B. Mampassi, B. Saley and B. Somé

Solving Some Nonlinear Reaction-Diffusion EquationsUsing the New Adomian Decomposition Method

ABSTRACT. We present a numerical scheme based on the Adomian decomposition method (ADM) for the discretization of nonlinear diffusion problems, the solution of which may blow up in a finite time. The proposed scheme involves numerical solution that has the same blow up properties as the exact solution. In comparison with a Spectral-Runge Kutta scheme (SRK) we show that this method is well convergent.

H. Kh. Abdullah and K. T. Al Dosary

ABSTRACT. Some sufficient conditions are established for the oscillation of first order linear differential systems whose coefficients obey certain conditions. An example is given to illustrate the results.

L. Ragoub

ABSTRACT. Le premier résultat de ce papier est l'application du principe du maximum à un problème relatif à l'électrostatique. Nous montrons que la seule forme géométrique du domaine en question est un rectangle ou un secteur d'anneau. Pour le deuxième nous gènéralisons les résultats de Willms, Gladwell et Seigel. Willms a considéréle problème de St-Venant dans R² pour un doublement connexe. A l'aide de la technique des hyperplans mobiles, il a pu montrer que le domaine correspondant est un anneau de boules. Nous généralisons ce résultat dans Rⁿ en utilisant une approche différente. Notre technique est basèe sur les fonctions auxiliaires et n'utilise pas les principes du maximum de Hopf.

S. E. Rebiai

ABSTRACT.The boundary stabilization of the Schrödinger equation with non-constant coefficients in the principal part is studied. Dissipative boundary conditions are introduced. By using multiplier techniques, the exponential decay in H1(?) is established. Moreover, precise estimate on the decay rate is obtained.

P. P. Dey

ABSTRACT. In this paper we suggest a method that can be used to approximate the nth root of an arbitrary positive number p. This method makes use of the Monte Carlo Simulation Technique and rests on the determination of a sample size that is needed to apply the technique.

Volume 1, Number 2 (2004)

I. B. Risteski

ABSTRACT. In this paper the solutions of some nonlinear complex vector functional equations are given.

A. Diop and D. Guegan

ABSTRACT. We consider a class of linear regression model Y_t with (ζ_t) a white noise error process. We show by means of a point process technique that the asymptotic distribution of max_{{1 < k < n}} Y_k is the same as the one of \max_{{1 < k < n}}X_k under specific conditions on the noise process. The conditions say that the tail of (ζ_t) is lighter than the tail of (X_t).

N. Aissaoui

ABSTRACT. In this paper we establish a Wolff type inequality for the strongly nonlinear potential theory, i.e. when the underlying spaces are Orlicz. As applications, we give a relation between Bessel capacities and Hausdorff measure, and show that Riesz and Bessel capacities decrease under Lipschitz mapping in strongly nonlinear potential theory for reflexive Orlicz spaces. This generalizes the similar result in the nonlinear case and a result in the strongly one when the Lipschitz mapping is an orthogonal projection.

K. Bahlali, M. Eddahbi, and E. H. Essaky

ABSTRACT. We deal with quasi-linear parabolic stochastic partial differential equations. We prove that in the sense of Baire category, almost all quasi-linear parabolic stochastic partial differential equations (SPDE) with continuous coefficient have the properties of existence and uniqueness of solutions, as well as the continuous dependence of solutions on the coefficient and the L²-convergence of their Picard's approximations.

Volume 2, Number 1 (2004)

H. Chen, X. Chen, and H. Zhang

ABSTRACT. In this paper, a non-autonomous ratio-dependent multi-species competition predator-prey system is studied, where all parameters are time dependent. It is proved that the system is uniformly persistent under suitable conditions. Furthermore, the sufficient conditions are established for the existence of uniquely global asymptotically stable almost periodic solution of the system.

T. Kokou and N. I. Yurthuk

Classical Solution Weakened on the Axis to the Third Mixed Problem for the 3D Wave Equation with Central Symmetry in the Holder Spaces

ABSTRACT.We establish that necessary conditions on the initial functions are also sufficient conditions for the existence of the classical solution, weakened on the axis in Holder spaces of the third mixed problem with central symmetry for the tree-dimensional wave equation.

