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:

The Square Number by the Approximation

Author(s):

Masaki Hisasue

Asahikawa Fuji Girls' High School
Asahikawa Hanasaki-cho 6-3899
Hokkaido, Japan

masaki@fuji.ed.jp
 

Abstract:

In this paper, we give square numbers by using the solutions of Pell's equation.
 

Paper's Title:

Strong Convergence Theorem for a Common Fixed Point of an Infinite Family of J-nonexpansive Maps with Applications

Author(s):

Charlse Ejike Chidume, Otubo Emmanuel Ezzaka and Chinedu Godwin Ezea

African University of Science and Technology,
Abuja,
Nigeria.
E-mail: cchidume@aust.edu.ng

Ebonyi State University,
Abakaliki,
Nigeria.
E-mail: mrzzaka@yahoo.com

 Nnamdi Azikiwe University,
Awka,
Nigeria.
E-mail: chinedu.ezea@gmail.com

Abstract:

Let E be a uniformly convex and uniformly smooth real Banach space with dual space E^*. Let {T_i}^∞_i=1 be a family of J-nonexpansive maps, where, for each i,~T_i maps E to 2^E*. A new class of maps, J-nonexpansive maps from E to E^*, an analogue of nonexpansive self maps of E, is introduced. Assuming that the set of common J-fixed points of {T_i}^∞_i=1 is nonempty, an iterative scheme is constructed and proved to converge strongly to a point x^* in ∩^∞_n=1F_JT_i. This result is then applied, in the case that E is a real Hilbert space to obtain a strong convergence theorem for approximation of a common fixed point for an infinite family of nonexpansive maps, assuming existences. The theorem obtained is compared with some important results in the literature. Finally, the technique of proof is also of independent interest.