• Bulletin of the Korean Mathematical Society
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• 제57권5호
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• pp.1241-1249
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• 2020

Let Ω be a domain in ℂⁿ. Suppose that ∂Ω is smooth pseudoconvex of D'Angelo finite type near a boundary point ξ₀ ∈ ∂Ω and the Levi form has corank at most 1 at ξ₀. Our goal is to show that if the squeezing function s_Ω(𝜂_j) tends to 1 or the Fridman invariant h_Ω(𝜂_j) tends to 0 for some sequence {𝜂_j} ⊂ Ω converging to ξ₀, then this point must be strongly pseudoconvex.

• Communications of the Korean Mathematical Society
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• 제20권4호
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• pp.813-826
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• 2005

Regarding all particles at a fixed site as a cluster, the size of the largest cluster under the zero range invariant measures is well studied by Jeon et al.[5] for the case of density one. Here, the density of the finite zero-range process is given by the ratio between the number m of particles and the number n of sites. In this paper, we study the lower density case, i.e., the case m = o(n). Especially, when m ~ $n^{\beta}$,0 < ${\beta}$ < 1, we show that there is an interesting cutoff point around $\beta$ = 1/2.

• Bulletin of the Korean Mathematical Society
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• 제50권4호
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• pp.1193-1200
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• 2013

The center of the Lie group $SU(n)$ is isomorphic to $\mathbb{Z}_n$. If $d$ divides $n$, the quotient $SU(n)/\mathbb{Z}_d$ is also a Lie group. Such groups are locally isomorphic, and their Weyl groups $W(SU(n)/\mathbb{Z}_d)$ are the symmetric group ${\sum}_n$. However, the integral representations of the Weyl groups are not equivalent. Under the mod $p$ reductions, we consider the structure of invariant rings $H^*(BT^{n-1};\mathbb{F}_p)^W$ for $W=W(SU(n)/\mathbb{Z}_d)$. Particularly, we ask if each of them is a polynomial ring. Our results show some polynomial and non-polynomial cases.

• Communications of the Korean Mathematical Society
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• 제33권3호
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• pp.889-899
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• 2018

In this paper, we present some upper bounds for unitarily invariant norms inequalities. Among other inequalities, we show some upper bounds for the Hilbert-Schmidt norm. In particular, we prove $${\parallel}f(A)Xg(B){\pm}g(B)Xf(A){\parallel}_2{\leq}{\Large{\parallel}}{\frac{(I+{\mid}A{\mid})X(I+{\mid}B{\mid})+(I+{\mid}B{\mid})X(I+{\mid}A{\mid})}{^dA^dB}}{\Large{\parallel}}_2$$, where A, B, $X{\in}{\mathbb{M}}_n$ such that A, B are Hermitian with ${\sigma}(A){\cup}{\sigma}(B){\subset}{\mathbb{D}}$ and f, g are analytic on the complex unit disk ${\mathbb{D}}$, g(0) = f(0) = 1, Re(f) > 0 and Re(g) > 0.

• Communications of the Korean Mathematical Society
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• 제21권1호
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• pp.177-183
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• 2006

The purpose of this paper is to introduce an L-metrical non-linear connection $N_j^{*i}$ and investigate a conformal change in the Finsler space with $({\alpha},\;{\beta})-metric$. The (v)h-torsion and (v)hvtorsion in the Finsler space with L-metrical connection $F{\Gamma}^*$ are obtained. The conformal invariant connection and conformal invariant curvature are found in the above Finsler space.

• Communications of the Korean Mathematical Society
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• 제25권2호
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• pp.235-243
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• 2010

In a Riemannian manifold, the existence of a new connection is proved. In particular cases, this connection reduces to several symmetric, semi-symmetric and quarter symmetric connections, even some of them are not introduced so far. So, in this paper, we define a quarter symmetric semi-metric connection in an almost r-paracontact Riemannian manifold and consider invariant, non-invariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold with that connection.

• Bulletin of the Korean Mathematical Society
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• 제46권2호
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• pp.255-261
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• 2009

In this paper, we shall prove several results concerning Ricci curvature of a Riemannian manifold (M, g) := (SU(2), g) with an arbitrary given left invariant metric g. First of all, we obtain the maximum (resp. minimum) of {r(X) := Ric(X,X) | ${||X||}_g$ = 1,X ${\in}$ X(M)}, where Ric is the Ricci tensor field on (M, g), and then get a necessary and sufficient condition for the Levi-Civita connection ${\nabla}$ on the manifold (M, g) to be projectively flat. Furthermore, we obtain a necessary and sufficient condition for the Ricci curvature r(X) to be always positive (resp. negative), independently of the choice of unit vector field X.

• The Journal of Korean Institute of Communications and Information Sciences
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• 제22권2호
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• pp.392-400
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• 1997

In this paper we porposed WCHF-fSDF filter to obtain a roration and scale-invariant correlation output. WCHF-fSDF filter is synthesized by each single CHF exttracted from scale-changed and wavelet tranformed imagesfor a refereence image as tranining images. The wavelet transform is defined as the correlation of an input image with a wavelet function. Therefore two 4f optical correlation systems are needed for pattern recognition using wavelet transform. We here include the wavelet function for the input image in the process of the proposed filter design and substitute the two 4f optical correlation system with a single 4f optical correlation system. The Performances of the proposed filter are compared with conventional CHF-SDF, POCHF-SDF filters through the computer simulation. The results of computer simulation show that the proposed filter has the rotation and scale-invariant correlation output and it has better performances than thoseof the conventioanl filters.

• The Transactions of the Korean Institute of Electrical Engineers D
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• 제51권4호
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• pp.137-143
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• 2002

Because Block Pulse functions are used in a variety of fields such as the analysis and controller design of systems, it is necessary to find the more exact value of the Block Pulse series coefficients. This paper presents a method for the state estimation of the time-invariant linear systems via the improved estimation method for the Block Pulse coefficients by using the Simpson's rule. The proposed method using the Simpson's rule improve the accuracy of the Block Pulse coefficients.

• 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 ${\Delta}-moves$.