*Correspondence: [email protected] Department of Mathematics, Faculty of Science, Cumhuriyet University, Sivas, 58 410, Turkey Abstract The discrete generalized Cesàro matrix At = (ank) is the triangular matrix with nonzero entries ank = tn–k/(n + 1), where t ∈ [0, 1]. In this paper, boundedness, compactness, spectra, the fine spectra and subdivisions of the spectra of discrete gene...

We extend Atanassov’s methods for Halton sequences in two different directions: (1) in the direction of Niederreiter (t,s)−sequences, (2) in the direction of generating matrices for Halton sequences. It is quite remarkable that Atanassov’s method for classical Halton sequences applies almost “word for word” to (t,s)−sequences and gives an upper bound quite comparable to those of Sobol’, Faure a...

Suppose U is an upper-triangular matrix, and D a nonsingular diagonal matrix whose diagonal entries appear in nondescending order of magnitude down the diagonal. It is proved that kD UDk kUk for any matrix norm that is reduced by a pinching. In addition to known examples { weakly unitarily invariant norms { we show that any matrix norm de ned by kAk def = max x 6=0; y 6=0 Re (x Ay) (x) (y) ; wh...

; a ∈ A,m ∈ M, b ∈ B} equipped with the usual 2× 2 matrix-like addition and matrix-like multiplication is an algebra. An algebra T is called a triangular algebra if there exist algebras A and B and nonzero A−B-bimodule M such that T is (algebraically) isomorphic to Tri(A,M,B) under matrixlike addition and matrix-like multiplication; cf. [1]. For example, the algebra Tn of n × n upper triangular...

The hierarchical structure in the quark masses and mixings allows its ten physical parameters to be most conveniently encoded in mass matrices of the upper triangular form. We classify these matrices in the hierarchical, minimal parameter basis where the mismatch between the weak and mass eigenstates involves only small mixing angles. Ten such pairs are obtained for the up and down quarks. This...

We study the freeness problem for matrix semigroups. We show that the freeness problem is decidable for upper-triangular 2 × 2 matrices with rational entries when the products are restricted to certain bounded languages. We also show that this problem becomes undecidable for sufficiently large matrices.

We will restrict out attention to the simplest possible case, namely G = SL2(R), Γ = SL2(Z), and right K = SO(2)-invariant functions on Γ\G. That is, we neglect the finite primes and holomorphic automorphic forms. Let N be the subgroup of G consisting of upper-triangular unipotent matrices, and P the parabolic subgroup consisting of all upper-triangular matrices. For simplicity we give K total ...

Abstract. Let nn(C) be the algebra of strictly upper-triangular n × n matrices and X2 = {u ∈ nn(C) : u2 = 0} the subset of matrices of nilpotent order 2. Let Bn(C) be the group of invertible upper-triangular matrices acting on nn by conjugation. Let Bu be the orbit of u ∈ X2 with respect to this action. Let S2n be the subset of involutions in the symmetric group Sn. We define a new partial orde...

In studying the enumerative theory of super characters of the group of upper triangular matrices over a finite field we found that the moments (mean, variance and higher moments) of novel statistics on set partitions of [n] = {1, 2, · · · , n} have simple closed expressions as linear combinations of shifted bell numbers. It is shown here that families of other statistics have similar moments. T...

∣ p . Hardy’s inequality thus asserts that the Cesáro matrix operator C = (cj,k), given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤ p/(p − 1). (The norm is in fact p/(p − 1).) Hardy’s inequality leads naturally to the study on lp norms of general matrices. For example, we say a matrix A = (aj,k) is a weighted mean matrix if its entries satisfy aj,k = 0, k > j and aj,k ...