A weighted mean matrix, denoted by (N , pn), is a lower triangular matrix with entries pk/Pn, where {pk} is a nonnegative sequence with p0 > 0, and Pn := ∑n k=0 pk. Mishra and Srivastava [1] obtained sufficient conditions on a sequence {pk} and a sequence {λn} for the series ∑ anPnλn/npn to be absolutely summable by the weighted mean matrix (N , pn). Bor [2] extended this result to absolute sum...

Aweighted mean matrix, denoted by N,pn , is a lower triangular matrix with entries pk/Pn, where {pk} is a nonnegative sequence with p0 > 0, and Pn : ∑n k 0 pk. Mishra and Srivastava 1 obtained sufficient conditions on a sequence {pk} and a sequence {λn} for the series ∑ anPnλn/npn to be absolutely summable by the weighted mean matrix N,pn . Recently Savaş and Rhoades 2 established the correspon...

In this paper, we first consider n × n upper-triangular matrices with entries in a given semiring k. Matrices of this form with invertible diagonal entries form a monoid Bn(k). We show that Bn(k) splits as a semidirect product of the monoid of unitriangular matrices Un(k) by the group of diagonal matrices. When the semiring is a field, Bn(k) is actually a group and we recover a well-known resul...

Let G be the group of n×n upper-triangular matrices with elements in a finite field and ones on the diagonal. This paper applies the character theory of Andre, Carter and Yan to analyze a natural random walk based on adding or subtracting a random row from the row above.

Let T be an operator-weighted shift whose weights are 2-by-2 matrices. We say that, given > 0, T is in the -canonical form if each weight is an upper triangular matrix (aij), with 0 ≤ a11, a22 ≤ 1 and a12 6= 0 implies a11, a22 < . We generalize this concept to operator-weighted shifts whose weights are n-by-n matrices and we show that every polynomially bounded weighted shift, whose weights are...

Let A be a local commutative principal ideal ring. We study the double coset space of GLn(A) with respect to the subgroup of upper triangular matrices. Geometrically, these cosets describe the relative position of two full flags of free primitive submodules of A. We introduce some invariants of the double cosets. If k is the length of the ring, we determine for which of the pairs (n, k) the dou...

We resolve a 25 year old problem by showing that The Paving Conjecture is equivalent to The Paving Conjecture for Triangular Matrices.

The shape of interfacial voids formed in the epitaxial SiC/Si(111) heterosystem just underneath the SiC film has been investigated using optical microscopy and transmission electron microscopy (TEM). SiC films are grown on Si(111) substrates at two different substrate temperatures (specimen type 1 at 850°C, specimen type 2 at 1050°C) using solid-source molecular-beam epitaxy (MBE). At 850°C sub...

This paper presents a dual-band planar antenna array for ISM band applications (2.4 GHz and 2.45 GHz). This antenna is proposed for indoor applications and enables adaptive beamforming and angle of arrival (AOA) estimation. An adaptive beamforming algorithm is applied for a planar antenna array, which is able to steer its main beam and nulls in azimuth and elevation planes over a wide frequency...

Generators are found for the field of invariants of coadjoint representations for the Lie algebras that are factors of a unitriangular Lie algebra by some regular ideal.