J. Dhar

Modeling and Analysis: The effect of Industrialization on Diffusive Forestry Ressource Biomass in Closed Habitat

ABSTRACT. In this paper, a mathematical model is proposed to study the depletion of forest biomass by different levels of industrialization in two different adjoining regions of the habitat leading to patchiness. In the model it is assumed that the density of forestry resource biomass is governed by the same logistic equation with the prescribed intrinsic growth rate and carrying capacity in both the regions. It is shown that the steady state distributions of the forestry resource as well as industrialization are positive, continuous and monotonic from one end to the other end of the linear closed habitat. The model is analyzed by using the stability theory of differential equation. Further, it is shown that the steady state distributions of biomass in the two regions are stable under certain conditions and decrease as density of industrialization or rate of depletion due to industrialization increases in each of the two adjoining region.

X. Zhang

Additive Preservers on Group Inverses of Matrices Over Fields of Characteristic Not 2

ABSTRACT. Suppose F is a field of characteristic not 2 and n greater than or equal to 2 is a positive integer. Let M_n(F) and S_n(F) be the linear spaces of n x n full matrices and symmetric matrices over F, respectively. We first characterize all additive maps from S_n(F) to M_n(F) preserving group inverses of matrices, and thereby all, additive maps from S_n(F) to itself preserving group inverses of matrices are characterized.

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Volume 2, Number 2 (2004)

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P. H. Bezandry

Limiting Law of the Fluctuation Processes Associated with the Systems of Randomly Interacting Particles with Collisions

ABSTRACT. We consider large systems of interacting particles with collisions related to a nonlinear Boltzmann-type equation. Under suitable reasonable initial assumptions, we show that the limiting law of the fluctuation processes associated with this model is gaussian.

A. El Arni

General KKM Theorem with Applications to Minimax Inequalities and Generalized Quasi-variational Inequalities

ABSTRACT. In this paper we present a general version of the KKM theorem by relaxing the compactness condition. We generalize the Ky Fan minimax inequality and we give some applications to the generalized quasi-variational inequalities.

S. Al Ghour

SLH Fuzzy Spaces

ABSTRACT. We introduce and study fuzzy homogeneous components. Various results concerning them are obtained. We extend the concept of being strongly locally homogeneous to include fuzzy topological spaces. Our extension is proved to be a good extension in the sense of Lowen. We study the relation between fuzzy SLH spaces and some ordinary topological spaces generated by these fuzzy spaces.

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Volume 3, Number 1 (2005)

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P. N. Mwita

On Conditional Scale Function: Estimate and Asymptotic Properties

ABSTRACT. This paper considers the problem of nonparametric estimation of conditional scale function of time series, based on quantile regression methodology of Koenker and Bassett. We discuss an estimate which we get by inverting a kernel estimate of the conditional distribution function, and prove its consistency and asymptotic normality. We illustrate the good performance of the estimate for light and heavy-tailed distribution of the innovation with a small simulation study.

A. Rashid

Convergence of Spectral Method in Time for Benjamin-Bonna-Mahony Equation

ABSTRACT. A spectral method for the approximation of the initial and boundary value problem for the Benjamin-Bona-Mahony Equation is proposed. A Fourier Galerkin approximation is used in the spatial direction, while the Chebyshev Pseudospectral approximation in the time direction. The expansion coefficients are determined by means of minimizing an object functional, and rapid convergence of the method is proved.

M. Bezzarga and N. B. Rhouma

Potentials of Additive Functionals in Unstable Semidynamical Systems

ABSTRACT. We consider a global continuous semidynamical system (X,T,Φ) on a locally compact space (X,T) with countable base and an additive functional A defined on X. We characterize unstable semidynamical systems by the associated additive functionals. In this situation, given an additive functional A, we give necessary and sufficient condition on (X,T, Φ) to get the continuity of the associated potential U_A.

X. Zhang

Linear Maps On Symmetric Matrix Spaces Preserving Inverses of Matrices

ABSTRACT. In this paper we consider linear maps from S_n(F) to M_n(F) (respectively S_n(F) preserving inverses of matrices when F is a field of characteristic not 2. It is shown that every linear map f: S_n(F) -----> M_n(F) preserving inverses of matrices is of the form f(X)=ePXP^-1 for any X in S_n(F) , where e belongs to { 1,-1 } and P is a nonsingular n x n matrix. Thereby, all linear maps from S_n(F) to itself preserving inverses of matrices are characterized.

