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Bulletin of the Korean Mathematical Society
Journal Basic Information
pISSN :
1015-8634
eISSN :
2234-3016
Journal DOI :
10.4134/BKMS
Frequency :
Others
Publisher:
The Korean Mathematical Society
Editor in Chief :
Yongnam Lee
Volume & Issues
Volume 48, Issue 6 - Nov 2011
Volume 48, Issue 5 - Sep 2011
Volume 48, Issue 4 - Jul 2011
Volume 48, Issue 3 - May 2011
Volume 48, Issue 2 - Mar 2011
Volume 48, Issue 1 - Jan 2011
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1
A DIFFERENTIAL EQUATION FOR MULTIPLE BESSEL POLYNOMIALS WITH RAISING AND LOWERING OPERATORS
Baek, Jin-Ok ; Lee, Dong-Won ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 445~454
DOI : 10.4134/BKMS.2011.48.3.445
Abstract
In this paper, we first find a raising operator and a lowering operator for multiple Bessel polynomials and then give a differential equation having multiple Bessel polynomials as solutions. Thus the differential equations were found for all multiple orthogonal polynomials that are orthogonal with respect to the same type of classical weights introduced by Aptekarev et al.
2
REFINEMENT RINGS, EXCHANGE PROPERTY AND COMPARABILITY
Huang, Chaoling ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 455~468
DOI : 10.4134/BKMS.2011.48.3.455
Abstract
We introduce the notion of refinement rings, and generalize some comparability properties of regular rings to the setting of refinement rings.
3
ON THE CHARACTER RINGS OF TWIST KNOTS
Nagasato, Fumikazu ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 469~474
DOI : 10.4134/BKMS.2011.48.3.469
Abstract
The Kauffman bracket skein module
(M) of a 3-manifold M becomes an algebra for t
4
GENERALIZED ANALYTIC FEYNMAN INTEGRAL VIA FUNCTION SPACE INTEGRAL OF BOUNDED CYLINDER FUNCTIONALS
Chang, Seung-Jun ; Choi, Jae-Gil ; Chung, Hyun-Soo ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 475~489
DOI : 10.4134/BKMS.2011.48.3.475
Abstract
In this paper, we use a generalized Brownian motion to define a generalized analytic Feynman integral. We then obtain some results for the generalized analytic Feynman integral of bounded cylinder functionals of the form F(x)
5
FUZZY STABILITY OF A CUBIC-QUARTIC FUNCTIONAL EQUATION: A FIXED POINT APPROACH
Jang, Sun-Young ; Park, Choon-Kil ; Shin, Dong-Yun ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 491~503
DOI : 10.4134/BKMS.2011.48.3.491
Abstract
Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quartic functional equation (0.1) f(2x + y) + f(2x - y)
6
A REMARK ON GEL`FAND DUALITY FOR SPECTRAL TRIPLES
Bertozzini, Paolo ; Conti, Roberto ; Lewkeeratiyutkul, Wicharn ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 505~521
DOI : 10.4134/BKMS.2011.48.3.505
Abstract
We present a duality between the category of compact Riemannian spin manifolds (equipped with a given spin bundle and charge conjugation) with isometries as morphisms and a suitable "metric" category of spectral triples over commutative pre-
-algebras. We also construct an embedding of a "quotient" of the category of spectral triples introduced in [5] into the latter metric category. Finally we discuss a further related duality in the case of orientation and spin-preserving maps between manifolds of fixed dimension.
7
NONPARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION OF A CONCAVE RECEIVER OPERATING CHARACTERISTIC CURVE VIA GEOMETRIC PROGRAMMING
Lee, Kyeong-Eun ; Lim, Johan ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 523~537
DOI : 10.4134/BKMS.2011.48.3.523
Abstract
A receiver operating characteristic (ROC) curve plots the true positive rate of a classier against its false positive rate, both of which are accuracy measures of the classier. The ROC curve has several interesting geometrical properties, including concavity which is a necessary condition for a classier to be optimal. In this paper, we study the nonparametric maximum likelihood estimator (NPMLE) of a concave ROC curve and its modification to reduce bias. We characterize the NPMLE as a solution to a geometric programming, a special type of a mathematical optimization problem. We find that the NPMLE is close to the convex hull of the empirical ROC curve and, thus, has smaller variance but positive bias at a given false positive rate. To reduce the bias, we propose a modification of the NPMLE which minimizes the
distance from the empirical ROC curve. We numerically compare the finite sample performance of three estimators, the empirical ROC curve, the NMPLE, and the modified NPMLE. Finally, we apply the estimators to estimating the optimal ROC curve of the variance-threshold classier to segment a low depth of field image and to finding a diagnostic tool with multiple tests for detection of hemophilia A carrier.
8
EXISTENCE AND ASYMPTOTIC STABILITY OF SOLUTIONS OF A PERTURBED FRACTIONAL FUNCTIONAL-INTEGRAL EQUATION WITH LINEAR MODIFICATION OF THE ARGUMENT
Darwish, Mohamed Abdalla ; Henderson, Johnny ; O`Regan, Donal ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 539~553
DOI : 10.4134/BKMS.2011.48.3.539
Abstract
We study the solvability of a perturbed quadratic functional-integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions.
