On the iterative solution of some decomposable nonlinear operator equations

Author: Vasile Berinde

Abstract: The aimof this note is to extend a recent result concerning the solvability of a nonlinear equation that can be decomposed under the formAu = Pu,
where one of the two operators A and P has richer properties than the other one.
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Abstract: The metric regularity is a central concept in variational analysis. This concept is frequently used for the study of solutions to some generalized equations, to variational inequalities and to parametrized constraints systems. Fundamental theorems of this field are Eckart-Young's, Robinson-Ursescu's and Lyusternyk-Grave's theorem. They have applications in single valuedness functions theory and also in set-valuedmappings theory. The purpose of this article is to analize the metric regularity property of some sublinear applications.
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About approximation of B-continuous and B-differentiable functions of three variables by GBS operators of Bernstein type

Author: Mircea D. FarcaČ™

Abstract: In this article, using a method from the paper [4], the sequence of GBS operators of Bernstein type for B-continuous and B-differentiable functions of three variables is constructed and some approximation properties of this sequence are established.
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Some convergence results for two new iteration processes in uniformly convex Banach space

Author: M. O. Olatinwo / O. O. Owojori / A. P. Akinola

Abstract: In this paper, following the concepts in [7, 9],we shall establish some convergence results for nonexpansive operators in a uniformly convex Banach space. Two new iteration processes will be considered for this purpose. Our results improve, generalize and extend those of [5, 8, 9, 10, 13, 14].
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Abstract: A ring R is called right FGF-ring if every finitely generated right R-module embeds in a free (projective) . A ring is called right simple-injective if RR is simple R-injective, that is, if I is a right ideal of R and
: I ! R is an R-morphismwith simple image, then
(x) = c:x, is leftmultiplication by an element c 2 R. There is a conjecture due to Carl Faith which asserts that every right FGF-ring is a Quasi-Frobenius ring (QF). In this paper we establish the conjecture in case that the ring is a simple injective ring by showing that the right simple-injective FGF ring is a right self- injective.
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Monotone semilinear equations in Hilbert spaces and applications

Author: Silviu Sburlan

Abstract: Consider a abstract semilinear equation of the formAu+F(u) = 0, where A is amaximalmonotonemap acting into a real Hilbert spaceH, and F is a Lipschitz strongly monotone map on H. Such equations were studied by H. Amann (1982), T. Bartsch (1988), C. Mortici and S. Sburlan (2005, 2006), D. Teodorescu (2005). By standard arguments we can reformulate the problem as a ?xed point equation and prove easier some existence
results. Based on these abstract results some applications to partial differential equations are also appended. The method can be adapted for teaching PDE in Technical Universities.
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Symbolic approach for the generalized airfoil equation

Author: Elena Bautu / Elena Pelican

Abstract: The generalized airfoil equation governs the pressure across an airfoil oscillating in a wind tunnel. In this paper we analyze the problem for an airfoil with a fiap, by means of Gene Expression Programming (GEP). We present the main traits of the GEP metaheuristic and then we de?ne its elements in order to be used for integral equations of the first kind. The results obtained by our symbolic approach con?rm the suitability of this method for problems modeled by Fredholm first kind integral equations.
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Singularity of a boundary value problem of the elasticity equations in a polyhedron

Author: Benabderrahmane Benyattou / Nouiri Brahim

Abstract: In this work we are looking at the study of the regularity of a boundary value problem governed by the Lame equations in a cylindrical domain. By studying the longitudinal displacement singularity along an edge and the perpendicular displacement singularity to the same edge, we arrive to describe the behavior of singular solutions of the Lame equations in a polyhedron.
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Shape preserving quadratic interpolation at Greville abscissae

Author: Paul A. Kupan

Abstract: The paper presents a method to construct a C1 quadratic approximation function that combine the shape preserving properties of the variation diminishing spline function with the approximation properties of the interpolation function.
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The order of convergence of some families of iterative methods for solving nonlinear equations

Author: Raluca Anamaria Pomian

Abstract: We focus on some families of iterative methods. A few particular cases of these families are: Newton's method, Halley's method, Euler's method, Osculating parabola method, Chebyshev's method and others. For each families we started with a definition, we continue with particular cases and examples. For each these families we get their convergence order. We also obtain for some polynomials the attraction basins of the studied
methods.
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Statistical approximation properties of Kantorovich operators based on q-integers

Author: Cristina Radu

Abstract: In this paper we present two new generalizations of Kantorovich operators based on q-calculus. With the help of Bohman-Korovkin type theorem we obtain some statistical approximation properties for these operators. Also, by using the modulus of continuity, the statistical rate of convergence is established.
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Abstract: In the present work a numerical method is developed for the determination of the J in (0; infinity) interval in the three critical points theorem. The
critical surfaces are also approximated.
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Abstract: Compression is very important for multimedia applications, because it reduces the amount of space for depositing the information, and the bandwidth required for sending it through a computer network. Multiresolution analysis performs a wavelet decomposition that decorrelates the signal data, in preparation for the quantization step and the final redundancy reduction. This article presents a simple algorithm for performing the decomposition of images and propounds a quantization method that takes into account the human eye contrast sensitivity function.
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Abstract: This paper presents an Electronic Transaction System (ETS) that can interact with different communication languages using a context-free language. ETS can be used in many economical and cultural projects. This concept is already implemented in construction of two projects from commodities exchange and library information exchange.
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Developmental teaching experiment in the field of geometry

Author: Ibola Szilagyine Szinger

Abstract: Our research question is how lower primary geometry teaching in Hungary, particularly the concept of symmetry is related to the levels formulated by van Hiele. Moreover to what extent are the concrete activities effectively carried out at these levels in evolving the concept of symmetry. Our hypothesis is that in the lower primary geometry teaching (classes 1-4) the ?rst two stages of the van Hiele levels can be put into practice. By
the completion of lower primary classes level 3 cannot be reached. Children do not see the logical relationship between the properties of a given shape. They cannot come to a conclusion from one property of shapes to another. In the lower primary the basics of geometrical concepts are laid down. In this paper the development of the concept of symmetry is examined. The evolvement of several geometrical concepts - among which the concept of symmetry as well - were examined in educational development experiments conducted with fourth class students.
In our paper we present the developing teaching experiment and its observations which we support with measurement results.
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