• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.353-359
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• 1998

Factorial designs with two-level factors represent the smallest factorial experiments. The system of notation and confounding and fractional factorial schemes developed for the $2^N$system are found in standard textbooks of experimental designs. Just as in the $2^N$ system, the general confounding and fractional factorial schemes are possible in $3^N,5^N$, .... , and $\rho^N$ where $\rho$ is a prime number. Hence, we have the $\rho^N$ system. In this article, the author proposes a new algorithm for constructing fractional factorial plans in the $\rho^N$ system.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.269-277
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• 2019

Let X be a nonempty set, ${\rho}$ be an equivalence on X, T(X) be the semigroup of all transformations from X into itself, and $T_{\rho}(X)=\{f{\in}T(X)|(x,y){\in}{\rho}{\text{ implies }}((x)f,\;(y)f){\in}{\rho}\}$. In this paper, we investigate some necessary and sufficient conditions for elements in $T_{\rho}(X)$ to be left or right magnifying.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.789-795
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• 1995

For nonintegrable weight $-\rho$, some weight multiplicities of the irreducible module $L(-\rho)$ over $A^{(1)}_{(1)}$ affine Lie algebras are expressed in terms of the colored partition functions. Also we find the multiplicity of $L(-\rho)$ in ther Verma module $M(-\rho)$ for any affine Lie algebras.

• Kyungpook Mathematical Journal
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• v.52 no.1
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• pp.99-107
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• 2012

The purpose of this paper is to introduce two new types of irresolute functions called, completely ${\rho}$-irresolute functions and weakly ${\rho}$-irresolute functions. We obtain their characterizations and their basic properties.

• Journal of Microbiology
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• v.44 no.1
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• pp.11-22
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• 2006

Escherichia coli protein Rho is required for the factor-dependent transcription termination by an RNA polymerase and is essential for the viability of the cell. It is a homohexameric protein that recognizes and binds preferably to C-rich sites in the transcribed RNA. Once bound to RNA, it utilizes RNA-dependent ATPase activity and subsequently ATPase-dependent helicase activity to unwind RNA-DNA hybrids and release RNA from a transcribing elongation complex. Studies over the past few decades have highlighted Rho as a molecule and have revealed much of its mechanistic properties. The recently solved crystal structure could explain many of its physiological functions in terms of its structure. Despite all these efforts, many of the fundamental questions pertaining to Rho recognition sites, differential ATPase activity in response to different RNAs, translocation of Rho along the nascent transcript, interactions with elongation complex and finally unwinding and release of RNA remain obscure. In the present review we have attempted to summarize 'the knowns' and 'the unknowns' of the Rho protein revealed by the recent developments in this field. An attempt has also been made to understand the physiology of Rho in the light of its phylogeny.

• Journal of Plant Biology
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• v.39 no.2
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• pp.85-92
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• 1996

Small GTP-binding proteins are divided into three major group: Ras, Rho and Ypt/Rab. They have the conserved regions designed G1 to G5 that are critical in GDP/GTP exchange, GTP-induced conformational change and GTP hydrolysis. We isolated and characterized genomic DNA or cDNAfragments encoding G1 to G3 domains of small GTP-binding protein Rab and Rho from several plant species using two different PCR-based cloning strategies. Seven rab DNA fragments were isolated from 4 different plants, mung-bean, tobacco, rice and pepper using two degenerate primers corresponding to the GTP-binding domain G1 and G3 in small GTP-binding proteins. The amino acid sequences among these rab DNA fragments and other known small GTP-binding proteins shows that they belong to the Ypt/Rab family. Six rho DNA fragments were isolated from 5 different plants, mung-bean, rice, Arabidopsis, Allium and Gonyaulax using the nested PCR method that involves four degenerate primers corresponding to the GTP-binding domain G1, G3 and G4. The rho DNA fragments cloned show more than 90% homology to each other. Sequence comparison between plant and other known Rho family genes suggests that they are closely related (67 to 82% amino acid identity). Sequence analysis and southern blot analysis of rab and rho in mung-bean suggest than thses genes are encoded by multigene family in mung-bean.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.175-178
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• 2005

In the present paper, we observe a relation between fuzzy norms and induced crisp norms on a linear space. We first prove that if $\rho_1,\;\rho_2$ are equivalent fuzzy norms on a linear space, then for every $\varepsilon\in(0.1)$, the induced crisp norms $P_\varepsilon^1,\;and\;P_\varepsilon^2$, respectively are equivalent. Since the converse does not hold, we prove it under some strict conditions. And consider the following theorem proved in [8]: Let $\rho$ be a lower semicontinuous fuzzy norm on a normed linear space X, and have the bounded support. Then $\rho$ is equivalent to the fuzzy norm $\chi_B$ where B is the closed unit ball of X. The lower semi-continuity of $\rho$ is an essential condition which guarantees the continuity of $P_\varepsilon$, where 0 < e < 1. As the last result, we prove that : if $\rho$ is a fuzzy norm on a finite dimensional vector space, then $\rho$ is equivalent to $\chi_B$ if and only if the support of $\rho$ is bounded.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.139-144
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• 2000

