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...

Given a length function L on the R-modules of a unital ring R, for any sofic group Γ, we define a mean length for every locally L-finite RΓ-module relative to a bigger RΓ-module. We establish an addition formula for the mean length. We give two applications. The first one shows that for any unital left Noetherian ring R, RΓ is stably direct finite. The second one shows that for any ZΓ-module M,...

The object of the present paper is to investigate coefficient estimates for functions belonging to the subclasses Rγ [α, β ] and C p γ [α, β ] of p-valent γ -prestarlike functions of order α and type β with negative coefficients. We obtain extreme points, distortion theorems, integral operators and radii of starlikeness and convexity for functions belonging to the classes Rγ [α, β ] and C γ [α,...

By Theorem 2.1 the product φ1φ2 is of bounded variation and by Theorem 2.24 all three Riemann–Stieltjes integrals involved exist as the limit of Riemann–Stieltjes sums as |Γ| → 0. In particular we can find a δ1 > 0 such that ∣∣∣∣∫ b a fφ2 dφ1 −RΓ(fφ2, φ1) ∣∣∣∣ < ε , ∣∣∣∣∫ b a fφ1 dφ2 −RΓ(fφ1, φ2) ∣∣∣∣ < ε for all partitions with |Γ| < δ1. Let Γ = {xi}i=0 be any partition of [a, b] with intermed...

The conformational properties of foldamers generated from Rγ hybrid peptide sequences have been probed in the model sequence Boc-Aib-Gpn-Aib-Gpn-NHMe. The choice of R-aminoisobutyryl (Aib) and gabapentin (Gpn) residues greatly restricts sterically accessible conformational space. This model sequence was anticipated to be a short segment of the Rγ C12 helix, stabilized by three successive 4f1 hy...

Let R be any ring (with 1), Γ a group and RΓ the corresponding group ring. Let H be a subgroup of Γ of finite index. Let M be an RΓ−module, whose restriction to RH is projective. Moore’s conjecture [5]: Assume for every nontrivial element x in Γ, at least one of the following two conditions holds: M1) 〈x〉 ∩ H 6= {e} (in particular this holds if Γ is torsion free) M2) ord(x) is finite and invert...

The ratios Rγ,l = B(Z → l+l−) ·σ(Zγ)/B(W → lν) ·σ(W±γ), Rγ,ν = B(Z → ν̄ν) · σ(Zγ)/B(W → lν) · σ(Wγ), RWγ = σ(Wγ)/σ(W), and RZγ = σ(Zγ)/ σ(Z) are studied as tools to probe the electroweak boson self-interactions. As a function of the minimum photon transverse momentum, Rγ,l and Rγ,ν are found to directly reflect the radiation zero present in Wγ production in the Standard Model. All four ratios ar...

Let R be a commutative noetherian ring and Γ a finite group. In this paper,we study Gorenstein homological dimensions of modules with respect to a semi-dualizing module over the group ring  . It is shown that Gorenstein homological dimensions  of an  -RΓ module M with respect to a semi-dualizing module,  are equal over R and RΓ  .