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4: Paper Source PDF document

Paper's Title:

Positive Solutions to a System of Boundary Value Problems for Higher-Dimensional Dynamic Equations on Time Scales


I. Y. Karaca

Department of Mathematics,
Ege University,
35100 Bornova, Izmir,



In this paper, we consider the system of boundary value problems for higher-dimensional dynamic equations on time scales. We establish criteria for the existence of at least one or two positive solutions. We shall also obtain criteria which lead to nonexistence of positive solutions. Examples applying our results are also given.

1: Paper Source PDF document

Paper's Title:

On Ruled Surfaces According to Quasi-Frame in Euclidean 3-Space


M. Khalifa Saad and R. A. Abdel-Baky

Department of Mathematics, Faculty of Science,
Islamic University of Madinah,
Department of Mathematics, Faculty of Science,
Sohag University, Sohag,

Department of Mathematics, Faculty of Science,
Assiut University, Assiut,


This paper aims to study the skew ruled surfaces by using the quasi-frame of Smarandache curves in the Euclidean 3-space. Also, we reveal the relationship between Serret-Frenet and quasi-frames and give a parametric representation of a directional ruled surface using the quasi-frame. Besides, some comparative examples are given and plotted which support our method and main results.

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