Invariant points of maps between Grassmannians

We show that for a very large class of integers and any map between Grassmannians, there is some -plane of which is mapped into a subspace of itself.

     

Temperature tunability of size in CdS nanoparticles and size dependent photocatalytic degradation of nitroaromatics

Size tunability of thiophenol capped CdS nanoparticles (NPs) has been achieved by controlling the temperatures in situ. Synthesis at 5 degrees C produced stable particles of smallest size having narrow size distribution and high photoluminescence quantum yield. The photoluminescence of thiophenol capped CdS NPs was quenched by the nitroaromatic compounds. The Stern-Volmer constant of dinitrobenzene was about 15-fold higher than nitrobenzene, which indicates that introduction of nitro groups in the benzene ring increases the quenching efficiency. Further, the as-prepared CdS NPs were found to display size dependent photocatalytic activity towards degradation of nitroaromatics. The catalytic efficiency of CdS quantum particles was quintupled with decrease in particle size from 5.8 to 3.8 nm. An empirical equation has been derived to correlate the catalytic efficiency of the nanoparticles with the twin factors operating in the quantum confinement regime: (i) change in surface to volume ratio and (ii) shift in conduction band edge.     

Solution of a problem on the identification of parameters by the distribution of the maximum random variable: a multivariate normal case

In this paper we solve the problem of unique factorization of products ofn-variate nonsingular normal distributions with covariance matrices of the form , _ij =p _{i j} forij, = _i ² ,j=j,p0.     

Biophysical,spectroscopic vis-à-vis biochemical investigation on DNA–metalloprotein interaction: a model study involving cobalt(II)-glutathione complex

Abstract  The interaction of cobalt(II)-glutathione (CoGSH) with deoxyribonucleic acid (DNA) has been studied by UV–vis, fluorescence, circular dichroism (CD), thin-film infrared (IR), and viscometric techniques. From the UV-spectroscopic method, binding constant (K _b) was determined and was found to be 2.3 × 10⁶ M⁻¹. In fluorimetric analysis, the quenching of fluorescence intensity of DNA bound to ethidium bromide (EB) was investigated. The Stern–Volmer quenching constant (K _sv) was also estimated from this study and was found to be 2.8 × 10⁶ M⁻¹at 37 °C. The solution CD spectra of DNA and DNA–CoGSH indicate that in each case, DNA exists in the ‘B’ conformation and suggested an intercalative binding mode. Thin-film IR data also reveal that DNA attains the ‘B’ family of conformations after interaction with CoGSH complex. The increase in DNA viscosity in the presence of CoGSH complexes is attributed to the lengthening of DNA helix due to intercalation. Graphical Abstract  The spectrophotometric, CD, thin film IR, viscometric and fluorimetric studies on the interaction of CoGSH with DNA indicated an intercalative binding mode with the retention of ‘B’ conformation of DNA.      

Upper packing dimension of a measure and the limit distribution of products of i.i.d. stochastic matrices

This article gives sufficient conditions for the limit distribution of products of i.i.d. 2 × 2 stochastic matrices to be continuous singular, when the support of the distribution of the individual random matrices is countably infinite. It extends a previous result for which the support of the random matrices is finite. The result is based on adapting existing proofs in the context of attractors and iterated function systems to the case of infinite iterated function systems.     

Identification of parameters and the distribution of the minimum of the tri-variate normal

In this note, for tri-variate normal distributions, we consider the problem of the identification of parameters when only the distribution of the minimum is known.     

Identification of parameters by the distribution of the maximum random variable: The general multivariate normal case

Summary LetX ₁,X ₂, ...,X _r ber independentn-dimensional random vectors each with a non-singular normal distribution with zero means and positive partial correlations. Suppose thatX _i =(X _i1 , ...,X _in ) and the random vectorY=(Y ₁, ...,Y _n ), their maximum, is defined byY _j =max{X _ij :1ir}. LetW be another randomn-vector which is the maximum of another such family of independentn-vectorsZ ₁,Z ₂, ...,Z _s . It is then shown in this paper that the distributions of theZ _i 's are simply a rearrangement of those of theZ _j 's (and of course,r=s), whenever their maximaY andW have the same distribution. This problem was initially studied by Anderson and Ghurye [2] in the univariate and bivariate cases and motivated by a supply-demand problem in econometrics.     

On certain conjectures on invariant measures on semigroups

A conjecture stating that a locally compact semigroup admits a twosided semi-invariant measure iff it contains a kernel which is a unimodular group, is proven. Also a conjecture stating that the support of an r^*-invariant measure is a left group, is proven under the condition that for some a ε F (=support of the measure), aF is right cancellative. Moreover four types of invariance for regular probability measures are shown to be equivalent. Also a new proof of the equivalence of a two-sided semi-invariant probability measure and the existence of a kernel which is a compact group, is given.