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871.
Fei Teng Zhengdong Luo Jing Yang 《Mathematical Methods in the Applied Sciences》2019,42(12):4273-4291
In this article, we primarily focuses to study the order‐reduction for the classical natural boundary element (NBE) method for the two‐dimensional (2D) hyperbolic equation in unbounded domain. To this end, we first build a semi‐discretized format about time for the hyperbolic equation and discuss the existence, stability, and convergence of the time semi‐discretized solutions. We then establish the classical fully discretized NBE format from the time semi‐discretized one and analyze the existence, stability, and convergence of the classical NBE solutions. Next, using proper orthogonal decomposition method, we build a reduced‐order extrapolated NBE (ROENBE) format containing very few unknowns but having adequately high accuracy, and we also discuss the existence, stability, and convergence of the ROENBE solutions. Finally, we use some numerical examples to show that the ROENBE method is far superior to the classical NBE one. It shows that the ROENBE method is reliable and effective for solving the 2D hyperbolic equation with the unbounded domain. 相似文献
872.
Qing MENG 《数学年刊B辑(英文版)》2019,40(3):429-438
In this paper, the author first introduces the concept of
generalized algebraic cone metric spaces and some elementary results
concerning generalized algebraic cone metric spaces. Next, by using
these results, some new fixed point theorems on generalized
(complete) algebraic cone metric spaces are proved and an example is
given. As a consequence, the main results generalize the
corresponding results in complete algebraic cone metric spaces and
generalized complete metric spaces. 相似文献
873.
Philip A. Ernst Wilfrid S. Kendall Gareth O. Roberts Jeffrey S. Rosenthal 《Stochastic Processes and their Applications》2019,129(2):355-380
Classical coupling constructions arrange for copies of the same Markov process started at two different initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two different Markov (or other stochastic) processes to remain equal for as long as possible, when started in the same state. We refer to this “un-coupling” or “maximal agreement” construction as MEXIT, standing for “maximal exit”. After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of MEXIT for Brownian motions with two different constant drifts. 相似文献
874.
In this article, we introduce the algebra of block-symmetric cylinders and we show that symmetric cylindrical constructions on base-graphs admitting commutative decompositions behave as generalized tensor products. We compute the characteristic polynomial of such symmetric cylindrical constructions in terms of the spectra of the base-graph and the cylinders in a general setting. This gives rise to a simultaneous generalization of some well-known results on the spectra of a variety of graph amalgams, as various graph products, graph subdivisions and generalized Petersen graph constructions. While our main result introduces a connection between spectral graph theory and commutative decompositions of graphs, we focus on commutative cyclic decompositions of complete graphs and tree-cylinders along with a subtle group labeling of trees to introduce a class of highly symmetric graphs containing the Petersen and the Coxeter graphs. Also, using techniques based on recursive polynomials we compute the characteristic polynomials of these highly symmetric graphs as an application of our main result. 相似文献
875.
《Journal of Pure and Applied Algebra》2019,223(11):4888-4900
We construct families of prime ideals in polynomial rings for which the number of associated primes of the second power (or higher powers) is exponential in the number of variables in the ring. 相似文献
876.
提高数据的完备与真实性是水资源监控能力建设的关键。针对国家水资源监控能力建设项目实施以来其监测数据呈现出的异常特征,按照“先粗筛后精选”逻辑,并考虑取用水季节性周期波动的特点,提出采用拉依达准则-模态分解-傅里叶残差修正的水监测数据异常值识别方法,并根据粒子群优化最小二乘支持向量机模型实现对异常数据的重构恢复。通过对企业取用水数据的实例分析,结果表明分段式拉依达准则在其监测异常数据的粗筛中具有较好的适用性,利用傅里叶修正集合模态分解的监测数据序列可取得更佳的拟合效果,从而达到异常数据精选的目的;而粒子群优化最小二乘支持向量机模型对异常数据重构恢复的可信度高于普通最小二乘支持向量机及传统曲线拟合数据重构方法,即该类取用水监测异常数据重构方法可有助于进一步推进其监测数据对实际水资源状态的客观反映。 相似文献
877.
878.
Fernando De Tern Bruno Iannazzo Federico Poloni Leonardo Robol 《Numerical Linear Algebra with Applications》2019,26(5)
We consider the uniqueness of solution (i.e., nonsingularity) of systems of r generalized Sylvester and ?‐Sylvester equations with n×n coefficients. After several reductions, we show that it is sufficient to analyze periodic systems having, at most, one generalized ?‐Sylvester equation. We provide characterizations for the nonsingularity in terms of spectral properties of either matrix pencils or formal matrix products, both constructed from the coefficients of the system. The proposed approach uses the periodic Schur decomposition and leads to a backward stable O(n3r) algorithm for computing the (unique) solution. 相似文献
879.
880.
针对具有不确定参数结构,提出时域不确定性传播和量化的多项式维数分解法,确定了结构响应统计量的演变过程.首先,采用参数概率模型来描述结构参数的不确定性,建立结构动力学方程,将结构响应表达为不确定参数的函数;进一步,将所关心的结构响应采用成员函数进行维数分解,并利用正交多项式基底对成员函数进行Fourier展开;最后,应用降维积分方法进行展开系数的求解,给出了响应均值和标准差的计算表达式.在数值算例中,将本文方法与蒙特卡洛方法进行对比,结果表明所建立方法具有较高的求解效率和计算精度. 相似文献