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Online Edition: ISSN 1843 - 4401

Carpathian J. Math. is a category A journal in the CNCSIS classification

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Vol. 29 (2013), No. 1, 15 March 2013
Some numerical integration methods based on interpolation polynomials
Author: Ana Maria Acu / Daniel Florin Sofonea
Abstract: In this paper we have considered the asymptotic expressions for remainder term of quadrature formulas of the interpolator type. We derive some corrected versions of the quadrature formulas of interpolatory type, which provide a better approximation accuracy than the original rules. A method to improve the degree of exactness of the quadrature formulas is also considered. A numerical example of the proposed method is given
No. of downloads: 375
Convergence theorems for fixed point iterative methods defined as admissible perturbations of a nonlinear operator
Author: Vasile Berinde
Abstract: The aim of this paper is to prove some convergence theorems for a general fixed point iterative method defined by means of the new concept of admissible perturbation of a nonlinear operator, introduced in [Rus, I. A., An abstract point of view on iterative approximation of fixed points, Fixed Point Theory 13 (2012), No. 1, 179--192]. The obtained convergence theorems extend and unify some fundamental results in the iterative approximation of fixed points due to Petryshyn [Petryshyn, W. V., Construction of fixed points of demicompact mappings in Hilbert space, J. Math. Anal. Appl. 14 (1966), 276--284] and Browder and Petryshyn [Browder, F. E. and Petryshyn, W. V., Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), No. 2, 197--228].
No. of downloads: 249
New proofs of some properties of essential submodules
Author: Daniela Adriana Heuberger
Abstract: In 1986, Lambek [Lambek, J., Lectures on rings and modules, Chelsea Publishing Company New York, 1986] studied the connections between essential submodules and quotient rings, and in 2009, Steinberg [Steinberg, S. A., Lattice-ordered rings and modules, Springer New York Dordrecht Heidelberg London, 2009, 1--307] presented some interesting results in this field. The main aim of this paper is to provide proofs for those of these results for which we did not found old ones in the literature we studied, using the same techniques as in the mentioned books
No. of downloads: 189
Minimal number of crossings in strong product of paths
Author: Marián Klešč / Jana Petrillová / Matúš Valo
Abstract: The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of $G$ in the plane. The exact crossing number is known only for few specific families of graphs. Cartesian products of two graphs belong to the first families of graphs for which the crossing number has been studied. Some results concerning crossing numbers are also known for join products of two graphs. In the paper, we start to collect the crossing numbers for the strong product of graphs, namely for the strong product of two paths.
No. of downloads: 194
Weak solutions in Elasticity of dipolar bodies with stretch
Author: Marin Marin / Gabriel Stan
Abstract: In the present paper we generalize the results obtained by Iesan and Quintanilla for microstretch elastic bodies in order to cover the dipolar elastic materials with stretch. For the boundary value problem considered in this context, we use some results from the theory of semigroups of the linear operators in order to prove the existence and uniqueness of a weak solution.
No. of downloads: 175
Gamma function by $x^{x-1}$
Author: Cristinel Mortici
Abstract: The aim of this paper is to give new asymptotic formulas for gamma function which refine some results of Anderson and Qiu [A monotoneity property of the gamma function, Proc. Amer. Math. Soc., 125 (1997) 3355--3362].
No. of downloads: 205
On some special classes of Gronwall lemmas
Author: Anton S. Mureșan
Abstract: Problem 9 in [Rus, I. A., Gronwall lemmas: ten open problems, Scientiae Math. Jpn., 70 (2009), No. 2, 221--228] is the following: ”Give new concrete and abstract Gronwall lemmas”. The aim of this paper is to give and study some special classes of Gronwall lemmas.
No. of downloads: 163
Differential equations with modified argument, via weakly Picard operators' theory
Author: Viorica Mureșan
Abstract: In this paper we use Picard and weakly Picard operatorsÂ’ technique, introduced by Ioan A. Rus, to study a class of differential equations with modified argument and a boundary value problem for this kind of equations. We obtain existence, uniqueness, comparison and data dependence results
No. of downloads: 164
On the (n,m)- semirings derived polynomially from infinite semidomains
Author: Adina Pop / Maria Sânziana Pop
Abstract: In the paper [Marichal, J.-L. and Mathonet, P., A description of n-ary semigroups polynomial-derived from integral domains, Semigroup Forum, 83 (2011), No. 2, 241--249] the authors provide a complete classification of the n-semigroups, defined by polynomial functions over infinite commutative integral domains with identity (i.e., the $n$-semigroup structures polynomial derived from integral domains). We remark that some results from that paper can be extended for the n-semigroups polynomial-derived defined over infinite semidomains with zerosumfree element. Furthermore, in this note we give a description of (n, m)- semiring structures defined by polynomial functions over such semidomains.
No. of downloads: 164
Extensions of n-groups by m-groups
Author: Vasile Pop
Abstract: By juxtaposition of a (n+1)-operation with a (m+1)-operation on G we obtain a (m+n+1)-operation on G. In this paper we study the reciprocal associativity of these operations and the conditions that the obtained operation determine on G a (m+n+1)-group.
No. of downloads: 180
Polynomial instability of evolution operators in Banach spaces
Author: Magda Luminița Râmneanșu / Mihail Megan / Traian Ceaușu
Abstract: In this paper we consider two concepts of polynomial instability for evolution operators in Banach spaces. Our approach is based on the extension of techniques for exponential instability to the case of polynomial instability. The obtained results are generalizations of some theorems about uniform and nonuniform exponential instability.
No. of downloads: 170
Asymptotic relations for the Bernstein-Schnabl operators on the unit interval
Author: Ioan Rața
Abstract: Asymptotic relations are established for the Bernstein-Schnabl operators on the unit interval. The general results are applied to special sequences of operators, and some known results are obtained as particular cases.
No. of downloads: 147
On constructive investigation of a class of non-linear boundary value problems for functional differential equations
Author: A. Ronto / M. Ronto
Abstract: We consider a two-point boundary value problem for a non-linear system of functional differential equations, for which a scheme of efficient investigation using certain iteration process is constructed. A new convergence condition is established in the case where a certain additional property of the Lipschitz operator is present, which may lead one to weaker assumptions.
No. of downloads: 551 Full access PDF |
Optimization methods for $l^1$-energy minimization in the estimation of optical flow
Author: Mircea Dan Rus
Abstract: The aim of this paper is to present a new approach for solving the minimization problem for a large class of energy functionals that appear in the differential models of optical flow estimation problems, and which are expressed using the discrete l1-norm. The choice of l1-energy minimization is motivated by the fact that quadratic l2 optimization is not robust to outliers and that l1-norm is a better choice for modeling real problems involving discrete signals. The method described in this paper is very general, thus the advantage of being applicable to almost every differential model that has been proposed so far for the optical flow estimation problem. In order to test and validate our method, a Matlab implementation on several optical flow models is currently under development. Also, a multi-core implementation on GP-GPU is to be considered in the near future.
No. of downloads: 167
A remark on a theorem of Browder
Author: Corneliu Udrea
No. of downloads: 467 Full access PDF |
On the probabilistic stability of some functional equations
Author: Claudia Zaharia / Dorel Miheș
No. of downloads: 216

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