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VARIOUS CONTINUITIES OF A MAP f ; (X, k, TnX) → (Y, 2, TY) IN COMPUTER TOPOLOGY

  • HAN, SANG-EON
    • Honam Mathematical Journal
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    • v.28 no.4
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    • pp.591-603
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    • 2006
  • For a set $X{\subset}{\mathbb{Z}}^n$ let $(X,\;T^n_X)$ be the subspace of the Khalimsky n-dimensional space $({\mathbb{Z}}^n,\;T^n)$, $n{\in}N$. Considering a k-adjacency of $(X,\;T^n_X)$, we use the notation $(X,\;k,\;T^n_X)$. In this paper for a map $$f:(X,\;k,\;T^n_X){\rightarrow}(Y,\;2\;T_Y)$$, we find the condition that weak (k, 2)-continuity of the map f implies strong (k, 2)-continuity of f.

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Analysis of Water Quality Pollutants Proximated to sediment in Lake (호소내 퇴적물의 근접도에 따른 수질오염물질 분석(I) - COD, T-N, T-P, pH -)

  • Park, Sun-Ku;Yang, Young-Mo
    • Analytical Science and Technology
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    • v.14 no.3
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    • pp.238-243
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    • 2001
  • The study was carried out to analysis of the pollutant $COD_{Mn}$, T-N, T-P for water quality proximated to sediment in lake of K river basin. water extracted from sediment showed higher $COD_{Mn}$, T-N, T-P datas than water proximated to sediment. Also, water proximated to sediment and water 5-10cm proximated to sediment showed the following data : $COD_{Mn}$, 1.2~1.9mg/L, T-N, 1.3~6.2mg/L, TP, 0.05~0.26mg/L, respectively. From this results, we have known the fact that the pollution degree of sediment have an effect on the water quality in lake and stream.

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CONDITIONAL INTEGRAL TRANSFORMS AND CONVOLUTIONS OF BOUNDED FUNCTIONS ON AN ANALOGUE OF WIENER SPACE

  • Cho, Dong Hyun
    • Journal of the Chungcheong Mathematical Society
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    • v.26 no.2
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    • pp.323-342
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    • 2013
  • Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $Xn:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}:C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\cdots},x(t_n),x(t_{n+1}))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions which have the form $${\int}_{L_2[0,t]}{{\exp}\{i(v,x)\}d{\sigma}(v)}{{\int}_{\mathbb{R}^r}}\;{\exp}\{i{\sum_{j=1}^{r}z_j(v_j,x)\}dp(z_1,{\cdots},z_r)$$ for $x{\in}C[0,t]$, where $\{v_1,{\cdots},v_r\}$ is an orthonormal subset of $L_2[0,t]$ and ${\sigma}$ and ${\rho}$ are the complex Borel measures of bounded variations on $L_2[0,t]$ and $\mathbb{R}^r$, respectively. We then investigate the inverse transforms of the function with their relationships and finally prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the products of the conditional Fourier-Feynman transforms of each function.

OSCILLATORY BEHAVIOR AND COMPARISON FOR HIGHER ORDER NONLINEAR DYNAMIC EQUATIONS ON TIME SCALES

  • Sun, Taixiang;Yu, Weiyong;Xi, Hongjian
    • Journal of applied mathematics & informatics
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    • v.30 no.1_2
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    • pp.289-304
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    • 2012
  • In this paper, we study asymptotic behaviour of solutions of the following higher order nonlinear dynamic equations $$S_n^{\Delta}(t,x)+{\delta}p(t)f(x(g(t)))=0$$ and $$S_n^{\Delta}(t,x)+{\delta}p(t)f(x(h(t)))=0$$ on an arbitrary time scale $\mathbb{T}$ with sup $\mathbb{T}={\infty}$, where n is a positive integer, ${\delta}=1$ or -1 and $$S_k(t,x)=\{\array x(t),\;if\;k=0,\\a_k(t)S_{{\kappa}-1}^{\Delta}(t),\;if\;1{\leq}k{\leq}n-1,\\a_n(t)[S_{{\kappa}-1}^{\Delta}(t)]^{\alpha},\;if\;k=n,$$ with ${\alpha}$ being a quotient of two odd positive integers and every $a_k$ ($1{\leq}k{\leq}n$) being positive rd-continuous function. We obtain some sufficient conditions for the equivalence of the oscillation of the above equations.

