In this paper we introduce a special form of symmetric matrices that is called central symmetric $X$-form matrix and study some properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.

It is well known that the matrix exponential function has practical applications in engineering and applied sciences. In this paper, we present some new explicit identities to the exponential functions of a special class of matrices that are known as central-symmetric $X$-form. For instance, $e^{mathbf{A}t}$, $t^{mathbf{A}}$ and $a^{mathbf{A}t}$ will be evaluated by the new formulas in this par...

the matrix functions appear in several applications in engineering and sciences. the computation of these functions almost involved complicated theory. thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. the aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. more...

it is well known that the matrix exponential function has practical applications in engineering and applied sciences. in this paper, we present some new explicit identities to the exponential functions of a special class of matrices that are known as central-symmetric $x$-form. for instance, $e^{mathbf{a}t}$, $t^{mathbf{a}}$ and $a^{mathbf{a}t}$ will be evaluated by the new formulas in this par...

Some probability distributions (e.g., Gaussian) are symmetric, some (e.g., lognormal) are non-symmetric (skewed). How can we gauge the skeweness? For symmetric distributions, the third central moment C3 def = E[(x − E(x))] is equal to 0; thus, this moment is used to characterize skewness. This moment is usually estimated, based on the observed (sample) values x1, . . . , xn, as C3 = 1 n · n ∑ i...

We say that X = [xij ]i,j=1 is symmetric centrosymmetric if xij = xji and xn−j+1,n−i+1, 1 ≤ i, j ≤ n. In this paper we present an efficient algorithm for minimizing ‖AXB + CY D − E‖ where ‖ · ‖ is the Frobenius norm, A ∈ Rt×n, B ∈ Rn×s, C ∈ Rt×m, D ∈ Rm×s, E ∈ Rt×s and X ∈ Rn×n is symmetric centrosymmetric with a specified central submatrix [xij ]r≤i,j≤n−r, Y ∈ Rm×m is symmetric with a specifie...

In this paper, using a quantum superalgebra associated with the universal central extension of sl(2, 2)(1), we introduce new R-matrices having an extra parameter x. As x → 0, they become those associated with the symmetric and anti-symmetric tensor products of the copies of the vector representation of Uqsl(2, 2) (1).

In this paper, using a quantum superalgebra associated with the universal central extension of sl(2, 2)(1), we introduce new R-matrices having an extra parameter x. As x → 0, they become those associated with the symmetric and anti-symmetric tensor products of the copies of the vector representation of Uqsl(2, 2) (1).

We prove some results on the kernel of the Abel transform on an irreducible Riemannian symmetric space X = G=K with G noncompact and complex, in particular an estimate of this kernel. We also study the behaviour of spherical functions near the walls of Weyl chambers. We show how these harmonic spherical analysis results lead to a new proof of a central limit theorem of Guivarc'h and Raugi in th...

Introduction: Physical wedge as a useful tool has been utilized in radiotherapy to modify photon beam shape and intensity such that it distributes dose uniformly in tumor site and reduces hot points. Since during Linac commissioning dosimetric parameters like output factors and lateral dose profiles are measured only for symmetric open and wedged fields, so calculation the par...