for $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...

for vectors x, y ∈ rn, it is said that x is left matrix majorizedby y if for some row stochastic matrix r; x = ry. the relationx ∼` y, is defined as follows: x ∼` y if and only if x is leftmatrix majorized by y and y is left matrix majorized by x. alinear operator t : rp → rn is said to be a linear preserver ofa given relation ≺ if x ≺ y on rp implies that t x ≺ ty onrn. the linear preservers o...

The large-scale use of sustainable energy necessitates the latent heat storage (LHS). This study aims to increase melting performance an LHS system by designing and optimizing cesaro fins. To examine behaviours PCM (i.e., RT-82) in a finned system, 2-D transfer model is developed numerically solved. As per literature, there very literature including NC (Natural Convection) represents coordinati...

in this article, we characterize the involutiveness of the linear combination of the forma1a1 +a2a2 when a1, a2 are nonzero complex numbers, a1 is a quadratic or tripotent matrix,and a2 is arbitrary, under certain properties imposed on a1 and a2.

in this paper, at rst for a given set of real or complex numbers  with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which  is its spectrum. in continue we present some conditions for existence such nonnegative tridiagonal matrices.

Abstract Change of boundary is a method that iteratively downward continues data from star-shaped to regular surface, such as the sphere or ellipsoid revolution, and then solves value problem using continued on changed boundary. Although belongs concepts involved in development recent high-degree Earth’s gravity models, it still unclear whether iterations converge true solution for boundaries c...

Some pointwise properties of (C,α) kernel (−1 < α < 0) with respect to the Walsh–Paley system are established.

3/a) On peut éliminer le cas où bn est nul à partir d’un certain rang (ceci ne peut se produire que si tous le an sont nuls) ; dans ce cas il suffit de prendre un = 1/n. Posons vn = supp≥n bp et un = √ vn. La suite (vn) est une suite décroissante de réels strictement positifs, tend vers 0 car bn → 0, et bn ≤ vn pour tout n ∈ N∗. La suite (un) tend donc vers 0 en décroissant, et puisque bn/un ≤ ...