Families of Increasing Sequences Possessing the Harmonic Series Property

We prove in this paper that any maximal, with respect to inclusion, subset of N – the family of all increasing sequences of positive integers – possessing the harmonic series property has the cardinality of the continuum. Moreover, we prove that for any countable (infinite) set exists an "orthogonal" family such that it hold some facts. All facts are proved constructively, by using the modified version of the classical Sierpiński family of increasing sequences having the cardinality of the continuum

A stronger version of the second mean value theorem for integrals

AbstractWe prove a stronger version of the classic second mean value theorem for integrals

Bridges between different known integer sequences

In this paper a new method of generating identities for Fibonacci and Lu- cas numbers is presented. This method is based on some fundamental identities for powers of the golden ratio and its conjugate. These identities give interesting connections between Fibonacci and Lucas numbers and Bernoulli numbers, Catalan numbers, binomial coefficients, δ-Fibonacci numbers, etc. Keywords: Fibonacci and Lucas numbers, Bernoulli numbers, Bell numbers, Dobinski’s formul

Comparison of the Adomian decomposition method and the variational iteration method in solving the moving boundary problem

AbstractIn this paper, a comparison between two methods: the Adomian decomposition method and the variational iteration method, used for solving the moving boundary problem, is presented. Both of the methods consist in constructing the appropriate iterative or recurrence formulas, on the basis of the equation considered and additional conditions, enabling one to determine the successive elements of a series or sequence approximating the function sought. The precision and speed of convergence of the procedures compared are verified with an example

ON SIMILARITIES BETWEEN EXPONENTIAL POLYNOMIALS AND HERMITE POLYNOMIALS

Abstract. The aim of this paper is to introduce and compare some fundamental analytical properties of the title polynomials. Many similarities between them are emphasized in the paper. Moreover, the authors present many isolated results, new proofs and identities

Application of the Homotopy Analysis Method for Solving the Systems of Linear and Nonlinear Integral Equations

In this paper we indicate some applications of homotopy analysis method for solving the systems of linear and nonlinear integral equations. The method is based on the concept of creating function series. If the series converges, its sum is the solution of this system of equations. The paper presents conditions to ensure the convergence of this series and estimation of the error of approximate solution obtained when the partial sum of the series is used. Application of the method will be illustrated by examples

A boson approach to the structure of A=22 nuclei

AbstractWe discuss a procedure to transfer the description of a fermion system from a subspace of the full shell model space built in terms of collective pairs onto a space of corresponding bosons. We apply the procedure to systems of six nucleons in the 1s0d major shell. We perform exact shell model calculations and compare them with calculations in the collective pair and boson approximations. The effects of the truncation of the boson Hamiltonian and of the consequent violation of the Pauli principle are examined

Artificial bee colony algorithm in the solution of selected inverse problem of the binary alloy solidification

The paper presents a procedure for reconstructing, on the basis of known measurements of temperature, the heat transfer coefficient and the distribution of temperature in given region of solidifying binary alloy in the casting mould. Solution of the considered inverse problem is found by applying the finite element method for solving the corresponding direct problem and the Artificial Bee Colony algorithm for minimizing the functional representing the error of approximate solution