Strong Convergence of an Iterative Scheme by a New Type of Projection Method for a Family of Quasinonexpansive Mappings

We deal with a common fixed point problem for a family of quasinonexpansive mappings defined on a Hilbert space with a certain closedness assumption and obtain strongly convergent iterative sequences to a solution to this problem. We propose a new type of iterative scheme for this problem. A feature of this scheme is that we do not use any projections, which in general creates some difficulties in practical calculation of the iterative sequence. We also prove a strong convergence theorem by the shrinking projection method for a family of such mappings. These results can be applied to common zero point problems for families of monotone operators.     

Note – Uncrossing a Family of Set-Pairs

Frank and Jordán [1] proved an important min-max result on covering a crossing family of set-pairs. As an application, among others they can solve the unweighted node-connectivity augmentation problem for directed graphs in polynomial time. In this paper, we show how to solve the dual packing problem in polynomial time. To decompose a fractional dual optimum as a convex combination of integer vertices, besides the ellipsoid method, we use a polynomial-time algorithm for uncrossing a family of set-pairs. Our main result is this uncrossing algorithm. Received November 9, 1998 / Revised October 18, 1999     

Group of Self-Equivalences of Sum Object

In general category, the group of self-equivalences of sum object can decompose as the product of its two subgroups under certain conditions and also several split short exact sequences are obtained. Subsequently, we apply the above results to the category of space under a space and get some results which are dual to those in fibrewise category.     

When Is a Sum of Partial Reflections Equal to a Scalar Operator?

We describe the set of values of the parameter for which there exists a Hilbert space H and n partial reflections A ₁,...,A _n (self-adjoint operators such that A _k ³ =A_k or, which is the same, self-adjoint operators whose spectra belong to the set {-1,0,1}) whose sum is equal to the scalar operator I _H .     

Lie Bialgebras of a Family of Lie Algebras of Block Type

Lie bialgebra structures on a family of Lie algebras of Block type are shown to be triangular coboundary.     

Gauss Sum of Index Four

Let p be a prime number, q=p^f and m|q-1. For a multiplicative character x of Fq with order m, the Gauss sum G(x) over Fq is defined by     

A New Bound for the Fejér-Jackson Sum

We establish a new positive functional estimate for the Fejér-Jackson sum Sn() = k=1n k-1 sin k. This result enables us to give a simple proof of a result of Askey and Steinig on a monotonic sine sum associated with the sum Sn().     

On a Conjecture of Drasin Concerning Functions With Maximum Deficiency Sum

Let f be a meromorphic function of finite order in the plane. If its Nevanlinnadeficiency sum is 2,then we say that f has maximum deficiency sum. Drasin con-jectured that if f has maximum deficiency sum and the infinity is not its Nevanlinna'sdeficient value, then zero is the only Nevaulinna's deficient value of f' with defi-ciency 1. Yang Lo gave a positive answer of this conjecture by proving that under theabove assumption, zero is the only Nevanlinna's deficient value of f(h) with,deficie-ncy 2/(1 + k) for k = 1,2,…. Now, omitting the condition δ(∞,f) = 0, we prove     

When is a Sum of Annihilator Ideals an Annihilator Ideal?

We call a ring R a right SA-ring if for any ideals I and J of R there is an ideal K of R such that r(I) + r(J) = r(K). This class of rings is exactly the class of rings for which the lattice of right annihilator ideals is a sublattice of the lattice of ideals. The class of right SA-rings includes all quasi-Baer (hence all Baer) rings and all right IN-rings (hence all right selfinjective rings). This class is closed under direct products, full and upper triangular matrix rings, certain polynomial rings, and two-sided rings of quotients. The right SA-ring property is a Morita invariant. For a semiprime ring R, it is shown that R is a right SA-ring if and only if R is a quasi-Baer ring if and only if r(I) + r(J) = r(I ∩ J) for all ideals I and J of R if and only if Spec(R) is extremally disconnected. Examples are provided to illustrate and delimit our results.     

Turán Number of the Family Consisting of a Blow-up of a Cycle and a Blow-up of a Star

Let F={H₁,...,H_k}(k> 1) be a family of graphs.The Turán number of the family F is the maximum number of edges in an n-vertex {H₁,...,H_k)-free graph,denoted by ex(n,F) or ex(n,{H₁,H₂,...,H_k}).The blow-up of a graph H is the graph obtained from H by replacing each edge in H by a clique of the same size where the new vertices of the cliques are all different.In this paper we determine the Turán number of the family cons...     

Extending Theorems of Göllnitz,A New Family of Partition Identities

A new family of partition identities is given which include as special cases two theorems of Göllnitz. We show, also, a relation between our result and a theorem given by Sylvester.     

Stochastic Processes Associated with a Sum of the Lévy Laplacians

Abstract

In this paper, we give a stochastic expression of a semigroup generated by a sum of the Lévy Laplacians acting on a class of S-transforms of white noise distributions in terms of an infinite sequence of independent Brownian motions.     

An Explicit Computation of a Family of Trivializing Étale Covers

We explicitly compute étale covers of the smooth Fermat curves Y _p+1 = Proj k[u, v, w]/(u ^p+1 + v ^p+1 ? w ^p+1) which trivialize the vector bundles Syz(u ², v ², w ²)(3), where k is a field of characteristic p ≥ 3.     

Nonexistence of UMVUE for the Parameter of a Two-sided Trancated Family

§1 The main result The classical Rao-Blackwell-Lehmann-Scheffe theorm guarantees the existence of uniform minimum variance unbiased estimate (UMVUE) for any estimable parameterfunctions, in case there is a sufficient and complete statistic. The situation becomes complicated when such statistics do not exist. For example, UMVUE does not exist for a function g of the parameter of the family     

The Degree Theory of a New Operator

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Spectra of Tensor Triangulated Categories over a Category Algebra—A New Approach

Applied Categorical Structures - We provide a new method to compute the Balmer spectra of the bounded derived category and the singularity category of the category algebra of a finite EI category...     

On a New Approach to the Problem of Distribution of Zeros of Hermite—Padé Polynomials for a Nikishin System

A new approach to the problem of the zero distribution of type I Hermite—Padé polynomials for a pair of functions f₁, f₂ forming a Nikishin system is discussed. Unlike the traditional vector approach, we give an answer in terms of a scalar equilibrium problem with harmonic external field which is posed on a two-sheeted Riemann surface.     

Proof of the Volume Conjecture for Whitehead Doubles of a Family of Torus Knots

A technique to compute the colored Jones polynomials of satellite knots,illus- trated by the Whitehead doubles of knots,is presented.Then the author proves the volume conjecture for Whitehead doubles of a family of torus knots and shows some interesting observations.     

Comparison of Certain Complexes of Modules of Generalized Fractions and Čech Complexes

We establish an explicit quasi-isomorphism of complexes, which is homogeneous in graded situation, from a given ?ech complex to a certain complex of modules of generalized fractions. This leads to characterizations of local cohomology and ideal transforms of a module. Also, in this note, we study the behavior of generalized fraction formation along exact sequences and vanishing of modules of generalized fractions in certain cases.