• 대한수학회지
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• 제35권1호
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• pp.177-189
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• 1998

In this paper, weighted Bloch spaces $B_q (q > 0)$ are considered on the open unit ball in $C^n$. These spaces extend the notion of Bloch spaces to wider classes of holomorphic functions. It is proved that the functions in a weighted Bloch space admit certain integral representation. This representation formula is then used to determine the degree of growth of the functions in the space $B_q$. It is also proved that weighted Bloch space is a Banach space for each weight q > 0, and the little Bloch space $B_q,0$ associated with $B_q$ is a separable subspace of $B_q$ which is the closure of the polynomials for each $q \geq 1$.

• 대한수학회지
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• 제56권5호
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• pp.1265-1283
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• 2019

We develop a framework to construct geometric representations of finite groups G through the correspondence between real toric spaces $X^{\mathbb{R}}$ and simplicial complexes with characteristic matrices. We give a combinatorial description of the G-module structure of the homology of $X^{\mathbb{R}}$. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type A and B, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representation geometrically as the homology of real toric varieties.

• 호남수학학술지
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• 제41권2호
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• pp.421-433
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• 2019

Let n denote an integer greater than 2 and let c denote a nonzero complex number. In this paper, we introduce a family of elements of the rational Cherednik algebra $H^{sl_n}(c)$ of type $sl_n$, which are analogous to the Dunkl-Cherednik elements of the rational Cherednik algebra $H^{gl_n}(c)$ of type $gl_n$. We also introduce the raising and lowering element of $H^{sl_n}(c)$ which are useful in the representation theory of the algebra $H^{sl_n}(c)$, and provide simple results related to these elements.

• 호남수학학술지
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• 제46권3호
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• pp.407-427
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• 2024

The purpose of this article is to bring together the Horadam numbers and 3-parameter generalized quaternions, which are a general form of the quaternion algebra according to 3-parameters. With this purpose, we introduce and examine a new type of quite big special numbers system, which is called Horadam 3-parameter generalized quaternions (shortly, Horadam 3PGQs), and special cases of them. Besides, we compute both some new equations and classical well-known equations such as; Binet formulas, generating function, exponential generating function, Poisson generating function, sum formulas, Cassini identity, polar representation, and matrix equation. Furthermore, this article concludes by presenting the determinant, characteristic polynomial, characteristic equation, eigenvalues, and eigenvectors in relation to the matrix representation of Horadam 3PGQ.

• 대한수학회보
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• 제61권4호
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• pp.907-915
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• 2024

Let f be an integral quadratic form in k variables, F the Gram matrix corresponding to a ℤ-basis of ℤ^k. For r ∈ F^-1ℤ^k, a rational number n with f(r) ≡ n mod ℤ and a positive integer c, set N_f(n, r; c) := #{x ∈ ℤ^k/cℤ^k : f(x + r) ≡ n mod c}. Siegel showed that for each prime p, there is a number w depending on r and n such that N_f(n, r; p^ν+1) = p^k-1N_f(n, r; p^ν) holds for every integer ν > w and gave a rough estimation on the upper bound for such w. In this short note, we give a more explicit estimation on this bound than Siegel's.

• Korean Journal of Mathematics
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• 제17권1호
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• pp.25-36
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• 2009

We compute spectrums of left regular isometries and weighted left regular isometries of a strongly perforated semigroup $P=\{0,2,3,4,{\cdots}\}$.

• Kyungpook Mathematical Journal
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• 제57권4호
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• pp.601-612
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• 2017

Let Q be the frame g-loop quiver, i.e. a generalized ADHM quiver obtained by replacing the two loops into g loops. The vector space M of representations of Q admits an involution ${\ast}$ if orthogonal and symplectic structures on the representation spaces are endowed. We prove equivalence between semisimplicity of representations of the ${\ast}-invariant$ subspace N of M and the orbit-closedness with respect to the natural adjoint action on N. We also explain this equivalence in terms of King's stability [8] and orthogonal decomposition of representations.

• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.7-14
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• 2009

In this short note, we consider a family of linear representations of the braid group and the fundamental group of a punctured torus bundle over the circle. We construct an irreducible (special) unitary representation of the fundamental group of a closed 3-manifold obtained by the Dehn filling.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권4호
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• pp.377-383
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• 2016

The set of priors in the representation of coherent risk measure is expressed in terms of quantile function and increasing concave function. We show that the set of prior, $\mathcal{Q}_c$ in (1.2) is equal to the set of $\mathcal{Q}_m$ in (1.6), as maximal representing set $\mathcal{Q}_{max}$ defined in (1.7).

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.331-347
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• 2017

Soft sets are fantastic mathematical tools to handle imprecise and uncertain information in complicated situations. In this paper, we defined the hybrid structure which is the combination of soft set and complex number representation of intuitionistic fuzzy set. We defined basic set theoretic operations such as complement, union, intersection, restricted union, restricted intersection etc. for this hybrid structure. Moreover, we developed this theory to establish some more set theoretic operations like Disjunctive sum, difference, product, conjugate etc.