插值问题和特殊矩阵及矩阵不等式研究

In this period, the research team published 34 papers, where SCI 17. Main results are as follows: Proved that two classes of inverse M-matrices are closed under the Hadamard multiplication, in particular, the case of triangular inverse M-matrices which has highly technique and very interesting identity; Defining two new functions on a poset gave some explicit expressions of Smith’s determinant; The research team has.successfully realized the transformations from the Nevanlinna-Pick problem with infinitely many interpolation data and boundary Nevanlinna-Pick problem to Hamburger moment problems, basing on the use of the Hankel/Toeplitz vector approach, and gave a brief method to solve these types of interpolation problems. Presented a unified treatment for nondegenerate and degenerate Stieltjes moment problem, and the general.solution formula for the Stieltjes moment problem with odd moments was first.given. Completely determined Ringel-Hall algebra structure, gave its R-matrix, Showed that they satisfy a fundamental symmetry relation: Yang-Baxter equation; Defining Lusztig’s symmetries and proved that they satisfy the braid group relations, this answered a question of Sevenhant and Van den Bergh; gave a new proof of famous Kac Theorem.

研究各种插值问题（解析矩阵函数类上的N－P插值，非切与带切的有理插值，数值与矩阵值的矩量问题等）；研究相关的特殊矩阵（数值与块Hankel,Toeplitz,Bezout,Loewner,pick卣螅┑男灾始捌湎嗷ス叵担谎芯縎chur 补与广义Schur补，矩阵的Hadamard积与Fan积及矩蟾髦至康牟坏仁降取Ｕ庑┒际羌扔欣砺奂壑涤钟惺涤靡庖宓难芯靠翁狻?.