Almost locatedness in uniform spaces

A weak form of the constructively important notion of locatedness is lifted from the context of a metric space to that of a uniform space. Certain fundamental results about almost located and totally bounded sets are then proved.     

Uncertainty principles on two step nilpotent Lie groups

We extend an uncertainty principle due to Cowling and Price to two step nilpotent Lie groups, which generalizes a classical theorem of Hardy. We also prove an analogue of Heisenberg inequality on two step nilpotent Lie groups.     

On Haar wavelet operational matrix of general order and its application for the numerical solution of fractional Bagley Torvik equation

In the present analysis, the motion of an immersed plate in a Newtonian fluid described by Torvik and Bagley’s fractional differential equation [1] has been considered. This Bagley Torvik equation has been solved by operational matrix of Haar wavelet method. The obtained result is compared with analytical solution suggested by Podlubny [2]. Haar wavelet method is used because its computation is simple as it converts the problem into algebraic matrix equation.     

On (q 2 + q + 2, q + 2)-arcs in the Projective Plane PG(2, q)

A (k,n)-arc in PG(2,q) is usually defined to be a set of k points in the plane such that some line meets in n points but such that no line meets in more than n points. There is an extensive literature on the topic of (k,n)-arcs. Here we keep the same definition but allow to be a multiset, that is, permit to contain multiple points. The case k=q ²+q+2 is of interest because it is the first value of k for which a (k,n)-arc must be a multiset. The problem of classifying (q ²+q+2,q+2)-arcs is of importance in coding theory, since it is equivalent to classifying 3-dimensional q-ary error-correcting codes of length q ²+q+2 and minimum distance q ². Indeed, it was the coding theory problem which provided the initial motivation for our study. It turns out that such arcs are surprisingly rich in geometric structure. Here we construct several families of (q ²+q+2,q+2)-arcs as well as obtain some bounds and non-existence results. A complete classification of such arcs seems to be a difficult problem.     

Explicit ring-theoretic presentation of Iwasawa algebras

Iwasawa algebras are completed group algebras of compact p-adic Lie groups. Ardakov and Venjakob have studied the structure theory and the ring-theoretic properties of such algebras. This article gives an explicit presentation by generators and relations of the Iwasawa algebras of uniform pro-p groups, i.e. the pro-p groups that admit a p-adic analytic manifold structure.     

Chebyshev Centers that are Not Farthest Points

In this paper, we address the question whether in a given Banach space, a Chebyshev center of a nonempty bounded subset can be a farthest point of the set. We obtain a characterization of two-dimensional real strictly convex spaces as those ones where a Chebyshev center cannot contribute to the set of farthest points of a subset. In dimension greater than two, every non-Hilbert smooth space contains a subset whose Chebyshev center is a farthest point. We explore the scenario in uniformly convex Banach spaces and further study the roles played by centerability and Mcompactness in the scheme of things to obtain a step by step characterization of strictly convex Banach spaces.     

Hopf algebras of set systems

Hopf algebras play a major rôle in such diverse mathematical areas as algebraic topology, formal group theory, and theoretical physics, and they are achieving prominence in combinatorics through the influence of G.-C. Rota and his school. Our primary purpose in this article is to build on work of Schmitt [18,19], and establish combinatorial models for several of the Hopf algebras associated with umbral calculus and formal group laws. In so doing, we incorporate and extend certain invariants of simple graphs such as the umbral chromatic polynomial, and Stanley's [21] recently introduced symmetric function. Our fundamental combinatorial components are finite set systems, together with a versatile generalization in which they are equipped with a group of automorphisms. Interactions with the Roman-Rota umbral calculus over graded rings of scalars which may contain torsion are a significant feature of our presentation.     

Mixed norm estimate for Radon transform on weighted <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> spaces

We will discuss about the mapping property of Radon transform on L ^p spaces with power weight. It will be shown that the Pitt’s inequality together with the weighted version of Hardy-Littlewood-Sobolev lemma imply weighted inequality for the Radon transform.     

Copper(I) Derivative of Pyridine-3-carbaldehyde-N-ethylthiosemicarbazone and Triphenylphosphine—First Case of Crystal Structure Study

The synthesis and crystal structure of pyridine-3-carbaldehyde-N-ethylthiosemicarbazone (3-pytscH-NHEt) 1, and its Cu^I complex of stoichiometry, [CuCl(3-pytscH-NHEt)(PPh₃)₂] 2, studied using single crystal X-ray crystallography, are reported in this paper. Crystal data: 1, monoclinic, P2₁/n, a?=?6.6322(3), b?=?21.1200(8), c?=?7.2989(3) Å; β?=?91.883(4), T?=?173(2), R factor?=?0.0457; 2: triclinic, P-1, a?=?19.3600(5), b?=?20.6241(6), c?=?23.8015(6) Å,α?=?92.647(2), β?=?104.388(2), γ?=?114.377(3), R factor?=?0.0662. The thio-ligand, as a neutral entity, is coordinating to Cu through its S donor atom in complex 2. It has exhibited an unusual feature of forming four independent molecules (A, B, C, D) in the unit cell, with minor differences in the bond angles / distances / torsion angles. The geometry of each molecule of 2 is distorted tetrahedral. Crystal packing, as well as Infrared, electronic absorption and proton NMR spectroscopic studies, are also reported. Copper compound 2 represents the first example of a structurally studied copper coordination compound of 3-pyridyl based thiosemicarbazones.

Graphical Abstract

Copper(I) chloride with pyridine-3-carbaldehyde-N-ethylthiosemicarbazone and PPh₃ in CH₃CN yielded a copper compound, 2 (Green-Cl, blue-N; aqua-Cu, orange-S, magneta-P).

     

An equilibrium solution for a fluid saturated porous elastic solid

This work concerns the behavior of a binary mixture of a fluid and an isotropic elastic solid in static equilibrium. The displacements are assumed to be small. Thus, the governing partial differential equations are linear. The physical model is sufficiently general to allow for a nonconstant fluid pressure when the mixture is in static equilibrium. The model is applied to the problem of an arbitrary pressure distribution on an isothermal half-space. Among the results of this calculation is an explicit formula for the surface porosity. This parameter gives the fraction of the applied pressure transmitted to the fluid.

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Zusammenfassung Diese Arbeit behandelt das Verhalten einer binären Mischung eines Flüssigkeit und eines isotropen elastischen Festkorgers im statischen Gleichgewicht. Deformationen sind als klein angenommen. Die beschreibenden partiellen Differentialgleichungen sind dadurch linear. Das physikalische Modell ist allgemein genügend um einen nichtkonstanten Druck zuzulassen, wenn die Mischung im statischen Gleichgewicht ist. Das Modell wird auf das Problem einer willkürlichen druckverteilung auf dem isothermen halbraum angewandt. Unter den Ergebnissen dieser Berechnung ist eine explizite Formel für die Oberflächen porosität. Dieser Parameter gibt den Bruchteil des ausgeübten Druckes an, der auf die Flüssigkeit übertragen wird.

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Presently employed at Johnson Space Center National Aeronautics and Space Administration Houston, Texas.