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¡¤Chang-Jiang Bu ¡¤Chi-Kwong Li
¡¤Xiaomin Tang ¡¤Qingwen Wang
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Abstracts

 Name£ºChongguang Cao Institutions£ºHeilongjiang University Title£ºMapping preserve classical adjoint of product of two matrices

 Name£ºChangjiang Bu Institutions£ºHarbin Engineering University Title£ºSome old and new results in HEU Abstract£ºIn recent years, many results on matrix and graph theory are given by the research group of Harbin Engineering University. In this talk, we mainly introduce our some new results on Drazin (group) inverse of matrices, sign pattern of generalized inverse and graph spectra.

 Name£ºZhoujiang Institutions£ºHarbin Engineering University Title£ºSignless Laplacian spectral characterization of starlike trees Abstract£ºThe multiset of eigenvalues of the signless Laplacian matrix of graph  is called the signless Laplacian spectrum of . A graph is said to be determined by its signless Laplacian spectrum if there is no other non-isomorphic graph with the same signless Laplacian spectrum. A tree is called starlike if it has exactly one vertex of degree greater than 2. In this talk, we show that starlike trees with maximum degree at least 5 are determined by their signless Laplacian spectra. (This is joint work with Changjiang Bu.)

 Name£ºMinghua Lin Institutions£ºUniversity of Waterloo Title£ºThe generalized Wielandt inequality in inner product spaces Abstract£ºA new inequality between angles in inner product spaces is formulated and proved. It leads directly to a concise statement and proof of the generalized Wielandt inequality, including a simple description of all cases of equality. As a consequence, several recent results in matrix analysis and inner product spaces are improved. The talk is based on this manuscript http://arxiv.org/abs/1201.6294

 Name£ºüSÒãÇà Institutions£ºÌ¨ž³‡øÁ¢ÖÐÉ½´óŒW Title£ºCompact disjointness preserving operators Abstract£ºWe show that the compactness, the weak compactness, and the complete continuity of a disjointness preserving linear operator between continuous function spaces are equivalent. They provide a nuclear representation of the operator, and implement a tree structure on the underlying spectral space. This makes graph theoretic technique is applicable in studying these kind of operators.

 Name£ºQingxiang Xu Institutions£ºShanghai Normal University Title£ºExplicit characterization of the Drazin index Abstract: Let $\mathbb{B}\,(X)$ be the set of bounded linear operators on a Banach space $X$, and $A\in\mathbb{B}\,(X)$ be Drazin invertible.  An element $B\in\mathbb{B}\,(X)$ is  said to be a stable perturbation of $A$ if $B$ is Drazin invertible and $I-A^\pi-B^ pi$I-A^\pi-B^\pi$is invertible,where$I$is the identity operator on$X$,$A^\pi$and$B^\pi$where$I$is the identity operator on$X$,$A^\pi$and$B^\pi$arethe spectral projectors of$A$and$B$respectively. Under thecondition that$B$is a stable perturbation of$A$, a formula forthe Drazin inverse$B^D$is derived. Based on this formula, a newapproach is provided to the computation of the explicit Drazin indices of certain$2\times 2$operator matrices.  Name£ºJianlong Chen Institutions£ºSoutheast University Title£ºGeneralized Drazin inverses in rings and Banach algebras Abstract£ºThe notion of the generalized Drazin inverse in Banach algebras and rings are introduced in 1996 and 2002, respectively. Because of desirable spectral property, the generalized Drazin inverse attracted widely concern. In this talk, we introduce additive and multiplicative property of (generalized) Drazin invertibility of elements in a ring. In particular, we present Cline's formula and Jacobson's lemma for the generalized Drazin inverse in rings, and the applications of the related results of generalized Drazin inverses in Banach algebras.  Name£º¹ùîÚ Institutions£ºÌ«Ô­Àí¹¤´óÑ§ Title£ºLocal channel preserving quantum correlations  Name£ºÑà×Ó×Ú Institutions£º³¤½­´óÑ§ÐÅÏ¢ÓëÊýÑ§Ñ§Ôº Title£ºThe SNIEP with prescribed diagonal entries: a necessary and sufficient condition Abstract£ºWith the help of the inverse of the interlacing theorem, this paper presents a necessary and sufficient condition for the symmetric nonnegative inverse eigenvalue problem. Meanwhile, we present a family of matrixes with prescribed diagonal entries.  