• 대한수학회보
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• 제36권2호
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• pp.239-246
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• 1999

We extend the Ding's vanishing theorem of $\delta$-invariant slightly on a Cohen-Macaulay local ring using the concept of Golod paris. we also investigate the relation between the vanishing of $\delta$-invariant and Hochster's Monomial Conjecture.

• 대한수학회보
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• 제56권3호
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• pp.675-680
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• 2019

We, in this note, decompose the invariant Laplacian of the unit complex ball of ${\mathbb{C} }^n$ by the radial part and tangential part as ${\tilde{\Delta}}={\tilde{\Delta}}_{rad}+{\tilde{\Delta}}_{tan}$. We give several properties and interpretations involved with this decomposition.

• Kyungpook Mathematical Journal
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• 제58권1호
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• pp.183-202
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• 2018

${\Delta}-moves$ are closely related with a Vassiliev invariant of degree 2. For classical knots, M. Okada showed that the second coefficients of the Conway polynomials of two knots differ by 1 if the two knots are related by a single ${\Delta}-move$. The first author extended the Okada's result for virtual knots by using a Vassiliev invariant of virtual knots of type 2 which is induced from the Kauffman polynomial of a virtual knot. The arrow polynomial is a generalization of the Kauffman polynomial. We will generalize this result by using Vassiliev invariants of type 2 induced from the arrow polynomial of a virtual knot and give a lower bound for the number of ${\Delta}-moves$ transforming $K_1$ to $K_2$ if two virtual knots $K_1$ and $K_2$ are related by a finite sequence of ${\Delta}-moves$.

• 대한수학회보
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• 제48권6호
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• pp.1129-1135
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• 2011

In this note, we prove that every subscalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent subscala operator is nilpotent. We also prove that every subscalar operator with property (${\delta}$) on a Banach space of dimension greater than 1 has a nontrivial invariant closed linear subspace.

• Kyungpook Mathematical Journal
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• 제51권4호
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• pp.385-393
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• 2011

The aim of this paper is to introduce and study the sequence spaces [w, ${\theta}$, F, p, q]$_{\infty}({\Delta}_{\upsilon}^m)$, [w, ${\theta}$, F, p, q]$_1({\Delta}_{\upsilon}^m)$ and [w, ${\theta}$, F, p, q]$_0({\Delta}_{\upsilon}^m)$, which arise from the notions of generalized difference sequence space, lacunary convergence, invariant mean and a sequence of Moduli $F=(f_k)$. We establish some inclusion relations between these spaces under some conditions.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.942-944
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• 2004

This paper proposes a delta-operator-based digital redesign (DR) technique. An asymptotic property of the delta-operator-based DR is analyzed. The performance recovery is proved as a sampling time approaches zero.

• IMMUNE NETWORK
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• 제11권6호
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• pp.406-411
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• 2011

Background: Invariant Natural killer T (iNKT) cells, a distinct subset of CD1d-restricted T cells with invariant $V{\alpha}{\beta}$ TCR, functionally bridge innate and adaptive immunity. While iNKT cells share features with conventional T cells in some functional aspects, they simultaneously produce large amount of Th1 and Th2 cytokines upon T-cell receptor (TCR) ligation. However, gene expression pattern in two types of cells has not been well characterized. Methods: we performed comparative microarray analyses of gene expression in murine iNKT cells and conventional $CD4^+CD25^-$ ${\gamma}{\delta}TCR^-$ T cells by using Gene Set Enrichment Analysis (GSEA) method. Results: Here, we describe profound differences in gene expression pattern between iNKT cells and conventional $CD4^+CD25^-$ ${\gamma}{\delta}TCR^-$ T cells. Conclusion: Our results provide new insights into the functional competence of iNKT cells and a better understanding of their various roles during immune responses.

• 충청수학회지
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• 제24권1호
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• pp.19-34
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• 2011

A bounded linear operator T on a complex Banach space X is said to have property (I) provided that T has Bishop's property (${\beta}$) and there exists an integer p > 0 such that for a closed subset F of ${\mathbb{C}}$ ${X_T}(F)={E_T}(F)=\bigcap_{{\lambda}{\in}{\mathbb{C}}{\backslash}F}(T-{\lambda})^PX$ for all closed sets $F{\subseteq}{\mathbb{C}}$, where $X_T$(F) denote the analytic spectral subspace and $E_T$(F) denote the algebraic spectral subspace of T. Easy examples are provided by normal operators and hyponormal operators in Hilbert spaces, and more generally, generalized scalar operators and subscalar operators in Banach spaces. In this paper, we prove that if T has property (I), then the quasi-nilpotent part $H_0$(T) of T is given by $$KerT^P=\{x{\in}X:r_T(x)=0\}={\bigcap_{{\lambda}{\neq}0}(T-{\lambda})^PX$$ for all sufficiently large integers p, where ${r_T(x)}=lim\;sup_{n{\rightarrow}{\infty}}{\parallel}T^nx{\parallel}^{\frac{1}{n}}$. We also prove that if T has property (I) and the spectrum ${\sigma}$(T) is finite, then T is algebraic. Finally, we prove that if $T{\in}L$(X) has property (I) and has decomposition property (${\delta}$) then T has a non-trivial invariant closed linear subspace.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.985-994
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• 2021

The object of this paper is to study non-invariant hypersurface of a (𝜖, 𝛿)-trans Sasakian manifolds equipped with (f, g, u, v, λ)-structure. Some properties obeyed by this structure are obtained. The necessary and sufficient conditions also have been obtained for totally umbilical non-invariant hypersurface with (f, g, u, v, λ)-structure of a (𝜖, 𝛿)-trans Sasakian manifolds to be totally geodesic. The second fundamental form of a non-invariant hypersurface of a (𝜖, 𝛿)-trans Sasakian manifolds with (f, g, u, v, λ)-structure has been traced under the condition when f is parallel.

• 대한수학회보
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• 제40권3호
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• pp.411-423
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• 2003

Some B.-Y. Chen inequalities for different kind of submanifolds of generalized complex space forms are established.