Sp(4,K)的WEYL模分解

给出了G=Sp(4，K)时WEYL模的分解模式，给出了Sp(4，K)的WEYL模分解。     

ON THE CONJECTURE OF GOLOMB(Ⅱ) 关于Golomb猜想(Ⅱ)

本文证明了: 定理1.若p=2~αoq_1~αq_2~α2…q_m~αm+1,α_0≥2,且multiply from t=1 to m qi-1/qi>2/3, 则在有限域GF(p)中,Golomb猜想成立。推论.设p=2~α0q_2~α2…q_m~αm+1,α_0≥2, ①若m=1,则当q_1>3时: ②若m=2,则当q_2>q_1>3时; ③若m=3,则当q_3>q_2>q_1>5时,在有限域GF(p)中,Golomb猜想成立。定理2.若p=2~α03~α1,α_0≥2,且模p的最小正平方非剩余不是原根,则在有限域GF(p)中,Golomb猜想成立。     

Sp(4,p~n)的Cartan不变量

本文给出了Sp(4,p~n)的Cartan不变量的一种计算方法。首先考虑n=1的情形,然后再推广到任意的正整数n的情形。并计算了Sp(4,7)的Cartan矩阵。     

Sp(4,p~n)的Cartan不变量

本文给出了Sp(4,p~n)的Cartan不变量的一种计算方法.首先考虑n=1的情形,然后再推广到任意的正整数n的情形.并计算了Sp(4,7)的Cartan矩阵.     

CALCULATIONS OF OPTIMUM PHASE MATCH PARAMETERS FOR THE BIAXIAL CRYSTAL KTiOPO_4

The expression for the effective nonlinear coefficient d_(eff) of a biaxial crystal such as KTiOPO_4 (KTP) is presented and numerically calculated. The theoretical walk-off angle, the influence of mismatching, and critical crystal length are discussed, alld finally the optimum phase matching angle is determined. The results provide some theoretical and practical guidance for optinum operation Of biaxial crystals.