Name£ºÑîÁ¦ Institutions£ºÎ÷°²¹¤Òµ´óÑ§ÀíÑ§Ôº Title£ºA theorem on the decomposability of high-order linear differential operators with variable coefficients Abstract£ºIn this paper, we study the decomposability of high-order linear differential operators with variable coefficients, and obtain a decomposition theorem of high-order linear differential operators. Applying this result, we give out a sufficient condition that high-order linear differential equations can be reduced into lower order linear differential equations.  Name£ºDeyu Wu Institutions£ºSchool of Mathematical Science Title£ºOn the Adjoint of Operator Matrices with Unbounded Entries Abstract£ºIn this report, the adjoint of an densely defined block operator matrix is studied ,and by applying perturbation theory of linear operator and Frobenius-Schur factorization, the sufficient conditions under which the conclusion holds are obtained.  Name£ºµó»³°² Institutions£º¶«±±Ê¦·¶´óÑ§ÊýÑ§ÓëÍ³¼ÆÑ§Ôº Title£ºOn Condition Numbers for Constrained Linear Least Squares Problems Abstract£ºCondition numbers are important in numerical linear algebra, who can tell us the poste-rior error bounds for the computed solution. Classical condition numbers are normwise, but they ignore the input data sparsity and/or scaling. Componentwise analysis had been introduced, which gives a powerful tool to study the perturbations on input and output data regarding on the sparsity and scaling. In this paper under componentwise perturbation analysis we will study the condition numbers for constrained linear least squares problems. The obtained expressions of the condition numbers avoid the explicit formingKronecker products, which can be estimated by power methods eﬃciently. Numerical examples show that our condition numbers can give better error bounds.  Name£º°×Õý¼ò Institutions£ºÏÃÃÅ´óÑ§ Title£ºApplications of the Alternating Direction Method of Multipliers to the Semidenite Inverse Quadratic Eigenvalue Problem with Partial Eigenstructure Abstract£ºThis paper shows that the alternating direction method of multipliers (ADMM) is an efficient approach to solving the semidefinite inverse quadratic eigenvalue problem (SDIQEP) with partial eigenstructure. We derive several ADMM-based iterative schemes for SDIQEP,and demonstrate their efficiency for large-scale cases of SDIQEP numerically.  Name£ºÍõ‡øÖÙ Institutions£º‡øÁ¢½»Í¨´óŒW Title£ºMaximizing Numerical Radii of Weighted Shifts under Weight Permutations Abstract£ºLet ( ) and , the symmetric group of all permutations of 1, 2, ¡­, n. Suppose is the weighted cyclic matrix with the weight and denotes its numerical radius. We characterize those which satisfy The characterizations for unilateral and bilateral weighted (backward) shifts are also obtained.  Name£ºMao-Ting Chien Institutions£ºSoochow University Taiwan Title£ºNumerical range and central force Abstract£ºLetA be an n ¡Á n matrix. A homogeneous polynomial associated with A is defined by FA(t, x, y) = det(t In + x(A + A*)/2+ y(A ¨C A*)/(2i)). It is known that the numerical range of A, which is defined as the set W(A) = {¦Î*A¦Î : ¦Î ¡Ê Cn, ¦Î* ¦Î =1}, is the convex hull of the real part of the dual curve of FA(t, x, y) = 0. In this talk, I will discuss orbits of some central forces which are interpreted as the algebraic curves FA(1, x, y) = 0 for some matrix A. It is shown that the orbit of a point mass under a central force f(r) = − r−3 with angular momentum M, satisfying M/(M2 − 1)1/2 = m/p, is represented by the algebraic curve FA(1, x, y) = 0 for some  Name: …ÇÅàÔª Institutions£º‡øÁ¢½»Í¨´óŒW Title£ºNumerical ranges of nilpotent operators Abstract£ºIn this talk, we present properties of the numerical ranges of nilpotent operators on a (possibly infinite-dimensional) Hilbert space. More precisely, we show that (1) if A is a nonzero nilpotent operator, then 0 is always in the interior of its numerical range W(A) and the boundary of W(A) is a differentiable curve, (2) if A is as in (1) with nilpotency n, then its numerical radius w(A ) is at most the product of n-1 and the (generalized) Crawford number (i.e., the distance from the origin to the boundary of W(A)), and (3) in contrast to the finite-dimensional case, a noncircular elliptic disc can be the numerical range of a nilpotent operator with nilpotency 3 on an infinite-dimensional space.  