• Journal of the Korean Mathematical Society
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• 제34권3호
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• pp.581-598
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• 1997

This paper is concerned with the impulsive control problem $$ \dot{x}(t) = f(t, x) + g(t, x)\dot{u}(t), t \in [0, T], x(0) = \overline{x}, $$ where u is a possibly discontinuous control function of bounded variation, $f : R \times R^n \mapsto R^n$ is a bounded and Lipschitz continuous function, and $g : R \times R^n \mapsto R^n$ is continuously differentiable w.r.t. the variable x and satisfies $\mid$g(t,\cdot) - g(s,\cdot)$\mid$ \leq \phi(t) - \phi(s)$, for some increasing function $\phi$ and every s < t. We show that the map $u \mapsto x_u$ is Lipschitz continuous when u ranges in the set of step functions whose total variations are uniformly bounded, where $x_u$ is the solution of the impulsive control system corresponding to u. We also define the generalized solution of the impulsive control system corresponding to a measurable control functin of bounded variation.

• Journal of the Korean Mathematical Society
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• 제45권5호
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• pp.1393-1404
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• 2008

Let K be a nonempty closed convex subset of a Banach space E. Suppose $\{T_{n}\}$ (n = 1,2,...) is a uniformly asymptotically regular sequence of nonexpansive mappings from K to K such that ${\cap}_{n=1}^{\infty}$ F$\(T_n){\neq}{\phi}$. For $x_0{\in}K$, define $x_{n+1}={\lambda}_{n+1}x_{n}+(1-{\lambda}_{n+1})T_{n+1}x_{n},n{\geq}0$. If ${\lambda}_n{\subset}[0,1]$ satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n=0$, we proved that $\{x_n\}$ weakly converges to some $z{\in}F\;as\;n{\rightarrow}{\infty}$ in the framework of reflexive Banach space E which satisfies the Opial's condition or has $Fr{\acute{e}}chet$ differentiable norm or its dual $E^*$ has the Kadec-Klee property. We also obtain that $\{x_n\}$ strongly converges to some $z{\in}F$ in Banach space E if K is a compact subset of E or there exists one map $T{\in}\{T_{n};n=1,2,...\}$ satisfy some compact conditions such as T is semi compact or satisfy Condition A or $lim_{n{\rightarrow}{\infty}}d(x_{n},F(T))=0$ and so on.

• Proceedings of the KOSOMBE Conference
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• 대한의용생체공학회 1998년도 추계학술대회
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• pp.291-292
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• 1998

The purpose of the study was aimed to evaluate the BOLD contrast fMRI in occipital lobe and compare this imaging with metabolite changes based on $^1H$ MRS and MRSI before and after visual stimulation. As a result, the activation map were sucessfully produced by thresholding with minimum cross-correlate value of 0.45. In MRS, NAA/Cr ratio is almost same. however, latate was elevated almost 9 times higher than before activation. Lactate metabolic images were consistent with the BOLD effect map. The BOLD contrast fMRI is not enough to detect the activation area in human brain. so, the other modality was required such as lactate metabolic map.

• Honam Mathematical Journal
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• 제34권2호
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• pp.279-287
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• 2012

Let $k$ be a field containing the field $\mathbb{Q}$ of rational numbers and let $R=k[x_{ij}{\mid}1{\leq}i{\leq}m,\;1{\leq}j{\leq}n]$ be the polynomial ring over a field $k$ with indeterminates $x_{ij}$. Let $I_t(X)$ be the determinantal ideal generated by the $t$-minors of an $m{\times}n$ matrix $X=(x_{ij})$. Eagon and Hochster proved that $I_t(X)$ is a perfect ideal of grade $(m-t+1)(n-t+1)$. We give a structure theorem for a class of determinantal ideals of grade 3. This gives us a characterization that $I_t(X)$ has grade 3 if and only if $n=m+2$ and $I_t(X)$ has the minimal free resolution $\mathbb{F}$ such that the second dierential map of $\mathbb{F}$ is a matrix defined by complete matrices of grade $n+2$.

