miRNAs as one of the potential therapeutic agents have been recently considered for cancer treatment. AS1411 (aptNCL) is a DNA aptamer specifically binding to nucleolin protein on the cancer cell surface with antiproliferative effect. The aim of the study was to develop a conjugate consisted of aptNCL (as targeted delivery of therapeutic agent) and miRNA let-7d (as a tumor suppressor) using two...

In this paper, the matrix equation AX + XB = C is considered, where the matrices A and B have sizes m × n and n × m, respectively, the size of the unknown X is n × m, and the operator (·) denotes either the transpose or the conjugate transpose of a matrix. In the first part of the paper, necessary and sufficient conditions for the existence and uniqueness of solutions are reviewed. These condit...

Sturmian eigenstates specified by stationary scattering boundary conditions are particularly useful in contexts such as forming simple separable two nu-cleon t matrices, and are determined via solution of generalised eigenvalue equation using real and symmetric matrices. In general, the spectrum of such an equation may contain complex eigenvalues. But to each complex eigenvalue there is a corre...

Recently, many mathematicians have studied in the area of the Euler numbers and polynomials see 1–15 . The Euler numbers and polynomials possess many interesting properties and arising in many areas of mathematics and physics. In 14 , we introduced that Euler equation En x 0 has symmetrical roots for x 1/2 see 14 . It is the aim of this paper to observe an interesting phenomenon of “scattering”...

In this work, we are concerned with (R, S) – conjugate solutions to coupled Sylvester complex matrix equations of two unknowns. When the considered consistent, it is demonstrated that can be obtained by utilizing iterative algorithm for any initial arbitrary (R,S) matrices V1,W1. A necessary and sufficient condition established guarantee proposed method converges solutions. Finally, numerical e...

We show that for each element g of a Garside group, there exists a positive integer m such that gm is conjugate to a periodically geodesic element h, an element with |hn|D = |n|·|h|D for all integers n, where |g|D denotes the shortest word length of g with respect to the set D of simple elements. We also show that there is a finite-time algorithm that computes, given an element of a Garside gro...

If H denotes the classical Hilbert transform and Hu(x) = v(x), then the functions u(x) and v(x) are the values on the real axis of a pair of conjugate functions, harmonic in the upper half-plane. This note gives a generalization of the above concepts in which the Laplace equation Deltau = 0 is replaced by the Yukawa equation Deltau = mu(2)u and in which the Cauchy-Riemann equations have a corre...

Throughout this paper we use the following notations. By Zp we denote the ring of p-adic rational integers, Q denotes the field of rational numbers, Qp denotes the field of p-adic rational numbers, C denotes the complex number field, and Cp denotes the completion of algebraic closure of Qp. Let νp be the normalized exponential valuation of Cp with |p|p = p−νp(p) = p−1. When one talks of q-exten...

We study the problem of complex-valued independent subspace analysis (ISA). We introduce complex flag manifolds to tackle this problem, and, based on Riemannian geometry, propose the natural conjugate gradient method on this class of manifolds. Numerical experiments demonstrate that the natural conjugate gradient method yields better convergence compared to the natural gradient geodesic search ...