Name: Ðì°²±ª Institutions£º¹ðÁÖµç×Ó¿Æ¼¼´óÑ§ Title£ºNorm-constrained least-squares solutions to the matrix equation AXB=C Abstract£ºIn this paper, an iterative method to compute the norm-constrained least-squares solutions of the matrix AXB=C is proposed. Numerical experiments are performed to illustrate the efficiency of the algorithm.  Name: ÕÅÃôæõ Institutions£º±±¾©ÓÊµç´óÑ§¹ú¼ÊÑ§Ôº Title£ºNorm-constrained least-squares solutions to the matrix equation AXB=C Abstract£ºIn this note we consider the classical gambler's ruin problem with two players as a random walk problem. Ruin probability in matrix form is expressed and it can be easily calculate in MATLAB. This two-gambler's ruin model can be also extended to multiple transition states. And an in-depth analysis is given  Name£ºChi-Kwong Li Institutions£ºCollege of William and Mary Title£ºPhysical transformation of quantum states Abstract£ºGiven two sets of quantum states$\{A_1, \dots, A_k\}$and$\{B_1, \dots, B_k\}$, represented as sets as density matrices, necessary and sufficient conditions are obtained for the existence of a physical transformation$T$, represented as a trace-preserving completely positive map, such that$T(A_i) = B_i$for$i = 1, \dots, k$.General completely positive maps without the trace-preserving requirement, and unital completely positive maps transforming the states are also considered.  Name£ºZejun Huang Institutions£ºPolytechnic University Title£ºPartial matrices all of whose completions have the same rank Abstract£ºWe characterize the partial matrices all of whose completions have the same rank, determinethe largest number of indeterminates in such partial matrices of a given size, and determine the partial matrices that attain this largest number  Name£ºChunyuan Deng Institutions£ºSouth China Normal University Title£ºOn invertibility of combinations of k-potent operators Abstract£ºIn this talk, we will report some recent results on the general invertibility of the prod-ucts and di®erences of projectors and generalized projectors. The invertibility, the group invertibility and the k-potency of the linear combinations of k-potents are investigated, under certain commutativity properties imposed on them. In addition, the range relations of projectors and the detailed representations for various inverses are presented.  Name£º¶ÅË¨Æ½ Institutions£ºÏÃÃÅ´óÑ§ Title£ºThe structure of nonlinear -Lie derivations on von Neumann algebras Abstract£ºThe structures of nonlinear -Lie derivations( including nonlinear derivations, Lie derivations, Jordan derivations) on von Neumann algebras with no central summands of type are given.  Name£ºKarol Zyczkowski Institutions£ºUniwersytet Jagielloñski Title£ºAlmost Hadamard matrices Abstract£ºWe analyze "almost Hadamard matrices"- orthogonal matrices of a given order N with modulus of all elements distributed as uniform as possible. Formally an Almost Hadamard matrix is an orthogonal matrix, for which the 1-norm on O(N) achieves a local maximum of. Our study includes a detailed discussion of the circulant case and of the two-entry case, with the construction of several families of examples, and some 1-norm computations.  