Pseudoframes for Subspaces with Applications

A notion of pseudoframes for subspaces (PFFS) is defined and characterized in a separable Hilbert space H. PFFS functions in a manner of a frame for a subspace X in H. Yet none of the pair of sequences {x_n} and {x*_n} is necessarily contained in X. This gives rise to attractive properties that center around the flexibility. A necessary and sufficient characterization of PFFSs is provided. Analytical formulae for the constructions of PFFSs in two directions are derived. Examples are considered. Some insight relationships of an PFFS for X and a frame of X are also observed thanks to a private communication with Casazza. Further applications of PFFSs are also discussed.     

A Theory of Generalized Multiresolution Structure and Pseudoframes of Translates

The notion of a Generalized Multiresolution Structure (GMS) in LL is introduced. Basically, it consists of an increasing sequence of closed subspaces of LL, with a textit{pseudoframe of translates} at each level. Using their shift-invariance a frame-like decomposition is derived based on such a GMS. As a major new contribution the construction of affine frames for LtwoRLtwoR based on an GMS is presented. A fast algorithm for the GMS-based affine frame decomposition and reconstruction using filter banks is presented as well.     

Beurling Dimension of Gabor Pseudoframes for Affine Subspaces

Pseudoframes for subspaces have been recently introduced by Li and Ogawa as a tool to analyze lower dimensional data with arbitrary flexibility of both the analyzing and the dual sequence. In this paper we study Gabor pseudoframes for affine subspaces by focusing on geometrical properties of their associated sets of parameters. We first introduce a new notion of Beurling dimension for discrete subsets of ℝ ^d by employing a certain generalized Beurling density. We present several properties of Beurling dimension including a comparison with other notions of dimension showing, for instance, that our notion includes the mass dimension as a special case. Then we prove that Gabor pseudoframes for affine subspaces satisfy a certain Homogeneous Approximation Property, which implies invariance under time–frequency shifts of an approximation by elements from the pseudoframe. The main result of this paper is a classification of Gabor pseudoframes for affine subspaces by means of the Beurling dimension of their sets of parameters. This provides us, in particular, with a Nyquist dimension which separates sets of parameters of pseudoframes from those of non-pseudoframes and which links a fixed value to sets of parameters of pseudo-Riesz sequences. These results are even new for the special case of Gabor frames for an affine subspace.      

Topology Optimization for Continuum Structure with Decreasing Mass

This paper deals with the proper distribution of material in a structure whose available mass decreases in the working time, i.e. part of the structure undergoes degradation and loses mass. This means, the other part of the structure must bear the load. Therefore the structure's mass should be redistributed to replace the degraded material. The present analysis is carried out for the so‐called smart structures which are able to shift their mass within a certain previously fixed area and this research falls within the analysing and decision system. Minimization of the mean compliance under the mass constraints with the artificial approach for updating the material properties is used [1], [2]. As a numerical realization of the problem FEM examples are presented. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Möbius立方体的拓扑结构性质

超立方体网络是目前在超级计算机处理器结构中应用得最广泛的拓扑结构,M(o)bius立方体是超立方体的一种变形,已经被证明它在某些方面具有优于超立方体的拓扑性质.本文指出了n维M(o)bius立方体递归结构的一些重要拓扑性质.     

平方可积函数空间的仿射框架

推广了双正交小波的概念.引进了多尺度平移伪框架的概念.给出了它的塔式分解格式及其存在的条件.进而得到平方可积函数空间的函数仿射伪框架展式.     

Topology Optimization Procedure Based on Structure Stress History

The structure design points stress analysis for succeeding optimization steps is the base of the topology optimization algorithm. Because the material density of the material is proportional to the strain energy we can predict how to change the density for each design point for the next optimization steps. Proposed procedure make the optimization process faster and final topology is finally more optimal than topology obtained using standard optimization procedures. This stress analyzing procedure, can be treated as a hardware of the sensors being the part of the smart structure for the real time structure reconstruction. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Topology Optimization of Structure with Growing Mass and Expanding Shape

The problem of obtaining the optimal topology for the shape expanding continuum structure with the growing mass is considered. Such stated real‐world problem exists in the case of bridges, which are two cantilevers during the construction process. The FEM mesh is fixed for the whole growing process and covers the final structure. This enable using the same algorithm for each stage. A properly defined threshold function lets us obtain the optimal topology within small number of steps. The detailed history ‐ the set of optimal topologies of the structure with changing mass and changing shape ‐ is obtained. This set is needed to get the final topology of the structure including the stages of structure set‐up.     

One Setting for All: Metric, Topology, Uniformity, Approach Structure

For a complete lattice V which, as a category, is monoidal closed, and for a suitable Set-monad T we consider (T,V)-algebras and introduce (T,V)-proalgebras, in generalization of Lawvere's presentation of metric spaces and Barr's presentation of topological spaces. In this lax-algebraic setting, uniform spaces appear as proalgebras. Since the corresponding categories behave functorially both in T and in V, one establishes a network of functors at the general level which describe the basic connections between the structures mentioned by the title. Categories of (T,V)-algebras and of (T,V)-proalgebras turn out to be topological over Set.     

