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WEAK AND STRONG CONVERGENCE FOR QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES

  • Kim, Gang-Eun
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.4
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    • pp.799-813
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    • 2012
  • In this paper, we first show that the iteration {$x_n$} defined by $x_{n+1}=P((1-{\alpha}_n)x_n +{\alpha}_nTP[{\beta}_nTx_n+(1-{\beta}_n)x_n])$ converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {$x_n$} defined by $x_{n+1}={\alpha}_nSx_n+{\beta}_nT[{\alpha}^{\prime}_nSx_n+{\beta}^{\prime}_nTx_n+{\gamma}^{\prime}_n{\upsilon}_n]+{\gamma}_nu_n$ converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].

Assessment of Posterior Globe Flattening: Two-Dimensional versus Three-Dimensional T2-Weighted Imaging

  • Ann, Jun Hyung;Kim, Eung Yeop
    • Investigative Magnetic Resonance Imaging
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    • v.19 no.3
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    • pp.178-185
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    • 2015
  • Purpose: To compare the frequency of posterior globe flattening between two-dimensional T2-weighted imaging (2D T2WI) and three-dimensional (3D T2WI). Materials and Methods: Sixty-nine patients (31 female; mean age, 44.4 years) who had undergone both 5-mm axial T2WI and sagittal 3D 1-mm isovoxel T2WI of the whole brain for evaluation of various diseases (headache [n = 30], large hemorrhage [n = 19], large tumor or leptomeningeal tumor spread [n = 15], large infarct [n = 3], and bacterial meningitis [n = 2]) were used in this study. Two radiologists independently reviewed both sets of images at separate sessions. Axial T2WI and multi-planar imaging of 3D T2WI were visually assessed for the presence of globe flattening. The optic nerve sheath diameter (ONSD) was measured at a location 4 mm posterior to each globe on oblique coronal imaging reformatted from 3D T2WI. Results: There were significantly more globes showing posterior flattening on 3D T2WI (105/138 [76.1%]) than on 2D T2WI (27/138 [19.6%], P = 0.001). Inter-observer agreement was excellent for both 2D T2WI and 3D T2WI (Cohen's kappa = 0.928 and 0.962, respectively). Intra-class correlation coefficient for the ONSD was almost perfect (Cohen's kappa = 0.839). The globes with posterior flattening had significantly larger ONSD than those without on both 2D and 3D T2WI (P < 0.001; $6.14mm{\pm}0.44$ vs. $5.74mm{\pm}0.44$ on 2D T2WI; $5.90mm{\pm}0.47$ vs. $5.56mm{\pm}0.34$ on 3D T2WI). Optic nerve protrusion was significantly more frequent on reformatted 1-mm 3D T2WI than on 5-mm 2D T2WI (8 out of 138 globes on 3D T2WI versus one on 2D T2WI; P = 0.018). Conclusion: Posterior globe flattening is more frequently observed on 3D T2WI than on 2D T2WI in patients suspected of having increased intracranial pressure. The globes with posterior flattening have significantly larger ONSD than those without.

THE LATTICE DISTRIBUTIONS INDUCED BY THE SUM OF I.I.D. UNIFORM (0, 1) RANDOM VARIABLES

  • PARK, C.J.;CHUNG, H.Y.
    • Journal of the Korean Mathematical Society
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    • v.15 no.1
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    • pp.59-61
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    • 1978
  • Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be i.i.d. uniform (0,1) random variables. Let $f_n(x)$ denote the probability density function (p.d.f.) of $T_n={\sum}^n_{i=1}X_i$. Consider a set S(x ; ${\delta}$) of lattice points defined by S(x ; ${\delta}$) = $x{\mid}x={\delta}+j$, j=0, 1, ${\cdots}$, n-1, $0{\leq}{\delta}{\leq}1$} The lattice distribution induced by the p.d.f. of $T_n$ is defined as follow: (1) $f_n^{(\delta)}(x)=\{f_n(x)\;if\;x{\in}S(x;{\delta})\\0\;otherwise.$. In this paper we show that $f_n{^{(\delta)}}(x)$ is a probability function thus we obtain a family of lattice distributions {$f_n{^{(\delta)}}(x)$ : $0{\leq}{\delta}{\leq}1$}, that the mean and variance of the lattice distributions are independent of ${\delta}$.

