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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
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Bulletin of the Korean Mathematical Society
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Journal DOI :
The Korean Mathematical Society
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Volume & Issues
Volume 51, Issue 6 - Nov 2014
Volume 51, Issue 5 - Sep 2014
Volume 51, Issue 4 - Jul 2014
Volume 51, Issue 3 - May 2014
Volume 51, Issue 2 - Mar 2014
Volume 51, Issue 1 - Jan 2014
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A LYAPUNOV CHARACTERIZATION OF ASYMPTOTIC CONTROLLABILITY FOR NONLINEAR SWITCHED SYSTEMS
Wang, Yanling ; Qi, Ailing ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 1~11
DOI : 10.4134/BKMS.2014.51.1.001
In this paper, we show that general nonlinear switched systems are asymptotically controllable if and only if there exist control-Lyapunov functions for their relaxation systems. If the switching signal is dependent on the time, then the control-Lyapunov functions are continuous. And if the switching signal is dependent on the state, then the control-Lyapunov functions are
-smooth. We obtain the results from the viewpoint of control system theory. Our approach is based on the relaxation theorems of differential inclusions and the classic Lyapunov characterization.
PERTURBATION RESULTS FOR HYPERBOLIC EVOLUTION SYSTEMS IN HILBERT SPACES
Kang, Yong Han ; Jeong, Jin-Mun ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 13~27
DOI : 10.4134/BKMS.2014.51.1.013
The purpose of this paper is to derive a perturbation theory of evolution systems of the hyperbolic second order hyperbolic equations. We give an example of a partial functional equation as an application of the preceding result in case of the mixed problems for hyperbolic equations of second order with unbounded principal operators.
ON SOME SOLUTIONS OF A FUNCTIONAL EQUATION RELATED TO THE PARTIAL SUMS OF THE RIEMANN ZETA FUNCTION
Martinez, Juan Matias Sepulcre ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 29~41
DOI : 10.4134/BKMS.2014.51.1.029
In this paper, we prove that infinite-dimensional vector spaces of -dense curves are generated by means of the functional equations f(x)+f(2x)+
+f(nx) = 0, with
, which are related to the partial sums of the Riemann zeta function. These curves
-densify a large class of compact sets of the plane for arbitrary small
, extending the known result that this holds for the cases n = 2, 3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the
power of the density approaches the Jordan content of the compact set which the curve densifies.
EXISTENCE OF SOLUTIONS FOR NONLINEAR EVOLUTION EQUATIONS WITH INFINITE DELAY
Dong, Qixiang ; Li, Gang ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 43~54
DOI : 10.4134/BKMS.2014.51.1.043
This paper is concerned with nonlinear evolution differential equations with infinite delay in Banach spaces. Using Kato's approximating approach, existence and uniqueness of strong solutions are obtained.
EXTINCTION AND NON-EXTINCTION OF SOLUTIONS TO A FAST DIFFUSIVE p-LAPLACE EQUATION WITH A NONLOCAL SOURCE
Han, Yuzhu ; Gao, Wenjie ; Li, Haixia ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 55~66
DOI : 10.4134/BKMS.2014.51.1.055
In this paper, the authors establish the conditions for the extinction of solutions, in finite time, of the fast diffusive p-Laplace equation
, 1 < p < 2, in a bounded domain
. More precisely, it is shown that if q > p-1, any solution vanishes in finite time when the initial datum or the coefficient a or the Lebesgue measure of the domain is small, and if 0 < q < p-1, there exists a solution which is positive in
for all t > 0. For the critical case q = p-1, whether the solutions vanish in finite time or not depends crucially on the value of
is the unique positive solution of the elliptic problem -div(
) = 1,
. This is a main difference between equations with local and nonlocal sources.
SHADOWING, EXPANSIVENESS AND STABILITY OF DIVERGENCE-FREE VECTOR FIELDS
Ferreira, Celia ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 67~76
DOI : 10.4134/BKMS.2014.51.1.067
Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions:
X is a divergence-free vector field satisfying the shadowing property.
X is a divergence-free vector field satisfying the Lipschitz shadowing property.
X is an expansive divergence-free vector field.
X has no singularities and is Anosov.
STABILITY OF ZEROS OF POWER SERIES EQUATIONS
Wang, Zhihua ; Dong, Xiuming ; Rassias, Themistocles M. ; Jung, Soon-Mo ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 77~82
DOI : 10.4134/BKMS.2014.51.1.077
We prove that if
is large and
is small enough, then every approximate zero of power series equation
=0 can be approximated by a true zero within a good error bound. Further, we obtain Hyers-Ulam stability of zeros of the polynomial equation of degree n,
= 0 for a given integer n > 1.
