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ISSN : 1226-0657
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Vol.20 No.3
Abstract
In this paper, we study the Lie-generalized Fibonacci sequence and the root system of rank 2 symmetric hyperbolic Kac-Moody algebras. We derive several interesting properties of the Lie-Fibonacci sequence and relationship between them. We also give a couple of sufficient conditions for the existence of the integral points on the hyperbola <TEX>$\mathfrak{h}^a:x^2-axy+y^2=1$</TEX> and <TEX>$\mathfrak{h}_k:x^2-axy+y^2=-k$</TEX> (<TEX>$k{\in}\mathbb{Z}_{</TEX><TEX>></TEX><TEX>0}$</TEX>). To list all the integral points on that hyperbola, we find the number of elements of <TEX>${\Omega}_k$</TEX>.
Abstract
In this article, we study the Gauss map of generalized slant cylindrical surfaces (GSCS's) in the 3-dimensional Euclidean space <TEX>$\mathbb{E}^3$</TEX>. Surfaces of revolution, cylindrical surfaces and tubes along a plane curve are special cases of GSCS's. Our main results state that the only GSCS's with Gauss map G satisfying <TEX>${\Delta}G=AG$</TEX> for some <TEX>$3{\times}3$</TEX> matrix A are the planes, the spheres and the circular cylinders.
Abstract
We establish a common fixed point theorem for mappings under <TEX>${\phi}$</TEX>-contractive conditions on intuitionistic fuzzy metric spaces. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. We also give an example to validate our result.
Abstract
C. Vetro [4] gave the concept of weak non-Archimedean in fuzzy metric space. Using the same concept for Menger PM spaces, Mishra et al. [22] proved the common fixed point theorem for six maps, Also they introduced semi-compatibility. In this paper, we generalized the theorem [22] for family of maps and proved the common fixed point theorems using the pair of semi-compatible and reciprocally continuous maps for one pair and R-weakly commuting maps for another pair in Menger WNAPM-spaces. Our results extends and generalizes several known results in metric spaces, probabilistic metric spaces and the similar spaces.
Abstract
We present a 4-dimensional nil-manifold as the first example of a closed non-K<TEX>$\ddot{a}$</TEX>hlerian symplectic manifold with the following property: a function is the scalar curvature of some almost K<TEX>$\ddot{a}$</TEX>hler metric iff it is negative somewhere. This is motivated by the Kazdan-Warner's work on classifying smooth closed manifolds according to the possible scalar curvature functions.
Abstract
In this work we study the tribonacci numbers. We find a tribonacci triangle which is an analog of Pascal triangle. We also investigate an efficient method to compute any <TEX>$n$</TEX>th tribonacci numbers by matrix method, and find periods of the sequence by taking modular tribonacci number.
Abstract
Alexseev's formula generalizes the variation of constants formula and permits the study of a nonlinear perturbation of a system with certain stability properties. In recent years M. Pinto introduced the notion of <TEX>$h$</TEX>-stability. S.K. Choi et al. investigated <TEX>$h$</TEX>-stability for the nonlinear differential systems using the notion of <TEX>$t_{\infty}$</TEX>-similarity. Applying these two notions, we study bounds for solutions of the perturbed differential systems.