A Study of Individual Number Process Under Continuous-Time Markov Chains (시간이 연속인 마르코프 체인하에서 개체수 과정에 관한 연구)

  • 박춘일;김명철
    • Journal of the Korean Institute of Navigation
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    • v.16 no.1
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    • pp.94-97
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    • 1992
  • In this paper, the individual number of the future has depended not only upon the present individual number but upon the present individual age, considering the stochastic process model of individual number when the life span of each individual number and the individual age as a set, this becomes a Markovian. Therefore, in this paper the individual is treated as invariable, without depending upon the whole record of each individual since its birth. As a result, suppose {N(t), t>0} be a counting process and also suppose $Z_n$ denote the life span between the (n-1)st and the nth event of this process, (n{$geq}1$) : that is, when the first individual is established at n=1(time, 0), the Z$Z_n$ at time nth individual breaks, down. Random walk $Z_n$ is $Z_n=X_1+X_2+{\cdots}{\cdots}+X_A, Z_0=0$ So, fixed time t, the stochastic model is made up as follows ; A) Recurrence (Regeneration)number between(0.t) $N_t=max{n ; Z_n{\leq}t}$ B) Forwardrecurrence time(Excess life) $T^-I_t=Z_{Nt+1}-t$ C) Backward recurrence time(Current life) $T^-_t=t-Z_{Nt}$

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Construction of a Relation Between the Triadic Min(N, T, D) and Max(N, T, D) Operating Policies Based on their Corresponding Expected Busy Periods (Busy Period 기대값을 사용하여 삼변수 Min(N, T, D)와 Max(N, T, D) 운용방침사이의 관계식 설정)

  • Rhee, Hahn-Kyou
    • Journal of the Society of Korea Industrial and Systems Engineering
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    • v.33 no.3
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    • pp.63-70
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    • 2010
  • Based on the known results of the expected busy periods for the triadic Min (N, T, D) and Max (N, T, D) operating policies applied to a controllable M/G/1 queueing model, a relation between them is constructed. Such relation is represented in terms of the expected busy periods for the simple N, T and D, and the dyadic Min (N, T), Min (T, D) and Min (N, D) operating policies. Hence, if any system characteristics for one of the two triadic operating policies are known, unknown corresponding system characteristics for the other triadic operating policy could be obtained easily from the constructed relation.

AN ERDŐS-KO-RADO THEOREM FOR MINIMAL COVERS

  • Ku, Cheng Yeaw;Wong, Kok Bin
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.875-894
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    • 2017
  • Let $[n]=\{1,2,{\ldots},n\}$. A set ${\mathbf{A}}=\{A_1,A_2,{\ldots},A_l\}$ is a minimal cover of [n] if ${\cup}_{1{\leq}i{\leq}l}A_i=[n]$ and $$\bigcup_{{1{\leq}i{\leq}l,}\\{i{\neq}j_0}}A_i{\neq}[n]\text{ for all }j_0{\in}[l]$$. Let ${\mathcal{C}}(n)$ denote the collection of all minimal covers of [n], and write $C_n={\mid}{\mathcal{C}}(n){\mid}$. Let ${\mathbf{A}}{\in}{\mathcal{C}}(n)$. An element $u{\in}[n]$ is critical in ${\mathbf{A}}$ if it appears exactly once in ${\mathbf{A}}$. Two minimal covers ${\mathbf{A}},{\mathbf{B}}{\in}{\mathcal{C}}(n)$ are said to be restricted t-intersecting if they share at least t sets each containing an element which is critical in both ${\mathbf{A}}$ and ${\mathbf{B}}$. A family ${\mathcal{A}}{\subseteq}{\mathcal{C}}(n)$ is said to be restricted t-intersecting if every pair of distinct elements in ${\mathcal{A}}$ are restricted t-intersecting. In this paper, we prove that there exists a constant $n_0=n_0(t)$ depending on t, such that for all $n{\geq}n_0$, if ${\mathcal{A}}{\subseteq}{\mathcal{C}}(n)$ is restricted t-intersecting, then ${\mid}{\mathcal{A}}{\mid}{\leq}{\mathcal{C}}_{n-t}$. Moreover, the bound is attained if and only if ${\mathcal{A}}$ is isomorphic to the family ${\mathcal{D}}_0(t)$ consisting of all minimal covers which contain the singleton parts $\{1\},{\ldots},\{t\}$. A similar result also holds for restricted r-cross intersecting families of minimal covers.

