• Title/Summary/Keyword: [r,s,t

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Ptr,s)-CLOSED SPACES AND PRE-(ωr,s)t-θf-CLUSTER SETS

  • Afsan, Bin Mostakim Uzzal;Basu, Chanchal Kumar
    • Communications of the Korean Mathematical Society
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    • v.26 no.1
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    • pp.135-149
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    • 2011
  • Using (r, s)-preopen sets [14] and pre-${\omega}_t$-closures [6], a new kind of covering property $P^t_{({\omega}_r,s)}$-closedness is introduced in a bitopological space and several characterizations via filter bases, nets and grills [30] along with various properties of such concept are investigated. Two new types of cluster sets, namely pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets and (r, s)t-${\theta}_f$-precluster sets of functions and multifunctions between two bitopological spaces are introduced. Several properties of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets are investigated and using the degeneracy of such cluster sets, some new characterizations of some separation axioms in topological spaces or in bitopological spaces are obtained. A sufficient condition for $P^t_{({\omega}_r,s)}$-closedness has also been established in terms of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets.

ON SOME NEW CLASSES OF COMPACT-LIKE BITOPOLOGICAL SPACES

  • Afsan, BM Uzzal
    • Journal of the Chungcheong Mathematical Society
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    • v.33 no.2
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    • pp.271-285
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    • 2020
  • In this paper, we have introduced a new type of covering property ${\beta}^t_{({\omega}_r,s)}$-closedness, stronger than $P^t_{({\omega}_r,s)}$-closedness [3] in terms of (r, s)-β-open sets [9] and β-ωt-closures in bitopological spaces along with its several characterizations via filter bases and grills [15] and various properties. Further grill generalizations of ${\beta}^t_{({\omega}_r,s)}$-closedness (namely, ${\beta}^t_{({\omega}_r,s)}$-closedness modulo grill) and associated concepts have also been investigated.

([r, s], [t, u])-INTERVAL-VALUED INTUITIONISTIC FUZZY GENERALIZED PRECONTINUOUS MAPPINGS

  • Park, Chun-Kee
    • Korean Journal of Mathematics
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    • v.25 no.1
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    • pp.1-18
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    • 2017
  • In this paper, we introduce the concepts of ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preclosed sets and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preopen sets in the interval-valued intuitionistic smooth topological space and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized pre-continuous mappings and then investigate some of their properties.

Conditional Integral Transforms on a Function Space

  • Cho, Dong Hyun
    • Kyungpook Mathematical Journal
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    • v.52 no.4
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    • pp.413-431
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    • 2012
  • Let $C^r[0,t]$ be the function space of the vector-valued continuous paths $x:[0,t]{\rightarrow}\mathbb{R}^r$ and define $X_t:C^r[0,t]{\rightarrow}\mathbb{R}^{(n+1)r}$ and $Y_t:C^r[0,t]{\rightarrow}\mathbb{R}^{nr}$ by $X_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}),\;x(t_n))$ and $Y_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}))$, respectively, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n=t$. In the present paper, using two simple formulas for the conditional expectations over $C^r[0,t]$ with the conditioning functions $X_t$ and $Y_t$, we establish evaluation formulas for the analogue of the conditional analytic Fourier-Feynman transform for the function of the form $${\exp}\{{\int_o}^t{\theta}(s,\;x(s))\;d{\eta}(s)\}{\psi}(x(t)),\;x{\in}C^r[0,t]$$ where ${\eta}$ is a complex Borel measure on [0, t] and both ${\theta}(s,{\cdot})$ and ${\psi}$ are the Fourier-Stieltjes transforms of the complex Borel measures on $\mathbb{R}^r$.

EVALUATION FORMULAS FOR AN ANALOGUE OF CONDITIONAL ANALYTIC FEYNMAN INTEGRALS OVER A FUNCTION SPACE

  • Cho, Dong-Hyun
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.3
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    • pp.655-672
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    • 2011
  • Let $C^r$[0,t] be the function space of the vector-valued continuous paths x : [0,t] ${\rightarrow}$ $R^r$ and define $X_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{(n+1)r}$ and $Y_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{nr}$ by $X_t(x)$ = (x($t_0$), x($t_1$), ..., x($t_{n-1}$), x($t_n$)) and $Y_t$(x) = (x($t_0$), x($t_1$), ..., x($t_{n-1}$)), respectively, where 0 = $t_0$ < $t_1$ < ... < $t_n$ = t. In the present paper, with the conditioning functions $X_t$ and $Y_t$, we introduce two simple formulas for the conditional expectations over $C^r$[0,t], an analogue of the r-dimensional Wiener space. We establish evaluation formulas for the analogues of the analytic Wiener and Feynman integrals for the function $G(x)=\exp{{\int}_0^t{\theta}(s,x(s))d{\eta}(s)}{\psi}(x(t))$, where ${\theta}(s,{\cdot})$ and are the Fourier-Stieltjes transforms of the complex Borel measures on ${\mathbb{R}}^r$. Using the simple formulas, we evaluate the analogues of the conditional analytic Wiener and Feynman integrals of the functional G.