The generalized noncommutative torus $T_{\rho}^d$ of rank m was defined in [2]. Assume that for the completely irrational noncommutative subtorus $A_{\rho}$ of rank m of $T_{\rho}^d$ there is no integer q > 1 such that $tr(K_0(A_{\rho}))=\frac{1}{q}{\cdot}tr(K_0(A_{\rho^{\prime}}))$ for $A_{\rho^{\prime}}$ a completely irrational noncommutative torus of rank m. All $C^*$-algebras ${\Gamma}({\eta})$ of sections of locally trivial $C^*$-algebra bundles ${\eta}$ over $M=\prod_{i=1}^{e}S^{2k_i}{\times}\prod_{i=1}^{s}S^{2n_i+1}$, $\prod_{i=1}^{s}\mathbb{PR}_{2n_i}$, or $\prod_{i=1}^{s}L_{k_i}(n_i)$ with fibres $T_{\rho}^d{\otimes}M_c(\mathbb{C})$ were constructed in [6, 7, 8]. We prove that ${\Gamma}({\eta}){\otimes}M_{p^{\infty}}$ is isomorphic to $C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C}){\otimes}M_{p^{\infty}}$ if and only if the set of prime factors of cd is a subset of the set of prime factors of p, that $\mathcal{O}_{2u}{\otimes}{\Gamma}({\eta})$ is isomorphic to $\mathcal{O}_{2u}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if and only if cd and 2u - 1 are relatively prime, and that $\mathcal{O}_{\infty}{\otimes}{\Gamma}({\eta})$ is not isomorphic to $\mathcal{O}_{\infty}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if cd > 1 when no non-trivial matrix algebra can be ${\Gamma}({\eta})$.

• The Korean Journal of Physiology and Pharmacology
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• v.13 no.3
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• pp.201-207
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• 2009

Our previous study demonstrated that flavone inhibits vascular contractions by decreasing the phosphorylation levelof the myosin phosphatase target subunit (MYPT1). In the present study, we hypothesized that flavone attenuates vascular contractions through the inhibition of the RhoA/Rho kinase pathway. Rat aortic rings were denuded of endothelium, mounted in organ baths, and contracted with either 30 nM U46619 (a thromboxane A2 analogue) or 8.0 mM NaF 30 min after pretreatment with either flavone (100 or 300 $({\mu}M$) or vehicle. We determined the phosphorylation level of the myosin light chain ($MLC_{20}$), the myosin phophatase targeting subunit 1 (MYPT1) and the protein kinase C-potentiated inhibitory protein for heterotrimeric myosin light chain phophatase of 17-kDa (CPI17) by means of Western blot analysis. Flavone inhibited, not only vascular contractions induced by these contractors, but also the levels of $MLC_{20}$ phosphorylation. Furthermore, flavone inhibited the activation of RhoA which had been induced by either U46619 or NaF. Incubation with flavone attenuated U46619 or NaF-induced phosphorylation of $MYPT1^{Thr855}$ and $CPI17^{Thr38}$, the downstream effectors of Rho-kinase. In regards to the $Ca^{2+}$-free solution, flavone inhibited the phosphorylation of $MYPT1^{Thr855}$ and $CPI17^{Thr38}$, as well as vascular contractions induced by U 46619. These results indicate that flavone attenuates vascular contractions, at least in part, through the inhibition of the RhoA/Rho-kinase pathway.

• Korean Journal of Applied Biomechanics
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• v.24 no.3
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• pp.217-227
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• 2014

The purpose of this study was to investigate the relationship between distance and factors of javelin in korean male's javelin throwing. To accomplish this purpose, the analyzed trail selected total 29 trails (subjects 9) recorded more than 65 m in the 93rd National Sports Festival. The Kwon3D 3.1 version was used to obtain the three dimensional coordinates about the top, grip, end of javelin. And the kinematic data such as projection factors and direction angle of javelin calculated using Matlab2009a program. The statical analysis on the records (n=29) were used to Pearson's product moment correlation coefficient. There was a statistically positive relationship between the records and horizontal velocity (r=.866, ${\rho}$<.01), height (r=.541, ${\rho}$ <.001), height rate (r=.373, ${\rho}$ <.05) and horizontal displacement of javelin (r=.749, ${\rho}$ <.01), but the medial/lateral velocity showed a negative relationship to r=-.663 (${\rho}$ <.01). The attack and yaw angle showed not a significant relationship between the records, but the medial-lateral tilt (E1:r =-.557 [p<.01)] E2:r=-.629 [${\rho}$<.01], E3:r=-.528 [${\rho}$ <.01]) and attitude angle (E2:r=-.629 [[${\rho}$<.01], E3:r=-.619 [${\rho}$ <.01]) of javelin showed a negative relationship between the records, as well as the projection angle of javelin (r=-.419, ${\rho}$ <.05) showed a negative relationship between the records.