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A Renewal Theorem for Random Walks with Time Stationary Random Distribution Function

  • Hong, Dug-Hun
    • Journal of the Korean Statistical Society
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    • v.25 no.1
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    • pp.153-159
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    • 1996
  • Sums of independent random variables $S_n = X_1 + X_ + cdots + X_n$ are considered, where the X$_{n}$ are chosen according to a stationary process of distributions. Given the time t .geq. O, let N (t) be the number of indices n for which O < $S_n$ $\geq$ t. In this set up we prove that N (t)/t converges almost surely and in $L^1$ as t longrightarrow $\infty$, which generalizes classical renewal theorem.m.

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Optimal Rates of Convergence in Tensor Sobolev Space Regression

  • Koo, Ja-Yong
    • Journal of the Korean Statistical Society
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    • v.21 no.2
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    • pp.153-166
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    • 1992
  • Consider an unknown regression function f of the response Y on a d-dimensional measurement variable X. It is assumed that f belongs to a tensor Sobolev space. Let T denote a differential operator. Let $\hat{T}_n$ denote an estimator of T(f) based on a random sample of size n from the distribution of (X, Y), and let $\Vert \hat{T}_n - T(f) \Vert_2$ be the usual $L_2$ norm of the restriction of $\hat{T}_n - T(f)$ to a subset of $R^d$. Under appropriate regularity conditions, the optimal rate of convergence for $\Vert \hat{T}_n - T(f) \Vert_2$ is discussed.

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APPROXIMATION OF COMMON FIXED POINTS OF NON-SELF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

  • Kim, Jong-Kyu;Dashputre, Samir;Diwan, S.D.
    • East Asian mathematical journal
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    • v.25 no.2
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    • pp.179-196
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    • 2009
  • Let E be a uniformly convex Banach space and K a nonempty closed convex subset which is also a nonexpansive retract of E. For i = 1, 2, 3, let $T_i:K{\rightarrow}E$ be an asymptotically nonexpansive mappings with sequence ${\{k_n^{(i)}\}\subset[1,{\infty})$ such that $\sum_{n-1}^{\infty}(k_n^{(i)}-1)$ < ${\infty},\;k_{n}^{(i)}{\rightarrow}1$, as $n{\rightarrow}\infty$ and F(T)=$\bigcap_{i=3}^3F(T_i){\neq}{\phi}$ (the set of all common xed points of $T_i$, i = 1, 2, 3). Let {$a_n$},{$b_n$} and {$c_n$} are three real sequences in [0, 1] such that $\in{\leq}\;a_n,\;b_n,\;c_n\;{\leq}\;1-\in$ for $n{\in}N$ and some ${\in}{\geq}0$. Starting with arbitrary $x_1{\in}K$, define sequence {$x_n$} by setting {$$x_{n+1}=P((1-a_n)x_n+a_nT_1(PT_1)^{n-1}y_n)$$ $$y_n=P((1-b_n)x_n+a_nT_2(PT_2)^{n-1}z_n)$$ $$z_n=P((1-c_n)x_n+c_nT_3(PT_3)^{n-1}x_n)$$. Assume that one of the following conditions holds: (1) E satises the Opial property, (2) E has Frechet dierentiable norm, (3) $E^*$ has Kedec -Klee property, where $E^*$ is dual of E. Then sequence {$x_n$} converges weakly to some p${\in}$F(T).

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Two New Marine Sponges of Genus Tedania (Demospongiae: Poecilosclerida: Tedaniidae) from Korea (한국 테다니해면속 (보통해면강: 다골해면목: 테다니해면과)의 2신종)

  • Kim, Hyung-June;Sim, Chung-Ja
    • Animal Systematics, Evolution and Diversity
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    • v.21 no.2
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    • pp.233-241
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    • 2005
  • Two new marine sponges of family Tedaniidae, Tedania (Tedon iu) songakensis n. sp. and Tedania (Tedonia) sasuensis n. sp. were collected from Jeju Island and Chuja Island, Korea between 2004 and 2005. T. (T.) songakensis n. sp. is similar to T (T.) purpurescen Bergquist and Fromont, 1988 based on its type of spicules, but is distinguished from growth form and size of small onychaetes. The growth form of this species is massive, and is compared with thin encrusting of Tedania (T.) purpurescen. The onychaetes of the new species is twice as long as that of T. (T.) purpurescen. T. (T.) sasuensis n. sp. is closely related to T. (T.) connectens (Bronsted, 1924) in type of spicules. However, it is different in size of onychaetes and growth form. The large onychaetes of new species is larger than that of T (T.) connectens. The small onychaetes of new species is smaller than that of T. (T.) connectens. The growth form is massive in new species, but thick encrustins in T.(T.) connectens. And T. (T.) songakensis n. sp. is similar to T. (T.) sasuensis n. sp. in growth form. However, the former is widely different from the latter in shape, color and size of all spicules.

