The optimality Kuhn-Tucker condition and the wolfe duality for the prein-vex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.
A sequence of spherical zonal translation networks based on the Bochner-Riesz means of spherical harmonics and the Riesz means of Jacobi polynomials is introduced, and its degree of approximation is achieved. The results obtained in the present paper actually imply that the approximation of zonal translation networks is convergent if the action functions have certain smoothness.
想 { X (t) ；t ≥ 0 } 是有出生率 q_(ii+1 ) 的一个单个出生过程(i ≥ 0 ) 并且死亡率 qij (i >
j ≥ 0 ) 。它在这篇论文被证明(ⅰ)如果在那里存在经常的 c ≥ 0 以便 b (i)-(i)+ ci 关于 i 和(i)+ u (i)是不减少的- ci ≥ 0 ( i ≥ 0 )，那么 Var X (t)-前(t)≥ -X(0)e^(-2ct), t ≥ 0 ，或(ⅱ)如果在那里存在经常的 c ≥ 0 以便 b (i)-(i)+ ci 关于 i 和(i)+ u (i)是非增加的- ci ≤ 0 ( i ≥0 )，然后 Var X (t)-前(t)≤ -X(0)e^(-2ct), t ≥ 0 。这里 b (i)=q_( i i + 1 )，一( 0 )= 0 ，(i)=∑_( j =1 )~ i jq_( i i - j )( i ≥ 1 )， u ( 0 )= u ( 1 )= 0 并且 u (i)= 1/2 ∑_( j=2 )~ i j ( j - 1 )q_( i i - j )( i ≥ 2 )。这结果为获得在的出生死亡过程盖住结果[7 ] 。
