The product of affine orthogonal projections

In the case of a finite number of subspaces in a given Hilbert space, by a theorem of J. von Neumann, the iteration of the product of projectors is always convergent. In a finite dimensional Hilbert space, this theorem has been generalized for affine subspaces. In this paper we construct an example which shows that this result does not hold in the infinite dimensional case.     

求解多孔介质中可压缩混溶驱动问题的一类满足极大值原理的数值方法

多孔介质中可压缩混溶驱动问题是用非线性抛物型方程组来描述的．用Ｐｏｔｅｍｐａ格式求其数值解．证明了构造的求解方法满足极大值原理，从而可以保证饱和度的数值解在［０，１］范围内这一物理特性，同时还得到了解的收敛性．     

A partial order for the set of meanders

In this paper, we present a new approach for studying meanders in terms of noncrossing partitions. We show how this approach leads to a natural partial order on the set of meanders. In particular, meanders form a graded poset with regard to this partial order.     

图的完全正则自同态

作为图的代数分析的一部分，对图的自同态幺半群的研究近年来有一定的进展（参见［３］及［４］）。这类研究的主要目的在于将半群理论应用于图论。文献［５］研究了图的正则自同态及其逆。在此基础上本文进一步描述了图的完全正则自同态的组合特征；同时对含有完全正则自同态ｆ的极大子群，文中也明确给出了其单位元素及ｆ的逆     

Finite capacity assembly-like queues

In assembly lines, service involves assembling units coming from more than one source. In queue terminology, we may consider this situation as one in which service is rendered only to groups of customers — one from each class. In this paper we give procedures to determine response time characteristics of such a system under Markovian assumptions when a finite capacity restriction is imposed. This restriction is imposed to reflect reality as well as to make analysis tractable. In the course of this study, we also give a recursive technique to determine the distribution of the time taken for a specific number of departures in a Poisson queue from an arbitrary initial state. We demonstrate that this distribution is related to the response time distribution of the assembly-like queue. We believe that this procedure will also be of independent interest.     

Addendum to “Distribution of points on the circle” [J. Number Theory 127 (1) (2007) 127-135]

In an earlier paper we gave a result relating the value of an exponential sum with the distribution of summands in the arcs of the unit circle in the complex plane. In a marginal case, this result is superseded by a result of Lev. In this addendum we use an idea of Lev to give a new proof of our earlier result and to improve upon the marginal result.     

Finding GM-estimators with global optimization techniques

In this note we address the problem of finding the GM-estimator for the location parameter of a univariate random variable. When this problem is non-convex but d.c. one can use a standard covering method, which, in the one-dimensional case has a simple form. In this paper we exploit the structure of the problem in order to obtain d.c. decompositions with certain optimality properties in the application of the algorithm. Numerical results show that this general-purpose algorithm outperforms previous ad-hoc methods for this problem.     

Linear recurrent subsequences of generalized meta-Fibonacci sequences

In a recent paper, Frank Ruskey asked whether every linear recurrent sequence can occur in some solution of a meta-Fibonacci sequence. In this paper, we consider the natural generalization of meta-Fibonacci recurrences to more than two terms. In this context, we show, using an explicit construction, that any sequence satisfying a linear recurrence with positive coefficients occurs as an evenly-spaced subsequence in some generalized meta-Fibonacci sequence.     

Complexity of 3-edge-coloring in the class of cubic graphs with a polyhedral embedding in an orientable surface

A polyhedral embedding in a surface is one in which any two faces have boundaries that are either disjoint or simply connected. In a cubic (3-regular) graph this is equivalent to the dual being a simple graph. In 1968, Grünbaum conjectured that every cubic graph with a polyhedral embedding in an orientable surface is 3-edge-colorable. For the sphere, this is equivalent to the Four-Color Theorem, but we have disproved the conjecture in the general form. In this paper we extend this result and show that if we restrict our attention to a class of cubic graphs with a polyhedral embedding in an orientable surface, then the computational complexity of the 3-edge-coloring problem and its approximation does not improve.     