• East Asian mathematical journal
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• 제24권1호
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• pp.35-43
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• 2008

Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let ${\{T_i\}}^N_{i=1}$ be N nonexpansive self-mappings of K with $F\;=\;{\cap}^N_{i=1}F(T_i)\;{\neq}\;{\theta}$ (here $F(T_i)$ denotes the set of fixed points of $T_i$). Suppose that one of the mappings in ${\{T_i\}}^N_{i=1}$ is semi-compact. Let $\{{\alpha}_n\}\;{\subset}\;[{\delta},\;1-{\delta}]$ for some ${\delta}\;{\in}\;(0,\;1)$ and $\{{\beta}_n\}\;{\subset}\;[\tau,\;1]$ for some ${\tau}\;{\in}\;(0,\;1]$. For arbitrary $x_0\;{\in}\;K$, let the sequence {$x_n$} be defined iteratively by $\{{x_n\;=\;{\alpha}_nx_{n-1}\;+\;(1-{\alpha}_n)T_ny_n,\;\;\;\;\;\;\;\;\; \atop {y_n\;=\;{\beta}nx_{n-1}\;+\;(1-{\beta}_n)T_nx_n},\;{\forall}_n{\geq}1,}$, where $T_n\;=\;T_{n(modN)}$. Then {$x_n$} convergence strongly to a common fixed point of the mappings family ${\{T_i\}}^N_{i=1}$. The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of ${\beta}_n\;{\equiv}\;1$ or N=1 are also new.

• Korean Journal of Environment and Ecology
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• 제37권3호
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• pp.209-220
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• 2023

Over the past few centuries, widespread changes to natural ecosystems caused by human activities have severely threatened biodiversity worldwide. Understanding changes in ecosystems is essential to identifying and managing threats to biodiversity. In line with this need, the IUCN Council formed the IUCN Global Ecosystem Typology (GET) in 2019, taking into account the functions and types of ecosystems. The IUCN provides maps of 10 ecosystem groups and 108 ecological functional groups (EFGs) on a global scale. According to the type classification of IUCN GET ecosystems, Korea's ecosystem is classified into 8 types of Realm (level 1), 18 types of Biome (level 2), and 41 types of Group (level 3). GETs provided by IUCN have low resolution and often do not match the actual land status because it was produced globally. This study aimed to increase the accuracy of Korean IUCN GET type classification by using land cover maps and producing maps that reflected the actual situation. To this end, we ① reviewed the Korean GET data system provided by IUCN GET and ② compared and analyzed it with the current situation in Korea. We evaluated the limitations and usability of the GET through the process and then ③ classified Korea's new Get type reflecting the current situation in Korea by using the national data as much as possible. This study classified Korean GETs into 25 types by using land cover maps and existing national data (Territorial realm: 9, Freshwater: 9, Marine-territorial: 5, Terrestrial-freshwater: 1, and Marine-freshwater-territorial: 1). Compared to the existing map, "F3.2 Constructed lacustrine wetlands", "F3.3 Rice paddies", "F3.4 Freshwater aquafarms", and "T7.3 Plantations" showed the largest area reduction in the modified Korean GET. The area of "T2.2 Temperate Forests" showed the largest area increase, and the "MFT1.3 Coastal saltmarshes and reedbeds" and "F2.2 Small permanent freshwater lakes" types also showed an increase in GET area after modification. Through this process, the existing map, in which the sum of all EFGs in the existing GET accounted for 8.33 times the national area, was modified so that the total sum becomes 1.22 times the national area using the land cover map. This study confirmed that the existing EFG, which had small differences by type and low accuracy, was improved and corrected. This study is significant in that it produced a GET map of Korea that met the GET standard using data reflecting the field conditions. 

