Weak Cayley Tables

In [1] Brauer puts forward a series of questions on group representationtheory in order to point out areas which were not well understood.One of these, which we denote by (B1), is the following: whatinformation in addition to the character table determines a(finite) group? In previous papers [5, 7–13], the originalwork of Frobenius on group characters has been re-examined andhas shed light on some of Brauer's questions, in particularan answer to (B1) has been given as follows. Frobenius defined for each character of a group G functions^(k):G^(k) C for k = 1, ..., deg with ⁽¹⁾ = . These functionsare called the k-characters (see [10] or [11] for their definition).The 1-, 2- and 3-characters of the irreducible representationsdetermine a group [7, 8] but the 1- and 2-characters do not[12]. Summaries of this work are given in [11] and [13].     

Mechanical Motion in Crystals Triggered by Solid State Photochemical [2+2] Cycloaddition Reaction

Some special crystals respond to light by jumping, scattering or bursting just like popping of popcorn kernels on a hot surface. This rare phenomenon is called the photosalient (PS) effect. Molecular level control over the arrangement of light-responsive molecules in microscopic crystals for macroscale deformation or mechanical motion offers the possibility of using light to control smart material structures across the length scales. Photochemical [2+2] cycloaddition has recently emerged as a promising route to obtain photoswitchable structures and a wide variety of frameworks, but such reaction in crystals leading to macroscopic mechanical motion is relatively less explored. Study of chemistry of such novel soft crystals for the generation of smart materials is an imperative task. This minireview highlights recent advances in solid-state [2+2] cycloaddition in crystals to induce macroscale mechanical motion and thereby transduction of light into kinetic energy.     

Coherent production of photons by neutrinos

The reaction ν+N→ν+N+γ, involving the coherent emission of a photon in a neutrino-nucleus collision, can produce “single shower” events that simulate the reaction ν+e→ν+e. The ratio of coherent photons to electrons (for an ²⁷Al target) is estimated to be 40% at E_ν=20GeV and 10% at E_ν=20 GeV. We examine the extent to which the “excess” of showers seen in the Aachen-Padova experiment could be understood by this mechanism.     

An extension of building sets and relative difference sets

Building sets are a successful tool for constructing semi‐regular divisible difference sets and, in particular, semi‐regular relative difference sets. In this paper, we present an extension theorem for building sets under simple conditions. Some of the semi‐regular relative difference sets obtained using the extension theorem are new in the sense that their ambient groups have smaller ranks than previously known. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 50–57, 2000     

Unimodular polynomial matrices over finite fields

Journal of Algebraic Combinatorics - We consider some combinatorial problems on matrix polynomials over finite fields. Using results from control theory, we give a proof of a result of Lieb, Jordan...     

Lie nilpotence of group rings

Let FG be the group algebra of a group G over a field F. Denote by ? the natural involution, (∑f_i g_i ^-1. Let S and K denote the set of symmetric and skew symmetric and skew symmetric elements respectively with respect to this involutin. It is proved that if the characteristic of F is zero p≠2 and G has no 2-elements, then the Lie nilpotence of S or K implies the Lie nilpotence of FG.     

Experimental Investigation of the Effect of Flow Arrangements on the Performance of a Micro-Channel Heat Sink

Abstract

An experimental study is carried out to investigate the effect of entrance and exit conditions that prevail due to different flow arrangements on the thermal performance of a copper micro-channel heat sink. Three flow arrangements—U-type, S-type, and P-type—were considered for the analysis with a test piece having inlet and outlet plenum dimensions of 10 mm × 30 mm × 2.5 mm with an array of parallel micro-channels having an individual width of 330 μm and a uniform channel depth of 2.5 mm. Performance evaluations for different flow conditions at inlet and outlet plenums were made by maintaining constant heat supply at 125 W, 225 W, and 375 W with varying Reynolds number ranging from 224 to 1,121. Nusselt number and pressure drop were computed by measuring temperature difference and pressure drop across the inlet and outlet plenum for various test combinations. Maximum heat transfer was observed for the U-type flow arrangement, followed by the P-type and S-type; maximum pressure drop was noted for the S-type flow arrangement, followed by the U-type and P-type arrangements for a constant Reynolds number. A detailed analysis of the experimental results indicate that from a pressure drop point of view, the P-type flow arrangement is preferred, whereas from the heat transfer point of view, the U-type is found to be a better option.