Abstract:

We study the existence of large solutions of the semilinear elliptic equation Δu=p(x)f(u) where f is not monotonic. We prove existence, on bounded and unbounded domains, under the assumption that f is Lipschitz continuous, f(0) = 0, f(s) > 0 for s > 0 and there exists a nonnegative, nondecreasing Hölder continuous function g and a constant M such that g(s) ≤ f(s) ≤ Mg(s) for large s. The nonnegative function p is allowed to be zero on much of the domain.

Paper's Title:

Analysis of the Dynamic Response of the Soil-pile Behavioral Model Under Lateral Load

Author(s):

Ibrahima Mbaye, Mamadou Diop, Aliou Sonko and Malick Ba

University of Thies,
Department of Mathematics, Bp 967 Thies,
Senegal.
E-mail: imbaye@univ-thies.sn
mamadou.diop@univ-thies.sn
aliousonko59@gmail.com
mmalickba@hotmail.fr
URL: https://www.univ-thies.sn
 

Abstract:

This work aims to extend and improve our previous study on mathematical and numerical analysis of stationary Pasternak model. In this paper a dynamic response of Pasternak model is considered. On the one hand we establish the existence and uniqueness of the solution by using the Lax-Milgram theorem and the spectral theory thus the existence of a Hilbert basis is shown and the spectral decomposition of any solution of the problem can be established and on the other hand the finite element method is used to determinate the numerical results. Furthermore, the influence of soil parameters G_p and K_p on the displacement of the pious is studied numerically at any time t_n.

Paper's Title:

Numerical Approximation by the Method of Lines with Finite-volume Approach of a Solute Transport Equation in Periodic Heterogeneous Porous Medium

Author(s):

D. J. Bambi Pemba and B. Ondami

Université Marien Ngouabi,
Factuté des Sciences et Techniques,
BP 69, Brazzaville,
Congo.
E-mail: bondami@gmail.com

Abstract:

In this paper we are interested in the numerical approximation of a two-dimensional solute transport equation in heterogeneous porous media having periodic structures. It is a class of problems which has been the subject of various works in the literature, where different methods are proposed for the determination of the so-called homogenized problem. We are interested in this paper, in the direct resolution of the problem, and we use the method of lines with a finite volume approach to discretize this equation. This discretization leads to an ordinary differential equation (ODE) that we discretize by the Euler implicit scheme. Numerical experiments comparing the obtained solution and the homogenized problem solution are presented. They show that the precision and robustness of this method depend on the ratio between, the mesh size and the parameter involved in the periodic homogenization.

Paper's Title:

The successive approximations method and error estimation in terms of at most the first derivative for delay ordinary differential equations

Author(s):

Alexandru Mihai Bica

Department of Mathematics,
University of Oradea,
Str. Armatei Romane no.5,
410087, Oradea,
Romania
smbica@yahoo.com
abica@uoradea.ro

Abstract:

We present here a numerical method for first order delay ordinary differential equations, which use the Banach's fixed point theorem, the sequence of successive approximations and the trapezoidal quadrature rule. The error estimation of the method uses a recent result of P. Cerone and S.S. Dragomir about the remainder of the trapezoidal quadrature rule for Lipchitzian functions and for functions with continuous first derivative.

Paper's Title:

On Stan Ulam and his Mathematics

Author(s):

Krzysztof Ciesielski and Themistocles M. Rassias

Mathematics Institute, Jagiellonian University,
Łjasiewicza 6, 30-348 Kraków,
Poland
Department of Mathematics. National Technical University of Athens,
Zografou Campus, 15780 Athens,
Greece
Krzysztof.Ciesielski@im.uj.edu.pl
trassias@math.ntua.gr

Abstract:

In this note we give a glimpse of the curriculum vitae of Stan Ulam, his personality and some of the mathematics he was involved in.

Paper's Title:

Ulam Stability of Functional Equations

Author(s):

Stefan Czerwik and Krzysztof Król

Abstract:

In this survey paper we present some of the main results on Ulam-Hyers-Rassias stability for important functional equations.

Paper's Title:

Bounds on the Jensen Gap, and Implications for Mean-Concentrated Distributions

Author(s):

Xiang Gao, Meera Sitharam, Adrian E. Roitberg

Department of Chemistry, and Department of Computer & Information Science & Engineering,
University of Florida,
Gainesville, FL 32611,
USA.
E-mail: qasdfgtyuiop@gmail.com
URL: https://scholar.google.com/citations?user=t2nOdxQAAAAJ

Abstract:

This paper gives upper and lower bounds on the gap in Jensen's inequality, i.e., the difference between the expected value of a function of a random variable and the value of the function at the expected value of the random variable. The bounds depend only on growth properties of the function and specific moments of the random variable. The bounds are particularly useful for distributions that are concentrated around the mean, a commonly occurring scenario such as the average of i.i.d. samples and in statistical mechanics.

