• Journal of the Korean School Mathematics Society
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• v.13 no.2
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• pp.243-262
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• 2010

CRESST(the National Center for Research on Evaluation, Standards, and Student Testing at UCLA) is now carrying out the research, which was scheduled for a five year period from 2007 to 2011. This research aimed at testing the effectiveness of the formative assessment program by continuously conducting the program on the target group and steadily applying the recurring feedback, in order to reform the teachers' teaching and to facilitate students' learning. To do this, CRESST has set out to develop the material for 7th graders since January 2007, and KICE(Korea Institute of Curriculum and Evaluation) have been running a collaborated research since July 2007, while sharing the instructional materials developed by CRESST. In 2008, the pre-test was conducted prior to this study in 2009. Especially, this paper deals with the Korean 7th graders' scholastic achievements in algebra domain measured by PowerSource(c). In addition, this study would examine the responses of teachers and students on its application.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.83-90
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• 2009

In this paper, we investigate isomorphisms between $C^*$-ternary algebras and derivations on $C^*$-ternary algebras associated with the Cauchy-Jensen functional equation $$2f(\frac{x+y}{2}+z)=f(x)+f(y)+2f(z)$$, which was introduced and investigated by Baak in [2].

• The Pure and Applied Mathematics
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• v.24 no.3
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• pp.171-178
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• 2017

In this paper, we define $C^*-ternary$ quadratic 3-Jordan homomorphisms associated with the quadratic mapping f(x + y) + f(x - y) = 2f(x) + 2f(y), and prove the Hyers-Ulam stability of $C^*-ternary$ quadratic 3-Jordan homomorphisms.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.195-209
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• 2010

In this paper, we prove the generalized Hyers-Ulam stability of bi-homomorphisms in $C^*$-ternary algebras and of bi-derivations on $C^*$-ternary algebras for the following bi-additive functional equation f(x + y, z - w) + f(x - y, z + w) = 2f(x, z) - 2f(y, w). This is applied to investigate bi-isomorphisms between $C^*$-ternary algebras.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.243-250
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• 2005

Given operators X and Y acting on a separable Hilbert space ${\mathcal{H}}$, an interpolating operator is a bounded operator A such that AX = Y. We show the following: Let ${\mathcal{L}}$ be a subspace lattice acting on a separable complex Hilbert space ${\mathcal{H}}$. and let $X=(x_{ij})$ and $Y=(y_{ij})$ be operators acting on ${\mathcal{H}}$. Then the following are equivalent: (1) There exists an invertible operator $A=(a_{ij})$ in $Alg{\mathcal{L}}$ such that AX = Y. (2) There exist bounded sequences {${\alpha}_n$} and {${\beta}_n$} in ${\mathbb{C}}$ such that $${\alpha}_{2k-1}{\neq}0,\;{\beta}_{2k-1}=\frac{1}{{\alpha}_{2k-1}},\;{\beta}_{2k}=-\frac{{\alpha}_{2k}}{{\alpha}_{2k-1}{\alpha}_{2k+1}}$$ and $$y_{i1}={\alpha}_1x_{i1}+{\alpha}_2x_{i2}$$ $$y_{i\;2k}={\alpha}_{4k-1}x_{i\;2k}$$ $$y_{i\;2k+1}={\alpha}_{4k}x_{i\;2k}+{\alpha}_{4k+1}x_{i\;2k+1}+{\alpha}_{4k+2}x_{i\;2k+2}$$ for $$k{\in}N$$.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.115-120
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• 2011

Given vectors x and y in a separable complex Hilbert space $\cal{H}$, an interpolating operator is a bounded operator A such that Ax = y. We show the following : Let Alg$\cal{L}$ be a tridiagonal algebra on a separable complex Hilbert space H and let x = ($x_i$) and y = ($y_i$) be vectors in H. Then the following are equivalent: (1) There exists an invertible operator A = ($a_{kj}$) in Alg$\cal{L}$ such that Ax = y. (2) There exist bounded sequences $\{{\alpha}_n\}$ and $\{{{\beta}}_n\}$ in $\mathbb{C}$ such that for all $k\in\mathbb{N}$, ${\alpha}_{2k-1}\neq0,\;{\beta}_{2k-1}=\frac{1}{{\alpha}_{2k-1}},\;{\beta}_{2k}=\frac{\alpha_{2k}}{{\alpha}_{2k-1}\alpha_{2k+1}}$ and $$y_1={\alpha}_1x_1+{\alpha}_2x_2$$ $$y_{2k}={\alpha}_{4k-1}x_{2k}$$ $$y_{2k+1}={\alpha}_{4k}x_{2k}+{\alpha}_{4k+1}x_{2k+1}+{\alpha}_{4k+2}x_{2k+2}$$.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.661-679
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• 1995

The concept of the structure conformal vector field C on a Sasakian manifold M is defined. The existence of such a C on M is determined by an exterior differential system in involution. In this case M is a foliate manifold and the vector field C enjoys the property to be exterior concurrent. This allows to prove some interesting properties of the Ricci tensor and Obata's theorem concerning isometries to a sphere. Different properties of the conformal Lie algebra induced by C are also discussed.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.641-650
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• 2021

The notions of skew-commuting/commuting/semi-commuting/skew-centralizing/semi-centralizing mappings play an important role in ring theory. ${\mathfrak{C}}^*$-algebras with these properties have been studied considerably less and the existing results are motivating the researchers. This article elaborates the structure of prime rings and ${\mathfrak{C}}^*$-algebras satisfying certain functional identities involving automorphisms.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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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.

• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.219-233
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• 2024

In this paper, we study the generalized Fourier-Feynman transform (GFFT) for functions on the general Wiener space C_a,b[0, T]. We establish an explicit evaluation formula for the analytic GFFT of bounded cylinder functions on C_a,b[0, T]. We start by examining certain cylinder functions which belong in a Banach algebra of bounded functions on C_a,b[0, T]. We then obtain an explicit formula for the analytic GFFT of the bounded cylinder functions.