批次在处理之前都需要一个设置时间。兼容性意味着来自不同代理的作业可以在一个共同的批处理中处理;否则,来自不同代理的作业是不兼容的。在批量可用性和项目可用性假设下,同时考虑了兼容和不兼容模型。批可用性是指批处理中的任何作业在此批处理中的所有作业完成之前都不可用。项目可用性意味着批处理中的作业在完成处理后立即可用。作业的完成时间被定义为它可用的时刻。目标是同时最小化代理A的完工时间和代理B的最大延迟时间。对于具有批量可用性的兼容模型,提出了一种$ O(n_A+n_B^2log n_B) $ time算法,改进了现有的$ O(n_A+n_B^4log n_B) $ time算法。对算法稍加修改,在$ O(n_A+n_B^2log n_B) $ time内解决了具有批处理可用性的不兼容模型,其时间复杂度与现有算法相同。对于具有物品可用性的兼容模型,分析表明该模型易于实现,并且允许$ O(n_A+n_Blog n_B) $时间算法。对于具有物品可用性的不兼容模型,提出了一种$ O(n_A+n_Blog n_B) $ time算法,改进了已有的$ O(n_A+n_B^2) $ time算法。该算法可以生成所有的Pareto最优点,并为每个Pareto最优点找到相应的Pareto最优调度。
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引用次数: 0
A model of voting dynamics under bounded confidence with nonstandard norming 非标准规范下有界置信度下的投票动力学模型
IF 1 4区 数学 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.3934/nhm.2022032
S. Pilyugin, M. Tarasova, Aleksandr S. Tarasov, G. Monakov
In this paper, we study a model of opinion dynamics based on the so-called "bounded confidence" principle introduced by Hegselmann and Krause. Following this principle, voters participating in an electoral decision with two options are influenced by individuals sharing an opinion similar to their own.We consider a modification of this model where the operator generating the dynamical system which describes the process of formation the final distribution of opinions in the society is defined in two steps. First, to the opinion of an agent, a value proportional to opinions in his/her "influence group" is added, and then the elements of the resulting array are divided by the maximal absolute value of elements to keep the opinions in the prescribed interval. We show that under appropriate conditions, any trajectory tends to a fixed point, and all the remaining fixed points are Lyapunov stable.
本文研究了基于Hegselmann和Krause提出的“有界置信”原理的意见动态模型。根据这一原则,选民参与有两个选择的选举决策时,会受到与自己观点相似的个人的影响。我们考虑了对该模型的一种修改,其中将生成描述社会意见最终分布形成过程的动力系统的算子定义为两个步骤。首先,对代理人的意见加上与其“影响组”中的意见成比例的值,然后将结果数组中的元素除以元素的最大绝对值,使意见保持在规定的区间内。我们证明了在适当的条件下,任何轨迹都趋向于一个不动点,并且所有剩余的不动点都是李雅普诺夫稳定的。
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引用次数: 0
Compactness property of the linearized Boltzmann operator for a diatomic single gas model 双原子单气体模型线性化Boltzmann算子的紧性
IF 1 4区 数学 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.3934/nhm.2022029
S. Brull, Marwa Shahine, P. Thieullen

In the following work, we consider the Boltzmann equation that models a diatomic gas by representing the microscopic internal energy by a continuous variable I. Under some convenient assumptions on the collision cross-section begin{document}$ mathcal{B} $end{document}, we prove that the linearized Boltzmann operator begin{document}$ mathcal{L} $end{document} of this model is a Fredholm operator. For this, we write begin{document}$ mathcal{L} $end{document} as a perturbation of the collision frequency multiplication operator, and we prove that the perturbation operator begin{document}$ mathcal{K} $end{document} is compact. The result is established after inspecting the kernel form of begin{document}$ mathcal{K} $end{document} and proving it to be begin{document}$ L^2 $end{document} integrable over its domain using elementary arguments.This implies that begin{document}$ mathcal{K} $end{document} is a Hilbert-Schmidt operator.

In the following work, we consider the Boltzmann equation that models a diatomic gas by representing the microscopic internal energy by a continuous variable I. Under some convenient assumptions on the collision cross-section begin{document}$ mathcal{B} $end{document}, we prove that the linearized Boltzmann operator begin{document}$ mathcal{L} $end{document} of this model is a Fredholm operator. For this, we write begin{document}$ mathcal{L} $end{document} as a perturbation of the collision frequency multiplication operator, and we prove that the perturbation operator begin{document}$ mathcal{K} $end{document} is compact. The result is established after inspecting the kernel form of begin{document}$ mathcal{K} $end{document} and proving it to be begin{document}$ L^2 $end{document} integrable over its domain using elementary arguments.This implies that begin{document}$ mathcal{K} $end{document} is a Hilbert-Schmidt operator.
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引用次数: 8
Smooth Transonic Flows Around Cones 圆锥体周围的平滑跨音速流
IF 1 4区 数学 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.3934/nhm.2022028
W. Lien, Yu-Yu Liu, Chen-Chang Peng
We consider a conical body facing a supersonic stream of air at a uniform velocity. When the opening angle of the obstacle cone is small, the conical shock wave is attached to the vertex. Under the assumption of self-similarity for irrotational motions, the Euler system is transformed into the nonlinear ODE system. We reformulate the problem in a non-dimensional form and analyze the corresponding ODE system. The initial data is given on the obstacle cone and the solution is integrated until the Rankine-Hugoniot condition is satisfied on the shock cone. By applying the fundamental theory of ODE systems and technical estimates, we construct supersonic solutions and also show that no matter how small the opening angle is, a smooth transonic solution always exists as long as the speed of the incoming flow is suitably chosen for this given angle.
我们考虑一个面对匀速超音速气流的锥形物体。当障碍物锥开口角度较小时,锥形激波附着在障碍物锥顶点。在无旋转运动自相似假设下,将欧拉系统转化为非线性ODE系统。我们用无量纲形式重新表述了这个问题,并分析了相应的ODE系统。在障碍物锥上给出初始数据,积分解,直到激波锥上满足Rankine-Hugoniot条件。通过应用ODE系统的基本理论和技术估计,我们构造了超声速解,并证明了无论开口角有多小,只要在给定的角度下选择合适的来流速度,总是存在一个平滑的跨声速解。
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引用次数: 0
Notations 符号
IF 1 4区 数学 Q2 Mathematics Pub Date : 2021-07-05 DOI: 10.1016/b978-0-12-819880-3.00007-x
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引用次数: 16
Cracks in heterogeneous media 非均质介质中的裂纹
IF 1 4区 数学 Q2 Mathematics Pub Date : 2021-01-01 DOI: 10.1016/B978-0-12-819880-3.00013-5
S. Kanaun
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引用次数: 0
Index 指数
IF 1 4区 数学 Q2 Mathematics Pub Date : 2021-01-01 DOI: 10.1016/b978-0-12-819880-3.00017-2
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引用次数: 0
期刊
Networks and Heterogeneous Media
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