Abstract:
In \cite{St3} H. Stetk\ae r obtained the solutions of Van Vleck's functional equation for the sine $$f(x\tau(y)z_0)-f(xyz_0) =2f(x)f(y),\; x,y\in G,$$ where $G$ is a semigroup, $\tau$ is an involution of $G$ and $z_0$ is a fixed element in the center of $G$. The purpose of this paper is to determine the complex-valued solutions of the following extension of Van Vleck's functional equation for the sine $$\mu(y)f(x\tau(y)z_0)-f(xyz_0) =2f(x)f(y), \;x,y\in G,$$ where $\mu$ : $G\longrightarrow \mathbb{C}$ is a multiplicative function such that $\mu(x\tau(x))=1$ for all $x\in G$. Furthermore, we obtain the solutions of a variant of Van Vleck's functional equation for the sine $$\mu(y)f(\sigma(y)xz_0)-f(xyz_0) = 2f(x)f(y), \;x,y\in G$$ on monoids, and where $\sigma$ is an automorphism involutive of $G$.

Abstract:
In this paper we study the solutions and stability of the generalized Wilson's functional equation $\int_{G}f(xty)d\mu(t)+\int_{G}f(xt\sigma(y))d\mu(t)=2f(x)g(y),\; x,y\in G$, where $G$ is a locally compact group, $\sigma$ is a continuous involution of $G$ and $\mu$ is an idempotent complex measure with compact support and which is $\sigma$-invariant. We show that $\int_{G}g(xty)d\mu(t)+\int_{G}g(xt\sigma(y))d\mu(t)=2g(x)g(y),\; x,y\in G$ if $f\neq 0$ and $\int_{G}f(t.)d\mu(t)\neq 0$. We also study some stability theorems of that equation and we establish the stability on noncommutaive groups of the classical Wilson's functional equation $f(xy)+\chi(y)f(x\sigma(y))=2f(x)g(y)\; x,y\in G$, where $\chi$ is a unitary character of $G$.

Abstract:
In this paper, we give a proof of the Hyers-Ulam stability of the Jensen functional equation $$f(xy)+f(x\sigma(y))=2f(x),\phantom{+} x,y\in{G},$$ where $G$ is an amenable semigroup and $\sigma$ is an involution of $G.$

Abstract:
In \cite{bbb} the authors obtained the Hyers-Ulam stability of the functional equation $$ \int_{K}\int_{G} f(xtk\cdot y)d\mu(t)dk=f(x)g(y), \; x, y \in G ,$$ where $G$ is a Hausdorff locally compact topological group, $K$ is a copmact subgroup of morphisms of $G$, $\mu$ is a $K$-invariant complex measure with compact support, provided that the continuous function $f$ satisfies some Kannappan Type condition. The purpose of this paper is to remove this restriction.

Abstract:
In this paper, we present an off line Tifinaghe characters recognition system. Texts are scannedusing a flatbed scanner. Digitized text are normalised, noise is reduced using a median filter,baseline skew is corrected by the use of the Hough transform, and text is segmented into line andlines into words. Features are extracted using the Walsh Transformation. Finally characters arerecognized by a multilayer neural network.

Abstract:
In this paper, we present a comparison of two few extraction methods based on the raw form and the skeleton. The experimental results show the benefit of using these methods compared with other conventional approaches; the findings have been applied on the MNIST database. The paper presents the evaluation work for the comparison of the two methods and provides conclusions based on the study outcomes.

Abstract:
This paper contributes to the literature on comparative performance of family and non-family businesses by accounting for self-selection and by comparing performance within and across sectors. Using an extensive data set of Dubai businesses in the four different major sectors in the Dubai economy (construction, manufacturing, services, and trading); we find that the sector matters. Family businesses outperform nonfamily businesses in trading, followed by construction as a far second. Performance of family businesses is weakest in manufacturing and services, only in trading did family businesses outperform nonfamily exporting businesses in other sectors. Reasons for that are discussed and policy implications are drawn. We also find strong evidence of self-selection bias.

This paper deals with spaces such that their compactification is a resolvable space. A characterization of space such that its one point compactification (resp. Wallman compactification) is a resolvable space is given.

Abstract:
Image analysis by topological gradient approach is a technique based upon the historic application of the topological asymptotic expansion to crack localization problem from boundary measurements. This paper aims at reviewing this methodology through various applications in image processing; in particular image restoration with edge detection, classification and segmentation problems for both grey level and color images is presented in this work. The numerical experiments show the efficiency of the topological gradient approach for modelling and solving different image analysis problems. However, the topological gradient approach presents a major drawback: the identified edges are not connected and then the results obtained particularly for the segmentation problem can be degraded. To overcome this inconvenience, we propose an alternative solution by combining the topological gradient approach with the watershed technique. The numerical results obtained using the coupled method are very interesting. 1. Introduction The goal of topological optimization is to find the optimal decomposition of a given domain in two parts: the optimal design and its complementary. Similarly in image processing, the goal is to split an image in several parts, in particular, in image restoration the detection of edges makes this operation straightforward. The goal of this work is to show how it is possible to solve some image analysis problems using topological optimization tools. Let us recall that the basic and first idea is based on the work of Amstutz et al. [1] in which the authors propose a solution for crack detection problem using the topological gradient approach. Then, this approach was extended to different problems in image processing like restoration, classification, segmentation, inpainting, and tomography application [2–6]. This paper presents an overview of the applications of the topological gradient approach to major image processing problems with an illustration of both inconveniences and advantages of this technique in image analysis. Let be a given noisy image defined in a domain and the restored image. We recall that a classical way to restore the image is to solve the following partial differential equations (PDE) problems where is a small positive constant and denotes the outward unit normal to . This method is well known to give poor results: it blurs important structures like edges and in order to improve this method, nonlinear isotropic and anisotropic methods were introduced. In our topological optimization approach, takes only two values: in the

Abstract:
Using the fixed point theorem we establish the Hyers-Ulam-Rassias stability of the generalized Pexider functional equation $$\frac{1}{\mid K\mid}\sum_{k\in K}f(x+k\cdot y)=g(x)+h(y),\;\;x,y\in E$$ from a normed space $E$ into a complete $\beta$-normed space $F$, where $K$ is a finite abelian subgroup of the automorphism group of the group $(E,+)$.