Name£ºFangyan Lu Institutions£ºSuzhou University Title£ºSimilarity-preserving linear maps on B(X) Abstract£ºLet$X$be an infinite-dimensional Banach space,$B(X)$the algebra of all bounded linear operators on$X$. Then a bijective linear map$\phi: B(X)\to B(X)$is similarity-preserving if and only if one of the following holds: \begin{itemize} \item[(1).] There exist a nonzero complex number$c$, an invertible bounded operator$T$in$B(X)$and a similarity-invariant linear functional$h$on$B(X)$with$h(I)\ne -c$such that$\phi(A)=cTAT^{-1}+h(A)I$for all$A\in B(X)$;\item[(2).] There exist a nonzero complex number$c$, an invertible bounded operator$T: X^*\to X$and a similarity-invariant linear functional$h$on$B(X)$with$h(I)\ne -c$such that$\phi(A)=cTA^*T^{-1}+h(A)I$for all$A\in B(X)$. \end{itemize}  Name£ºMan-Duen Choi Institutions£ºMath Department, University of Toronto Title£º The Taming of the Shrew with Positive Linear Maps Abstract£ºI look into the full structure of positive linear maps between matrix algebras. In particular, I wish to tame the quantum entanglements, from the pure mathematical point of view. Note that the research work along these lines, has been proven to be useful to the foundation of abstract quantum information in the light of (the reality of) quantum computers.  Name£ºChangqing Xu Institutions£ºZhejiang A&F University Title£ºNonnegative Matrix Factorization and its Applications in Compressive sensing Abstract£ºThe study of the recovery of sparse signals from limited measurements of signals (which have relatively few nonzero terms or whose coefficients in some fixed basis have relatively few nonzero entries ) has been blooming in recent few years since 2006 when E.Candes, J. Romberg, T. Tao, D. Donoho jointly gave deep investigation. The core idea of this relatively young field appeared in a pioneering work by Stephane Mallat and Zhifeng Zhang in 1993. In this talk we will introduce the method of nonnegative matrix factorization (NMF) to achieve the low rank approximation (LRA) of the data matrix, by which we can facilitate the progress of the traditional OMP (orthogonal matching pursuit), and thus improve the performance of the algorithm.  Name£ºTin-Yau Tam Institutions£ºDepartment of Mathematics, Auburn University Title£ºOn Ky Fan's Result on Eigenvalues and Real Singular Values Abstract£ºKy Fan's result states that the real parts of the eigenvalues of an$n\times n$complex matrix$A$is majorized by the real singular values of$A$. The converse was established independently by Amir-Mo\'ez and Horn, and Mirsky. We extend the results in the context of complex semisimple Lie algebras. The real semisimple case is also discussed. The complex skew symmetric case and the symplectic case are explicitly worked out in terms of inequalities. The symplectic case and the odd dimensional skew symmetric case can be stated in terms of weak majorization. The even dimensional skew symmetric case involves Pfaffian. Name£ºXiaofei Qi Institutions: Shanxi University Title£ºCharacterizations of Lie ($\xi$-Lie) derivations on some rings and algebras Abstract£ºLet$\mathcal A$be an algebra over a field$\mathbb F$. For any scalar$\xi\in {\mathbb F}$, a map$L : {\mathcal A}\rightarrow{\mathcal A}$is called a$\xi$-Lie derivation if$ [L(A);B]_\xi + [A;L(B)]_\xi = L([A;B]_\xi)$, where$[A;B]_\xi= AB-\xi BA$is the$\xi$-Lie product of$A,B \in {\mathcal A}$. In this talk, such maps on some rings and algebras are characterized and the relations$L$to the derivations are revealed.  Name£ºHwa-Long Gau Institutions£ºNational Central University Title£ºWeighted Shift Matrices Abstract£ºAn$n$-by-$n$($n\ge 3$) weighted shift matrix$A$is one of the form $$\left[\begin{array}{cccc}0 & a_1 & & \\ & 0 & \ddots & \\ & & \ddots & a_{n-1} \\ a_n & & & 0\end{array}\right],$$ where the$a_j$'s, called the weights of$A$, are complex numbers. Assume that all$a_j$'s are nonzero and$B$is an$n$-by-$n$weighted shift matrix with weights$b_1, \ldots, b_n$. We show that$B$is unitarily equivalent to$A$if and only if$b_1\cdots b_n=a_1\cdots a_n$and, for some fixed$k$,$1\le k \le n$,$|b_j| = |a_{k+j}|$($a_{n+j}\equiv a_j$) for all$j$. Next, we show that$A$is reducible if and only if$A$has periodic weights, that is, for some fixed$k$,$1\le k \le \lfloor n/2\rfloor$,$n$is divisible by$k$, and$|a_j|=|a_{k+j}|$for all$1\le j\le n-k$. Finally, we prove that$A$and$B$have the same numerical range if and only if$a_1\cdots a_n=b_1\cdots b_n$and$S_r(|a_1|^2, \ldots, |a_n|^2)=S_r(|b_1|^2, \ldots, |b_n|^2)$for all$1\le r\le \lfloor n/2\rfloor$, where$S_r$'s are the circularly symmetric functions.  