A Riemannian Invariant and its Applications to Submanifold Theory

In a previous paper the author has defined a Riemannian invariant δ for Riemannian manifolds and has obtained some of its applications. In this article, we investigate this invariant in more details and provide further applications of this invariant to submanifold theory.     

一类条件变分问题解的存在性

本文对一类有广泛应用价值的不规则的条件泛函极值问题的解的存在性及解的解析表示式进行了深入系统的讨论,得到了一系列在理论及应用上颇有价值的结果.对该类问题最优解的存在性的证明填补了这方面的空白.     

Flatness of CR submanifolds in a sphere

In Euclidean geometry, for a real submanifold M in E n+a , M is a piece of E n if and only if its second fundamental form is identically zero. In projective geometry, for a complex submanifold M in CP n+a , M is a piece of CP n if and only if its projective second fundamental form is identically zero. In CR geometry, we prove the CR analogue of this fact in this paper.     

Relationships between upper exhausters and the basic subdifferential in variational analysis

In this paper we establish a relationship between the basic subdifferential and upper exhausters of positively homogeneous and polyhedral functions. In the case of a finite exhauster this relationship is represented in a form of an equality, and in the case of a Lipschitz function an inclusion formula is obtained.     

Coven和Hedlund一个定理的较简单的证明

Coven和Hedlund在[1]中证明：若区间映射的周期集为有限集,则它的每一个非游荡点都是周期点。本给出了这一定理的一个较简单的证明。此外,我们还用“同伦”的方法简化了该的一个关键引理的证明。     

Prüfer Conditions and the Total Quotient Ring

In this article, we consider two of the five well-studied extensions of the Prüfer domain notion to arbitrary commutative rings. In particular, we consider a class of rings that lies properly between Gaussian and Prüfer rings. We give a characterization of this property in terms of the total quotient ring and show that this property behaves nicely in conductor squares.     

Some properties of functional algebras from the point of view of orthogonal measures

In this article we establish a connection between some properties of a functional algebra and the space of measures orthogonal to the algebra. In particular, certain results in [1] follow from the results in this work.     

A primal-dual interior-point algorithm for symmetric optimization based on a new method for finding search directions

We introduce an interior-point method for symmetric optimization based on a new method for determining search directions. In order to accomplish this, we use a new equivalent algebraic transformation on the centring equation of the system which characterizes the central path. In this way, we obtain a new class of directions. We analyse a special case of this class, which leads to the new interior-point algorithm mentioned before. Another way to find the search directions is using barriers derived from kernel functions. We show that in our case the corresponding direction cannot be deduced from a usual kernel function. In spite of this fact, we prove the polynomial complexity of the proposed algorithm.     

有限族非扩张映象的公共不动点的具误差和具扰动映射的迭代程序

本文在实一致凸和q-一致光滑Banach空间中研究了一类新的有限族非扩张映象的公共不动点的具误差和具扰动映射的显式迭代程序并且得到了一些收敛性定理.特别地,获得了该显式迭代程序强收敛性的充要条件.本文所得到结果推广了文[1]中的相应结果.     

不可约圈与路之并补图的色唯一性

讨论了形如ｋＣＲＵｒＰＲ的一类图的补图的色性．在一定的条件下证明了这类图是色唯一的．本文推广了文［１］的结果．     

Global BV solution for a non-local coupled system modeling the dynamics of dislocation densities

In this paper, we study a non-local coupled system arising in the modeling of the dynamics of dislocation densities in crystals. For this system, the global existence and uniqueness are available only for continuous viscosity solutions. In the present paper, we investigate the global time existence of this system by considering BV initial data. Based on a fundamental uniform BV estimate and the finite speed of propagation property of this system, we show, in a particular setting, the global existence of discontinuous viscosity solutions of this problem.