FINITE LOGARITHMIC ORDER SOLUTIONS OF LINEAR q-DIFFERENCE EQUATIONS
Wen, Zhi-Tao ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 83~98
DOI : 10.4134/BKMS.2014.51.1.083
During the last decade, several papers have focused on linear q-difference equations of the form
with entire or meromorphic coefficients. A tool for studying these equations is a q-difference analogue of the lemma on the logarithmic derivative, valid for meromorphic functions of finite logarithmic order
. It is shown, under certain assumptions, that
+ 1. Moreover, it is illustrated that a q-Casorati determinant plays a similar role in the theory of linear q-difference equations as a Wronskian determinant in the theory of linear differential equations. As a consequence of the main results, it follows that the q-gamma function and the q-exponential functions all have logarithmic order two.
MULTIPLE SOLUTIONS FOR A p-LAPLACIAN SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS
Zhou, Jun ; Kim, Chan-Gyun ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 99~113
DOI : 10.4134/BKMS.2014.51.1.099
A nonlinear elliptic problem involving p-Laplacian and nonlinear boundary condition is considered in this paper. By using the method of Nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameter is small enough.
ON THE SECOND APPROXIMATE MATSUMOTO METRIC
Tayebi, Akbar ; Tabatabaeifar, Tayebeh ; Peyghan, Esmaeil ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 115~128
DOI : 10.4134/BKMS.2014.51.1.115
In this paper, we study the second approximate Matsumoto metric F =
on a manifold M. We prove that F is of scalar flag curvature and isotropic S-curvature if and only if it is isotropic Berwald metric with almost isotropic flag curvature.
ORIGIN-SYMMETRIC CONVEX BODIES WITH MINIMAL MAHLER VOLUME IN ℝ
Lin, Youjiang ; Leng, Gangsong ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 129~137
DOI : 10.4134/BKMS.2014.51.1.129
In this paper, a new proof of the following result is given: The product of the volumes of an origin-symmetric convex bodies K in
and of its polar body is minimal if and only if K is a parallelogram.
ERROR ESTIMATES OF RT1 MIXED METHODS FOR DISTRIBUTED OPTIMAL CONTROL PROBLEMS
Hou, Tianliang ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 139~156
DOI : 10.4134/BKMS.2014.51.1.139
In this paper, we investigate the error estimates of a quadratic elliptic control problem with pointwise control constraints. The state and the co-state variables are approximated by the order k = 1 Raviart-Thomas mixed finite element and the control variable is discretized by piecewise linear but discontinuous functions. Approximations of order
-norm and order h in the
-norm for the control variable are proved.
METRIC THEOREM AND HAUSDORFF DIMENSION ON RECURRENCE RATE OF LAURENT SERIES
Hu, Xue-Hai ; Li, Bing ; Xu, Jian ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 157~171
DOI : 10.4134/BKMS.2014.51.1.157
We show that the recurrence rates of Laurent series about continued fractions almost surely coincide with their pointwise dimensions of the Haar measure. Moreover, let
be the set of points with lower and upper recurrence rates
), we prove that all the sets
, are of full Hausdorff dimension. Then the recurrence sets
have constant multifractal spectra.
ON GORENSTEIN COTORSION DIMENSION OVER GF-CLOSED RINGS
Gao, Zenghui ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 173~187
DOI : 10.4134/BKMS.2014.51.1.173
In this article, we introduce and study the Gorenstein cotorsion dimension of modules and rings. It is shown that this dimension has nice properties when the ring in question is left GF-closed. The relations between the Gorenstein cotorsion dimension and other homological dimensions are discussed. Finally, we give some new characterizations of weak Gorenstein global dimension of coherent rings in terms of Gorenstein cotorsion modules.
ON SOLVABILITY OF THE DISSIPATIVE KIRCHHOFF EQUATION WITH NONLINEAR BOUNDARY DAMPING
Zhang, Zai-Yun ; Huang, Jian-Hua ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 189~206
DOI : 10.4134/BKMS.2014.51.1.189
In this paper, we prove the global existence and uniqueness of the dissipative Kirchhoff equation
with nonlinear boundary damping by Galerkin approximation benefited from the ideas of Zhang et al. . Furthermore,we overcome some difficulties due to the presence of nonlinear terms
by introducing a new variables and we can transform the boundary value problem into an equivalent one with zero initial data by argument of compacity and monotonicity.
