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ISSN : 1226-0657
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Vol.19 No.4
Abstract
Let A and B denote a point, a line or a circle, respectively. For a positive constant <TEX>$a$</TEX>, we examine the locus <TEX>$C_{AB}$</TEX>(<TEX>$a$</TEX>) of points P whose distances from A and B are, respectively, in a constant ratio <TEX>$a$</TEX>. As a result, we establish some equivalent conditions for conic sections. As a byproduct, we give an easy way to plot points of conic sections exactly by a compass and a straightedge.
Abstract
We study half lightlike submanifolds M of semi-Riemannian manifolds <TEX>$\widetilde{M}$</TEX> of quasi-constant curvatures. The main result is a characterization theorem for screen homothetic Einstein half lightlike submanifolds of a Lorentzian manifold of quasi-constant curvature subject to the conditions; (1) the curvature vector field of <TEX>$\widetilde{M}$</TEX> is tangent to M, and (2) the co-screen distribution is a conformal Killing one.
Abstract
The taxicab distance and Chinese-checker distance in the plane are practical distance notions with a wide range of applications compared to the Euclidean distance. The <TEX>${\alpha}$</TEX>-distance was introduced as a generalization of these two distance functions. In this paper, we study alpha circle, trigonometry, and the area of a triangle in the plane with <TEX>${\alpha}$</TEX>-distance.
Abstract
CAT(0) cubical complexes are a key to formulate geodesic spaces with nonpositive curvatures. The paper discusses the median structure of CAT90) cubical complexes. Especially, the underlying graph of a CAT(0) cubical complex is a median graph. Using the idea of median structure, this paper shows that groups acting on median complexes L(<TEX>${\delta}$</TEX>) groups and, in addition, work L(0) groups are closed under free product.
Abstract
Shortfall risk is considered by taking some exposed risks because the superhedging price is too expensive to be used in practice. Minimizing shortfall risk can be reduced to the problem of finding a randomized test <TEX>${\psi}$</TEX> in the static problem. The optimization problem can be solved via the classical Neyman-Pearson theory, and can be also explained in terms of hypothesis testing. We introduce the classical Neyman-Pearson lemma expressed in terms of mathematics and see how it is applied to shortfall risk in finance.
Abstract
In this paper, we investigate a fuzzy version of stability for the functional equation <TEX>$$f(x+2y)-3f(x+y)+3f(x)-f(x-y)-3f(y)+3f(-y)=0$$</TEX> in the sense of M. Mirmostafaee and M. S. Moslehian.
Abstract
Let X and Y be vector spaces. We introduce a new type of a cubic functional equation <TEX>$f$</TEX> : <TEX>$X{\rightarrow}Y$</TEX>. Furthermore, we assume X is a vector space and (Y, N) is a fuzzy Banach space and then investigate a fuzzy version of the generalized Hyers-Ulam stability in fuzzy Banach space by using fixed point method for the cubic functional equation.
Abstract
In this paper, using an efficient change of variables we refine the Hyers-Ulam stability of the alternative Jensen functional equations of J. M. Rassias and M. J. Rassias and obtain much better bounds and remove some unnecessary conditions imposed in the previous result. Also, viewing the fundamentals of what our method works, we establish an abstract version of the result and consider the functional equations defined in restricted domains of a group and prove their stabilities.
Abstract
We give some properties of weak Bloch functions and also give some properties of <TEX>${\phi}$</TEX>-uniform domains and <TEX>${\phi}$</TEX>-John domains in terms of moduli of continuity of Bloch functions and weak Bloch functions.