Generalization of tangential trace spaces of H(curl,Ω) for curvilinear Lipschitz polyhedral domains Ω

For curvilinear Lipschitz polyhedral domains Ω, explicit characterizations of the tangential trace spaces of H ¹(Ω) are presented. These extend the original characterizations given by Buffa and Ciarlet that hold on Lipschitz polyhedral domains with plane faces. The tangential trace spaces of H ¹(Ω) are fundamental for the definition, analysis and intuitive understanding of the trace spaces of H ( curl ,Ω) and therefore, more general characterizations of the latter are obtained at the same time. Copyright © 2013 John Wiley & Sons, Ltd.     

On Burenkov's extension operator preserving Sobolev–Morrey spaces on Lipschitz domains

We prove that Burenkov's extension operator preserves Sobolev spaces built on general Morrey spaces, including classical Morrey spaces. The analysis concerns bounded and unbounded open sets with Lipschitz boundaries in the n‐dimensional Euclidean space.     

A three‐dimensional cadmium coordination polymer based on 1,4‐bis(1,2,4‐triazol‐1‐yl)but‐2‐ene and benzene‐1,3,5‐tricarboxylic acid

The Cd^II three‐dimensional coordination poly[[[μ₄‐1,4‐bis(1,2,4‐triazol‐1‐yl)but‐2‐ene]bis(μ₃‐5‐carboxybenzene‐1,3‐dicarboxylato)dicadmium(II)] dihydrate], {[Cd₂(C₉H₄O₆)₂(C₈H₁₀N₆)]·2H₂O}_n , (I), has been synthesized by the hydrothermal reaction of Cd(NO₃)₂·4H₂O, benzene‐1,3,5‐tricarboxylic acid (1,3,5‐H₃BTC) and 1,4‐bis(1,2,4‐triazol‐1‐yl)but‐2‐ene (1,4‐btbe). The IR spectrum suggests the presence of protonated carboxylic acid, deprotonated carboxylate and triazolyl groups. The purity of the bulk sample was confirmed by elemental analysis and X‐ray powder diffraction. Single‐crystal X‐ray diffraction analysis reveals that the Cd^II ions adopt a five‐coordinated distorted trigonal–bipyramidal geometry, coordinated by three O atoms from three different 1,3,5‐HBTC²⁻ ligands and two N atoms from two different 1,4‐btbe ligands; the latter are situated on centres of inversion. The Cd^II centres are bridged by 1,3,5‐HBTC²⁻ and 1,4‐btbe ligands into an overall three‐dimensional framework. When the Cd^II centres and the tetradentate 1,4‐btbe ligands are regarded as nodes, the three‐dimensional topology can be simplified as a binodal 4,6‐connected network. Thermogravimetric analysis confirms the presence of lattice water in (I). Photoluminescence studies imply that the emission of (I) may be ascribed to intraligand fluorescence.     

Maximizing H‐Colorings of Connected Graphs with Fixed Minimum Degree

For graphs G and H , an H‐coloring of G is a map from the vertices of G to the vertices of H that preserves edge adjacency. We consider the following extremal enumerative question: for a given H , which connected n‐vertex graph with minimum degree δ maximizes the number of H‐colorings? We show that for nonregular H and sufficiently large n , the complete bipartite graph is the unique maximizer. As a corollary, for nonregular H and sufficiently large n the graph is the unique k‐connected graph that maximizes the number of H‐colorings among all k‐connected graphs. Finally, we show that this conclusion does not hold for all regular H by exhibiting a connected n‐vertex graph with minimum degree δ that has more ‐colorings (for sufficiently large q and n ) than .     

Well‐posedness and regularity results for a 2m‐th order parabolic equation in symmetric conical domains of ℝN+1

In this paper, we use the domain decomposition method to prove well‐posedness and smoothness results in anisotropic weighted Sobolev spaces for a multidimensional high‐order parabolic equation set in conical time‐dependent domains of . Copyright © 2017 John Wiley & Sons, Ltd.     

