On the simultaneous determination of the zeros of an analytic function inside a simple smooth closed contour in the complex plane

A family of higher-order iterative methods for the simultaneous determination of all simple or multiple zeros of an analytic function (inside a simple smooth closed contour) is obtained using earlier results of the author. With the help of circular arithmetic, the interval variant of this family is proposed. Many parallel iterative methods of the literature are special cases of this family.     

Characterization of the skew-normal distribution

Two characterization results for the skew-normal distribution based on quadratic statistics have been obtained. The results specialize to known characterizations of the standard normal distribution and generalize to the characterizations of members of a larger family of distributions. Results on the decomposition of the family of distributions of random variables whose square is distributed as χ ₁ ² are obtained. Research supported by a non-service fellowship at Bowling Green State University.     

超凸度量空间中非扩张可交换映象族的几乎不动点

获得了关于超凸度量空间中非扩张可交换映象族不动点存在性的更一般结果.证明了可数个非扩张可交换映象的公共ε-几乎不动点集的超凸性,并在一定条件下证明了任意个非扩张可交换映象的公共ε-几乎不动点集的超凸性.还讨论了Baillon的两个重要结果间的等价关系.     

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．     

Robust statistical inference based on the C-divergence family

This paper describes a family of divergences, named herein as the C-divergence family, which is a generalized version of the power divergence family and also includes the density power divergence family as a particular member of this class. We explore the connection of this family with other divergence families and establish several characteristics of the corresponding minimum distance estimator including its asymptotic distribution under both discrete and continuous models; we also explore the use of the C-divergence family in parametric tests of hypothesis. We study the influence function of these minimum distance estimators, in both the first and second order, and indicate the possible limitations of the first-order influence function in this case. We also briefly study the breakdown results of the corresponding estimators. Some simulation results and real data examples demonstrate the small sample efficiency and robustness properties of the estimators.

     

The spectrum of the Burnside Tambara functor of a cyclic group

We derive a family of prime ideals of the Burnside Tambara functor for a finite group G. In the case of cyclic groups, this family comprises the entire prime spectrum. We include some partial results towards the same result for a larger class of groups.     

Fiducial inference in the pivotal family of distributions

In this paper a family, called the pivotal family, of distributions is considered. A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is given. The method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.     

The hybrid projection algorithm for finding the common fixed points of nonexpansive mappings and the zeroes of maximal monotone operators in Banach spaces

The proposal of this article is to construct a new modified block by using the hybrid projection method and prove the strong convergence theorem for this method, which include the fixed point set of an infinite family of weak relatively nonexpansive mappings and zeroes of a finite family of maximal monotone operators in a uniformly smooth and strictly convex Banach space with the Kadec–Klee property. The results presented in this article improve and generalize some well-known results in the literature.     

On the Helly Number for Line Transversals to Parallel Triangles

We prove two results about the problem of finding the Helly number for line transversals to a family of parallel triangles in the plane: (1) If each three triangles of a family of parallel right triangles are intersected by an ascending (or a descending) line, then there is an ascending (or a descending) line that intersects all     

Oscillations near a separatrix in the duffing equation

A small periodic perturbation results in a complicated dynamics near separatrices and saddle points. A two-parameter family of asymptotic solutions staying near separatrices for a long time is constructed. Solutions from this family depend nonsmoothly on the perturbation parameter. An example is given in which the values of the perturbation parameter for this family of solutions are determined by a set with structure of the type of the Cantor set.     

On the Bartle-Graves theorem

The Bartle-Graves theorem extends the Banach open mapping principle to a family of linear and bounded mappings, thus showing that surjectivity of each member of the family is equivalent to the openness of the whole family. In this paper we place this theorem in the perspective of recent concepts and results, and present a general Bartle-Graves theorem for set-valued mappings. As applications, we obtain versions of this theorem for mappings defined by systems of inequalities, and for monotone variational inequalities.

