Some Symmetric Identities Involving Fubini Polynomials and Euler Numbers

The aim of this paper is to use elementary methods and the recursive properties of a special sequence to study the computational problem of one kind symmetric sums involving Fubini polynomials and Euler numbers, and give an interesting computational formula for it. At the same time, we also give a recursive calculation method for the general case.

ON EXACT SOLUTION OF OPTIMIZATION TASK GENERATED BY THE LAPLACE EQUATION

A one-parameter family of finite-dimensional spaces consisting of special two-dimensional splines of Lagrangian type is defined (the parameter N is related to the dimension of the space). The Laplace equation generates in each such space the problem of minimizing the residual functional. The existence and uniqueness of optimal splines are proved. For their coefficients and residuals, exact formulas are obtained. It is shown that with increasing N; the minimum of the residual functional is O(N^(-5) ); and the special sequence consisting of optimal splines is fundamental.

On the properties of k-balancing and k-Lucas-balancing numbers

The k-Lucas-balancing numbers are obtained from a special sequence of squares of k-balancing numbers in a natural form. In this paper, we will study some properties of k-Lucas-balancing numbers and establish relationship between these numbers and k-balancing numbers.

Research Progress in the Typical Structure of Human Telomeric G-Quadruplex

Telomeric DNA of human chromosomes plays a significant role in physiological processes such as cell cycle, aging, cancer and genetic stability due to its special sequence and structure. The research on small molecule ligands targeting G-quadruplex formed by such special sequence has attracted considerable attention, and has achieved great breakthrough. In this paper, we summarize the DNA sequences and structures of three kinds of typical human telomeric G-quadruplex, providing an important reference for further research.

Expansions with Poisson kernels and related topics

Let P(r, θ) be the two-dimensional Poisson kernel in the unit disc D. It is proved that there exists a special sequence {ak} of points of D which is non-tangentially dense for ∂D and such that any function on ∂D can be expanded in series of P(|ak|, (·)–arg ak) with coefficients depending continuously on f in various classes of functions. The result is used to solve a Cauchy-type problem for Δu = μ, where μ is a measure supported on {ak}.