• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.915-935
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• 2001

Let V be any valuation domain and let E be a subset of the quotient field K of V. We study the ring of integer-valued polynomials on E, that is, Int(E, V)={f$\in$K[X]｜f(E)⊆V}. We show that, if E is precompact, then Int(E, V) has many properties similar to those of the classical ring Int(Z).In particular, Int(E, V) is dense in the ring of continuous functions C(E, V); each finitely generated ideal of Int(E, V) may be generated by two elements; and finally, Int(E, V) is a Prufer domain.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.903-921
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• 2008

A continuous linear operator $T\;:\;X{\rightarrow}X$ is called hypercyclic if there exists an $x\;{\in}\;X$ such that the orbit ${T^nx}_{n{\geq}0}$ is dense. We consider the problem: given an operator $T\;:\;X{\rightarrow}X$, hypercyclic or not, is the restriction $T|y$ to some closed invariant subspace $y{\subset}X$ hypercyclic? In particular, it is well-known that any non-constant partial differential operator p(D) on $H({\mathbb{C}}^d)$ (entire functions) is hypercyclic. Now, if q(D) is another such operator, p(D) maps ker q(D) invariantly (by commutativity), and we obtain a necessary and sufficient condition on p and q in order that the restriction p(D) : ker q(D) $\rightarrow$ ker q(D) is hypercyclic. We also study hypercyclicity for other types of operators on subspaces of $H({\mathbb{C}}^d)$.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1435-1449
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• 2020

In this article we make a local classification of n-dimensional Riemannian manifolds (M, g) with harmonic curvature and less than four Ricci eigenvalues which admit a smooth non constant solution f to the following equation $$(1)\hspace{20}{\nabla}df=f(r-{\frac{R}{n-1}}g)+x{\cdot} r+y(R)g,$$ where ∇ is the Levi-Civita connection of g, r is the Ricci tensor of g, x is a constant and y(R) a function of the scalar curvature R. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, either (i) or (ii) below holds; (i) (V, g, f + x) is a static space and isometric to a domain in the Riemannian product of an Einstein manifold N and a static space (W, gW, f + x), where gW is a warped product metric of an interval and an Einstein manifold. (ii) (V, g) is isometric to a domain in the warped product of an interval and an Einstein manifold. For the proof we use eigenvalue analysis based on the Codazzi tensor properties of the Ricci tensor.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1261-1273
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• 2016

In this paper, we analyze the necessary and sufficient condition introduced in [5]: that a functional F in $L^2(C_{a,b}[0,T])$ has an integral transform ${\mathcal{F}}_{{\gamma},{\beta}}F$, also belonging to $L^2(C_{a,b}[0,T])$. We then establish the inverse integral transforms of the functionals in $L^2(C_{a,b}[0,T])$ and then examine various properties with respect to the inverse integral transforms via the translation theorem. Several possible outcomes are presented as remarks. Our approach is a new method to solve some difficulties with respect to the inverse integral transform.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.585-594
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• 2022

In this article we classify four dimensional gradient Ricci solitons (M, g, f) with half harmonic Weyl curvature and at most two distinct Ricci-eigenvalues at each point. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, (V, g) is isometric to one of the following: (i) an Einstein manifold. (ii) a domain in the Riemannian product (ℝ², g₀) × (N, ${\tilde{g}}$), where g₀ is the flat metric on ℝ² and (N, ${\tilde{g}}$) is a two dimensional Riemannian manifold of constant curvature λ ≠ 0. (iii) a domain in ℝ × W with the warped product metric $ds^2+h(s)^2{\tilde{g}}$, where ${\tilde{g}}$ is a constant curved metric on a three dimensional manifold W.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.259-266
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• 2024

The purpose of this note is a wide generalization of the topological results of various classes of ideals of rings, semirings, and modules, endowed with Zariski topologies, to r-strongly irreducible r-ideals (endowed with Zariski topologies) of monoids, called terminal spaces. We show that terminal spaces are T₀, quasi-compact, and every nonempty irreducible closed subset has a unique generic point. We characterize rarithmetic monoids in terms of terminal spaces. Finally, we provide necessary and sufficient conditions for the subspaces of r-maximal r-ideals and r-prime r-ideals to be dense in the corresponding terminal spaces.