Studies on the Primary Structure of the Alkaline Protease in Neungee [Sarcodon aspratus (Berk.) S. Ito] I. Amino Acid Composition, Chemical Modification and Sequence of the N-terminal Amino Acid (능이[Sarcodon aspratus(Berk.) S. Ito]중 알카리성 단백질가수분해효소의 1차구조에 관한 연구 I. 아미노산 조성, 활성부위 아미노산 및 N-말단 부위의 아미노산 배열)

  • 이태규
    • Journal of the Korean Society of Food Science and Nutrition
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    • v.22 no.6
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    • pp.811-814
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    • 1993
  • Properties of a protease purified from Sarcodon asparatus(Berk.) S. Ito have been investigated. The enzyme displays as a glycosylated serine protease. The sequence for the 21 amino acids of the N-terminal side in the enzyme was determined by automated sequence analysis. The sequence was V-T-T-K-Q-T-N-A-P-W-G-L-G-N-I-S-T-T-N-K-L-.

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GENERALIZED EULER POWER SERIES

  • KIM, MIN-SOO
    • Journal of applied mathematics & informatics
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    • v.38 no.5_6
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    • pp.591-600
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    • 2020
  • This work is a continuation of our investigations for p-adic analogue of the alternating form Dirichlet L-functions $$L_E(s,{\chi})={\sum\limits_{n=1}^{\infty}}{\frac{(-1)^n{\chi}(n)}{n^s}},\;Re(s)>0$$. Let Lp,E(s, t; χ) be the p-adic Euler L-function of two variables. In this paper, for any α ∈ ℂp, |α|p ≤ 1, we give a power series expansion of Lp,E(s, t; χ) in terms of the variable t. From this, we derive a power series expansion of the generalized Euler polynomials with negative index, that is, we prove that $$E_{-n,{\chi}}(t)={\sum\limits_{m=0}^{\infty}}\(\array{-n\\m}\)E_{-(m+n),{\chi}^{t^m}},\;n{\in}{\mathbb{N}}$$, where t ∈ ℂp with |t|p < 1. Some further properties for Lp,E(s, t; χ) has also been shown.

MINIMUM RANK OF THE LINE GRAPH OF CORONA CnoKt

  • Im, Bokhee;Lee, Hwa-Young
    • Communications of the Korean Mathematical Society
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    • v.30 no.2
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    • pp.65-72
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    • 2015
  • The minimum rank mr(G) of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose (i, j)-th entry (for $i{\neq}j$) is nonzero whenever {i, j} is an edge in G and is zero otherwise. The corona $C_n{\circ}K_t$ is obtained by joining all the vertices of the complete graph $K_t$ to each n vertex of the cycle $C_n$. For any t, we obtain an upper bound of zero forcing number of $L(C_n{\circ}K_t)$, the line graph of $C_n{\circ}K_t$, and get some bounds of $mr(L(C_n{\circ}K_t))$. Specially for t = 1, 2, we have calculated $mr(L(C_n{\circ}K_t))$ by the cut-vertex reduction method.

BLOCK THNSOR PRODUCT

  • Lee, Sa-Ge
    • Communications of the Korean Mathematical Society
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    • v.10 no.1
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    • pp.109-113
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    • 1995
  • For a Hilbert space H, let L(H) denote the algebra of all bounded operators on H. For an $n \in N$, it is well known that any element $T \in L(\oplus^n H)$ is expressed as an $n \times n$ matrix each of whose entries lies in L(H) so that T is written as $$ (1) T = (T_{ij}), i, j = 1, 2, ..., n, T_{ij} \in L(H), $$ where $\oplus^n H$ is the direct sum Hilbert space of n copies of H.

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Effect of Pre-NH3 Stripping on the Advanced Sewerage Treatment by BNR (BNR에 의한 하수의 고도처리에 미치는 NH3 스트리핑 전처리의 영향)

  • Seo, Jeong-Beom;An, Kwang-Ho
    • Journal of Korean Society on Water Environment
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    • v.22 no.5
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    • pp.846-850
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    • 2006
  • The biological nutrient removal from domestic wastewater with low C/N ratio is difficult. Therefore, this study was performed to increase influent C/N ratio by ammonia stripping without required carbon source and for improving treatment efficiencies of sewerage by the combination process of ammonia stripping and BNR (StripBNR). The results of this study were summarized as follows. BOD removal efficiencies of BNR and StripBNR were 95.3% and 93.2%, respectively. T-N and T-P removal efficiencies of BNR were 53.3% and 40.8%, respectively. T-N and T-P removal efficiencies of StripBNR were 72.8% and 62.9%, respectively. Concentrations of $NH_3-N$, $NO_2-N$ and $NO_3-N$ at BNR effluent were 0.03 mg/L, 0.08 mg/L and 9.12 mg/L, respectively. On the other hands, concentrations of $NH_3-N$, $NO_2-N$ and $NO_3-N$ at StripBNR effluent were 5.79 mg/L, 0.01 mg/L and 0.14 mg/L, respectively. Consequently, influent C/N ratio of BNR process was increased by ammonia stripping. Removal efficiency of T-N and T-P was improved about 20% by the process of StripBNR.

WEAKTYPE $L^1(R^n)$-ESTIMATE FOR CRETAIN MAXIMAL OPERATORS

  • Kim, Yong-Cheol
    • Journal of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.1029-1036
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    • 1997
  • Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

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