we survey some recent results on cocharacters of upper triangular matrices. in particular, we deal both with ordinary and graded cocharacter sequence; we list the principal combinatorial results; we show di erent tech-niques in order to solve similar problems.

In this paper, some elementary operations on triangular fuzzynumbers (TFNs) are defined. We also define some operations on triangularfuzzy matrices (TFMs) such as trace and triangular fuzzy determinant(TFD). Using elementary operations, some important properties of TFMs arepresented. The concept of adjoints on TFM is discussed and some of theirproperties are. Some special types of TFMs (e.g. pu...

For large classes of Schrodinger operators and Jacobi matrices we prove that if h has only one point spectrum then for φo of compact support

Let H0 be an arbitrary self-adjoint n × n matrix and H(n) be an n × n (random) Wigner matrix. We show that t 7→ Tr exp(H(n)−itH0) is positive definite in the average. This partially answers a long-standing conjecture. On the basis of asymptotic freeness our result implies that t 7→ τ(exp(a − itb)) is positive definite whenever the noncommutative random variables a and b are in free relation, wi...

O R IG IN A L A R T IC L E

‎In this paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$‎, ‎where $A_1...

Let µ be a measure with support on the real line and n ≥ 1, β > 0. In the theory of random matrices, one considers a probability distribution on the eigenvalues t1, t2,. .. , tn of random matrices, of the form P (n) (tj − ti). This is the so-called β ensemble with temperature 1/β. We explicitly evaluate the m−point correlation functions when µ is a Gauss quad-rature type measure, and use this t...