Some vanishing sums involving binomial coefficients in the denominator

Identities involving binomial coeffcients usually arise in situations where counting is carried out in two different ways. For instance, some identities obtained by William Horrace [1] using probability theory turn out to be special cases of the Chu-Vandermonde identities. Here, we obtain some generalizations of the identities observed by Horrace and give different types of proofs; these, in turn, give rise to some other new identities. In particular, we evaluate sums of the form Pm j=0 (1) j j d (mj) (n+jj ) and deduce that they vanish when d is even and m = n > d=2. It is well-known [2] that sums involving binomial coeffcients can usually be expressed in terms of the hypergeometric functions but it is more interesting if such a function can be evaluated explicitly at a given argument. Identities such as the ones we prove could perhaps be of some interest due to the explicit evaluation possible. The papers [3], [4] are among many which deal with identities for sums where the binomial coeffcients occur in the denominator and we use similar methods here

Evaluation of buprofezin 70 DF an insect growth regulator for eco-friendly management of jassid (Amrasca bigutulla bigutulla Ishida) in okra, Abelmoschus esculentus (L.) Moench

Field experiments were carried out for two seasons in 2012 to evaluate the efficacy of a new formulation of buprofezin (buprofezin 70 DF) against jassid (Amarasca biguttula biguttula Ishida) in okra, Abelmoschus esculentus (L.) Moench. The insecticide was applied at 200 and 150 g a.i./ha at the ETL level of the insect (2 Jassids/leaf) and the performance of the same was compared with imidacloprid 17.8 SL @ 20 g a.i./ha, acephate 75 SP @ 562.5g a.i./ha and an untreated control. Results revealed that both the dosages of buprofezin 70 DF were significantly superior over the untreated control at 5 % level of significance. Buprofezin 70 DF at 200 and 150 g a.i./ha performed better over the other treatments with 88.81 and 85.96 % reduction during first season and 89.60 and 84.73% reduction during second season, respectively. Buprofezin , an insect growth regulator which had less or no hazardous effects on human health and environment and thus it can be incorporated in Integrated Pest Management programme in okra cultivation

Rotational Surfaces in L3\mathbb{L}^3 and Solutions in the Nonlinear Sigma Model

The Gauss map of non-degenerate surfaces in the three-dimensional Minkowski space are viewed as dynamical fields of the two-dimensional O(2,1) Nonlinear Sigma Model. In this setting, the moduli space of solutions with rotational symmetry is completely determined. Essentially, the solutions are warped products of orbits of the 1-dimensional groups of isometries and elastic curves in either a de Sitter plane, a hyperbolic plane or an anti de Sitter plane. The main tools are the equivalence of the two-dimensional O(2,1) Nonlinear Sigma Model and the Willmore problem, and the description of the surfaces with rotational symmetry. A complete classification of such surfaces is obtained in this paper. Indeed, a huge new family of Lorentzian rotational surfaces with a space-like axis is presented. The description of this new class of surfaces is based on a technique of surgery and a gluing process, which is illustrated by an algorithm.Comment: PACS: 11.10.Lm; 11.10.Ef; 11.15.-q; 11.30.-j; 02.30.-f; 02.40.-k. 45 pages, 11 figure

Sterol 14α-demethylase mutation leads to amphotericin B resistance in Leishmania mexicana

Amphotericin B has emerged as the therapy of choice for use against the leishmaniases. Administration of the drug in its liposomal formulation as a single injection is being promoted in a campaign to bring the leishmaniases under control. Understanding the risks and mechanisms of resistance is therefore of great importance. Here we select amphotericin B-resistant Leishmania mexicana parasites with relative ease. Metabolomic analysis demonstrated that ergosterol, the sterol known to bind the drug, is prevalent in wild-type cells, but diminished in the resistant line, where alternative sterols become prevalent. This indicates that the resistance phenotype is related to loss of drug binding. Comparing sequences of the parasites’ genomes revealed a plethora of single nucleotide polymorphisms that distinguish wild-type and resistant cells, but only one of these was found to be homozygous and associated with a gene encoding an enzyme in the sterol biosynthetic pathway, sterol 14α-demethylase (CYP51). The mutation, N176I, is found outside of the enzyme’s active site, consistent with the fact that the resistant line continues to produce the enzyme’s product. Expression of wild-type sterol 14α-demethylase in the resistant cells caused reversion to drug sensitivity and a restoration of ergosterol synthesis, showing that the mutation is indeed responsible for resistance. The amphotericin B resistant parasites become hypersensitive to pentamidine and also agents that induce oxidative stress. This work reveals the power of combining polyomics approaches, to discover the mechanism underlying drug resistance as well as offering novel insights into the selection of resistance to amphotericin B itself

Low-field conduction in the D-region of the ionosphere in the presence of a high-field signal

The theory of conduction in the lower ionosphere, due to a low-field probing signal, in the presence of a high-field disturbing signal, has been developed, neglecting the effect of earth's magnetic field and considering elastic collisions with neutral molecules. It is found that the value of the conductivity obtained from the assumption of the Maxwellian velocity distribution of the electrons is considerably higher than that obtained for the actually existing non-Maxwellian distribution. It is also observed that the ratio of these two values decreases with the increase in the amplitude of the high-field signal. The importance of this result in relation to the interpretation of cross-modulation results has been discussed