Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.

Special issue on Current Trends in Physics

In 1974, the Russian physicist Vitaly Ginzburg wrote a book entitled `Key Problems of Physics and Astrophysics' in which he presented a selection of important and challenging problems along with speculations on what the future holds. The selection had a broad range, was highly personalized, and was aimed at the general scientist, for whom it made very interesting reading

On a Special Co-cycle Basis of Graphs

In this paper we consider the problems of computing a minimum co-cycle basis and a minimum weakly fundamental co-cycle basis of a directed graph G. A co-cycle in G corresponds to a vertex partition (S,V ∖ S) and a { − 1,0,1} edge incidence vector is associated with each co-cycle. The vector space over ℚ generated by these vectors is the co-cycle space of G. Alternately, the co-cycle space is the orthogonal complement of the cycle space of G. The minimum co-cycle basis problem asks for a set of co-cycles that span the co-cycle space of G and whose sum of weights is minimum. Weakly fundamental co-cycle bases are a special class of co-cycle bases, these form a natural superclass of strictly fundamental co-cycle bases and it is known that computing a minimum weight strictly fundamental co-cycle basis is NP-hard. We show that the co-cycle basis corresponding to the cuts of a Gomory-Hu tree of the underlying undirected graph of G is a minimum co-cycle basis of G and it is also weakly fundamental.

Soft condensed matter -A special issue of solid state communications -Foreword

It is a policy of Solid State Communications’ Executive Editorial Board to organize special issues from time to time on topics of current interests. The present issue focuses on soft condensed matter, a rapidly developing and diverse area of importance not only for the basic science, but also for its potential applications. The ten articles in this issue are intended to give the readers a snapshot of some latest developments in soft condensed matter, mainly from the point of view of basic science. As the special issues are intended for a broad audience, most articles are short reviews that introduce the readers to the relevant topics. Hence this special issue can be especially helpful to readers who might not be specialists in this area but would like to have a quick grasp on some of the interesting research directions.

Hierarchy of structures in the family of amine templated open-framework gallium arsenates

Five new gallium arsenate compounds C2N2H10]Ga(H2AsO4)(HAsO4)(2)]center dot H2O, I; C2N2H10]Ga(OH)(AsO4)](2), II; C2N2H10]GaF(AsO4)](2), III; C3N2H12]Ga(OH)(AsO4)](2), IV; Ga2F3(AsO4)(HAsO4)]center dot 2H(3)O, V, have been synthesized under hydrothermal conditions and the structures determined employing single crystal X-ray diffraction studies. All the structures consist of octahedral gallium and tetrahedral arsenate units connected together forming a hierarchy of structures. Thus, one- (I), two- (II and IV) and three-dimensionally (III and V) extended structures have been observed. The Ga-O(H)/F-Ga connectivity in some of the structures suggests the coordination requirements posed by the octahedral gallium in these compounds. The observation of only one type of secondary building unit in the structures of III (SBU-4) and V (spiro-5) is unique and noteworthy. All the compounds have been characterized by a variety of techniques that include powder XRD, IR, and TGA. (C) 2010 Elsevier B. V. All rights reserved.

Liquid-Liquid Interphase (Biphasic) as the Reaction Medium in the Assembly of a Hierarchy of Structures of 4,4 `-Azodibenzoic Acid with Zinc and Cadmium

The compounds Zn(C12H8N2)](2)C12N2H8(COO)(2)](2)center dot(C6H12O)center dot(H2O), I, Zn(C12H8N2)]C12N2H8(COO)(2)], II, Cd(C12H8N2)(H2O)]C12N2H8(COO)(2)]center dot(H2O), III, Zn(C10N2H8)]C12N2H8(COO)(2)]center dot 0.5(C10N2H8), IV, Cd(C12N2H8(COO)(2)center dot H2O], V, and Zn-3(mu(2)-O)(mu(3)-O)(3)]C12N2H8(COO)(2)], VI, have been synthesized by using a biphasic approach (I, III, V, VI) or regular hydrothermal method (II, IV). The compounds exhibit one (I and II), two (In), and three dimensionally (IV, V, VI) extended structures. The flexible azodibenzoate ligand gives rise to a 3-fold interpenetration (IV) when the synthesis was carried out using normal hydrothermal methods. The biphasic approach forms structures without any interpenetrations, especially in the three-dimensional structures of V and VI. Formation of Cd2O2 dimers in V and extended M-O(H)-M two-dimensional layers in VI suggests the subtle structural control achieved by the biphasic method. Transformation studies indicate that it is possible to transform I to II. Lewis acid catalytic studies have been performed to evaluate the role of the coordination environment in such reactions. All the compounds have been characterized by a variety of techniques that includes powder X-ray diffraction, infrared, thermogravitric analysis, UV-vis, photoluminescence studies.