Paper's Title:

The Jacobson Density Theorem for Non-Commutative Ordered Banach Algebras

Author(s):

Kelvin Muzundu

University of Zambia,
Deparment of Mathematics and Statistics,
P.O. Box 32379, Lusaka,
Zambia.
E-mail: kmzundu@gmail.com

Abstract:

The Jacobson density theorem for general non-commutative Banach algebras states as follows: Let π be a continuous, irreducible representation of a non-commutative Banach algebra A on a Banach space X. If x₁,x₂,...,x_n are linearly independent in X and if y₁,y₂,...,y_n are in X, then there exists an a∈ A such that π(a)x_i=y_i for i=1,2,...,n. By considering ordered Banach algebras A and ordered Banach spaces X, we shall establish an order-theoretic version of the Jacobson density theorem.

Paper's Title:

A Caratheodory's Approximate Solutions of Stochastic Differential Equations Under the Hölder Condition

Author(s):

Bo-Kyeong Kim and Young-Ho Kim

Department of Mathematics,
Changwon National University,
Changwon, Gyeongsangnam-do 51140,
Korea.
E-mail: claire9576@naver.com
yhkim@changwon.ac.kr

Abstract:

In this paper, based on the theorem of the uniqueness of the solution of the stochastic differential equation, the convergence possibility of the Caratheodory's approximate solution was studied by approximating the unique solution. To obtain this convergence theorem, we used a Hölder condition and a weakened linear growth condition. Furthermore, The auxiliary theorems for the existence and continuity of the Caratheodory's approximate solution were investigated as a prerequisite.

Paper's Title:

Fractional Integral Inequalities of Hermite-Hadamard Type for P-convex and Quasi-Convex Stochastic Process

Author(s):

Oualid Rholam, Mohammed Barmaki and Driss Gretet

National School of Applied Sciences (ENSA),
University Ibn Tofail,
B.P 242 Kenitra 14000,
phone number : +212606257757,
Morocco.
E-mail: oualid.rholam@uit.ac.ma

 
Science Faculty Ben M'sik,
University Hassan II,
B.P 7955 Av Driss El Harti Sidi Othmane 20700,
phone number : +212 5 22 70 46 71 ,
Morocco.
E-mail:  mohammed.barmaki@uit.ac.ma

National School of Applied Sciences (ENSA),
University Ibn Tofail,
B.P 242 Kenitra 14000,
phone number : +212661403557,
Morocco.
E-mail: driss.gretete@uit.ac.ma 

Abstract:

In this paper we consider the class of P-convex and Quasi-convex stochastic processes on witch we apply a general class of generalized fractional integral operator in order to establish new integral inequalities of Hermite-Hadammard type. then we obtain some results for well known types of fractional integrals. Results obtained in this paper may be starting point as well as a useful source of inspiration for further research in convex analysis.

Paper's Title:

The Automatic Continuity of N-Homomorphisms in Certain *-Banach Algebras

Author(s):

M. Aboulekhlef, Y. Tidli

Laboratory of Applied Mathematics and Information and Communication Technology
Polydisciplinary Faculty of Khouribga
University of Sultan Moulay Slimane
Morocco.
E-mail: aboulekhlef@gmail.com y.tidli@gmail.com

Abstract:

In this study, we prove the automatic continuity of surjective n-homomorphism between complete p-normed algebras. We show also that if Α and Β are complete *-p-normed algebras, Β is *simple and ψ: Α → Β is a surjective n-homomorphism under certain conditions, then ψ is continuous.

Paper's Title:

On Infinite Unions and Intersections of Sets in a Metric Space

Author(s):

Spiros Konstantogiannis

Ronin Institute,
Montclair, New Jersey,
United States.
E-mail: spiros.konstantogiannis@ronininstitute.org
URL: https://www.researchgate.net/profile/Spiros-Konstantogiannis

Abstract:

The aim of this paper is to examine infinite unions and intersections of sets in a general metric space, with a view to explaining when an infinite intersection of open sets is an open set and when an infinite union of closed sets is a closed set.

Paper's Title:

Automatic Continuity of Generalized Derivations in Certain *-Banach Algebras

Author(s):

M. Aboulekhlef, Y. Tidli and M. Belam

Laboratory of Applied Mathematics and Information and Communication Technology Polydisciplinary
Faculty of Khouribga University of Sultan Moulay Slimane
Morocco.
E-mail: aboulekhlef@gmail.com y.tidli@gmail.com m.belam@gmail.com

Abstract:

Consider the map φ of the Banach algebra Β in Β, if there exists a derivation δ of Β in Β so that for every  x, y ∈ Β , φ(xy) =φ(x)y+xδ(y) . φ is called a generalized derivation of Β. In [9], Bresar introduced the concept of generalized derivations. We prove several results about the automatic continuity of generalized derivations on certain Banach algebras.

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