GENERALIZED CAYLEY GRAPH OF UPPER TRIANGULAR MATRIX RINGS

  • Afkhami, Mojgan;Hashemifar, Seyed Hosein;Khashyarmanesh, Kazem
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1017-1031
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    • 2016
  • Let R be a commutative ring with the non-zero identity and n be a natural number. ${\Gamma}^n_R$ is a simple graph with $R^n{\setminus}\{0\}$ as the vertex set and two distinct vertices X and Y in $R^n$ are adjacent if and only if there exists an $n{\times}n$ lower triangular matrix A over R whose entries on the main diagonal are non-zero such that $AX^t=Y^t$ or $AY^t=X^t$, where, for a matrix B, $B^t$ is the matrix transpose of B. ${\Gamma}^n_R$ is a generalization of Cayley graph. Let $T_n(R)$ denote the $n{\times}n$ upper triangular matrix ring over R. In this paper, for an arbitrary ring R, we investigate the properties of the graph ${\Gamma}^n_{T_n(R)}$.

WEAK AND STRONG CONVERGENCE OF MANN'S-TYPE ITERATIONS FOR A COUNTABLE FAMILY OF NONEXPANSIVE MAPPINGS

  • Song, Yisheng;Chen, Rudong
    • Journal of the Korean Mathematical Society
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    • v.45 no.5
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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.

Comparsion of Dst forecast models during intense geomagnetic storms (Dst $\leq$ -100 nT)

  • Ji, Eun-Young;Moon, Yong-Jae;Lee, Dong-Hun
    • The Bulletin of The Korean Astronomical Society
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    • v.35 no.2
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    • pp.51.2-51.2
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    • 2010
  • We have investigated 63 intense geomagnetic storms (Dst $\leq$ -100 nT) that occurred from 1998 to 2006. Using these events, we compared Dst forecast models: Burton et al. (1975), Fenrich and Luhmann (1998), O'Brien and McPherron (2000a), Wang et al. (2003), and Temerin and Li (2002, 2006) models. For comparison, we examined a linear correlation coefficient, RMS error, the difference of Dst minimum value (${\Delta}$peak), and the difference of Dst minimum time (${\Delta}$peak_time) between the observed and the predicted during geomagnetic storm period. As a result, we found that Temerin and Li model is mostly much better than other models. The model produces a linear correlation coefficient of 0.94, a RMS (Root Mean Square) error of 14.89 nT, a MAD (Mean Absolute Deviation) of ${\Delta}$peak of 12.54 nT, and a MAD of ${\Delta}$peak_time of 1.44 hour. Also, we classified storm events as five groups according to their interplanetary origin structures: 17 sMC events (IP shock and MC), 18 SH events (sheath field), 10 SH+MC events (Sheath field and MC), 8 CIR events, and 10 nonMC events (non-MC type ICME). We found that Temerin and Li model is also best for all structures. The RMS error and MAD of ${\Delta}$peak of their model depend on their associated interplanetary structures like; 19.1 nT and 16.7 nT for sMC, 12.5 nT and 7.8 nT for SH, 17.6 nT and 15.8 nT for SH+MC, 11.8 nT and 8.6 nT for CIR, and 11.9 nT and 10.5 nT for nonMC. One interesting thing is that MC-associated storms produce larger errors than the other-associated ones. Especially, the values of RMS error and MAD of ${\Delta}$peak of SH structure of Temerin and Li model are very lower than those of other models.

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