Name£ºZhongshan Li Institutions£ºGeorgia State University Title£ºSign patterns with minimum rank 2 and upper bounds on minimum ranks Abstract£ºA {sign pattern (matrix)} is a matrix whose entries are from the set$\{+, -, 0\}$. The minimum rank (resp., rational minimum rank) of a sign pattern matrix$\cal A$is the minimum of the ranks of the real (resp., rational) matrices whose entries have signs equal to the corresponding entries of$\cal A$. The notion of a condensed sign pattern is introduced.A new, insightful proof of the rational realizability of the minimum rank of a sign pattern with minimum rank 2 is obtained. Several characterizations of sign patterns with minimum rank 2 are established, along with linear upper bounds for the absolute values of an integer matrix achieving the minimum rank 2. A known upper bound for the minimum rank of a$(+,-)$sign pattern in terms of the maximum number of sign changes in the rows of the sign pattern is substantially extended to obtain upper bounds for the rational minimum ranks of general sign pattern matrices. The new concept of the number of polynomial sign changes of a sign vector is crucial for this extension. Another known upper bound for the minimum rank of a$(+,-)$sign pattern in terms of the smallest number of sign changes in the rows of the sign pattern is also extended to all sign patterns using the notion of the number of strict sign changes. Some examples and open problems are also presented.  Name£ºChi-Keung Ng Institutions£ºChern's Instutitute of Mathematics, Nankai University Title£ºA Murray-von Neumann type classification of$C^*$-algebras Abstract£º\noindent Abstract: We define type$\mathfrak{A}$, type$\mathfrak{B}$, type$\mathfrak{C}$as well as$C^*$-semi-finite$C^*$-algebras.It is shown that a von Neumann algebra is a type$\mathfrak{A}$, type$\mathfrak{B}$, type$\mathfrak{C}$or$C^*$-semi-finite$C^*$-algebra if and only if it is, respectively, a type I, type II, type III orsemi-finite von Neumann algebra.Any type I$C^*$-algebrais of type$\mathfrak{A}$(actually, type$\mathfrak{A}$coincides with the discreteness as defined by Peligrad and Zsid\'{o}), and any type II$C^*$-algebra (as defined by Cuntz and Pedersen) is of type$\mathfrak{B}$. Moreover, any type$\mathfrak{C}C^*$-algebra is of type III (in the sense of Cuntz and Pedersen). Conversely, any purely infinite$C^*$-algebra (in the sense of Kirchberg and R{\o}rdam) with real rank zero is of type$\mathfrak{C}$, and any separable purely infinite$C^*$-algebra with stable rank one is also of type$\mathfrak{C}$. We also prove that type$\mathfrak{A}$, type$\mathfrak{B}$, type$\mathfrak{C}$and$C^*$-semi-finiteness are stable under taking hereditary$C^*$-subalgebras, multiplier algebras and strong Morita equivalence. Furthermore, any$C^*$-algebra$A$contains a largest type$\mathfrak{A}$closed ideal$J_\mathfrak{A}$, a largest type$\mathfrak{B}$closed ideal$J_\mathfrak{B}$, a largest type$\mathfrak{C}$closed ideal$J_\mathfrak{C}$as well as a largest$C^*$-semi-finiteclosed ideal$J_\mathfrak{sf}$.Among them, we have$J_\mathfrak{A} + J_\mathfrak{B}$being anessential ideal of$J_\mathfrak{sf}$, and$J_\mathfrak{A} + J_\mathfrak{B} + J_\mathfrak{C}$being anessential ideal of$A$. On the other hand,$A/J_\mathfrak{C}$is always$C^*$-semi-finite, and if$A$is$C^*$-semi-finite, then$A/J_\mathfrak{B}$is of type$\mathfrak{A}$.Finally, we show that these results hold if type$\mathfrak{A}$, type$\mathfrak{B}$,type$\mathfrak{C}$and$C^*$-semi-finiteness are replaced by discreteness,type II, type III and semi-finiteness (as defined by Cuntz andPedersen), respectively \smallskip\noindent [It is a joint work with Ngai-Ching Wong]  Name£ºRaymond Sze Institutions£ºThe Hong Kong Polytechnic University Title£ºLinear Preservers of spectral radius of tensor products Abstract£ºIn this talk, characterization of linear maps leaving invariant the spectral radius of Hermitian matrices in tensor form$A\otimes B$will be presented. a brief survey of recent results on linear preserver problems relating to tensor product is given. In addition, some other related results will also be mentioned This talk is based on a joint work with A. Fo\v sner, Z. Huang, and C.K. Li.  