• 대한수학회논문집
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• 제32권2호
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• pp.261-266
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• 2017

H. R. Ebrahimi Vishki et al. conjectured in [1], that if every Jordan higher derivation on a trivial generalized matrix algebra $\mathcal{G}=(A,M,N,B)$ is a higher derivation, then either M = 0 or N = 0. In this note, we will give a class of counter examples.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.37-56
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• 2023

In this paper, we introduced the notions of ∗ - g-fusion frame and ∗ - K - g-fusion frame in Hilbert C^*-modules, we gives some properties and study the tensor product of ∗ - g-fusion frame. Non-trivial examples are further provided to support the hypotheses of our results.

• 대한수학회보
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• 제43권4호
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• pp.821-829
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• 2006

We determine reducibility points of degenerate principal series for exceptional p-adic groups of type $G_2$ via Jacquet module techniques and Hecke algebra isomorphisms.

• 대한수학회논문집
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• 제31권1호
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• pp.101-113
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• 2016

In this article, we considered the stability of the following (${\alpha}$, ${\beta}$, ${\gamma}$)-derivation $${\alpha}D[x,y]={\beta}[D(x),y]+{\gamma}[x,D(y)]$$ and homomorphisms associated to the quadratic type functional equation $$f(kx+y)+f(kx+{\sigma}(y))=2kg(x)+2g(y),\;x,y{\in}A$$, where ${\sigma}$ is an involution of the Lie $C^*$-algebra A and k is a fixed positive integer. The Hyers-Ulam stability on unbounded domains is also studied. Applications of the results for the asymptotic behavior of the generalized quadratic functional equation are provided.

• 대한수학회보
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• 제26권1호
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• pp.11-17
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• 1989

In [1], Johnson and Lapidus introduced a family { $A_{t}$ :t>0} of Banach algebras of functionals on Wiener space and showed that for every F in $A_{t}$ , the analytic operator-valued function space integral $K_{\lambda}$$^{t}$ (F) exists for all nonzero complex numbers .lambda. with nonnegative real part. In [2,3] Johnson and Lapidus introduced a noncommtative multiplication having the property that if F.mem. $A_{t}$ $_{1}$ and G.mem. $A_{t}$ $_{2}$ then $F^{*}$G.mem. A$t_{1}$+$_{t}$ $_{2}$ and (Fig.) Note that for F, G in $A_{t}$ , $F^{*}$G is not in $A_{t}$ but rather is in $A_{2t}$ and so the multiplication * is not internal to the Banach algebra $A_{t}$ . In this paper we introduce an internal noncommutative multiplication on $A_{t}$ having the property that for F, G in $A_{t}$ , F G is in $A_{t}$ and (Fig.) for all nonzero .lambda. with nonnegative real part. Thus is an auxiliary binary operator on $A_{t}$ .TEX> .

• 대한수학회지
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• 제37권4호
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• pp.645-655
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• 2000

We calculate the R(G)-algebra structure on the reduced equivariant K-groups of two-dimensional spheres on which a compact Lie group G acts as a reflection. In particular, the reduced equivariant K-groups are trivial if G is abelian, which shows that the previous Y. Yang's calculation in [8] is incorrect.

• Kyungpook Mathematical Journal
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• 제45권2호
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• pp.281-292
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• 2005

In this paper a nonlinear alternative of Leray-Schauder type is proved in a Banach algebra involving three operators and it is further applied to a functional nonlinear integral equation of mixed type $$x(t)=k(t,x({\mu}(t)))+[f(t,x({\theta}(t)))]\(q(t)+{\int}_0{^{\sigma}^{(t)}}v(t,s)g(s,x({\eta}\(s)))ds\)$$ for proving the existence results in Banach algebras under generalized Lipschitz and $Carath{\acute{e}}odory$ conditions.

• 대한수학회지
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• 제33권4호
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• pp.1047-1067
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• 1996

In this paper, we are interested in left invariant flat affine structures on Lie groups. These structures has been studied by many authors in different contexts. One of the fundamental questions is the existence of complete affine structures for solvable Lie groups G, raised by Minor [15]. But recently Benoist answered negatively even for the nilpotent case [1]. Also moduli space of such structures for lower dimensional cases has been studied by several authors, sometimes with compatible metrics [5,10,4,12].

• East Asian mathematical journal
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• 제33권1호
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• pp.45-52
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• 2017

Motivated by the problem of determining all right ideals of a group algebra FG for a finite group G over a finite field F, we explicitly determine the faithful irreducible representations of some finite metacylic groups over finite fields. By using that result, we determine the structure of all right ideals of the group algebra for the symmetric group $S_3$ over a finite field F, as an example.

• 대한수학회논문집
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• 제18권3호
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• pp.439-447
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• 2003

Let (equation omitted) be a symmetrizable Kac-Moody algebra with the indecomposable generalized Cartan matrix A and W be its Weyl group. Let $\theta$ be the highest root of the corresponding finite dimensional simple Lie algebra ${\gg}$ of g. For the type ${A_N}^{(r)}$, we give an element $\omega_{o}\;\in\;W$ such that ${{\omega}_o}^{-1}({\{\Delta\Delta}_{+}})\;=\;{\{\Delta\Delta}_{-}}$. And then we prove that the degree of nilpotency of the subalgebra (equation omitted) is greater than or equal to $ht{\theta}+1$.