Depending upon the various models and assumptions, the existing literature on Gamma Ray Bursts (GRBs) mentions that the gross theoretical value of the duration of the burst in the hydrodynamical models is τ ∼ rγ/2ηc, where rγ is the radius at which the blastwave associated with the fireball (FB) becomes radiative and sufficiently strong. Here η ≡ E/Mc, c is the speed of light, E is initial lab ...

Let R be a Γ-hyperring and M be an Γ-hypermodule over R. We introduce and study fuzzy RΓ-hypermodules. Also, we associate a Γhypermodule to every fuzzy Γ-hypermodule and investigate its basic properties.

We introduce notions of finiteness obstruction, Euler characteristic, L2-Euler characteristic, and Möbius inversion for wide classes of categories. The finiteness obstruction of a category Γ of type (FP) is a class in the projective class group K0(RΓ); the Euler characteristic and L2-Euler characteristic are respectively its RΓ-rank and L2-rank. We also extend the second author’s K-theoretic Mö...

We give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold X which satisfies the Witt condition. This construction is inductive. It is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index – the analytic signature of X – is well-defined. We then show how ...

Consider a countable group Γ acting ergodically by measure preserving transformations on a probability space (X,μ), and let RΓ be the corresponding orbit equivalence relation on X. The following rigidity phenomenon is shown: there exist group actions such that the equivalence relation RΓ on X determines the group Γ and the action (X,μ,Γ) uniquely, up to finite groups. The natural action of SLn(...

Present investigation was carried out to identify DNA polymorphism of IL-2Rγ and ChB6 genes. Sixty five birds belonging to the indigenous chicken of Himachal Pradesh were utilized. Good quality DNA samples were subjected to PCR-RFLP analysis using chicken specific primers. Overnight restriction enzyme digestion was carried out at 37°C with IU Hph I and Pvu II for IL-2Rγ and ChB6 genes, respecti...

We introduce the class of Rγ-convex functions and discuss that it relates to some other classes convexity. study in perspective trapezium-like inequalities, for which we also derive a new integral identity involving k-th order differentiable function. In show significance our results, several special cases offer interesting applications.

Consider a transformed linear mixed model (TLMM) obtained pre-multiplying (LMM) M : y = Zα + Rγ e by given matrix. This work concerns the problem of equalities predictors under considered two LMMs general assumptions. We characterize between best unbiased (BLUPs) LMM and its TLMM using various rank formulas block matrices elementary matrix operations.

Let G be a finite group. Suppose that Y is a projective algebraic variety over Z (i.e an integral scheme which is projective and flat over Spec (Z)) of relative dimension d. In this paper, we consider finite Galois covers π : X → Y with group G which are everywhere unramified, i.e “G-torsors”. Let F be a G-equivariant coherent sheaf on X. Consider the value of the right derived global section f...

This paper uses the theory of dual equivalence graphs to give explicit Schur expansions to several families of symmetric functions. We begin by giving a combinatorial definition of the modified Macdonald polynomials and modified Hall-Littlewood polynomials indexed by any diagram δ ⊂ Z × Z, written as H̃δ(X; q, t) and P̃δ(X; t), respectively. We then give an explicit Schur expansion of P̃δ(X; t) as...