• Structural Engineering and Mechanics
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• v.85 no.3
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• pp.381-391
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• 2023

The seismic performance of the tall building equipped with a tuned mass damper (TMD) considering soil-structure interaction (SSI) effects is well studied in the literature. However, these studies are performed on the nominal model of the seismic-excited structural system with SSI. Hence, the outcomes of the studies may not valid for the actual structural system. To address the study gap, the reliability theory as a useful and powerful method is utilized in the paper. The present study aims to carry out reliability analyses on tall buildings equipped with TMD under near-field pulse-like (NFPL) ground motions considering SSI effects using a subset simulation (SS) method. In the presence of uncertainties of the structural model, TMD device, foundation, soil, and near-field pulse-like ground motions, the numerical studies are performed on a benchmark 40-story building and the failure probabilities of the structures with and without TMD are evaluated. Three types of soils (dense, medium, and soft soils), different earthquake magnitudes (M_w = 7,0. 7,25. 7,5 ), different nearest fault distances (r = 5. 10 and 15 km), and three seismic performance levels of immediate occupancy (IO), life safety (LS), and collapse prevention (CP) are considered in this study. The results show that tall buildings built near faults and on soft soils are more affected by uncertainties of the structural and ground motion models. Hence, ignoring these uncertainties may result in an inaccurate estimation of the maximum seismic responses. Also, it is found the TMD is not able to reduce the failure probabilities of the structure in the IO seismic performance level, especially for high earthquake magnitudes and structures built near the fault. However, TMD is significantly effective in the reduction of failure probability for the LS and CP performance levels. For weak earthquakes and long fault distances, the failure probabilities of both structures with and without TMD are near zero, and the efficiency of the TMD in the reduction of failure probabilities is reduced by increasing earthquake magnitudes and the reduction of fault distance. As soil softness increases, the failure probability of structures both with and without TMD often increases, especially for severe near-fault earthquake motion.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.21 no.5
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• pp.197-202
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• 2021

Biometric technology using finger veins is receiving a lot of attention due to its high security, convenience and accuracy. And the recent development of deep learning technology has improved the processing speed and accuracy for authentication. However, the training data is a subset of real data not in a certain order or method and the results are not constant. so the amount of data and the complexity of the artificial neural network must be considered. In this paper, the deep learning model of Inception-Resnet-v2 was used to improve the high accuracy of the finger vein recognizer and the performance of the authentication system, We compared and analyzed the performance of the deep learning model of DenseNet-201. The simulations used data from MMCBNU_6000 of Jeonbuk National University and finger vein images taken directly. There is no preprocessing for the image in the finger vein authentication system, and the results are checked through EER.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.603-611
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• 1996

Let consider the following problem: find an element u(t) in a Banach space U from the equation $$ x'(t) = Ax(t) + f(t,x(t)) + \Phi_0 u(t), 0 \leq t \leq T $$ with initial and terminal conditions $$ x(0) = 0, x(T) = \phi $$ in a Banach space X where $\phi \in D(A)$. This problem is a kind of control engineering inverse problem and contains nonlinear term, so that it is difficult and interesting. Thee proof main result in this paper is based on the Fredholm property of [1] in section 3. Similar considerations of linear system have been dealt with in many references. Among these literatures, Suzuki[5] introduced this problem for heat equation with unknown spatially-varing conductivity. Nakagiri and Yamamoto[2] considered the identifiability problem, which A is a unknown operator to be identified, where the system is described by a linear retarded functional differential equation. We can also apply to determining the magnitude of the control set for approximate controllability if X is a reflexive space, i.e., we can consider whether a dense subset of X is covered by reachable set in section 4.

• IMMUNE NETWORK
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• v.6 no.1
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• pp.1-5
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• 2006

Background: B cell subset has been divided into B-1 cells and B-2 cells. B-1 cells are found most prominently in the peritoneal cavity, as well as constituting a small pro portion of splenic B cells and they are larger and less dense than B-2 cells in morphology. This study was designed to compare the differences in their proliferation and differentiation between B-1 and B-2 cell. Methods: We obtained sorted B-1 cells from peritoneal fluid and B-2 cells from spleens of mice. Secreted IgM was measured by enzyme-linked immunosorbent assay. Entering of S phase in response to LPS-stimuli was measured by proliferative assay. Cell cycle analysis by propidium iodide was performed. p21 expression was assessed by real time PCR. Results: Cell proliferation and cell cycle progression in B-1 and B-2 cells, which did not occur in the absence of LPS, required LPS stimulation. After LPS stimulation, B-1 and B-2 cells were shifted to Sand G2/M phases. p21 expression by resting B-1 cells was higher than that of resting B-2 cells. Conclusion: B-1 cells differ from conventional B-2 cells in proliferation, differentiation and cell cycle.