Bubble Divergences: Sorting out Topology from Cell Structure

We conclude our analysis of bubble divergences in the flat spinfoam model. In Bonzom and Smerlak, Comm. Math. Phys., (submitted), we showed that the divergence degree of an arbitrary 2-complex Γ can be evaluated exactly by means of twisted cohomology. Here, we specialize this result to the case where Γ is the 2-skeleton of the cell decomposition of a pseudomanifold, and sharpen it with a careful analysis of the cellular and topological structures involved. Moreover, we explain in detail how this approach reproduces all the previous powercounting results for the Boulatov–Ooguri (colored) tensor models, and sheds light on algebraic-topological aspects of Gurau’s 1/N expansion.     

一种新的光滑支持向量机的构造及其应用

光滑支持向量机模型是一个无约束、可微的最优化模型,人们可应用快速的最优化方法求解,从而降低计算复杂性.在前人工作的基础上研究基于样条函数的光滑支持向量机,采用广义三弯矩方法构造出六次样条光滑函数,分析了其性能及与正号函数的逼近精度,实现了求解六次样条光滑支持向量机的算法,与其它光滑支持向量机进行了比较,取得了较好的结果.最后将其应用于心脏病模型诊断,实验结果显示具有较高的精确度.     

Smooth格和强Smooth格

引入了强smooth格的概念,讨论了smooth格与强smooth格的一些基本性质,证明了强smooth格可用保任意交和Scott闭集之并的映射嵌入到某方体[0,1]X之中.     

The Scott Approach Structure: An Extension of the Scott Topology for Quantitative Domain Theory

In the study of partially ordered sets, topologies such as the Scott topology have shown to be of paramount importance. In order to have analogous topology-like tools in the more general setting of quantitative domains, we introduce the Scott distance, which is a canonical numerification of the Scott topology and at the same time allows for quantitative considerations. We show that the Scott distance shares the important features of the Scott topology.     

M(o)bius立方体的拓扑结构性质

超立方体网络是目前在超级计算机处理器结构中应用得最广泛的拓扑结构,M(o)bius立方体是超立方体的一种变形,已经被证明它在某些方面具有优于超立方体的拓扑性质.本文指出了n维M(o)bius立方体递归结构的一些重要拓扑性质.     

Mbius立方体的拓扑结构性质

超立方体网络是目前在超级计算机处理器结构中应用得最广泛的拓扑结构,Mbius立方体是超立方体的一种变形,已经被证明它在某些方面具有优于超立方体的拓扑性质.本文指出了n维Mbius立方体递归结构的一些重要拓扑性质.     

A Zariski Topology for Bicomodules and Corings

In this paper we introduce and investigate top (bi)comodules of corings, that can be considered as dual to top (bi)modules of rings. The fully coprime spectra of such (bi)comodules attains a Zariski topology, defined in a way dual to that of defining the Zariski topology on the prime spectra of (commutative) rings. We restrict our attention in this paper to duo (bi)comodules (satisfying suitable conditions) and study the interplay between the coalgebraic properties of such (bi)comodules and the introduced Zariski topology. In particular, we apply our results to introduce a Zariski topology on the fully coprime spectrum of a given non-zero coring considered canonically as duo object in its category of bicomodules. Supported by King Fahd University of Petroleum & Minerals, Research Project # INT/296.     

半连续格上的半Scott拓扑与半Lawson拓扑

在完备格上引入了半Scott拓扑与半Lawson拓扑,讨论了半连续格和强连续格上半Scott拓扑与半Lawson拓扑的一些基本性质。     

On the Topology of Singularities of the Set of Supporting Hyperplanes of a Smooth Submanifold in an Affine Space

Many new universal relations are obtained between the Eulernumbers of manifolds of singular supporting hyperplanes of anarbitrary generic smooth closed k-dimensional submanifold inRⁿ where n 7 or k = 1. These relations are applied to Barner-convexcurves in an odd-dimensional space Rⁿ. A universal (nontrivial)linear relation is established between the numbers of singularsupporting hyperplanes of various types but of the same totalmultiplicity n of tangency with a given generic smooth closedconnected Barner-convex curve in Rⁿ. The coefficients of thisrelation are defined by Catalan numbers.     

Finiteness Principles for Smooth Selection

In this paper we prove finiteness principles for \({C^m{({\mathbb{R}^n},{\mathbb{R}^D)}}}\) and \({C^{m-1,1}(\mathbb{R}^n,\mathbb{R}^D)}\) selections. In particular, we provide a proof for a conjecture of Brudnyi-Shvartsman (1994) on Lipschitz selections for the case when the domain is \({X=\mathbb{R}^n}\).