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RISS 인기검색어
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- 발행기관 : Department of Mathematics (검색결과 1,929 건)
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Langlands Functoriality Conjecture
Yang, Jae-Hyun Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.2
Functoriality conjecture is one of the central and influential subjects of the present day mathematics. Functoriality is the profound lifting problem formulated by Robert Langlands in the late 1960s in order to establish nonabelian class field theory. In this expository article, I describe the Langlands-Shahidi method, the local and global Langlands conjectures and the converse theorems which are powerful tools for the establishment of functoriality of some important cases, and survey the interesting results related to functoriality conjecture.
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Special Function Inverse Series Pairs
Alsardary, Salar Yaseen,Gould, Henry Wadsworth Department of Mathematics 2010 Kyungpook mathematical journal Vol.50 No.2
Working with the various special functions of mathematical physics and applied mathematics we often encounter inverse relations of the type $F_n(x)=\sum\limits_{k=0}^{n}A^n_kG_k(x)$ and $ G_n(x)=\sum\limits_{k=0}^{n}B_k^nF_k(x)$, where 0, 1, 2,$\cdots$. Here $F_n(x)$, $G_n(x)$ denote special polynomial functions, and $A_k^n$, $B_k^n$ denote coefficients found by use of the orthogonal properties of $F_n(x)$ and $G_n(x)$, or by skillful series manipulations. Typically $G_n(x)=x^n$ and $F_n(x)=P_n(x)$, the n-th Legendre polynomial. We give a collection of inverse series pairs of the type $f(n)=\sum\limits_{k=0}^{n}A_k^ng(k)$ if and only if $g(n)=\sum\limits_{k=0}^{n}B_k^nf(k)$, each pair being based on some reasonably well-known special function. We also state and prove an interesting generalization of a theorem of Rainville in this form.
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Fractional-Order Derivatives and Integrals: Introductory Overview and Recent Developments
Srivastava, Hari Mohan Department of Mathematics 2020 Kyungpook mathematical journal Vol.60 No.1
The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operators of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional "differintegral" equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind.
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Jun, Young Bae,Song, Seok Zun Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.1
Using the concept of fuzzy points, the notions of fuzzy point BCC-(sub) algebras, quasi BCC-(sub)algebras and quasi BCC-ideals are introduced. Some characterizations of them are discussed.
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On Semirings which are Distributive Lattices of Rings
Maity, S.K. Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.1
We introduce the notions of nilpotent element, quasi-regular element in a semiring which is a distributive lattice of rings. The concept of Jacobson radical is introduced for this kind of semirings.
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Extensing of Exponentially Convex Function on the Heisenberg Group
Zabel, A.M.,Bajnaid, Maha A. Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.4
The main purpose of this paper is to extend the exponentially convex functions which are defined and exponentially convex on a cylinderical neighborhood in the Heisenberg group. They are expanded in terms of an integral transform associated to the sub-Laplacian operator. Extension of such functions on abelian Lie group are studied in [15].
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Generalized Transformation Semigroups Whose Sets of Quasi-ideals and Bi-ideals Coincide
Chinram, Ronnason Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.2
Let BQ be the class of all semigroups whose bi-ideals are quasi-ideals. It is known that regular semigroups, right [left] 0-simple semigroups and right [left] 0-simple semigroups belong to BQ. Every zero semigroup is clearly a member of this class. In this paper, we characterize when generalized full transformation semigroups and generalized Baer-Levi semigroups are in BQ in terms of the cardinalities of sets.
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Triangular Normed Fuzzification of (Implicative) Filters in Lattice Implication Algebras
Beasley, Leroy B.,Cheon, Gi-Sang,Jun, Young-Bae,Song, Seok-Zun Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.2
We obtain characterizations of T-fuzzy (implicative) filters and some properties of T-product of fuzzy (implicative) filters in lattice implication algebras. We also establish the extension property for T-fuzzy implicative filters.
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Oscillation Criteria of Second-order Half-linear Delay Difference Equations
Saker, S.H. Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.4
In this paper, we will establish some new oscillation criteria for the second-order half-linear delay difference equation $${\Delta}(Pn ({\Delta}Xn)^{\gamma})+q_nx_\array{{\gamma}\\n-{\sigma}}=0,\;n{\geq}n_0$$, where ${\gamma}>0$ is a quotient of odd positive integers. Our results in this paper are sharp and improve some of the well known oscillation results in the literature. Some examples are considered to illustrate our main results.
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