S. A. Venetiaan

Estimating Fisher Information of Location

ABSTRACT. The problem of estimating Fisher information of location is studied. two estimators based on kernel estimators for the density and its derivative are constructed and a.s. convergence is shown. The first estimator is taken from Bickel(1982) and the second estimator is the natural one, namely the kernel estimator is substituted for the density in the functional which corresponds to Fisher information.

A. Belahmidi

Solvability of a Coupled System Arising in Image and Signal Processing

ABSTRACT. We study a coupled system proposed by Nitzberg and Shiota as a time-delay regularization of the Malik-Perona equation. For all dimensions, we show existence and uniqueness of classical solution. We also study the case where the initial datum is defined in a hypercube and investigate the asymptotic limit of the system when the time-delay tends to infinity.

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Volume 3, Number 2 (2005)

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A. M. Bijura

Transcendental Smallness in Singularly Perturbed Equations of Volterra Type

ABSTRACT. The application of different limit processes to a physical problem is an important tool in layer type techniques. Hence the study of initial layer correction functions is of central importance for understanding layer-type problems. It is shown that for singularly perturbed problems of Volterra type, the concept of transcendental smallness is an asymptotic one. Transcendentally small terms may be numerically important.

A. Ghanmi

Eigenprojector and Resolvent Kernels of the 2 D Pauli-Dirac Operator with Constant Magnetic Field

ABSTRACT. For Pauli-Dirac operators on the plane R²=C, in the presence of the constant magnetic field, we provide a concrete description of their L²-eigenforms and we give explicit formulae for their L²-eigenprojector and resolvent kernels.

R. Goonatilake

On Method of Statistical Differentials

ABSTRACT. The method of statistical differentials, which approximates the mean value and variance of transformations of random variables is used in many areas of mathematics. This paper will discuss the conditions under which such an approximation will be exact, and also explore their accuracy in terms of error bounds under certain moment conditions.

I. Bousrih

Families of Rational Functions Over Finite Fields and Construction of Optical Orthogonal Codes

ABSTRACT. We will go over the analysis of certain families of rational functions over F_q, introduced in [7] and [8] . We calculate their cardinalities by the introduction of a convolution of arithmetic functions defined over polynomial ring with coefficients in F_q and the study of the Mobius function over this ring. We examine, in a second time, a group action over those families of the product of a subgroup of F_q^* and the group generated by a cycling homography of the projective line of F_q. This permits to make effective constructions, cited in [8], of optical orthogonal codes from a representative system of orbits. We give in the end of this work two examples of optical orthogonal codes when q = 7 and q = 11.

C. Cao, L. Huang, and X. Tang

Additive Mapping Preserving Rank 2 of Alternate Matrices

ABSTRACT. Let F be a field, and K_n(F) be the set of n x n alternate matrices. This paper shows that φ is an additive surjective map preserving rank 2 from K_n(F) (n greater than or equal to 4) to itself if and only if φ is a bijective map and preserves ranks. Thus, by using the fundamental theorems of the geometry of alternate matrices, the characterization of φ is obtained.

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Volume 4, Number 1

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L. Noui

Une classe de groupes localement nilpotents

ABSTRACT. A group G is called SGN-group if every proper subgroup does not contain its centralizer. Here we are interested in these groups giving a description in many cases.

A. Senoussaoui

Opérateurs h-admissibles matriciels à symbole opérateur

ABSTRACT. This work is a generalization to the matrix case of the h-admissible operators with operator symbol notion introduced by Balazard-Konlein. We develop the formal matrix h-admissible with operator symbol calculus. We are interested in properties of composition, continuity, compactness and in the construction of the resolvent of these types of operators.

N. Mahdou

On P-Coherent Rings

ABSTRACT. In this paper, we introduce the notion of "P-coherent rings" which is a generalization of the notion of "coherent rings". Then we establish the transfer of this notion to pullbacks, direct products, and trivial ring extensions. We conclude with a brief discussion of the scope and limits of our results.

N. Midoune and L. Noui

Maximal Complexity of Trivectors

ABSTRACT. In this paper, by using the arithmetical invariant d₁(W ) of a trivector W we give an upper bound on maximal complexity C_n(F) where F is an arbitrary field. For n £ 8, C_n(F) is determined.