     

Hilbert空间中非扩张映象的最近的公共不动点的逼近问题

本文在Hilbert空间的框架下,研究无限族非扩张映象T_1,T_2,…的迭代程序x_n+1=λ_(n+1)y+(1-λ_(n+1))T_(n+1)x_n的收敛性问题．在适当的条件下,证明了该迭代序列收敛于这一非扩张映象族的最近的公共不动点．其结果改进和推广了引文中相应的结果．     

Polycondenser’s capacity and the module of a family of vector measures

The paper considers the capacity of a polycondenser and the module of a family of measures associated with the class of curves connecting the polycondenser’s plates. It is proved that these quantities are equal. Also a relation between the polycondenser’s capacity and the module of a family of vector measures associated with the class of functions admissible for the polycondenser’s capacity is established. The results obtained generalize the earlier results by M. Ohtsuka and H. Aikawa.     

Some families of generating functions for the extended Srivastava polynomials

Almost four decades ago, H.M. Srivastava considered a general family of univariate polynomials, the Srivastava polynomials, and initiated a systematic investigation for this family [10]. In 2001, B. González, J. Matera and H.M. Srivastava extended the Srivastava polynomials by inserting one more parameter [4]. In this study we obtain a family of linear generating functions for these extended polynomials. Some illustrative results including Jacobi, Laguerre and Bessel polynomials are also presented. Furthermore, mixed multilateral and multilinear generating functions are derived for these polynomials.     

On the periodic points of a two-parameter family of maps of the plane

We study the dynamics of a two-parameter family of noninvertible maps of the plane, derived from a model in population dynamics. We prove that, as one parameter varies with the other held fixed, the nonwandering set changes from the empty set to an unstable Cantor set on which the map is topologically equivalent to the shift endomorphism on two symbols. With the help of some numerical work, we trace the genealogies of the periodic points of the family of period 5, and describe their stability types and bifurcations. Among our results we find that the family has a fixed point which undergoes fold, flip and Hopf bifurcations, and that certain families of period five points are interconnected through a codimension-two cusp bifurcation.     

Extensions of the conjugate prior through the Kullback-Leibler separators

The conjugate prior for the exponential family, referred to also as the natural conjugate prior, is represented in terms of the Kullback-Leibler separator. This representation permits us to extend the conjugate prior to that for a general family of sampling distributions. Further, by replacing the Kullback-Leibler separator with its dual form, we define another form of a prior, which will be called the mean conjugate prior. Various results on duality between the two conjugate priors are shown. Implications of this approach include richer families of prior distributions induced by a sampling distribution and the empirical Bayes estimation of a high-dimensional mean parameter.     

On the family of meromorphic functions whose derivatives omit a holomorphic function

In this paper,we continue to study the normality of a family of meromorphic functions without simple zeros and simple poles such that their derivatives omit a given holomorphic function.Such a family in general is not normal at the zeros of the omitted function.Our main result is the characterization of the non-normal sequences,and hence some known results are its corollaries.     

New results on the invertibility of the finite interval convolution operator

Conditions for the invertibility and explicit formulas for the inverse of the convolution operator on a finite interval are obtained making use of solutions of corona problems. Using these results, a family of classes of functions is defined for which the study of invertibility can be carried through. An example of one class of this family is presented and a smaller class, for which the calculations are simpler, is more thoroughly studied.Work sponsored by F.C.T. (Portugal) under Project Praxis XXi/2/2.1/MAT/441/94     

Parametric Disjunctive Programming: One-Sided Differentiability of the Value Function

We consider a countable family of one-parameter convex programs and give sufficient conditions for the one-sided differentiability of its optimal value function. The analysis is based on the Borwein dual problem for a family of convex programs (a convex disjunctive program). We give conditions that assure stability of the situation of perfect duality in the Borwein theory.For the reader's convenience, we start with a review of duality results for families of convex programs. A parametric family of dual problems is introduced that contains the dual problems of Balas and Borwein as special cases. In addition, a vector optimization problem is defined as a dual problem. This generalizes a result by Helbig about families of linear programs.     

紧图的两个结果及其应用

双随机矩阵有许多重要的应用, 紧图族可以看作是组合矩阵论中关于双随机矩阵的著名的Birkhoff定理的拓广,具有重要的研究价值． 确定一个图是否紧图是个困难的问题,目前已知的紧图族尚且不多.给出了两个重要结果：任意紧图与任意多个孤立点的不交并是紧图;任意紧图的每一个顶点上各增加一条悬挂边的图是紧图． 利用这两个结果,从已知紧图可构造出无穷多个紧图族．