• The Journal of Korean Physical Therapy
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• 제23권6호
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• pp.49-53
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• 2011

Purpose: The purpose of this study is to investigate whether dual-hemisphere transcranial direct current stimulation (tDCS) could induce more cortical activity, compared to single-hemisphere, using functional MRI (fMRI). Methods: One right-handed healthy subject was recruited. Three phases of dual-hemisphere tDCS (i.e. anodal tDCS over the left-dominant primary sensoriomotor cortex (SM1) and cathodal tDCS over the right-non dominant SM(1) were consecutively delivered on to a subject, during fMRI scanning. The voxel count and the intensity index in the averaged cortical map were analyzed among the three tDCS phases. Results: Our result showed that cortical activation was observed on all the three phases of the dual-hemisphere tDCS. Voxel count and intensity index were as following; 912 and 4.07 in the first phase, 1102 and 3.90 in the second phase, 1031 and 3.80 in the third phase. Conclusion: This study demonstrated that application of the dual-hemisphere tDCS could induce cortical activity and maintain to recruit cortical neurons. Our findings suggested that application of dual-hemisphere tDCS could produce efficiency of the ongoing tDCS effect to facilitate cortical excitability.

• Bulletin of the Korean Mathematical Society
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• 제39권2호
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• pp.269-276
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• 2002

Let E be a real Banach space. Let T : E longrightarrow E be a map with F(T) : = { x $\in$ E : Tx = x} $\neq$ 0 and satisfying the accretive-type condition $\lambda\$\mid$x-Tx\$\mid$^2$, for all $x\inE,\;x^*\inf(T)\;and\;\lambda >0$. We prove some necessary and sufficient conditions for the convergence of the Mann iterative sequence to a fixed point of T.

• Bulletin of the Korean Mathematical Society
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• 제37권1호
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• pp.153-169
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• 2000

Let E be a real q-uniformly smooth Banach space which admits a weakly sequentially continuous duality map, and K a nonempty closed convex subset of E. Let T : K -> K be a mapping such that $F(T)\;=\;{x\;{\in}\;K\;:\;Tx\;=\;x}\;{\neq}\;0$ and (I - T) satisfies the accretive-type condition: $\;{\geq}\;{\lambda}$\mid$$\mid$x-Tx$\mid$$\mid$^2$, for all $x\;{\in}\;K,\;x^*\;{\in}\;F(T)$ and for some ${\lambda}\;>\;0$. The weak and strong convergence of the Ishikawa iteration method to a fixed point of T are investigated. An application of our results to the approximation of a solution of a certain linear operator equation is also given. Our results extend several important known results from the Mann iteration method to the Ishikawa iteration method. In particular, our results resolve in the affirmative an open problem posed by Naimpally and Singh (J. Math. Anal. Appl. 96 (1983), 437-446).

• Korean Journal of Breeding Science
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• 제40권2호
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• pp.97-100
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• 2008

Lectin protein and Kunitz trypsin inhibitor (KTI) protein of mature soybean seed are a main antinutritional factor in soybean seed. The Le gene controls a lectin protein and Ti gene controls the KTI protein in soybean. Ti locus has been located on linkage group 9 in the classical linkage map of soybean. Position of Le locus on linkage map was not identified. Genetic relationship between Ti locus and Le locus could be useful in soybean breeding program for the genetic elimination of these factors. The objective of this study was to determine the independent inheritance or linkage between Ti locus and Le locus in soybean seed. Two $F_2$ populations were developed from three parents (Gaechuck#1, T102, and PI548415). The $F_1$ seeds from Gaechuck#1 (titiLeLe) ${\times}$ T102 (TiTilele) and Gaechuck#1 (titiLeLe) ${\times}$ PI548415 (TiTilele) were obtained. The lectin and KTI protein were analysed from $F_2$ seeds harvested from the $F_1$ plants to find independent assortment or linkage between Ti locus and Le locus. The segregation ratios of 3 : 1 for Le locus (129 Le_ : 44 lele) and Ti locus (132 Ti_ : 41 titi) and were observed. The segregation ratios of 9 : 3 : 3 : 1 (95 Le_Li_ : 34 Le_titi: 37 leleTi_ : 7 leletiti) between Le gene and Ti gene in $F_2$ seeds were observed. This data showed that Ti gene was inherited independently with the Le gene in soybean. These results will be helpful in breeding program for selecting the line with lacking both KTI and lectin protein in soybean.