i-manager's Journal on Mathematics (JMAT)


Volume 1 Issue 4 October - December 2012

Article

Uniformly stable solutions of the functional inclusions

A.M.A. El-Sayed* , Fatma M.Gaffar**, Nesreen F.M.El-haddad***
* Faculty of Science, Alexandria University, Alexandria, Egypt.
**-*** Faculty of Science, Damanhour University, Egypt.
El-Sayed, A.M.A., Nesreen, F.M.G. and El-Haddad, F.M. (2012). Uniformly Stable Solutions of The Functional Inclusions. i-manager’s Journal on Mathematics, 1(4), 1-7. https://doi.org/10.26634/jmat.1.4.2043

Abstract

In this paper the authors concerned with the concept and the existence of the uniformly stable solution of the functional inclusion in the two classes C[0, T] and L1 [0, T].

Article

Biharmonic Curves With Bishop Frame In E3

Talat Körpinar* , Essin TURHAN**
*-** Firat University, Department of Mathematics 23119, Elazig, Turkey.
Körpinar, T., and Turhan, T. (2012). Biharmonic Curves With Bishop Frame in E3. i-manager’s Journal on Mathematics, 1(4), 8-11. https://doi.org/10.26634/jmat.1.4.2044

Abstract

In this paper, we study biharmonic curves in E3. We give some characterizations for curvature and torsion of a biharmonic curve in E3.

Article

International Judging System of Figure Skating: A Middle Grades Activity on Decimal Operations

Diana Cheng*
Assistant Professor, Towson University, Maryland, USA.
Cheng, D. (2012). International Judging System of Figure Skating: A Middle Grades Activity on Decimal Operations. i-manager’s Journal on Mathematics, 1(4), 12-17. https://doi.org/10.26634/jmat.1.4.2045

Abstract

The International Skating Union implemented a new judging system, the International Judging System (IJS), after it was revealed that the previously used 6.0 judging system accommodated for judging bias in figure skating events at the 2002 Olympic Winter Games. The 6.0 judging system required judges to rank figure skaters’ placements in an event relative to the other competitors; a controversy arose in the pairs event at the Olympic Games when it became clear that some of the judges were persuaded to influence the outcome irrespective of the actual performances of the skaters. The new IJS now requires judges to rate each element performed by each skater, without comparison to other skaters’ performances, in an effort to reduce judging bias.  The judges’ ratings are then averaged and a decimal score is accordingly assigned for each element.  The skaters earn a technical score, computed by finding the sum of the element scores.  In this article, the IJS is explained as an application of mathematics, and a skating judging activity suitable for middle grades students is presented.  The activity involves students’ rating a pairs team’s performance and computing the team’s score through a simplified version of the IJS.

Article

Position Vector of Null General Helices in the Lorentzian Heisenberg Group Heis3

Talat Körpinar* , Essin TURHAN**
*-** Firat University, Department of Mathematics 23119, Elazig, Turkey.
Körpinar, T., and Turhan, E. (2012). Position Vector Of Null General Helices In The Lorentzian Heisenberg Group Heis3. i-manager’s Journal on Mathematics, 1(4), 18-21. https://doi.org/10.26634/jmat.1.4.2046

Abstract

In this paper, the authors study characterizes null general helices in terms of their curvature and torsion in the Lorentzian Heisenberg group Heis3. They also gave their explicit parametrizations.

Research Paper

Oscillations in Lossy Transmission Lines Terminated By Exponential R-Load

Vasil G. Angelov* , Dafinka Angelova**
* Department of Mathematics, University of Mining and Geology, Bulgaria.
** Department of Mechanics and Mathematics, Higher School of Civil Engineering, Bulgaria
Angelov, V., and Angelova, D. (2012). Oscillations In Lossy Transmission Lines Terminated By Exponential R-Load. i-manager’s Journal on Mathematics, 1(4), 22-33. https://doi.org/10.26634/jmat.1.4.2047

Abstract

This present paper is devoted to investigation of lossy transmissions lines terminated by a nonlinear resistive element. The transmission line is terminated by an R-element with exponential nonlinearity in the V-I characteristic. The reducing of the mixed problem for Telegrapher hyperbolic system to an initial value problem for a nonlinear neutral equation on the boundary is made in [3]. The nonlinearity in the boundary condition is transferred to the neutral equation on the boundary. Then we introduce a suitable operator whose fixed point is an oscillatory solution of the neutral equation. The main existence-uniqueness theorem contains conditions which guarantee that the operator mentioned is contractive one in a uniform space. Finally, we demonstrate how to apply the results obtained to the circuit design.