A Set of Almost Automorphic Functions and Applications

For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.

Pseudo Almost Periodic Solutions of Nonlinear Hyperbolic Equations with Piecewise Constant Argument

In this paper, we investigate the pseudo almost periodicity of the unique bounded solution for a nonlinear hyperbolic equation with piecewise constant argument. The equation under consideration is a mathematical model for the dynamics of gas absorption,

Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods

Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.

ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS

This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.

ALMOST PERIODICITY AND EQUICONTINUITY OF THE TOPOLOGICAL TRANSFORMATION GROUP

In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.

TAUBERIAN THEOREMS FOR WEAK ALMOST CONVERGENT FUNCTIONS

The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R2＋ .

ON ALMOST PRECOVERS AND ALMOST PREENVELOPES

Let C be a class of R-modules closed under isomorphisms and finite direct sums. It is first shown that the finite direct sum of almost C-precovers is an almost C-precover and the direct sum of an almost C-cover and a weak C-cover is a weak C-cover. Then the notion of almost C-preenvelopes is introduced and studied.

Inverse limits of hereditarily almost expandable class

In this paper, the hereditarily almost expandability of inverse limits is investigated, with two results obtained. Let X be the inverse limit space of an inverse system （Xα, π^αβ, ∧}. （1） Suppose X is hereditarily κ-metacompact, if each Xα is hereditarily pointwise collectionwise normal （almost θ-expandable, almost discrete θ-expandable）, then so is X; （2） Suppose X is hereditarily κ-σ-metacompact, if each Xα is hereditarily almost σ-expandable （almost discrete σ-expandable = σ-pointwise collectionwise normal）, then so is X.

Almost Fuzzy Compactness in L-fuzzy Topological Spaces

In this paper, the notion of almost fuzzy compactness is dened in L-fuzzy topological spaces by means of inequality, where L is a completely distributiveDeMorgan algebra. Its properties are discussed and many characterizations of it arepresented.

Note on Almost Hermitian Manifolds

We give a necessary and sufficient condition for an almost Hermitian manifold to be a Kahler manifold. By making use of this condition, we give a new proof of Goldberg＇s theorem.

Existence and global attractivity of unique positive almost periodic solution for a model of hematopoiesis

Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and global attractivity of almost periodic solutions of almost periodic system.

OD-CHARACTERIZATION OF ALMOST SIMPLE GROUPS RELATED TO U_6(2)

Let G be a finite group and π（G） = {pl,p2,…… ,pk} be the set of the primes dividing the order of G. We define its prime graph F（G） as follows. The vertex set of this graph is 7r（G）, and two distinct vertices p, q are joined by an edge if and only if pq ∈ πe（G）. In this case, we write p - q. For p ∈π（G）, put deg（p） ：= ｜{q ∈ π（G）｜p - q}｜, which is called the degree of p. We also define D（G） ：= （deg（p1）, deg（p2）,..., deg（pk））, where pl 〈 p2 〈 -……〈 pk, which is called the degree pattern of G. We say a group G is k-fold OD-characterizable if there exist exactly k non-isomorphic finite groups with the same order and degree pattern as G. Specially, a l-fold OD-characterizable group is simply called an OD-characterizable group. Let L ：= U6（2）. In this article, we classify all finite groups with the same order and degree pattern as an almost simple groups related to L. In fact, we prove that L and L.2 are OD-characterizable, L.3 is 3-fold OD-characterizable, and L.S3 is 5-fold OD-characterizable.

Almost perfect sequences based on cyclic difference sets

The perfect sequences are so ideal that all out-of-phase autocorrelation coefficients are zero, and if the sequences are used as the coding modulating signal for the phase-modulated radar, there will be no interference of side lobes theoretically. However, it has been proved that there are no binary perfect sequences of period 4 〈 n ≤ 12100. Hence, the almost perfect sequences with all out-of-phase autocorrelation coefficients as zero except one are of great practice in engineering. Currently, the cyclic difference set is one of most effective tools to analyze the binary sequences with perfect periodic autocorrelation function. In this article, two characteristic formulas corresponding to the autocorrelation and symmetric structure of almost perfect sequences are calculated respectively. All almost perfect sequences with period n, which is a multiple of 4, can be figured out by the two formulas. Several almost perfect sequences with different periods have been hunted by the program based on the two formulas and then applied to the simulation program and practical application for ionospheric sounding.

