Radu Paltanea

Inequalities with second order moduli of continuity

We study some new type of estimates with second order moduli of continuity for positive linar operators and we study the optimality of the constants which appear in these estimates."

Adrian Branga

A Class of Parametric Quadrature Formulas with
Higher Degree of Exactness

In this paper is presented a new class of quadrature formulas depending on two real parameters, which is obtained using Taylor polynomials of even
degree. The value of the second parameter is found out such that the corresponding quadrature formulas have higher degree of exactness. Also we compute the coefficients and using the Peano's Theorem we find a representation of the remainder term. Particularly, the above formula
contains the Simpson, Maclaurin, Newton-Cotes and Gauss-Legendre quadrature formulas.
Keyword: Quadrature formula, Taylor polynomials, Peano's Theorem, Simpson formula, Maclaurin formula, Newton-Cotes formula, Gauss-Legendre formula

Mircea Ivan

A Simple Solution to Basel Problem

The Basel problem is a famous problem in number theory, first posed by Pietro Mengoli in 1644, and solved by Leonhard Euler in 1735.
The Basel problem asks for the precise sum of the  series
We present a simple proof of Euler's formula

Ioan Popa

A variant of A.Lupas inequality for Peano kernels.

In this paper we point out a companion of A.Lupas inequality for symmetric kernels and apply it for quadratures.

Andrei Vernescu

Some Results in Discrete Asymptotic Analysis

In this work we present some characterizations by two sided
estimations of the convergence of certain special sequences.

Bogdan Gavrea

Optimization based methods for the simulation of large multi-body
systems. A computational study

Traditional time-stepping schemes for simulation of multi-body systems are formulated as linear complementarity problems (LCPs) with copositive
matrices. Such LCPs are generally solved by means of Lemke-type algorithms, and solvers such as the PATH solver  have proven to be robust. However, for large systems, the PATH solver becomes unpractical from a computational point of view. The convex relaxation introduced by M. Anitescu in 2006 allows the formulation of the integration step as a quadratic program (QP), for which a wide variety of state-of-the-art solvers are available. In the present work we report results obtained when using several well known QP solvers. We investigate computational performance and we adress the correctness of the results from a modelling point of view.

Gancho Tachev

New Variants of Voronovskaja-type Theorems for Schoenberg-Spline
Operator

We represent new quantitative variants of Voronovskaja's Theorem,based on new Estimates for the second moment of Schoenberg Operator.Some conjectures are formulated.

  Ioan Gavrea

A representation theorem of Lupas type for Hermite-Hadamard Functionals

In 1974 A.Lupas proved a representation theorem for positive linear fuctionals in terms of divided differences.In this paper we give an extension of this theorem for Hermite-Hadamard functionals.

  Inna Nikolova

Lowering operators for Multiple Meixner Polynomials of first type

In this paper lowering operators  for multiple Meixner polynomials  of first type are found. There are two types  of lowering operators for this polynomial set: with fionite difference forward and finite difference backwards.

Ioana Chiorean

Remarks on some Parallel Computations for Spline Recurrence Formulas

It is known that many problems may be solved more accurate by using spline functions instead of finite differences methods. In this way, the computational effort is, also, reduced, even if serial algorithms are used, due to the tridiagonal matrices involved. But this effort can be even more improved by parallel calculus. The purpose of this paper is to give some parallel computation approaches for the recurrence formulas that appear in generating the cubic spline function.

Marian Olaru

Data dependence for some functional differential equation in a Banach space

Sorin G. Gal

Voronovskaja's Theorem and the Exact Degree of Approximation for the Derivatives of Complex Riesz-Zygmund Means

In this paper we obtain a quantitative Voronovskaja result and
the exact orders in approximation by the derivatives of complex Riesz-Zygmund means in compact disks.

Ioan Ţincu

A poof of Schur’s Conjecture and an improvement

In the paper I proved first Schur's Conjecture by using the properties of Bessel's functions of the first species. The second main result is an identity verified by the product , containing Schur’s Conjecture as a particular case  .

E.C. Popa

On an expansion theorem if finite operators calculus of G-C. Rota

Using so called Viskov method we present here the expansions theorems of the umbral calculus

Dana Simian, Corina Simian

ON AN APPLICATION OF IDEAL INTERPOLATION

Ideal interpolation is obtained when the interpolation conditions, Lambda, have the property that ker(Lambda) is an ideal of polynomials. In case of ideal interpolation we can switch between interpolation and reduction process with respect to a H-basis of the ideal  ker(Lambda). It is proved that the interpolation space, for an ideal interpolation scheme, is the same with the space of reduced polynomial modulo a H-basis of the ideal ker(Lambda) and the interpolation operator is the same with the reduction operator. The inner product used in the reduction process is very important Different inner products leads to different reduced spaces of polynomials and therefore to different polynomial interpolation spaces. The aim of this paper is to prove many properties of the polynomials which belong to different polynomial interpolation spaces for ideal interpolation schemes, using the reduction process with respect to a H-basis of the ideal ker(Lambda) and many inner products..

Adrian Holhos

Quantitative estimates for positive linear operators in weighted spaces

We give some quantitative estimates for positive linear operators in weighted spaces by introducing a new modulus of continuity and then apply these results to the Bernstein-Chlodowsky polynomials.
KEY WORDS: positive linear operators, weighted modulus of continuity, weighted spaces, Bernstein-Chlodowsky polynomials

Ana Maria Acu, Mugur Acu and Arif Rafiq

Extremal problems with polynomials

Using quadrature formulae of the Gauss-Lobatto and Gauss-Radau type, we give some new results for extremal problems with polynomials. Let ~H (®;¯) be the class of real polynomials pn¡1 2Q n¡1, such that
jpn¡1(xi)j · ¯~ P(®+1;¯+1)n¡1 (xi)¯¯¯; i = 1; n where by ~ P(®;¯) n we denote the nth Jacobi polynomial and the xi are the zeroes of ~ P(®;¯)n . We give exact estimation of certain weighted
L2-norms of the kth derivative of polynomials with there are in the
class ~H (®;¯).

Sofonea Florin

On a liniear and positive operators

Heiner Gonska

Quantitative Voronovskaya-type theorems

At the 2006 NAAT conference in Cluj we presented a new (?) estimate for the Taylor remainder which has many applications in Numerical Analysis and Approximation Theory.

Eugen Constantinescu

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Eugen Draghici, Daniel Pop,

Consider the problem:

The aim of this paper ist o present an approximate solution of this problem based on Pseudospectral methods. We constract the approximation using Chebyshev collocation methods and use Chebyshev-Gauss-Lobatto interpolation nodes. Using orthopoly polynomials techniques and a Maple implementation, we obtain an analytical expression of the approximation and give examples.