Detailed leading order QCD predictions are given for the scaling, angular, and helicity dependence of the reactions yy -f 6 (M=r, K, p, etc.) at large momentum transfer. In addition to providing a basic test of QCD at short distances, measurements can be used to determine the process-independent meson distribution amplitudes $M(x,Q). Other related two-photon channels such as yy+yp, y*y+rO, no, ...

In this chapter, we investigate the properties of domination parameters of Hypercubes and star graphs. For Hypercubes Q, we prove that if n = 1, then (Q) = = = n—k We also prove that -y(Q) = 7, y(Q) = 12, y(Q) = 16 and 'y(Q) 2 for all n 7. We determine the values of 'yj, Yt, 'Ye and yp for Qn where n 6 and obtain bounds for these parameters for n > 7. For n-star graph S we determine the values ...

Let K be a field of characteristic 0 and S = K[x1, . . . , xn] the polynomial ring over K with graded maximal ideal m = (x1, . . . , xn). Denote by βi(M) = Tor S i (K,M) the ith Betti number of a finitely generated graded module M and by Gin(I) the generic initial ideal of a graded ideal I with respect to the reverse lexicographical order. In this paper we answer (positively) a question raised ...

D uring male meiosis the X and Y chromosomes pair along much of their length, with a single obligatory recombination event usually occurring in the pseudoautosomal region (PAR) at the tip of Xp and Yp, thus maintaining identity of the sex chromosome PARs. Occasionally illegitimate crossover occurs outside the PAR, resulting in the transfer of Y specific sequences onto the X chromosome. Such tra...

D uring male meiosis the X and Y chromosomes pair along much of their length, with a single obligatory recombination event usually occurring in the pseudoautosomal region (PAR) at the tip of Xp and Yp, thus maintaining identity of the sex chromosome PARs. Occasionally illegitimate crossover occurs outside the PAR, resulting in the transfer of Y specific sequences onto the X chromosome. Such tra...

drought stress is one of the most important dangers for increasing the yield and good production of crops in iran and the world. to evaluate the genetic diversity of rapeseed genotypes, identifying the drought resistance indices and drought tolerant genotypes, 16 genotypes were tested in a randomized complete block design (rcbd) with three replications and two different water regimes (irrigated...

Positive-definite means that gp(v, v) > 0 for every v 6= 0, v ∈ TpM . Smoothly depending on p means that for every pair Xp,Yp of C ∞-smooth vector fields on M the expression gp(Xp, Yp) defines a C ∞-smooth function of p ∈M . Alternatively, consider a coordinate neighbourhood on M containing p and let x, i = 1, . . . , dimM be the local coordinates. Then any two tangent vectors u, v ∈ TpM may be...

Let Yl, , Yp be monomials over the indeterminates Xl, , xq. For every y (yl, , yp) there is some minimum number L(y) of multiplications sufficient to compute y 1, , Yo from x 1, , xq and the identity 1. Let L(p, q, N) denote the maximum of L(y) over all y for which the exponent of any indeterminate in any monomial is at most N. We show that if p (N+ 1) () and q (N+ 1)(), then L(p, q, N) min {p,...