ALMOST PERIODIC SOLUTION OF ONE DIMENSIONAL VISCOUS CAMASSA-HOLM EQUATION

This article studies one dimensional viscous Camassa-Holm equation with a periodic boundary condition. The existence of the almost periodic solution is investigated by using the Galerkin method.

Almost sure central limit theory for products of sums of partial sums

Consider a sequence of i.i.d.positive random variables.An universal result in almost sure limit theorem for products of sums of partial sums is established.We will show that the almost sure limit theorem holds under a fairly general condition on the weight dk= k-1 exp（lnβk）,0≤β〈1.And in a sense,our results have reached the optimal form.

EXISTENCE AND ATTRACTIVITY OF k-ALMOST AUTOMORPHIC SEQUENCE SOLUTION OF A MODEL OF CELLULAR NEURAL NETWORKS WITH DELAY

In this paper we discuss the existence and global attractivity of k-almost automorphic sequence solution of a model of cellular neural networks. We consider the corresponding difference equation analogue of the model system using suitable discretization method and obtain certain conditions for the existence of solution. Almost automorphic function is a good generalization of almost periodic function. This is the first paper considering such solutions of the neural networks.

关于Weakly Almost Clean环（英文）

定义了weakly almost clean环.交换环R叫做weakly almost clean环,如果对于任意一个元素x∈R可以写成x=r+e或x=r-e的形式,其中r∈reg(R)且e∈Id(R).首先,对于环Ri的非空集合{Ri},证明了直和R=∏i∈IRi为weakly almost clean当且仅当存在m∈I使Rm为weakly almost clean且对所有的n≠m,Rn为almost clean.然后,设R是一个环且M为一个R-模,得到了R和M的平凡扩张R(M)为weakly almost clean当且仅当每个x∈R可以写成x=r+e或x=r-e的形式,其中r∈R-(Z(R)∪Z(M))且e∈Id(R).进而推广了almost clean环的相应结果.

低位直肠癌新辅助治疗达到almost-cCR(near-cCR)的缩小手术和根治术疗效的对照研究

目的:总结低位直肠癌行新辅助治疗原发肿瘤达到almost-cCR(almost-clinical complete response)后,比较缩小手术和根治术两种术式的优缺点。方法:回顾性分析2013年1月至2018年10月间,辽宁省肿瘤医院大肠科收治的局部晚期低位直肠癌经新辅助治疗原发肿瘤达到almost-cCR(near-cCR)的共35例患者的临床和病理资料。采用Kaplan-Meier法绘制生存曲线。结果:35例病人中,缩小手术组共纳入9例患者,根治术组共纳入26例患者。缩小手术组未出现术后并发症,根治术组3例患者出现术后并发症,发生率11.5%。缩小手术组1年和2年无复发生存率均为100%。根治术组1年和2年无复发生存率分别为96.1%和88.4%。缩小手术组中位DFS和OS均为32.1个月。根治术组中位DFS和OS分别为43.2个月和39.6个月。结论:对于低位直肠癌新辅助治疗达到almost-cCR(near-cCR)的病人,缩小手术组可以取得不亚于根治术组的临床疗效。并且减少手术创伤,改善近期疗效和远期预后。

Existence of asymptotically almost periodic solutions and stability properties for functional difference equations

For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain limiting equation.

Asymptotic Behavior of Almost-orbits of Asymptotically Nonexpansive Semigroups in Banach Spaces(Dedicated to Professor You Zhaoyong for his 60th brithday)

Let C be a closed bounded convex subset of a uniformaly convex Banach space X with a Frechet differentiable norm, F= {T(t):t ≥0} an asymptotically noncxpansivc semigroup on C, and u:[0,∞)→ C an almost-orbit of F. Then we show that {u(t):t ≥ 0} is almost convergent weakly to a common fixed point y of F, that isweak - lim1/tdr - y uniformly in s≥ 0.This implies that {u(t):t≥ 0} converges weakly to y if and onlyif u is weakly asymptotically regular, i.e lim (u(t + s) - u(t) = 0 weakly for all s≥ 0.