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A Study on Value Orientation of Health of Rural Health Center Milieu (농촌지역 보건소 환경에 있어서의 건강가치관에 관한 일 조사연구)

  • 김순자
    • Journal of Korean Academy of Nursing
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    • v.5 no.1
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    • pp.17-30
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    • 1975
  • The concept and definition of nursing and her role have been changing in accordance with the socio-cultural factors of the initial society. At present, nursing is conceptualized as a health care profession assisting man to restore, maintain and promote health by providing knowledge, wilt strength and resources through various processes of interaction. Man′s behavior, of individual and group activities for health inclusive, is driven by the initial man′s value orientation. The purpose of this study is to investigate the value orientation regarding health of rural health center milieu in order to give data for; 1. the planning for the delivery of community nursing service, 2. the health education plan at all level of nursing care activities, and 3. the planning of curriculum for nursing education. A hundred opinion leaders among the labor population residing in rural areas (P-group), hundred and six professional nurses at rural health centers (N-group) were indirectly interviewed through questionaries. And ninety five of N-group were interviewed likewise of their perceptions of P-group (NP-group) from July 15, to October 15, 1974. The result is as follows: 1. Maintenance of health is revealed to be the most valued component for man′s happiness in all the three groups. (P-group: 7.30 S. D.=1.31), (N-group :7.84 S. D. =49), and (NP-group : 5.93 S. D. =2.28) 2. The average value score of the maintenance of health revealed significant difference by P〈.001 level between each of the three groups. (Between N-group and P-group : T= -4.07 P and NP ; T=-6.93, N and NP: T=-9.35) 3. Basic health maintenance activities necessary for maintenance and promotion of personal health were moderately valued by all the three groups, P-group ; 3.74 (S. D. =.43) , N-group: 3.52 (S. D. =.34), NP-group: 3.07 (S. D. :.55) Among the 8 categories of basic health maintenance activities, "food intake" was highly valued by P-group (mean value score; 4.00 S. D=.51) , "exercise and rest" and "personal cleanliness" was highly valued by both P-group (4.02, 4.08) and N-group (4.08, 4.22). 4. The mean value score of basic health maintenance activities revealed significant difference by P〈.001 level between each of the three groups (between P-group and N-group: T=-4, 07, N-and NP: T=-6.93, P and NP T=-9.35) 5. Among the 30 questionaries, dynamic activities for health maintenance were more valued in comparison to passive activities in an tile three groups. 6. In N-group, correlation between the value of basic health maintenance activities and the personal health status personal revealed moderate significance. Correlation between the value of basic health maintenance activities and the age revealed low significance. 7. In group, correlation between the value of basic health maintenance activities and; perception of personal health status revealed non significance, between the age and sex revealed low sign affiance, and between the educational status revealed moderate significance. Recommendations are as follows ; 1. The efforts towards alteration of value orientation concerning health in general in community nursing practice de focussed be that of family Planning. 2. In order to prepare professional nurses competent in understanding individual and group, social science and behavioral science be strength ended in planning nursing curriculum. 3. Milieu of nursing experience during nursing education be Planned to begin at simple nursing problem and move towards complex, f. e. home care towards health crisis situation in order to achieve dynamic role mastery.

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A Bottleneck Search Algorithm for Digraph Using Maximum Adjacency Merging Method (최대 인접 병합 방법을 적용한 방향 그래프의 병목지점 탐색 알고리즘)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.12 no.5
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    • pp.129-139
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    • 2012
  • Given digraph network $D=(N,A),n{\in}N,a=c(u,v){\in}A$ with source s and sink t, the maximum flow from s to t is determined by cut (S, T) that splits N to $s{\in}S$ and $t{\in}T$ disjoint sets with minimum cut value. The Ford-Fulkerson (F-F) algorithm with time complexity $O(NA^2)$ has been well known to this problem. The F-F algorithm finds all possible augmenting paths from s to t with residual capacity arcs and determines bottleneck arc that has a minimum residual capacity among the paths. After completion of algorithm, you should be determine the minimum cut by combination of bottleneck arcs. This paper suggests maximum adjacency merging and compute cut value method is called by MA-merging algorithm. We start the initial value to S={s}, T={t}, Then we select the maximum capacity $_{max}c(u,v)$ in the graph and merge to adjacent set S or T. Finally, we compute cut value of S or T. This algorithm runs n-1 times. We experiment Ford-Fulkerson and MA-merging algorithm for various 8 digraph. As a results, MA-merging algorithm can be finds minimum cut during the n-1 running times with time complexity O(N).

Analysis of cross-correlation functions of non-linear sequences (비선형수열의 상호상관함수 분석)

  • Cho, Sung-Jin;Yim, Ji-Mi
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.17 no.5
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    • pp.1138-1144
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    • 2013
  • Cross-correlation functions of maximal period sequences have been studied for decades. In this paper, we find the cross-correlation values of non-linear sequences $S_a^r(t)=Tr_1^m\{[Tr_m^n(a{\alpha}^t+{\alpha}^{dt})]^r\}$ having the maximal period $2^n-1$ for Niho type decimation $d=2^{m-2}(2^m+3)$, where n=2m. In particular, we call d Niho type decimation in case $d{\equiv}1(mod\;2^m-1)$. And we analyze the cross-correlation distributions of $S_a^r(t)$ when the phase shift ${\tau}=(2^m+1)k(0{\leq}k{\leq}2^m-2)$ and provide experiment results.

