球型平移网络逼近周期函数

研究了球型平移网络对周期函数的逼近问题．文章首先将基函数eimx分别表示成为两种球型平移网络．进一步,将有关多重Fourier级数的Bochner-Riesz平均表示成为球型平移网络的形式．在此基础上构造出了两类球型平移网络序列,并借助于有关Bochner-Riesz平均对Lp空间中函数的逼近结果给出了这两类球型平移网络序列在Lp空间中的逼近阶．     

球面带形平移网络逼近的Jackson定理

研究了球面带型平移网络逼近阶用球面调和多项式的最佳逼近及光滑模的刻画问题．借助于球调和多项式的最佳逼近多项式和Riesz平均构造出了单位球面Sq上的带形平移网络,并建立了球面带形平移网络对Lp(Sq)中函数一致逼近的Jackson型定理．所得结果表明球面带形平移网络可以达到球调和多项式的逼近阶．     

球面带形插值平移网络逼近的误差估计

构造了具有插值性质的球面带形平移网络, 并且给出了在一致范数下对连续函数逼近的上界估计.     

非周期神经网络及平移网络在L_w~p中的逼近

设s≥d≥1为整数, 1≤p≤+∞,借助于正交多元代数多项式系而构造了一类s维网络算子,并用于逼近Lpw[-1,1]s中的函数,给出了逼近的上界以及当此算子为平移网络算子及神经网络算子时的导数型估计.     

一类球面带形平移网络算子的逼近

借助于球调和多项式的de la Vallée Poussin和构造出了单位球面S^q上一类带形平移网络算子，并给出了其对L^p(S^q)中函数一致逼近的收敛速度.      

用平移网络逼近函数及其导数

若Х（ｘ）∈Ｗ１Ｍ（Ｒ＾ｄ），利用Х构造出具体的平移网络逼近Ｓｏｂｏｌｅｖ空间中的函数并给出逼近阶的估计。     

多-尺度加细函数及其性质的研究

引入伸缩因子为a的多-尺度加细函数和平移不变子空间的概念．研究了多-尺度加细方程解存在的条件．特别地,给出这种方程的解是正交的充分必要条件．建立了多-尺度加细函数与两尺度加细函数之间的关系．并讨论了它们的一些性质．最后给出相应的构造算例．     

交换半群上的次范整线性空间

为了刻画和研究平移空间的线性结构,给出了平移半群的概念,在平移半群为满足相消律的交换半群的平移空间上,引入了整数系数的线性结构;再加之,在平移空间上可利用距离在一定条件下构造出线性结构,引入了次范整线性空间的定义;并且证明了平移空间是次范整线性空间的充要条件是它的平移半群是满足相消律的交换半群.     

广义零程无穷质点过程的不变测度

本文研究了一类广义零程无穷质点马氏过程。给出了此类过程的一类不变测度;在平移不变情形下,构造了平移不变的不变测度集;而在重随机、常返的情形下,构造了不变测度集。这些结果自然推广了[3]的结果。     

k-紧优有向双环网络无限族的构建

本文给出了一种方法用于构造k-紧优双环网络无限族(k≥1),并用此方法构造出了4族3-紧优无限族,3族新的4-紧比无限族,3族5-紧优无限族及2族6-紧优无限族．     

Translations from natural deduction to sequent calculus

Gentzen's “Untersuchungen” [1] gave a translation from natural deduction to sequent calculus with the property that normal derivations may translate into derivations with cuts. Prawitz in [8] gave a translation that instead produced cut‐free derivations. It is shown that by writing all elimination rules in the manner of disjunction elimination, with an arbitrary consequence, an isomorphic translation between normal derivations and cut‐free derivations is achieved. The standard elimination rules do not permit a full normal form, which explains the cuts in Gentzen's translation. Likewise, it is shown that Prawitz' translation contains an implicit process of cut elimination.     

A translation plane of order 72 with a very small translation complement

A translation plane of order 7² is constructed whose left nucleus is a cyclic group of order 6. Generally the translation complement of a translation plane is quite large when compared to the order of the left nucleus. The plane discussed in this paper has the distinguished feature that its translation complement modulo the scalar collineations group is very small. In fact it is a Dihedral group of order 12 and is the smallest of all the known examples. The translation complement divides the set of ideal points into 9 orbits of lengths 1,1, 6, 6, 6, 6, 6, 6, and 12.     

Optimal use of the translation method and relaxations of variational problems

The translation method has been used with great success in bounding the effective moduli of composite materials. We consider here the analogous method for bounding the relaxations of variational problems. We optimize the bound over the set of all available translations. Our method is to cast this in the form of a minmax problem. Using techniques of nonsmooth analysis, we are able to identify the optimal translation bound, meanwhile proving the existence of at least one optimal combination rank-one convex quadratic and null-Lagrangian translation. The optimal translation bound proves to be a better general lower bound on relaxations of variational problems than is the polyconvexification in three dimensions. In two dimensions, we discuss the negative result that the optimal translation bound is exactly the polyconvexification. Several examples of optimal applications of translation bounds to non-convex nonlinear variational problems are given.     

平移空间的线性结构

本文证明了在平移空间上可利用距离在一定条件下构作出线性结构,引入了次范整线性空间的概念,还证明了平移空间是次范整线性空间当且仅当它的平移群是Abel群.泛函分析学中的有界线性算子定理,Hahn-Banach定理以及共鸣定理都可以移植于次范整线性空间之中.     

Translation Ovoids and Spreads of the Generalized Hexagon H(q)

Ovoids of the finite classical generalized hexagon H(q) that are translation with respect to a point are classified. By duality, translation spreads with respect to a line are classified when the characteristic is three. When the characteristic is not equal to three, it is shown that there are no ovoids that are translation with respect to a flag.     

An Affine Characterization of Moufang Projective Klingenberg Planes

It is shown that with minor exceptions all projective Klingenberg planes are Moufang exactly if they have a trilateral each of whose sides is the line at infinity of a translation plane; but there are non-Moufang projective Klingenberg planes which have a single line which produces an equiaffine translation plane or a point P so that all lines through P, except perhaps for some neighbour lines, produce translation planes.     

Translation quiver varieties

We introduce a framework of translation quiver varieties which includes Nakajima quiver varieties as well as their graded and cyclic versions. An important feature of translation quiver varieties is that the sets of their fixed points under toric actions can be again realized as translation quiver varieties. This allows one to simplify quiver varieties in several steps. We prove that translation quiver varieties are smooth, pure and have Tate motivic classes. We also describe an algorithm to compute those motivic classes.     

On affine translation divisible designs

We prove that a translation divisible design (TDD) with an abelian translation group can be embedded in PG (n,q) for some n2. Moreover we study affine TDD's showing that they have an (elementary) abelian translation group. A construction for TDD's with an abelian translation group which are not affine is given too.     

Some isomorphism results for Thompson-like groups <Emphasis Type="Italic">V</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>(<Emphasis Type="Italic">G</Emphasis>)

The natural automorphism group of a translation surface is its group of translations. For finite translation surfaces of genus g ≥ 2 the order of this group is naturally bounded in terms of g due to a Riemann–Hurwitz formula argument. In analogy with classical Hurwitz surfaces, we call surfaces which achieve the maximal bound Hurwitz translation surfaces. We study for which g there exist Hurwitz translation surfaces of genus g.