On distribution by rank of bases for vector spaces of matrices over a finite field

Let F^m×n_q denote the vector space of all m×n matrices over the finite field F_q of order q, and let $\text{B}\text{=(A}{}_1\text{,A}{}_2\text{,…,A}{}_{\mathrm{mn}}\text{)}$ denote an ordered basis for F^m×n_q. If the rank of A_i is r_i,i=1,2,…,mn, then $\text{B}$ is said to have rank (r₁,r₂,…,r_mn), and the number of ordered bases of F^mxn_q with rank (r₁,r₂,…,r_mn is denoted by N_q(r₁, r₂,…,r_mn). This paper determines formulas for the numbers N_q(r₁,r₂,…,r_mn) for the case m=n=2, q arbitrary, and while some of the techniques of the paper extend to arbitrary m and n, the general formulas for the numbers N_q(r₁,r₂,…,r_mn) seem quite complicated and remain unknown. An idea on a possible computer attack which may be feasible for low values of m and n is also discussed.     

FT-IR study of the effect of zinc exposure on the biochemical contents of the muscle of Labeo rohita

Heavy metal pollution is a major environmental problem in the modern world due to increasing human activities. Zinc is an essential element involved in a wide variety of cellular processes. However, it becomes toxic when elevated concentrations are introduced into the environment. The goal of the present study is to investigate the effect of zinc exposure on the biochemical contents of the muscle tissues of freshwater species Labeo rohita using Fourier transform infrared (FT-IR) spectroscopy. Since the muscle constitutes the greatest mass of the fish that is consumed, the present study has paid particular attention to muscle component. The result reveals that the zinc exposure causes significant changes in the biochemical contents of the L. rohita muscle tissues. In addition, it causes an alteration in the protein secondary structures by decreasing the α-helix and increasing the β-sheet contents of muscle tissues. Further, it has been observed that the administration of chelating agent D-penicillamine improves the protein and lipid contents in the muscle tissues compared to zinc exposed tissues. This result shows that D-penicillamine is the effective chelator of zinc in reducing the body burden of L. rohita fingerlings.     

Teleportation via decay

We present a rare example of a decay mechanism playing a constructive role in quantum information processing. We show how the state of an atom trapped in a cavity can be teleported to a second atom trapped in a distant cavity by the joint detection of photon leakage from the cavities. The scheme, which is probabilistic, requires only a single three level atom in a cavity. We also show how this scheme can be modified to a teleportation with insurance.     

The growth of a single crystal of Sr3CuIrO6 and its magnetic behavior compared to polycrystals

We have grown single crystals of the psuedo-one-dimensional compound Sr₃CuIrO₆, a K₄CdCl₆-derived monoclinic structure with Cu-Ir chains along the [101] direction. We present the ac and dc magnetization behavior of the single crystals in comparison with that of the polycrystalline form reported earlier. There is a distinct evidence for at least two magnetic transitions, at 5 K (T ₁) and 19 K (T ₂), with different relative magnitudes in the single and polycrystals. The low temperature magnetic relaxation behavior of both the forms is found to be widely different, exhibiting unexpected time dependence.