Let m2 < m1 be two given nonnegative integers with n = m1+m2+1. For suitably differentiable f , we let P,Q ∈ πn be the Hermite polynomial interpolants to f which satisfy P (a) = f (a), j = 0, 1, ..., m1 and P (b) = f (b), j = 0, 1, ..., m2, Q (a) = f (a), j = 0, 1, ..., m2 and Q(b) = f (b), j = 0, 1, ..., m1. Suppose that f ∈ C (I) with f (x) 6= 0 for x ∈ (a, b). If m1 − m2 is even, then there ...

The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. This method gives an analytic solution when ...

The concept of Lucky k-polynomials and in particular Lucky χ-polynomials was recently introduced. This paper introduces Stirling number of the fourth kind and Lucky partitions of a finite set in order to determine either the Lucky k- or Lucky χ-polynomial of a graph. The integer partitions influence Stirling partitions of the second kind.

We consider the max-plus analogue of the eigenproblem for matrix pencils, A ⊗ x = λ⊗ B ⊗ x. We show that the spectrum of (A, B) (i.e., the set of possible values of λ), which is a finite union of intervals, can be computed in pseudopolynomial number of operations, by a (pseudo-polynomial) number of calls to an oracle that computes the value of a mean payoff game. The proof relies on the introdu...

The trajectory planning, which is known as a movement from starting to end point by satisfying the constraints along the path is an essential part of robot motion planning. A common way to create trajectories is to deal with polynomials which have independent coefficients. This paper presents a trajectory formulation as well as a procedure to arrange the suitable trajectories for applications. ...

the main purpose of this article is to present an approximate solution for the two-dimensional nonlinear volterra integral equations using legendre orthogonal polynomials. first, the two-dimensional shifted legendre orthogonal polynomials are defined and the properties of these polynomials are presented. the operational matrix of integration and the product operational matrix are introduced. th...

assume that $(n,l)$, is a pair of finite dimensional nilpotent lie algebras, in which $l$ is non-abelian and $n$ is an ideal in $l$ and also $mathcal{m}(n,l)$ is the schur multiplier of the pair $(n,l)$. motivated by characterization of the pairs $(n,l)$ of finite dimensional nilpotent lie algebras by their schur multipliers (arabyani, et al. 2014) we prove some properties of a pair of nilpoten...

image analysis is an image processing technique that aims to extract features or information from images. image analysis in medicine has a special place because is a basis for disease diagnosis for physicians. electrophoresis is a laboratory separating technique. electrophoresis images are created during the electrophoresis process. serum protein and hemoglobin electrophoresis test are the most...