Name 
Title 
Abstract 
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, NewtonCotes and GaussLegendre quadrature formulas.
Keyword: Quadrature formula, Taylor polynomials, Peano's Theorem, Simpson formula, Maclaurin formula, NewtonCotes formula, GaussLegendre 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 multibody
systems. A computational study 
Traditional timestepping schemes for simulation of multibody systems are formulated as linear complementarity problems (LCPs) with copositive
matrices. Such LCPs are generally solved by means of Lemketype 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 stateoftheart 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 Voronovskajatype Theorems for SchoenbergSpline
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 HermiteHadamard 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 HermiteHadamard 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 RieszZygmund Means 
In this paper we obtain a quantitative Voronovskaja result and
the exact orders in approximation by the derivatives of complex RieszZygmund 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 GC. 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 Hbasis 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 Hbasis 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 Hbasis 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 BernsteinChlodowsky polynomials.
KEY WORDS: positive linear operators, weighted modulus of continuity, weighted spaces, BernsteinChlodowsky polynomials 
Ana Maria Acu, Mugur Acu and Arif Rafiq 
Extremal problems with polynomials 
Using quadrature formulae of the GaussLobatto and GaussRadau 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
L2norms of the kth derivative of polynomials with there are in the
class ~H (®;¯). 
Sofonea Florin 
On a liniear and positive operators 

Heiner Gonska 
Quantitative Voronovskayatype 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.
In our talk we will focus on just one group of applications, namely on extensions and generalizations of the classical Voronovskaya theorem for Bernstein operators. As one consequence we obtain several known quantitative Korovkintype theorems for positive linear operators defined on C[0,1].
More concrete applications will be given for the "genuine BernsteinDurrmeyer operators" U_n, for a class of operators which bridge the gap between them and the classical Bernstein operators B_n, and for one further class of mappings linking the U_n to the Durrmeyer operators M_n.
Time permitting, we also discuss Voronovskayatype theorems in terms of the DitzianTotik modulus, in simultaneous approximation, and such for the Schoenberg spline operator. 
Eugen Constantinescu 
. 
. 
Eugen Draghici, Daniel Pop, 
Approximation of solution of a polylocal problem using Chebyshev  polynomials
of first and second kind. 
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 ChebyshevGaussLobatto interpolation nodes. Using orthopoly polynomials techniques and a Maple implementation, we obtain an analytical expression of the approximation and give examples. 
Vasile Mihesan 
On A General Class of Beta Approximating Operators 
By using the generalized beta distribution(GB) we obtain general class
of Beta operators,which include both the Beta of the first and
second kind(see [5],[6],[9],[10]).We obtain a several positive
linear operators ,as a special of this Beta operator. 
Teodora Zapryanova 
A Characterization of Kfunctional for the Algebraic Version of Trigonometric Jackson Integrals and Kfunctionals for CaoGonska Operators 
We costruct moduli of functions which are a computable characteristic equivalent to the approximation error of algebraic version of trigonometric Jackson Integrals and CaoGonska operators. 
Lucian Beznea 


Carmen Violeta Muraru 


Dumitru Acu 
A note of Mathieu`s inequality 
In this note we obtain a generalization for Mathieu`s inequality 
Mioara Boncut 
On Some Properties of Box Spline Functions 
The work has two sections. The first section deals with some boxspline properties related with changing matrix $\Lambda$ in
$a\Lambda$} and the variale $x$ in $x/a, a>0$. The last section
contains the Fourier transform applied to boxspline functions and
some properties of this transformation. 
Nicolae Secelean 
The continuaity with respect to a parameter of Hutchinson
measure associated of an countable Iterated Functions System with
probabilities 
The continuaity with respect to a parameter of Hutchinson
measure associated of an countable Iterated Functions System with
probabilities 
Calin Gheorghiu 