[r, s, t; f]-COLORING OF GRAPHS

  • Yu, Yong;Liu, Guizhen
    • Journal of the Korean Mathematical Society
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    • v.48 no.1
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    • pp.105-115
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    • 2011
  • Let f be a function which assigns a positive integer f(v) to each vertex v $\in$ V (G), let r, s and t be non-negative integers. An f-coloring of G is an edge-coloring of G such that each vertex v $\in$ V (G) has at most f(v) incident edges colored with the same color. The minimum number of colors needed to f-color G is called the f-chromatic index of G and denoted by ${\chi}'_f$(G). An [r, s, t; f]-coloring of a graph G is a mapping c from V(G) $\bigcup$ E(G) to the color set C = {0, 1, $\ldots$; k - 1} such that |c($v_i$) - c($v_j$ )| $\geq$ r for every two adjacent vertices $v_i$ and $v_j$, |c($e_i$ - c($e_j$)| $\geq$ s and ${\alpha}(v_i)$ $\leq$ f($v_i$) for all $v_i$ $\in$ V (G), ${\alpha}$ $\in$ C where ${\alpha}(v_i)$ denotes the number of ${\alpha}$-edges incident with the vertex $v_i$ and $e_i$, $e_j$ are edges which are incident with $v_i$ but colored with different colors, |c($e_i$)-c($v_j$)| $\geq$ t for all pairs of incident vertices and edges. The minimum k such that G has an [r, s, t; f]-coloring with k colors is defined as the [r, s, t; f]-chromatic number and denoted by ${\chi}_{r,s,t;f}$ (G). In this paper, we present some general bounds for [r, s, t; f]-coloring firstly. After that, we obtain some important properties under the restriction min{r, s, t} = 0 or min{r, s, t} = 1. Finally, we present some problems for further research.

In vitro Selection of RNA Aptamers which Bind to Escherichia coli tRNAVal (대장균 tRNAVal에 결합하는 RNA Aptamer들의 시험관내 선별)

  • Jo, Bong Rae
    • Journal of the Korean Chemical Society
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    • v.46 no.2
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    • pp.157-163
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    • 2002
  • To identify RNA motifs interacting with $tRNA^{Val}$, a SELEX(Systematic Evolution of Ligands by Exponential Enrichment) was applied. Random DNA library which contains a region of ran-domized 48-mer oligonucleotide flanked by conserved sequ ence primers was transcribed into RNA pool using T7 RNA polymerase and RNA aptamers were selected with $tRNA^{Val}$ -immobilized affinity column through 14 rounds of SELEX. Some of the resulting aptamers contained a consensus sequence similar to the sequence in the loop regions of three rRNAs; C43GAAC47 sequence of 5S rRNA, G1491AAGU1495, G1379UUCC1383 sequence of 16S rRNA and C1064UUAG1068, G2110UGUA2114, C2480GACGG2485, A2600CAGU2604 sequence of 23S rRNA. These results suggest that $tRNA^{Val}$ can interact with 5S rRNA, 16S rRNA and 23S rRNA with variety in ribosome.

A Study for Identification of Nursing Diagnosis using the Roy's Adaptation Model in Maternity Unit (Roy's Adaptation Model에 의한 모성영역에서의 간호진단 확인연구)

  • Jo, Jeong-Ho
    • The Korean Nurse
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    • v.33 no.3
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    • pp.79-91
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    • 1994
  • The purpose of this study was to identify the meaningful nursing diagnosis in maternity unit and to suggest formally the basal data to the nursing service with scientific approach. The subject for this paper were 64 patients who admitted to Chung Ang University Hospital, Located in Seoul, from Mar. 10, to July 21, 1993. The results were as follows: 1. The number of nursing diagnosis from 64 patients were 892 and average number of nursing diagnosis per patient was 13.9. 2. Applying the division of nursing diagnosis to Roy's Adaptation Model, determined nursing diagnosis from the 64 patients were 621 (69.6%) in physiological adaptation mode and (Comfort, altered r/t), (Injury, potential for r/t), (Infection, potential for r/t), (Bowel elimination, altered patterns r/t), (Breathing pattern, ineffective r/t), (Nutrition, altered r/t less than body requirement) in order, and 139 (15.6%) in role function mode, (Self care deficit r/t), (Knowledge deficit r/t), (Mobility, impaired physical r/t) in order, 122 (13.7%) in interdependence adaptation mode, (Anxiety r/t), (Family Process, altered r/t) in order, 10(1.1%) in self concept adaptation mode, (Powerlessness r/t), (Grieving, dysfunctional r/t) in order. 3. Nursing diagnosis in maternity unit by the medical diagnosis, the average hospital dates were 3.8 days in normal delivery and majority of used nursing diagnosis, (Comfort, altered r/t) 64.6%, (Self care deficit r/t) 13.6% in order, and the average hospital dates were 9.6 days in cesarean section delivery and majority of used nursing diagnosis, (Comfort, altered r/t) 51.6%, (Self care deficit r/t) 15.2%, (Infection, potential for r/t) 9.9%, (Injury, potential "for r/t) 8.1%, (Anxiety r/t) 5.0%, (Mobility, impaired physical r/t) 3.3% in order, and the average hospital dates were 15.8days in preterm labor and majority of used nursing diagnosis, (Comfort, altered r/ t), (Anxiety r/t), (Injury, potential for r/t) in order, and the average short-term hospital dates were 2.5days, long-term hospital dates were 11.5days in gynecologic diseases and majority of used nursing diagnosis, (Comfort, altered r/t). (Self care deficit r/t), (Injury, potential for r/t), (Infection, potential for r/t) in order.

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