Approximation characteristics for diagonal operators in different computational settings

First we study several extremal problems on minimax, and prove that they are equivalent. Then we connect this result with the exact values of some approximation characteristics of diagonal operators in different settings, such as the best n-term approximation, the linear average and stochastic n-widths, and the Kolmogorov and linear n-widths. Most of these exact values were known before, but in terms of equivalence of these extremal problems, we present a unified approach to give them a direct proof.     

Extremal self-dual codes of length 64 through neighbors and covering radii

We construct extremal singly even self-dual [64,32,12] codes with weight enumerators which were not known to be attainable. In particular, we find some codes whose shadows have minimum weight 12. By considering their doubly even neighbors, extremal doubly even self-dual [64,32,12] codes with covering radius 12 are constructed for the first time.     

4维完备Einstein流形的一些注释

本文给出了在开的定向的4维流形上存在有界曲率的完备Einstein度量的障碍．     

The Existence of Infinitely Many Teichmuller Type Extremal Mappings with Special Boundary Correspondence

in the theory of quasiconformal mappings in the plane, tile problem about whetherthere exist infinitely many Teichmuller type extrmal mappings with special boundarycorrespondence is unsolved so far. In this paper an affirmative answer is given.     

Kähler Surfaces of Positive Scalar Curvature

We construct Kähler metrics of positive scalar curvature on almost all blown-up ruled surfaces of arbitrary genus. The metrics have an explicit form on ruled surfaces blown up at most twice successively from a minimal model. Our surfaces are generic in the sense that they make up a dense set in the deformations of a given ruled surface.     

Some Examples of Metrics with Positive Curvature and Negative Curvature on R￣n

ＳｏｍｅＥｘａｍｐｌｅｓｏｆＭｅｔｒｉｃｓｗｉｔｈＰｏｓｉｔｉｖｅＣｕｒｖａｔｕｒｅａｎｄＮｅｇａｔｉｖｅＣｕｒｖａｔｕｒｅｏｎＲ￣ｎ￥ＺｈｕＤａｘｉｎ；ＨｏｕＷｅｎｈｕａ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＴｉａｎｊｉｎＵｎｉｖｅｒｓ...     

Efficient estimates of the solutions of perturbed control problems

In this paper, we obtain estimates of the solutions for a sequence of strongly convex extremal problems. As applications of our abstract results, we consider optimal control problems with various types of perturbations. We estimate the solutions of problems with perturbations in the state equation and in the control constraining set. A singularly perturbed problem and a problem with perturbed time delay parameter are studied.     

On the positivity of symmetric polynomial functions. Part II: Lattice general results and positivity criteria for degrees 4 and 5

We prove that homogeneous symmetric polynomial inequalities of degree p∈{4,5} in n positive¹ variables can be algorithmically tested, on a finite set depending on the given inequality (Theorem 13); the test-set can be obtained by solving a finite number of equations of degree not exceeding p−2. Section 3 discusses the structure of the ordered vector spaces and . In Section 4, positivity criteria for degrees 4 and 5 are stated and proved. The main results are Theorems 10-14. Part III of this work will be concerned with the construction of extremal homogeneous symmetric polynomials (best inequalities) of degree 4 in n positive variables.