• Honam Mathematical Journal
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• v.36 no.1
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• pp.29-32
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• 2014

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. In this article, we investigate self-adjoint interpolation problems for operators in a tridiagonal algebra : 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 a self-adjoint operator A = ($a_{ij}$) in $Alg{\mathcal{L}}$ such that AX = Y. (2) There is a bounded real sequence {${\alpha}_n$} such that $y_{ij}={\alpha}_ix_{ij}$ for $i,j{\in}\mathbb{N}$.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.907-911
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• 2014

Given vectors x and y in a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that Ax = y. We show the following: Let $Alg{\mathcal{L}}$ be a tridiagonal algebra on $\mathcal{H}$ and let $x=(x_i)$ and $y=(y_i)$ be vectors in $\mathcal{H}$. Then the following are equivalent: (1) There exists a unitary operator $A=(a_{ij})$ in $Alg{\mathcal{L}}$ such that Ax = y. (2) There is a bounded sequence $\{{\alpha}_i\}$ in $\mathbb{C}$ such that ${\mid}{\alpha}_i{\mid}=1$ and $y_i={\alpha}_ix_i$ for $i{\in}\mathbb{N}$.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.443-450
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• 2011

In this paper, we construct a Gorenstein Artinian algebra R/J with non-unimodal Hilbert function h = (1, 13, 12, 13, 1) to investigate the algebraic structure of the ideal J in a polynomial ring R. For this purpose, we use a software system Macaulay 2, which is devoted to supporting research in algebraic geometry and commutative algebra.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.541-552
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• 2023

In 2005, Patterson studied lacunary statistical convergence of double sequences of real numbers and, in 2009, Mursaleen introduced notion of lacunary statistical convergence of single sequences in intuitionistic fuzzy normed space. The current work intends to investigate the lacunary statistical convergence of double sequences and some significant conclusions on the algebra of the lacunary statistical limit of double sequences in intuitionistic fuzzy normed space. In addition, we have studied some examples to support the definitions.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.617-626
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• 2000

We study the vectors related tro states on the Cuntz algebra Ο(sub)n and prove hat, for tow states $\omega$ and $\rho$ on Ο(sub)n with $\omega$│UHF(sub)n = $\rho$│UHF(sub)n, if ($\omega$(s$_1$), …, $\omega$(s(sub)n)) and ($\rho$(s$_1$),…, $\rho$(s(sub)n)) are unit vectors, then they and linearly dependent. We also study the linear functional on Ο(sub)n associated to a sequence of unit vectors in C(sup)n which is the generalization of the Cuntz state. We show that if the linear functional associated to a sequence of unit vectors with a certain condition is a state, then it is just the Cuntz state.

• Honam Mathematical Journal
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• v.32 no.2
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• pp.255-260
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• 2010

Given vectors x and y in a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that Ax = y. In this article, we investigate compact interpolation problems for vectors in a tridiagonal algebra. We show the following : Let Alg$\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let x = $(x_i)$ and y = $(y_i)$ be vectors in H. Then the following are equivalent: (1) There exists a compact operator A = $(a_{ij})$ in Alg$\mathcal{L}$ such that Ax = y. (2) There is a sequence ${{\alpha}_n}$ in $\mathbb{C}$ such that ${{\alpha}_n}$ converges to zero and for all k ${\in}$ $\mathbb{N}$, $y_1 = {\alpha}_1x_1 + {\alpha}_2x_2$ $y_{2k} = {\alpha}_{4k-1}x_{2k}$ $y_{2k+1}={\alpha}_{4k}x_{2k}+{\alpha}_{4k+1}x_{2k+1}+{\alpha}_{4k+2}+x_{2k+2}$.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.73-82
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• 2016

The utility of exponential generating functions is that they are relevant for combinatorial problems involving sets and subsets. Sequences of polynomials play a fundamental role in applied mathematics, such sequences can be described using the exponential generating functions. The actuarial polynomials ${\alpha}^{({\beta})}_n(x)$, n = 0, 1, 2, ${\cdots}$, which was suggested by Toscano, have the following exponential generating function: $${\limits\sum^{\infty}_{n=0}}{\frac{{\alpha}^{({\beta})}_n(x)}{n!}}t^n={\exp}({\beta}t+x(1-e^t))$$. A linear functional on polynomial space can be identified with a formal power series. The set of formal power series is usually given the structure of an algebra under formal addition and multiplication. This algebra structure, the additive part of which agree with the vector space structure on the space of linear functionals, which is transferred from the space of the linear functionals. The algebra so obtained is called the umbral algebra, and the umbral calculus is the study of this algebra. In this paper, we investigate some umbral representations in the actuarial polynomials.

• East Asian mathematical journal
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• v.17 no.1
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• pp.115-128
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• 2001

We present old unsolved problems on BCK-sequences connected with convex congruences on BCK-algebras. We posed also some new problems on subalgebras.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.405-411
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• 2003

We prove that 25 different Artinian O-Sequences of codimension 3 type 3 with length 7 among all possible 334 cases are not level.

• Honam Mathematical Journal
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• v.27 no.4
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• pp.649-654
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• 2005

Given operators X and Y acting on a separable complex Hilbert space ${\mathcal{H}}$, an interpolating operator is a bounded operator A such that AX = Y. We show the following: Let $Alg{\mathcal{L}}$ 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 a unitary operator $A=(a_{ij})$ in $Alg{\mathcal{L}}$ such that AX = Y. (2) There is a bounded sequence {${\alpha}_n$} in ${\mathbb{C}}$ such that ${\mid}{\alpha}_j{\mid}=1$ and $y_{ij}={\alpha}_jx_{ij}$ for $j{\in}{\mathbb{N}}$.