On the commutator of the Marcinkiewicz integral

boundedness is considered for the commutator of higher-dimensional Marcinkiewicz integral. Some conditions implying the and the boundedness for the commutator of the Marcinkiewicz integral are obtained.     

On the Ulam stability of Jensen and Jensen type mappings on restricted domains

In 1941 Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 Bourgin was the second author to treat this problem for additive mappings. In 1982-1998 Rassias established the Hyers-Ulam stability of linear and nonlinear mappings. In 1983 Skof was the first author to solve the same problem on a restricted domain. In 1998 Jung investigated the Hyers-Ulam stability of more general mappings on restricted domains. In this paper we introduce additive mappings of two forms: of “Jensen” and “Jensen type,” and achieve the Ulam stability of these mappings on restricted domains. Finally, we apply our results to the asymptotic behavior of the functional equations of these types.     

An example in holomorphic fixed point theory

If is the open unit ball in the Cartesian product furnished with the -norm , where and , then a holomorphic self-mapping of has a fixed point if and only if for some

     

Speeding up the FMMR perfect sampling algorithm: A case study revisited

In a previous paper by the second author, two Markov chain Monte Carlo perfect sampling algorithms—one called coupling from the past (CFTP) and the other (FMMR) based on rejection sampling—are compared using as a case study the move‐to‐front (MTF) self‐organizing list chain. Here we revisit that case study and, in particular, exploit the dependence of FMMR on the user‐chosen initial state. We give a stochastic monotonicity result for the running time of FMMR applied to MTF and thus identify the initial state that gives the stochastically smallest running time; by contrast, the initial state used in the previous study gives the stochastically largest running time. By changing from worst choice to best choice of initial state we achieve remarkable speedup of FMMR for MTF; for example, we reduce the running time (as measured in Markov chain steps) from exponential in the length n of the list nearly down to n when the items in the list are requested according to a geometric distribution. For this same example, the running time for CFTP grows exponentially in n. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2003     

Nuclearity of a nonnegative definite integral kernel on a separable metric space

The aim of this paper is to characterize the nuclearity of an integral operator, defined by a continuous non-negative definite square integrable kernel on a separable metric space, in terms of the integrability of the trace of the kernel function. Nuclearity here plays a role forU-statistics.     

Spatio-temporal symmetries and bifurcations via bi-orthogonal decompositions

Summary A tool for analyzing spatio-temporal complex physical phenomena was recently proposed by the authors, Aubry et al. [5]. This tool consists in decomposing a spatially and temporally evolving signal into orthogonal temporal modes (temporal “structures”) and orthogonal spatial modes (spatial “structures”) which are coupled. This allows the introduction of a temporal configuration space and a spatial one which are related to each other by an isomorphism. In this paper, we show how such a tool can be used to analyze space-time bifurcations, that is, qualitative changes in both space and time as a parameter varies. The Hopf bifurcation and various spatio-temporal symmetry related bifurcations, such as bifurcations to traveling waves, are studied in detail. In particular, it is shown that symmetry-breaking bifurcations can be detected by analyzing the temporal and spatial eigenspaces of the decomposition which then lose their degeneracy, namely their invariance under the symmetry. Furthermore, we show how an extension of the theory to “quasi-symmetries” permits the treatment of nondegenerate signals and leads to an exponentially decreasing law of the energy spectrum. Examples extracted from numerically obtained solutions of the Kuramoto-Sivashinsky equation, a coupled map lattice, and fully developed turbulence are given to illustrate the theory.     

Unconstrained and constrained global optimization of polynomial functions in one variable

In Floudas and Visweswaran (1990), a new global optimization algorithm (GOP) was proposed for solving constrained nonconvex problems involving quadratic and polynomial functions in the objective function and/or constraints. In this paper, the application of this algorithm to the special case of polynomial functions of one variable is discussed. The special nature of polynomial functions enables considerable simplification of the GOP algorithm. The primal problem is shown to reduce to a simple function evaluation, while the relaxed dual problem is equivalent to the simultaneous solution of two linear equations in two variables. In addition, the one-to-one correspondence between the x and y variables in the problem enables the iterative improvement of the bounds used in the relaxed dual problem. The simplified approach is illustrated through a simple example that shows the significant improvement in the underestimating function obtained from the application of the modified algorithm. The application of the algorithm to several unconstrained and constrained polynomial function problems is demonstrated.     

奇摄动Volterra型积分微分方程Robin问题

本文利用上、下解证明了Volterra型积分微分方程解的存在性。然后，应用所获得的微分不等式理论，在适当的假设下，通过构造特殊的上、下解函数，证明Volterra型 奇摄动积分微分方程解的存在性，并给出一致有效的解的渐近估计。     

Fuzzy集的基数

关于Fuzzy集的基数，[1]中曾对有限支集的Fuzzy集以及极苛刻条件下的无限Fuzzy集给出过一种定义。但是，正如本文将要指出的那样，该定义是不合理的。本文将从研究Fuzzy映射入手，给出Fuzzy集基数的一般性定义。基于这一定义，不但得到有关基数的大部分结论，而且有其自身的特殊性。     

复杂应力构件弹性失效疲劳失效新判据——动态静态八面体应力强度理论

本文,在研究现代和经典强度理论的基础之上,提出了一个在复杂应力下弹性失效与疲劳失效的总准则,即动态静态八面体应力强度理论,同时建立了并分析了一个独立的比较完整的理论体系,给出了36种材料广义失效系数,和一点复杂应力的11个状态的计算理论,导出了广义允许强度算子方程.给出了总准则能应用到静态、动态的计算方法,通过8个工程实例的计算,表明该方法有很高的精度,因而笔者建议广泛地应用到工程.