Spatial and Dynamical Chaos Generated by Reaction–Diffusion Systems in Unbounded Domains

We consider in this article a nonlinear reaction–diffusion system with a transport term (L,∇ _x )u, where L is a given vector field, in an unbounded domain Ω. We prove that, under natural assumptions, this system possesses a locally compact attractor in the corresponding phase space. Since the dimension of this attractor is usually infinite, we study its Kolmogorov’s ɛ-entropy and obtain upper and lower bounds of this entropy. Moreover, we give a more detailed study of the spatio-temporal chaos generated by the spatially homogeneous RDS in . In order to describe this chaos, we introduce an extended (n + 1)-parametrical semigroup, generated on the attractor by 1-parametrical temporal dynamics and by n-parametrical group of spatial shifts ( = spatial dynamics). We prove that this extended semigroup has finite topological entropy, in contrast to the case of purely temporal or purely spatial dynamics, where the topological entropy is infinite. We also modify the concept of topological entropy in such a way that the modified one is finite and strictly positive, in particular for purely temporal and for purely spatial dynamics on the attractor. In order to clarify the nature of the spatial and temporal chaos on the attractor, we use (following Zelik, 2003, Comm. Pure. Appl. Math. 56(5), 584–637) another model dynamical system, which is an adaptation of Bernoulli shifts to the case of infinite entropy and construct homeomorphic embeddings of it into the spatial and temporal dynamics on . As a corollary of the obtained embeddings, we finally prove that every finite dimensional dynamics can be realized (up to a homeomorphism) by restricting the temporal dynamics to the appropriate invariant subset of .     

宽音频扫描加载的电子剪切散斑技术在多层粘接板结构无损检测中的应用

本文利用宽音频自动扫描加载的电子剪切散斑干涉技术对多层粘接板结构进行了时实检测，结果表明，这种方法能够同时测定板的多个位置、大小和形状各不相同缺陷，迅速准确地对多层粘接板结构质量作出判断，同时根据到试过程中记录的共振频率等各种信息，可以进一步对被测部分的振动位移及缺陷深度进行定量分析．     

有限元网格自动生成及自动调整技术

本文给出了一种任意平面域内三角形网格自动生成及自动调整算法，并编制了相应的程序。通过对带Ｕ形槽的三点变曲试件的分析，证明本文算法是可行的，并且具有稳定性能好、收敛速度快的优点。     

Spectral Properties of Schrödinger Operators on Domains with Varying Orders of Thinness

We consider the Schrödinger operator on two types of domains depending on a small parameter : dumbbell domains and thin domains with varying orders of thinness. In both situations we compare the eigenvalues and eigenvectors of the Schrödinger operator with the corresponding eigenvalues and eigenvectors of a limit operator defined on the limit domain.     

The Mal'cev Rank for Modules over Pseudo-Valuation Domains

Let R be a commutative ring and A be an R-module. The Mal'cev rank μ(A) of A is the sup of genN, where N ranges over the finitely generated submodules of A, and genN is the minimum number of generators of N. We prove that μ is both sub-additive and pre-additive as an invariant of Mod(R). Our main goal is to investigate μ for modules over pseudo-valuation domains. Specifically, we establish which pseudo-valuation domains R satisfy the property that an R-module of finite Mal'cev rank must be finitely generated. We split the class 𝒞 of pseudo-valuation domains as a union 𝒞 = 𝒞₁ ∪ 𝒞₂ ∪ 𝒞₃ ∪ 𝒞₄ of suitably defined subclasses, and prove that the property holds if and only if R ∈ 𝒞₃ ∪ 𝒞₄. In that case we can describe the R-modules A where μ(A) < ∞. We also show that, for R ∈ 𝒞₄, there exist indecomposable R-modules of arbitrarily large finite Mal'cev rank.