The pure spinor formalism for the superstring has recently been used to compute massless four-point two-loop amplitudes in a manifestly super-Poincaré covariant manner. In this paper, we show that when all four external states are Neveu-Schwarz, the two-loop amplitude coincides with the RNS result.

Abstract Recently, Lovejoy introduced the construct of overpartition pairs which are a natural generalization of overpartitions. Here we generalize that idea to overpartition ktuples and prove several congruences related to them. We denote the number of overpartition k-tuples of a positive integer n by pk(n) and prove, for example, that for all n ≥ 0, pt−1(tn + r) ≡ 0 (mod t) where t is prime a...

Abstract. We prove two related concentration inequalities concerning the number of rational points of hyperelliptic curves over subsets of a finite field. In particular, we investigate the probability of a large discrepancy between the numbers of quadratic residues and non-residues in the image of such subsets over uniformly random hyperelliptic curves of given degrees. We find a constant proba...

In this paper, we introduce a new definitions of the Gray weight and the Gray map for linear codes over Z9+uZ9 with u 2 = u. Some results on self-dual codes over this ring are investigated. Further, the structural properties of quadratic residue codes are also considered. Two self-dual codes with parameters [22, 11, 5] and [24, 12, 9] over Z9 are obtained.

In this paper, a modification decoding algorithm for the (89, 45, 17) QR code is proposed to decode all error patterns with weight less than six and high percentage weight-6, weight-7, and weight-8 error patterns.

Binary optimal codes often contain optimal or near-optimal subcodes. In this paper we show that this is true for the family of self-dual codes. One approach is to compute the optimum distance profiles (ODPs) of linear codes, which was introduced by Luo, et. al. (2010). One of our main results is the development of general algorithms, called the Chain Algorithms, for finding ODPs of linear codes...

mulches often use for weed control, hold soil moisture, decrease soil temperature, soil fertility, soil conservation, soil against rain and soil quality in organic farming. a field experiment was conducted to evaluate the effect of different wheat residue and sunflower densities on sunflower growth and yield during 2007 growing season at the research field of birjand university. the experimenta...