H. K. Nashine

Existence of Random Best Approximation For Noncommutative Maps

ABSTRACT. Some existence results on common random fixed point as random best approximation for noncommutative maps in the setup of compact and weakly compact subset of Banach space are proved . The results of Beg and Shazad [5, 7] are improved and extended.

A. Rashid and L. Yuan

Legendre Pseudo Spectral Method For the Incompressible Navier-Stokes Equations on the Sphere

ABSTRACT. The Legendre pseudospectral approximation for numerical solution of the time-dependent incompressible Navier-Stokes equations on a spherical surface is presented. The fully discrete Legendre pseudospectral scheme is constructed. The stability of the scheme is analyzed and the convergence is proved.

A. Tsemo

Non-Abelian Cohomology: The Point of View of Gerbed Tower

ABSTRACT. We define in this paper the notion of gerbed tower. This enables us to interpret geometrically cohomology classes without using the notion of N-category. We use this theory to study sequences of affine maps between affine manifolds, and the cohomology of manifolds.

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Volume 4, Number 2

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T. A. Al-Hawary

A New Class of Matroids

ABSTRACT. In [1, 2], classes of graphs and matroids that are k-balanced were explored. Connections between k-balanced graphs and k-balanced matroids were also obtained. In this paper, we further study the operations that preserve matroid k -balance property. In particular, we show that the amalgam A of the uniform matroids M₁ and M₂ is k-balanced if and only if the k-density of M_i, i=1,2 is at most the k-density of A. We then obtain conditions for the parallel connection and consequently the series connection of uniform matroids to be k- balanced.

J. D. Lawson and A. T. Lisan

Isotropy Groups and Group Topologies

ABSTRACT. Let S be a topological semigroup acting on a compact phase space and consider the universal semigroup compactification of S. It is shown in [5] that the action of S can then be extended to the compactification such that all minimal flows are flow isomorphic to quotients of the compactification via closed left congruences. One can also associate a subgroup of the maximal group in any minimal left ideal of the compactification to each minimal flow. These subgroups are referred to as isotropy groups in the literature and are important to tower constructions of minimal flows. In this paper we will look at alternative topologies on the maximal group where every closed subgroup in these topologies is an isotropy group for some minimal flow.

S. Chaari and H. Ouerdiane

White Noise Analysis in the Poisson Space

ABSTRACT. We develop in this paper a general structure of Poissonian white noise analysis. Because the normalized exponential is a test function, we can define the S_{p}-transform and we characterize via the S-transform the spaces of test and generalized Poisson functional in terms of analytical functions with growth condition of exponential type.

R. P. Agarwal and S. Nadarajah

Skew Distributions I

ABSTRACT. Following the recent paper by Gupta et al. [1], we construct skew pdfs of the form 2 g(u) G (λ u), where pdf g and cdf G are taken to come from one of Laplace, logistic, student's t, uniform, exponential power or the Bessel function distribution. The mathematical properties of the resulting distributions are studied.

M. Erraoui and Y. Ouknine

Une représentation non canonique du drap brownien

ABSTRACT. Soit { B_s,t : s,t Î [0 , 1] } un drap brownien et f,g deux fonctions réelles. Nous construisons une classe de processus gaussiens a deux indices

{ B_s,t^f,g , B_s,t^f , B_s,t^g : s,t Î [0 , 1] }

qui sont des draps browniens mais qui donnent des représentations non-canoniques de B. Nous étudions aussi les propriétés ergodiques de la transformation: B ---> B^f,g qui laisse invariante la loi du drap brownien. Finalement, nous étendons cette construction a d'autres processus gaussiens, particuliérement aux draps browniens fractionnaires.

L. Honghai and L. Lanzhe

Sharp Function Estimates for Maximal Multilinear Commutator of Bochner-Riesz Operator

ABSTRACT. In this paper, we prove a sharp inequality for maximal multilinear commutator related to Bochner-Riesz operator. By using our (sharp) inequality we obtain the weighted L^p-norm inequality for the maximal multilinear commutator.

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Special Issue - Volume 4, Number 3 (Advances in Mathematics)

Editors: T. Diagana, G. M. N'Guérékata, and S. Zarati

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D. Bugajewska and D. O'Regan

Upper and Lower Solutions of Differential Equations via Approximate Derivatives and the Denjoy Integral

ABSTRACT. In this paper we deal with differential equations formulated in terms of approximate derivatives. We establish the existence of solutions to the n-th order equations as well as the Darboux problem between two functions s¹ (lower solution) and s⁰ (upper solution).