EVALUATION E(exp(∫0th(s)dx(s)) ON ANALOGUE OF WIENER MEASURE SPACE

  • Park, Yeon-Hee
    • Honam Mathematical Journal
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    • v.32 no.3
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    • pp.441-451
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    • 2010
  • In this paper we evaluate the analogue of Wiener integral ${\int\limits}_{C[0,t]}x(t_1){\cdots}x(t_n)d\omega_\rho(x)$ where 0 = $t_0$ < $t_1$ $\cdots$ < $t_n$ $\leq$ t and the Paley-Wiener-Zygmund integral ${\int\limits}_{C[0,t]}$ exp $({\int\limits}_0^t h(s)\tilde{d}x(s))d\omega_\rho(x)$ is the analogue of Wiener measure space.

Thermotropic Liquid Crystalline Behavior of Penta-O-4-{4'-(cyanophenylazo)phenoxy}alkyl-D-glucopyranoses (펜타-O-4-{4'-(시아노페닐아조)펜옥시}알킬-D-글루코피라노오스들의 열방성 액정 거동)

  • Jeong, Seung Yong;Kim, In Soo;Ma, Yung Dae
    • Applied Chemistry for Engineering
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    • v.20 no.6
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    • pp.603-611
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    • 2009
  • Thermotropic liquid crystalline behavior of a homologous series of penta-O-4-{4'-(cyanophenylazo)phenoxy}alkyl-D-glucopyranoses(CAGETn, n = 2~10, the number of methylene units in the spacer) has been investigated. The CAGETn with n of 2 and 7 exhibited enantiotropic nematic phases whereas other derivatives showed monotropic nematic phases. This is the first report of glucose derivatives that form thermotropic nematic phases. The isotropic-nematic transition temperatures ($T_{iNS}$) of CAGETns and their entropy variation at $T_{iN}$ showed the odd-even effect as a function of n. This behavior was rationalized in terms of the change in the average shape of the side chains as the parity of the spacer is varied. This rationalization also accounts for the observed variation of nematic-crystalline phase transition temperatures ($T_{NkS}$) and associoated entropy change at $T_{Nk}$. The entropy change at $T_{iN}$ or $T_{Nk}$ reaches a mininum at n = 3, before it increases again for n = 4. This may be attributed to the difference in the arrangement of the side groups. The mesophase properties of CAGETns were entirely different from those reported for partially or fully alkylated glucopyranoses. This result suggests that the degree of substitution and chemical structure of the substituents play an important role in the formation of the mesophase structures in the liquid crystals.

On the Almost Certain Rate of Convergence of Series of Independent Random Variables

  • Nam, Eun-Woo;Andrew Rosalsky
    • Journal of the Korean Statistical Society
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    • v.24 no.1
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    • pp.91-109
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    • 1995
  • The rate of convergence to a random variable S for an almost certainly convergent series $S_n = \sum^n_{j=1} X_j$ of independent random variables is studied in this paper. More specifically, when $S_n$ converges to S almost certainly, the tail series $T_n = \sum^{\infty}_{j=n} X_j$ is a well-defined sequence of random variable with $T_n \to 0$ a.c. Various sets of conditions are provided so that for a given numerical sequence $0 < b_n = o(1)$, the tail series strong law of large numbers $b^{-1}_n T_n \to 0$ a.c. holds. Moreover, these results are specialized to the case of the weighted i.i.d. random varialbes. Finally, example are provided and an open problem is posed.

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Association between a M-Iacking mutant D75N of pharaonis phoborhodopsin and its transducer is stronger than the complex of the wild-type pigment: Implication of the signal transduction

  • Sudo, Yuki;Iwamoto, Masayuki;Shimono, Kazumi;Kamo, Naoki
    • Journal of Photoscience
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    • v.9 no.2
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    • pp.314-316
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    • 2002
  • In halobacterial membrane, pharaonis phoborhodopsin (or pharaonis sensory rhdopsin II, psRII) forms a complex with its transducer pHtrII. Flash-photolyis of D75N mutant did not yield M-intermediate but an O-like intermediate is observed. We examined the interaction between D75N of ppR and t-Htr (truncated pHtrII). These formed a complex in the presence of n-dodecyl-$\beta$-D-maltoside, and the association accelerated the decay of the 0 of D75N from 15 to 56 s$\^$-1/. From the decay time constants under varying ratios of D75N and t-Htr, n, the molar ratio of D75N/t-Htr in the complex, and K$\_$D/, the dissociation constant, were estimated. The value of n was unity and K$\_$D/ was estimated to 146 nM. This K$\_$D/ value can be considered as the association between the photo-intermediate and t-Htr, which is deduced by the method of estimation. Previously we (Photochem. Photobiol. 74, 489-494 (2001)) reported K$\_$D/ of 15 $\mu$M for the interaction between the wild-type and t-Htr by means of the change of M-decay rates. Therefore, this value should be the K$\_$D/ value for the interaction between M of the wild-type and t-Htr.

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