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The Pure and Applied Mathematics
Journal Basic Information
pISSN :
1226-0657
eISSN :
2287-6081
Journal DOI :
10.7468/jksmeb
Frequency :
Others
Publisher:
Korea Society of Mathematical Education
Editor in Chief :
Moon-Ja Jeong
Volume & Issues
Volume 19, Issue 4 - Nov 2012
Volume 19, Issue 3 - Aug 2012
Volume 19, Issue 2 - May 2012
Volume 19, Issue 1 - Feb 2012
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1
SOME EQUIVALENT CONDITIONS FOR CONIC SECTIONS
Kim, Dong-Soo ; Seo, Soojeong ; Beom, Woo-In ; Yang, Deukju ; Kang, Juyeon ; Jeong, Jieun ; Song, Booseon ;
The Pure and Applied Mathematics, volume 19, issue 4, 2012, Pages 315~325
DOI : 10.7468/jksmeb.2012.19.4.315
Abstract
Let A and B denote a point, a line or a circle, respectively. For a positive constant
, we examine the locus
(
) of points P whose distances from A and B are, respectively, in a constant ratio
. 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.
2
THE CURVATURE OF HALF LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD OF QUASI-CONSTANT CURVATURE
Jin, Dae Ho ;
The Pure and Applied Mathematics, volume 19, issue 4, 2012, Pages 327~335
DOI : 10.7468/jksmeb.2012.19.4.327
Abstract
We study half lightlike submanifolds M of semi-Riemannian manifolds
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
is tangent to M, and (2) the co-screen distribution is a conformal Killing one.
3
AREA OF TRIANGLE IN THE PLANE WITH ALPHA DISTANCE FUNCTION
Oh, Chae Hee ; Ko, Il Seog ; Kim, Byung Hak ;
The Pure and Applied Mathematics, volume 19, issue 4, 2012, Pages 337~347
DOI : 10.7468/jksmeb.2012.19.4.337
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
-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
-distance.
4
GROUPS ACTING ON MEDIAN GRAPHS AND MEDIAN COMPLEXES
Ryang, Dohyoung ;
The Pure and Applied Mathematics, volume 19, issue 4, 2012, Pages 349~361
DOI : 10.7468/jksmeb.2012.19.4.349
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(
) groups and, in addition, work L(0) groups are closed under free product.
5
NEYMAN-PEARSON THEORY AND ITS APPLICATION TO SHORTFALL RISK IN FINANCE
Kim, Ju Hong ;
The Pure and Applied Mathematics, volume 19, issue 4, 2012, Pages 363~381
DOI : 10.7468/jksmeb.2012.19.4.363
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
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.
6
ON THE STABILITY OF A MIXED TYPE QUADRATIC AND CUBIC FUNCTIONAL EQUATION
Lee, Chang-Ju ; Lee, Yang-Hi ;
The Pure and Applied Mathematics, volume 19, issue 4, 2012, Pages 383~396
DOI : 10.7468/jksmeb.2012.19.4.383
Abstract
In this paper, we investigate a fuzzy version of stability for the functional equation $$f(x+2y)-3f(x+y)+3f(x)-f(x-y)-3f(y)+3f(-y)
7
ON THE FUZZY STABILITY OF CUBIC MAPPINGS USING FIXED POINT METHOD
Koh, Heejeong ;
The Pure and Applied Mathematics, volume 19, issue 4, 2012, Pages 397~407
DOI : 10.7468/jksmeb.2012.19.4.397
Abstract
Let X and Y be vector spaces. We introduce a new type of a cubic functional equation
:
. 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.
8
ASYMPTOTIC BEHAVIORS OF ALTERNATIVE JENSEN FUNCTIONAL EQUATIONS-REVISITED
Chung, Jaeyoung ; Choi, Chang-Kwon ;
The Pure and Applied Mathematics, volume 19, issue 4, 2012, Pages 409~421
DOI : 10.7468/jksmeb.2012.19.4.409
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.
9
WEAK BLOCH FUNCTIONS, ∅-UNIFORM AND ∅-JOHN DOMAINS
Kim, Ki Won ;
The Pure and Applied Mathematics, volume 19, issue 4, 2012, Pages 423~435
DOI : 10.7468/jksmeb.2012.19.4.423
Abstract
We give some properties of weak Bloch functions and also give some properties of
-uniform domains and
-John domains in terms of moduli of continuity of Bloch functions and weak Bloch functions.