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1.
《Discrete Mathematics》2022,345(5):112802
We study logical limit laws for uniform attachment random graphs. In this random graph model, vertices and edges are introduced recursively: at time , the vertex is introduced together with m edges joining the new vertex with m different vertices chosen uniformly at random from . We prove that this random graph obeys convergence law for first-order sentences with at most variables. 相似文献
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近年来拓扑学在量子力学中得到了广泛的运用.本文将安培环路定理积分式重新表达为一矢量场在轮胎参数面上的第一类陈数积分.数值模拟展示了该积分值为一整数即第一陈数,其代表矢量场的整体性质:当经历连续变换时,矢量场的局部数值发生改变但整体积分值即陈数仍保持不变;若陈数发生改变,则表明矢量场变换的连续性条件发生破坏,矢量场出现奇点.进一步通过高斯映射将该矢量场从参数轮胎面映射到单位球面上,并给出了第一陈数的直观几何意义.理论和数值结果揭示了安培环路定理的拓扑学本质,表明拓扑概念在经典物理学中也会有广泛应用. 相似文献
4.
Michele Colturato 《Mathematical Methods in the Applied Sciences》2020,43(10):6598-6626
We consider the sliding mode control (SMC) problem for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation perturbed by a maximal monotone nonlinearity. We prove existence and regularity of strong solutions and, under further assumptions, a uniqueness result. Then, we show that the chosen SMC law forces the system to reach within finite time a sliding manifold that we chose in order that the tumor phase remains constant in time. 相似文献
5.
《Stochastic Processes and their Applications》2020,130(1):394-430
We consider an affine process which is only observed up to an additive white noise, and we ask for the law of , for some , conditional on all observations up to time . This is a general, possibly high dimensional filtering problem which is not even locally approximately Gaussian, whence essentially only particle filtering methods remain as solution techniques. In this work we present an efficient numerical solution by introducing an approximate filter for which conditional characteristic functions can be calculated by solving a system of generalized Riccati differential equations depending on the observation and the process characteristics of . The quality of the approximation can be controlled by easily observable quantities in terms of a macro location of the signal in state space. Asymptotic techniques as well as maximization techniques can be directly applied to the solutions of the Riccati equations leading to novel very tractable filtering formulas. The efficiency of the method is illustrated with numerical experiments for Cox–Ingersoll–Ross and Wishart processes, for which Gaussian approximations usually fail. 相似文献
6.
《Physics letters. A》2020,384(26):126642
A novel method to make Lagrangians Galilean invariant is developed. The method, based on null Lagrangians and their gauge functions, is used to demonstrate the Galilean invariance of the Lagrangian for Newton's law of inertia. It is suggested that this new solution of an old physics problem may have implications and potential applications to all gauge-based theories of physics. 相似文献
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开放式、综合性量测实验的设计与应用,在巩固基础理论知识的同时,能够有效培养学生的动手实践能力、数据处理及分析能力,一定程度代表着大学物理实验课程的教学模式改革方向。以PN结物理特性的测量实验为例,基于通用型仪器与元器件的积木式组合,设计出简单、适用的实验电路;t=17.95℃时所采集的原始实验数据经三种模式回归分析,比较验证了PN结扩散电流与电压间遵循的玻尔兹曼分布律;计算出的玻尔兹曼常数与FD-PN-4测定仪的量测值相比,其结果说明了开放式测量实验方法的有效性。 相似文献
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Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn–Hilliard equations. However, often Stokes or Brinkman flows are more appropriate flow models. We introduce and mathematically analyse a new Cahn–Hilliard–Brinkman model for tumour growth allowing for chemotaxis. Outflow boundary conditions are considered in order not to influence tumour growth by artificial boundary conditions. Existence of global-in-time weak solutions is shown in a very general setting. 相似文献
9.
为了提高三阶WENO-Z格式在极值点处的计算精度,通过理论推导给出三阶WENO格式满足收敛精度的充分条件。采用泰勒级数展开的方式,推导给出所构造格式非线性权重的计算公式,并综合权衡计算精度和计算稳定性确定所构造格式的参数。通过两个典型的精度测试,验证了改进格式在光滑流场极值点区域逼近三阶精度。进一步选用激波与熵波相互作用和Richtmyer-Meshkov不稳定性等经典算例,证实了本文提出的改进格式WENO-PZ3相较其他格式(WENO-JS3和WENO-Z3)不仅具有较高的精度,而且降低了格式的耗散,提高了对流场结构的分辨率。 相似文献
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