IDENTITIES WITH ADDITIVE MAPPINGS IN SEMIPRIME RINGS
Fosner, Ajda ; Ur Rehman, Nadeem ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 207~211
DOI : 10.4134/BKMS.2014.51.1.207
The aim of this paper is to prove the next result. Let n > 1 be an integer and let R be a n!-torsion free semiprime ring. Suppose that f : R
R is an additive mapping satisfying the relation [f(x),
] = 0 for all
. Then f is commuting on R.
GRADIENT RICCI SOLITONS WITH SEMI-SYMMETRY
Cho, Jong Taek ; Park, Jiyeon ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 213~219
DOI : 10.4134/BKMS.2014.51.1.213
We prove that a semi-symmetric 3-dimensional gradient Ricci soliton is locally isometric to a space form
(Gaussian soliton); or a product space
, where the potential function depends only on the nullity.
A NOTE ON EXPONENTIAL ALMOST SURE STABILITY OF STOCHASTIC DIFFERENTIAL EQUATION
Mao, Xuerong ; Song, Qingshuo ; Yang, Dichuan ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 221~227
DOI : 10.4134/BKMS.2014.51.1.221
Our goal is to relax a sufficient condition for the exponential almost sure stability of a certain class of stochastic differential equations. Compared to the existing theory, we prove the almost sure stability, replacing Lipschitz continuity and linear growth conditions by the existence of a strong solution of the underlying stochastic differential equation. This result is extendable for the regime-switching system. An explicit example is provided for the illustration purpose.
HYBRID d-ARY TREES AND THEIR GENERALIZATION
Hong, SeoungJi ; Park, SeungKyung ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 229~235
DOI : 10.4134/BKMS.2014.51.1.229
We enumerate black and white colored d-ary trees with no leftmost
-edges, which is a generalization of hybrid binary trees. Then the multi-colored hybrid d-ary trees with the same condition is studied.
THE HYPONORMAL TOEPLITZ OPERATORS ON THE VECTOR VALUED BERGMAN SPACE
Lu, Yufeng ; Cui, Puyu ; Shi, Yanyue ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 237~252
DOI : 10.4134/BKMS.2014.51.1.237
In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators
, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space
. We also show some necessary conditions for the hyponormality of
MODULES WHOSE CLASSICAL PRIME SUBMODULES ARE INTERSECTIONS OF MAXIMAL SUBMODULES
Arabi-Kakavand, Marzieh ; Behboodi, Mahmood ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 253~266
DOI : 10.4134/BKMS.2014.51.1.253
Commutative rings in which every prime ideal is an intersection of maximal ideals are called Hilbert (or Jacobson) rings. We propose to define classical Hilbert modules by the property that classical prime submodules are intersections of maximal submodules. It is shown that all co-semisimple modules as well as all Artinian modules are classical Hilbert modules. Also, every module over a zero-dimensional ring is classical Hilbert. Results illustrating connections amongst the notions of classical Hilbert module and Hilbert ring are also provided. Rings R over which all modules are classical Hilbert are characterized. Furthermore, we determine the Noetherian rings R for which all finitely generated R-modules are classical Hilbert.
AN UPSTREAM PSEUDOSTRESS-VELOCITY MIXED FORMULATION FOR THE OSEEN EQUATIONS
Park, Eun-Jae ; Seo, Boyoon ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 267~285
DOI : 10.4134/BKMS.2014.51.1.267
An upstream scheme based on the pseudostress-velocity mixed formulation is studied to solve convection-dominated Oseen equations. Lagrange multipliers are introduced to treat the trace-free constraint and the lowest order Raviart-Thomas finite element space on rectangular mesh is used. Error analysis for several quantities of interest is given. Particularly, first-order convergence in
norm for the velocity is proved. Finally, numerical experiments for various cases are presented to show the efficiency of this method.
ON NONSMOOTH OPTIMALITY THEOREMS FOR ROBUST OPTIMIZATION PROBLEMS
Lee, Gue Myung ; Son, Pham Tien ;
Bulletin of the Korean Mathematical Society, volume 51, issue 1, 2014, Pages 287~301
DOI : 10.4134/BKMS.2014.51.1.287
In this paper, we prove a necessary optimality theorem for a nonsmooth optimization problem in the face of data uncertainty, which is called a robust optimization problem. Recently, the robust optimization problems have been intensively studied by many authors. Moreover, we give examples showing that the convexity of the uncertain sets and the concavity of the constraint functions are essential in the optimality theorem. We present an example illustrating that our main assumptions in the optimality theorem can be weakened.