D. Bourguiba, S. Hammouda and S. Zarati

Profondeur et Cohomologie Équivariante

ABSTRACT. Let V be an elementary abelian 2-group and X be a V-CW-complex. We denote by H^*_VX the mod. 2 equivariant cohomology of X; H^*_VX is naturally an H^*(BV; F₂)-module. If X is a finite V-CW-complex then, H^*_VX is an H^*(BV; F₂)-module of finite type; we denote by dth_VH^*_VX the depth of H^*_VX as an H^*(BV; F₂)-module. In this paper we compute, in certain cases, the depth of a tensor product and, as an application, we discuss the relation between dth_VH^*_VX and dth_WH^*_WX for W a subgroup of V. In particular, we prove: Theorem. Let V be an elementary abelian 2-group of rank 2 and X be a finite V-CW-complex such that H^*_VX is a monogenic H^*V-module. Then, for every subgroup W of V, we have: dth_WH^*_WX £ dth_VH^*_VX.

C. S. Gal, S. G. Gal, and G. M. N'Guérékata

Existence and Uniqueness of Almost Automorphic Mild Solutions to Semilinear Fuzzy Differential Equations

ABSTRACT. We consider the semilinear fuzzy differential equation

x'(t) = A x(t) Å f(t, x(t)), t Î R,

in a fuzzy-number kind space X, where A is the infinitesimal generator of an exponentially stable C₀-semigroup on X. Under suitable conditions on f, we prove the existence and uniqueness of an almost automorphic mild solution to the fuzzy equation. The results extends those of the classical case of Banach spaces in the recent paper [6].

M. Erraoui and Y. Ouknine

Note on the Smoothness of the Law of Fractional Brownian Sheet

ABSTRACT. Let (B_z^H,H', z Î [0,T]²) be a fractional Brownian sheet with Hurst parameter H, H^' Î (0 ,1). Using the local criterion, obtained by Florit and Nualart in [FN], for the smoothness of the density we prove that the maximum of the fractional Brownian sheet possesses an infinitely differentiable density.

S. M. Einstein-Matthews and C. H. Lutterodt

Rational Approximants in a Polydisk versus a Ball in C^N

ABSTRACT. The paper highlights the differences as well as the similarities in the approaches used in the construction of rational approximants to holomorphic functions based on their series expansions either in a polydisc or in a ball in C^N(N>1). It compares and contrasts some of the known results relating to the convergence of rational approximants to a certain class of meromorphic functions in a polydisc and its generalizations or in a ball and its analogous generalizations.

G. M. N'Guérékata

Almost Automorphic Solutions of Some Integrodifferential Equations in Fréchet Spaces

ABSTRACT. In this paper we study the existence of almost automorphic as well as asymptotically almost automorphic solutions of nonlinear and Volterra integral equations in Fréchet spaces. We also investigate a topological structure of the sets of such solutions. Throughout the paper, we use a recent Fixed point theorem due to D. Bugajewski.

C. C. Kokonendji and D. Pommeret

Characterization of Multivariate Exponential Families with Polynomial Variance Function

ABSTRACT. It exists different characterizations of natural exponential families with polynomial variance function. Some of them have been extended to the multivariate case (see for instance [19] for the quadratic case). Also, some connections between natural exponential families with polynomial variance functions and certain sequences of polynomials are obtained in [21]. Our purpose is to complete this result. We obtain a characterization of multivariate natural exponential families with k-th degree polynomial variance functions via a notion of k-orthogonality of some associated polynomials. This characterization may also be expressed in terms of the well known Bhattacharyya matrices.

C. C. Kokonendji and S. Marque

A Strict Arcsine Regression Model

ABSTRACT. The strict arcsine distribution has been recently studied as an alternative to negative binomial in univariate problems involving counts. We propose a strict arcsine regression model for regression analysis of overdispersed count data. The model can be derived from an attractive framework for incorporating random effect in Poisson regression models and in handling extra-Poisson variation. Comparison with negative binomial model is investigated by simulations and application on data concerning cardiovascular mortality among the elderly of the South-West of France.

M. Dammak, S. Hammouda, and S. Zarati