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Honam Mathematical Journal
Journal Basic Information
pISSN :
1225-293X
eISSN :
2288-6176
Journal DOI :
10.5831/HMJ
Frequency :
Others
Publisher:
The Honam Mathematical Society
Editor in Chief :
Volume & Issues
Volume 29, Issue 4 - Dec 2007
Volume 29, Issue 3 - Sep 2007
Volume 29, Issue 2 - Jun 2007
Volume 29, Issue 1 - Mar 2007
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1
TOWARDS UNIQUENESS OF MPR, THE MALVENUTO-POITIER-REUTENAUER HOPF ALGEBRA OF PERMUTATIONS
Hazewinkel, Michiel ;
Honam Mathematical Journal, volume 29, issue 2, 2007, Pages 119~192
DOI : 10.5831/HMJ.2007.29.2.119
Abstract
A very important Hopf algebra is the graded Hopf algebra Symm of symmetric functions. It can be characterized as the unique graded positive selfdual Hopf algebra with orthonormal graded distinguished basis and just one primitive element from the distinguished basis. This result is due to Andrei Zelevinsky. A noncommutative graded Hopf algebra of this type cannot exist. But there is a most important positive graded Hopf algebra with distinguished basis that is noncommutative and that is twisted selfdual, the Malvenuto-Poirier-Reutenauer Hopf algebra of permutations. Thus the question arises whether there is a corresponding uniqueness theorem for MPR. This prepreprint records initial investigations in this direction and proves that uniquenees holds up to and including the degree 4 which has rank 24.
2
STABILITY OF A QUADRATIC TYPE FUNCTIONAL EQUATION
Lee, Eun-Hwi ; Chang, Ick-Soon ; Jung, Yong-Soo ;
Honam Mathematical Journal, volume 29, issue 2, 2007, Pages 193~204
DOI : 10.5831/HMJ.2007.29.2.193
Abstract
In this paper, we investigate some results concerning the stability of the following quadratic type functional equation: f(x + y) + f(x - y) + f(y + z) + f(y - z) + f(z + x) + f(z - x) = 4f(x) + 4f(y) + 4f(z).
3
SOME PROPERTIES OF THE JULIA SETS OF QUADRATIC RATIONAL MAPS
Ahn, Young-Joon ;
Honam Mathematical Journal, volume 29, issue 2, 2007, Pages 205~212
DOI : 10.5831/HMJ.2007.29.2.205
Abstract
In this paper, we give some properties of the dynamics of quadratic rational maps. Using the properties we present the algorithm for drawing the Julia sets of the quadratic rational maps. We illustrate that they are fractals by computer graphics.
4
AN EXTENDED NON-ASSOCIATIVE ALGEBRA
Choi, Seul-Hee ;
Honam Mathematical Journal, volume 29, issue 2, 2007, Pages 213~222
DOI : 10.5831/HMJ.2007.29.2.213
Abstract
A Weyl type algebra is defined in the paper (see [2],[4], [6], [7]). A Weyl type non-associative algebra
and its restricted subalgebra
are defined in the papers (see [1], [14], [16]). Several authors find all the derivations of an associative (Lie or non-associative) algebra (see [3], [1], [5], [7], [10], [16]). We find Der(
) of the algebra
and show that the algebras
and
are not isomorphic in this work. We show that the associator of
is zero.
5
INTERVAL-VALUED FUZZY SEMI-PREOPEN SETS AND INTERVAL-VALUED FUZZY SEMI-PRECONTINUOUS MAPPINGS
Jun, Young-Bae ; Kim, Sung-Sook ; Kim, Chang-Su ;
Honam Mathematical Journal, volume 29, issue 2, 2007, Pages 223~244
DOI : 10.5831/HMJ.2007.29.2.223
Abstract
We introduce the notions of interval-valued fuzzy semipreopen sets (mappings), interval-valued fuzzy semi-pre interior and interval-valued fuzzy semi-pre-continuous mappings by using the notion of interval-valued fuzzy sets. We also investigate related properties and characterize interval-valued fuzzy semi-preopen sets (mappings) and interval-valued fuzzy semi-precontinuous mappings.
6
ERROR BOUNDS OF TRAPEZOIDAL RULE ON SUBINTERVALS USING DISTRIBUTION
Hong, Bum-Il ; Hahm, Nahm-Woo ;
Honam Mathematical Journal, volume 29, issue 2, 2007, Pages 245~257
DOI : 10.5831/HMJ.2007.29.2.245
Abstract
We showed in [2] that if
, then the average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is proportional to
using zero mean Gaussian distribution under the assumption that we have subintervals (for simplicity equal length) partitioning and that each subinterval has the length. In this paper, if
, we show that zero mean Gaussian distribution of average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is bounded by
.
7
INTUITIONISTIC FUZZY LIE IDEALS OF LIE ALGERBAS
Jun, Young-Bae ; Park, Chul-Hwan ;
Honam Mathematical Journal, volume 29, issue 2, 2007, Pages 259~268
DOI : 10.5831/HMJ.2007.29.2.259
Abstract
The notion of intuitionistic fuzzy Lie ideal of a Lie algebra is introduced, and related properties are investigated. Characterizations of an intuitionistic fuzzy Lie ideal are provided. Using a collection of Lie ideals, an intuitionistic fuzzy Lie ideal is established.
8
IRREDUCIBLE MODULES OVER THE E
_{6}
-TYPE LIE ALGEBRA
Kim, Yang-Gon ;
Honam Mathematical Journal, volume 29, issue 2, 2007, Pages 269~277
DOI : 10.5831/HMJ.2007.29.2.269
Abstract
Let L := L(G) denote the classical modular Lie algebra of
-type over an algebraically closed field F of characteristic p > 5 associated with some simple and simply connected algebraic group G. After the prototypes of those for
-type in [4], we shall search for irreducible (=simple) L-modules in this paper.
9
FUZZY FOLDNESS OF IMPLICATIVE ORDERED FILTERS IN IMPLICATIVE SEMIGROUPS
Jun, Young-Bae ; Park, Chul-Hwan ;
Honam Mathematical Journal, volume 29, issue 2, 2007, Pages 279~288
DOI : 10.5831/HMJ.2007.29.2.279
Abstract
The notion of fuzzy n-fold implicative ordered filters in implicative semigroups is introduced, and related properties are investigated. Relations between fuzzy ordered filters and fuzzy n-fold implicative ordered filters are provided. Characterizations of a fuzzy n-fold implicative ordered filter are given, and an extension property for a fuzzy n-fold implicative ordered filter is obtained.
10
ON INJECTIVE BCI-ALGEBRAS
Ahn, Sun-Shin ;
Honam Mathematical Journal, volume 29, issue 2, 2007, Pages 289~297
DOI : 10.5831/HMJ.2007.29.2.289
Abstract
In this paper, we show that BCI-algebras P and Q are injective if and only if its direct sum P
Q is injective. Moreover, we obtain the equivalent conditions for a p-semisimple BCI-algebra to be p-injective.
11
CARATHÉODORY FINITELY COMPACTNESS OF THE BOUNDED ATTRACTING BASIN OF THE ORIGIN
Park, Sung-Hee ;
Honam Mathematical Journal, volume 29, issue 2, 2007, Pages 299~305
DOI : 10.5831/HMJ.2007.29.2.299
Abstract
We prove that the bounded attracting basin of the origin for a complex homogeneous polynomial of degree larger than two is Carath
odory finitely compact.