He showed that for fully indecomposable A,logr(eDA) is strictly convex over D1,D2 if and only if D1-D2≠cI for any c∈R. Here the condition of full indecomposability is shown to be replaceable by the weaker condition that A and AA be irreducible, which is the sharpest possible ...
Since H is positive definite everywhere by Theorem 4.2 or Theorem 4.3, the cost function f(x) is strictly convex by Theorem 4.8. Therefore, the problem is convex and the solution x1 = 1, x2 = 1 satisfies sufficiency condition of Theorem 4.11. It is a strict global minimum point for the...
Most of this chapter is devoted to local existence theory for analytic solutions of the differential equation u/z 1 = f near a boundary point of a strictly pseudo-convex domain. This may seem like a very special problem, but in fact, via the transformation theory of microlocal analysis, it...
under the mixed boundary condition on a bounded domain Ω. In fact, this has remained an open problem for a few decades, even for the casef(u)=up. As a matter of fact, we prove: there is no global solution for any initial data if and only if∫0∞ψ(t)f(‖S(t)u0‖∞)‖S(t...
Liouville Equation and Spherical Convex Polytopes We study the Liouville equation Δ u = -e2uin the complex plane with prescribed singularities and obtain a necessary and sufficient condition for the exist... F Luo,G Tian - 《Proceedings of the American Mathematical Society》 被引量: 171发表: ...
利用k维凸体体积给出了局部凸空间中k-严格凸和k-光滑性的定义,证明了它们是B anach空间和偶对(X,P)相应概念的推广,并指出了它们之间的对偶关系。3) K-strictly convex K-严格凸 1. In this paper,we give two new sufficient and necessary conditions for Banach spaces to be K-strictly convex by us...
for all suitable test functions. It is, however, not so easy to show that a given function f is -quasiconvex. Therefore, one often studies functions of the form g(f(v)), where is a component-wise -quasiaffine function and is convex, which is, in the setting , referred to as poly...
本文给出了广义控制系统脉冲固定模的等价条件和必要条件。 更多例句>> 4) condition equivalence 条件等价5) equivalent conditionally 条件等价性 例句>> 6) Equivalent Condition 等价性条件 1. On the basis of a new class of equivalent conditions for the solution existence of convex programming problems...
For minimizing solutions, this was made precise using De Giorgi’s \Gamma -convergence theory by Modica [33] and Kohn-Sternberg [26]. They further used this idea to show the existence of stable solutions for (1.2) in two-dimensional non-convex domains such as a dumbbell. The existence of...
Thus, an efficient condition for a local optimal solution of the considered PDE&PDI-constrained variational control problem to be its global optimal solution is derived. The theoretical development is supported by a suitable example of nonconvex optimization problem....