Name£ºShigeru Furuichi Institutions£º Title£ºOn some refinements of Young inequalities for positive operators Abstract£ºWe show two different kinds of refinements of Young inequalities for positive operators.Based on one of refinements, we give two reverse Young inequalities. We also give alternative reverse Young inequalities. This talk is based on the following papers.[1] S.Furuichi, On refined Young inequalities and reverse inequalities, Journal of Mathematical inequalities,Vol.5(2011),pp.21-31.[2] S.Furuichi, Refined Young Inequalities with Specht's Ratio,J.Egypt.Math. Soc. (10.1016/j.joems.2011.12.010), in press.[3] S.Furuichi, and N. Minculete, Alternative reverse inequalities for Young's inequality, Journal of Mathematical inequalities, Vol.5(2011),pp. 595¨C600.  Name£ºNathaniel Johnston Institutions£ºUniversity of Guelph Title£ºRight CP-Invariant Cones of Superoperators Abstract£ºWe consider cones of superoperators (i.e., linear maps on matrices) that are closed under composition on one side by completely positive maps. We see that many results involving positive and superpositive maps follow from this simple property. We also consider other examples motivated by quantum information theory, and we show that every such cone corresponds to an abstract operator system  Name£ºYiu Tung Poon Institutions£ºIowa State University Title£ºLinear Preservers of Tensor Product of Unitary Orbits, and Product Numerical Range Abstract£ºIt is shown that the linear group of automorphism of Hermitian matrices whichpreserves the tensor product of unitary orbits is generated by {\bf natural} automorphisms: change of an orthonormal basis in each tensor factor, partial transpose in each tensor factor, and interchanging two tensor factors of the same dimension. The result is then applied to show that automorphisms of the product numerical ranges have the same structure  Name£ºTam, Bit-Shun Institutions£ºTamkang University µ­½­´óŒW”µŒWÏµ Title£ºEvery rational number is the sum of the entries of the inverse of the adjacency matrix of a nonsingular graph Abstract£ºFor a graph$G$we use$A(G)$to denote the adjacency matrix of$G$. It is proved that for any given integer$a$, every rational number can be attained as the sum of the entries of the inverse of the matrix$A(G)+aI$, where$G$is a connected graph for which$-a$is not an eigenvalue of$A(G)$. Our proof depends on a characterization of the non-singularity of a matrix in the$2\times 2$block form$\left[\begin{array}{cc}A_1&J\\ J^T&A_2\end{array}\right]$, where$A_1,A_2$are general real symmetric matrices with nullity$0$or$1$and$J$stands for a matrix of all$1$'s. As another application of the latter characterization, we find equivalent conditions for vertex-disjoint graphs$G_1,G_2$to satisfy${\rm rank}(A(G_1\vee G_2)) = {\rm dnzr}(A(G_1\vee G_2))$, where$G_1\vee G_2$is the join of$G_1$,$G_2$and for any matrix$A$,${\rm dnzr}(A)$denotes the number of distinct nonzero rows of$A$; thus we provide a new proof for Sillke's conjecture that for every cograph$G$,${\rm rank}(A(G)) = {\rm dnzr}(A(G))$. This talk is based on a joint work with Liang-Hao Huang  Name£ºÔøÇåÆ½ Institutions£º¸£½¨Ê¦·¶´óÑ§ Title£ºSpectra originated from semi-B-Fredholm theory and commuting perturbations Abstract£ºIn [\cite{Burgos-Kaidi-Mbekhta-Oudghiri}], Burgos, Kaidi, Mbekhta and Oudghiri provided an affirmative answer to a question of Kaashoek and Lay and proved that an operator$F$is power finite rank if and only if$\sigma_{dsc}(T+F) =\sigma_{dsc}(T)$for every operator$T$commuting with$F$. Later, several authors extended this result to the essential descent spectrum, the left Drazin spectrum and the left essentially Drazin spectrum. In this paper, using the theory of operator with eventual topological uniform descent and the technique used in [\cite{Burgos-Kaidi-Mbekhta-Oudghiri}], we generalize this result to various spectra originated from seni-B-Fredholm theory. As immediate consequences, we give affirmative answers to several questions posed by Berkani, Amouch and Zariouh. Besides, we provide a general framework which allows us to derive in a unify way commuting perturbational results of Weyl-Browder type theorems and properties (generalized or not). These commuting perturbational results, in particular, improve many recent results of [\cite{Berkani-Amouch}, \cite{Berkani-Zariouh partial}, \cite{Berkani Zariouh}, \cite{Berkani Zariouh Functional Analysis}, \cite{Rashid gw}] by removing certain extra assumptions.  