the new circuit consists of a subexponential number of circuits, each of which is of subex-ponential size, the new circuit is also of subexponential size. The depth of the new circuit family is the same as fC n g but the top layer of MOD p gates has been \absorbed" into the symmetric gate computing B and been replaced by a layer of AND gates of small fan-in. Now, by an appeal to Lemma 9, the ci...

Trong bài báo này, toán cân bằng vector được nghiên cứu theo nón thứ tự có phần trong đại số khác rỗng. Bằng cách sử dụng bổ đề nổi tiếng KKM-Fan cùng với tính nửa liên tục trên và lồi giảm nhẹ của các tập mức, điều kiện đủ cho nghiệm đang xét không là rỗng để ánh xạ thiết lập.

In this paper, the first part, we establish the fixed point theorems for a k-set contraction map on the class Q(X,Y ), (see [1]) . The second part, we generalize the KKM pproperty on a convex set [2] to the KKM∗ property on a nearly-convex set, and then we establish fixed point theorems, matching theorems and variational inequalities for this class. Mathematics Subject Classification: 47H10, 54...

Since the fundamental theory of variational inequality was founded in the 1960s, the variational inequality theory with applications has made powerful progress and has become an important part of nonlinear analysis. It has been applied intensively to mechanics, differential equation, cybernetics, quantitative economics, optimization theory, nonlinear programming, and so forth (see [2]). In virt...