9
GLOBAL STABILITY OF THE VIRAL DYNAMICS WITH CROWLEY-MARTIN FUNCTIONAL RESPONSE
Zhou, Xueyong ; Cui, Jingan ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 555~574
DOI : 10.4134/BKMS.2011.48.3.555
Abstract
It is well known that the mathematical models provide very important information for the research of human immunodeciency virus type. However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T-cells and the viral particles. In this paper, a differential equation model of HIV infection of
T-cells with Crowley-Martin function response is studied. We prove that if the basic reproduction number
< 1, the HIV infection is cleared from the T-cell population and the disease dies out; if
> 1, the HIV infection persists in the host. We find that the chronic disease steady state is globally asymptotically stable if
> 1. Numerical simulations are presented to illustrate the results.
10
SOME NOTES ON ISHIKAWA ITERATION FOR MULTI-VALUED MAPPINGS
Song, Yisheng ; Cho, Yeol-Je ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 575~584
DOI : 10.4134/BKMS.2011.48.3.575
Abstract
In Shahzad and Zegeye [Nonlinear Anal. 71 (2009), no. 3-4, 838-844], the authors introduced several Ishikawa iterative schemes for xed points of multi-valued mappings in Banach spaces, and proved some strong convergence theorems by using their iterations. In their proofs of the main results, it seems reasonable and simpler to prove for the iteration {
} to be a Cauchy sequence. In this paper, we modify and improve the proofs of the main results given by Shahzad and Zegeye. Two concrete examples also are given.
11
SCALAR CURVATURE OF CONTACT THREE CR-SUBMANIFOLDS IN A UNIT (4m + 3)-SPHERE
Kim, Hyang-Sook ; Pak, Jin-Suk ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 585~600
DOI : 10.4134/BKMS.2011.48.3.585
Abstract
In this paper we derive an integral formula on an (n + 3)-dimensional, compact, minimal contact three CR-submanifold M of (p-1) contact three CR-dimension immersed in a unit (4m+3)-sphere
. Using this integral formula, we give a sufficient condition concerning the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.
12
TENSOR PRODUCT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP
Arslan, Kadri ; Bulca, Betul ; Kilic, Bengu ; Kim, Young-Ho ; Murathan, Cengizhan ; Ozturk, Gunay ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 601~609
DOI : 10.4134/BKMS.2011.48.3.601
Abstract
Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle
centered at origin with an Euclidean planar curve
has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle
centered at origin with an Euclidean planar curve
to have pointwise 1-type Gauss map.
13
MINIMAL NONCOMMUTATIVE REVERSIBLE AND REFLEXIVE RINGS
Kim, Byung-Ok ; Lee, Yang ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 611~616
DOI : 10.4134/BKMS.2011.48.3.611
Abstract
The reflexiveness and reversibility were introduced by Mason and Cohn respectively. The structures of minimal reversible rings and minimal reflexive rings are completely determined. The term minimal means having smallest cardinality.
14
ON HYPONORMALITY OF TOEPLITZ OPERATORS WITH POLYNOMIAL AND SYMMETRIC TYPE SYMBOLS
Hazarika, Munmun ; Phukon, Ambeswar ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 617~625
DOI : 10.4134/BKMS.2011.48.3.617
Abstract
In [6], it was shown that hyponormality for Toeplitz operators with polynomial symbols can be reduced to classical Schur`s algorithm in function theory. In [6], Zhu has also given the explicit values of the Schur`s functions
,
and
. Here we explicitly evaluate the Schur`s function
. Using this value we find necessary and sufficient conditions under which the Toeplitz operator
is hyponormal, where
is a trigonometric polynomial given by
15
SANDWICH THEOREMS FOR HIGHER-ORDER DERIVATIVES OF p-VALENT FUNCTIONS DEFINED BY CERTAIN LINEAR OPERATOR
Aouf, Mohamed K. ; Seoudy, Tamer M. ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 627~636
DOI : 10.4134/BKMS.2011.48.3.627
Abstract
In this paper, we obtain some applications of first order differential subordination and superordination results for higher-order derivatives of p-valent functions involving certain linear operator. Some of our results improve and generalize previously known results.
16
COMPETITION INDICES OF STRONGLY CONNECTED DIGRAPHS
Cho, Han-Hyuk ; Kim, Hwa-Kyung ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 637~646
DOI : 10.4134/BKMS.2011.48.3.637
Abstract
Cho and Kim [4] and Kim [6] introduced the concept of the competition index of a digraph. Cho and Kim [4] and Akelbek and Kirkland [1] also studied the upper bound of competition indices of primitive digraphs. In this paper, we study the upper bound of competition indices of strongly connected digraphs. We also study the relation between competition index and ordinary index for a symmetric strongly connected digraph.
17
A NOTE ON HYPONORMAL TOEPLITZ OPERATORS
Kim, An-Hyun ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 647~653
DOI : 10.4134/BKMS.2011.48.3.647
Abstract
In this note we are concerned with the hyponormality of Toeplitz operators
with polynomial symbols ${\phi}
18
EVALUATION FORMULAS FOR AN ANALOGUE OF CONDITIONAL ANALYTIC FEYNMAN INTEGRALS OVER A FUNCTION SPACE
Cho, Dong-Hyun ;
Bulletin of the Korean Mathematical Society, volume 48, issue 3, 2011, Pages 655~672
DOI : 10.4134/BKMS.2011.48.3.655
Abstract
Let
[0,t] be the function space of the vector-valued continuous paths x : [0,t]
and define
:
[0,t]
and
:
[0,t]
by