If R-parity is not conserved, the SUSY-threshold production process e + e − → χ 0 1 χ 0 1 could be detectable with relatively low luminosity. Hence an interesting mass range for the lightest SUSY particle χ 0 1 could be explored at the CERN LEP collider during its intermediate energy development, even before the full LEP200 upgrade is completed. We present cross section formulas and discuss eve...

as χ varies over all multiplicative characters of k. For each χ, S(χ) is real, and (by Weil) has absolute value at most 2. Evans found empirically that, for large q = #k, these q − 1 sums were approximately equidistributed for the “Sato-Tate measure” (1/2π) √ 4− x2dx on the closed interval [−2, 2], and asked if this equidistribution was provably true. Rudnick had done numerics on the sums T (χ)...

Let q be a large prime and χ the quadratic character modulo q. Let φ be a self-dual cuspidal Hecke eigenform for SL(3,Z), and f a Hecke-Maaß cusp form for Γ0(q) ⊆ SL2(Z). We consider the twisted L-functions L(s, φ × f × χ) and L(s, φ × χ) on GL(3) × GL(2) and GL(3) with conductors q6 and q3, respectively. We prove the subconvexity bounds L(1/2, φ× f × χ) φ,f,ε q, L(1/2 + it, φ× χ) φ,t,ε q for a...

Given positive integers n⩾2k, the Kneser graph KGn,k is a whose vertex set collection of all k-element subsets {1,…,n}, with edges connecting pairs disjoint sets. One classical results in combinatorics, conjectured by and proved Lovász, states that chromatic number equal to n−2k+2. In this paper, we study random KGn,k(p), is, obtained from including each independently probability p. We prove th...

In this paper, we present appendices employed in the paper ”A geometric level-set formulation of a plasma-sheath interface” by the authors. Appendix A. Local existence of sheath solutions In this appendix, we present a series of a priori estimates for the approximate solutions constructed in Step 0 Step 7 in Section 7 and then give the proof Theorem 7.3. A.1. Basic a priori estimates. In this p...

SEAL was first introduced in [1] by Rogaway and Coppersmith as a fast software-oriented encryption algorithm. It is a pseudorandom function which stretches a short index into a much longer pseudorandom string under control of a secret key pre-processed into internal tables. In this paper we first describe an attack of a simplified version of SEAL, which provides large parts of the secret tables...

Explicit closed form expressions are derived for moments of order statistics from the chi square distribution. The expressions involve Lauricella functions of type A and type B. Some numerical tabulations are provided for selected parameter values.

(a) D: α0 = 1, α1 = 1, α2 = 1. χ(D ) = 1. (b) S: α0 = 1, α1 = 0, α2 = 1. χ(S ) = 2. (c) Möbius band: α0 = 1, α1 = 2, α2 = 1. χ(M) = 0. (d) Mg of genus g: α0 = 1, α1 = 2g, α2 = 1. χ(Mg) = 2− 2g. 6. RP n = (R − {0})/{z ∼ λz} = S/{z ∼ −z} = S/Z2 RP n = σ ∪ RP n−1 implies RP n = σ ∪ σn−1 ∪ · · · ∪ σ χ(RP ) = 1 for n even and 0 for n odd. 7. CP n = (C − {0})/{z ∼ λz} = S/{z ∼ λz||λ| = 1} CP n = σ ∪ ...