Name£ºShuchao Li Institutions£ºCentral China Normal University Title£ºOrdering trees by the minimum entry of their doubly stochastic graph matrices Abstract£º  Name£ºYongge Tian Institutions£ºCentral University of Finance and Economics Title£ºFormulas for the extremal ranks and inertias of the matrix-valued functions$A + BXC$and$A + BXB^*$when the rank of$X$is fixed Abstract£ºClosed-form formulas are established for calculating theÂ maximal and minimal ranks and inertias of the matrix-valued functionsÂ$A + BXC$and$A + BXB^*$under the restriction rank$(X) =k$Â by using certain simultaneous decompositions of$A$,$B$and$C$.  Name£ºXIAOMIN TANG Institutions£ºHeilongjiang University Title£ºROTA-BAXTER OPERATORS ON 4-DIMENSIONAL SIMPLE COMPLEX ASSOCIATIVE ALGEBRAS Abstract£ºRota-Baxter operators or relations were introduced to solve certain analytic and combinatorial problems and then applied to many fields in mathematics and mathematical physics. In this paper, we commence to study the Rota-Baxter operators of weight zero on 4-dimensional simple associative algebra. Such operators satisfy (the operator form of) the classical Yang-Baxter equation on the general linear Lie algebra.  Name£ºYimin Wei Institutions£ºFudan University Title£ºA sharp version of Bauer¨CFike's theorem Abstract: In this talk, we present a sharp version of Bauer¨CFike's theorem. We replace the matrix norm with its spectral radius or sign-complex spectral radius for diagonalizable matrices; 1-normand$\infty\$-norm for non-diagonalizable matrices.We also give thea pplications to the pole placement problem and the singular system Name£ºQingwen Wang Institutions£ºShanghai University Title£ºThe new developments of matrix equations Abstract: This talk gives some new developments of some systems of linear and nonlinear matrix equations, presents some applications of the new results

 Name£ºXiao Ji Liu Institutions£ºGuangxi University of Nationalities Title£ºThe perturbation of the generalized inverse Abstract: In this paper, we present the explicit expressions of the perturbation of the generalized inverse under different conditions, we give the upper bounds of generalized inverse .and apply the results to the relative errors of the solution of the general restricted linear equation

 Name£ºYang Zhang Institutions£ºUniversity of Manitoba Title£ºComputing the Hermite Form of a Quaternion Matrix Abstract: In this talk, we discuss an algorithm to compute the Hermite form of a quaternion matrix, and give a careful analysis of the complexity in terms of matrix size and entry degree.

 Name£ººî½ú´¨ Institutions£ºÌ«Ô­Àí¹¤´óÑ§ Title£ºConvex combination preserving maps and quangtum measurement Abstract: We show an essential relationship between quantum measurement and a convex combination preserving maps. This gives a geometric charactarization of invertible quantum measurment. Similar characterization of invertible local quantum measurement is also obtained.

 Name£º×ó¿ÉÕý Institutions£ºGeneralized inverses of combinations of idempotent operators Title£ºConvex combination preserving maps and quangtum measurement Abstract: Studied the criteria and representation of the Drazin inverse of combinations of two idempotent operators on a Hilbert space. By using the methods of splitting operator¡¯s matrix into blocks and space decompositions, the existence and calculation formulas of Drazin inverse of the combinations aP + bQ + cPQ of two idempotent operators P and Q are obtained under the conditions PQP = 0, PQP = P and PQP = PQ respectively. These generalized the related results of Deng Chunyuan¡¯s work, which characterized the Drazin inverse of the sumand difference of two idempotents.