• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.137-149
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• 2020

Let γ⁽ⁿ⁾ ≡ {γ_ij} (0 ≤ i+j ≤ 2n, |i-j| ≤ n) be a sequence in the complex number set ℂ and let E (n) be the Embry truncated moment matrices corresponding from γ⁽ⁿ⁾. For an odd number n, it is known that γ⁽ⁿ⁾ has a rank E (n)-atomic representing measure if and only if E(n) ≥ 0 and E(n) admits a flat extension E(n + 1). In this paper we suggest a related problem: if E(n) is positive and nonsingular, does E(n) have a flat extension E(n + 1)? and give a negative answer in the case of E(3). And we obtain some necessary conditions for positive and nonsingular matrix E (3), and also its sufficient conditions.

• Korean Journal of Plant Taxonomy
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• v.33 no.3
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• pp.279-293
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• 2003

Somatic chromosomes about 13 taxa of Korean Euphorbia L. was investigated to estimate its taxonomic significance. Somatic chromosome numbers of treated taxa were 2n= 12, 20, 22, 28, 40, 42, 56, therefore basic chromosome numbers of those were x=6, 7, 10, 11. The chromosome numbers of E. pallasii Turcz. (2n=20), E. hylonoma Hand.-Mazz (2n=20.), E. fauriei H. L$\acute{e}$v. & Vaniot ex H. L$\acute{e}$v (2n=28) and E. jolkini Boiss. (2n=28) were determined for the first time in this study. The chromosome numbers of four taxa were same as previous ones; E. sieboldiana Moor. & Decne. (2n=20), E. ebracteolata Hayata (2n=20), E. humifusa Willd. ex Schlecht. (2n=22). But those of six taxa were different; E. esula L (2n= 16, 20, 60, 64 vs 2n=20), E. helioscopia L. (2n=12, 42 vs 2n=42), E. lucorum Rupr. (2n=28, 40 vs 2n=56), E. pekinensis Rupr. in Maxim. (2n=24 vs 2n=28, 56), E. maculata L. (2n=28, 42 vs 2n=12), E. supina Raf. (n=7 vs 2n=40). E. ebracteolata, E. pallasii and E. hylonoma were distingushcd from the other taxa by the chromosome numbers, size and satellites, E. maculata, E. humifusa, E. supina had the different basic and somatic chromosome numbers in spite of the similar morphological. anatomical and palynological chracters. The chromosomal character of Korean Euphorbia was supported the Ma and Hu's systems, and as above results, it was found to be a good character in delimiting above sections and estimating relationships for some species.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.677-685
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• 2023

For n ≥ 2 and a real Banach space E, 𝓛(ⁿE : E) denotes the space of all continuous n-linear mappings from E to itself. Let Π (E) = {[x^*, (x₁, . . . , x_n)] : x^*(x_j) = ||x^*|| = ||x_j|| = 1 for j = 1, . . . , n }. An element [x^*, (x₁, . . . , x_n)] ∈ Π(E) is called a numerical radius point of T ∈ 𝓛(ⁿE : E) if |x^*(T(x₁, . . . , x_n))| = v(T), where the numerical radius v(T) = sup_{[y^*,y1,...,yn]∈Π(E)}|y^*(T(y₁, . . . , y_n))|. For T ∈ 𝓛(ⁿE : E), we define Nradius(T) = {[x^*, (x₁, . . . , x_n)] ∈ Π(E) : [x^*, (x₁, . . . , x_n)] is a numerical radius point of T}. T is called a numerical radius peak n-linear mapping if there is a unique [x^*, (x₁, . . . , x_n)] ∈ Π(E) such that Nradius(T) = {±[x^*, (x₁, . . . , x_n)]}. In this paper we present explicit formulae for the numerical radius of T for every T ∈ 𝓛(ⁿE : E) for E = c₀ or l_∞. Using these formulae we show that there are no numerical radius peak mappings of 𝓛(ⁿc₀ : c₀).

• Korean Journal of Animal Reproduction
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• v.6 no.1
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• pp.31-35
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• 1982

A study of 188 lactations of Holstein cows in Gwangju area was undertaken to establish the shape of lactation curve during the period from October in 1980 to January in 1982. The Gammafunction described by Wood(1967) was fitted to the lactations observed. The results obtained in the present study were summarized as follows; 1. The lactation curve of the 188 lactations was expressed by the equation based on Wood's model (1967) as follows; Yn=24.5m0.0762e-0.0944n(R2=0.99) 2. The lactation curves by parity were represented by the equations as follows; Yn=18.81n0.1486e-0.0741n(R2=0.98)……………parity 1 Yn=26.51n0.1161e-0.1200n(R2=0.96)……………parity 2 Yn=26.95n0.2804e-0.1703n(R2=0.99)……………parity 3 Yn=27.92n0.1429e-0.1427n(R2=0.98)……………parity 4 Yn=22.61n0.1985e-0.1211n(R2=0.94)……………parity 5 3. The lactation curves by calving seasons were represented by the equationes as follows; Yn=27.05n0.0739e-0.1005n(R2=0.98)……………spring Yn=23.08n0.2040e-0.1202n(R2=0.98)……………summer Yn=26.81n0.0460e-0.1134n(R2=0.98)……………autumn Yn=23.40n0.1299e-0.1101n(R2=0.95)……………winter

• The Journal of the Petrological Society of Korea
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• v.27 no.3
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• pp.109-120
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• 2018

The distributional characteristics of fault segments in Cretaceous and Tertiary rocks from southeastern Gyeongsang Basin were derived. The 267 sets of fault segments showing linear type were extracted from the curved fault lines delineated on the regional geological map. First, the directional angle(${\theta}$)-length(L) chart for the whole fault segments was made. From the related chart, the general d istribution pattern of fault segments was derived. The distribution curve in the chart was divided into four sections according to its overall shape. NNE, NNW and WNW directions, corresponding to the peaks of the above sections, indicate those of the Yangsan, Ulsan and Gaeum fault systems. The fault segment population show near symmetrical distribution with respect to $N19^{\circ}E$ direction corresponding to the maximum peak. Second, the directional angle-frequency(N), mean length(Lm), total length(Lt) and density(${\rho}$) chart was made. From the related chart, whole domain of the above chart was divided into 19 domains in terms of the phases of the distribution curve. The directions corresponding to the peaks of the above domains suggest the directions of representative stresses acted on rock body. Third, the length-cumulative frequency graphs for the 18 sub-populations were made. From the related chart, the value of exponent(${\lambda}$) increase in the clockwise direction($N10{\sim}20^{\circ}E{\rightarrow}N50{\sim}60^{\circ}E$) and counterclockwise direction ($N10{\sim}20^{\circ}W{\rightarrow}N50{\sim}60^{\circ}W$). On the other hand, the width of distribution of lengths and mean length decrease. The chart for the above sub-populations having mutually different evolution characteristics, reveals a cross section of evolutionary process. Fourth, the general distribution chart for the 18 graphs was made. From the related chart, the above graphs were classified into five groups(A~E) according to the distribution area. The lengths of fault segments increase in order of group E ($N80{\sim}90^{\circ}E{\cdot}N70{\sim}80^{\circ}E{\cdot}N80{\sim}90^{\circ}W{\cdot}N50{\sim}60^{\circ}W{\cdot}N30{\sim}40^{\circ}W{\cdot}N40{\sim}50^{\circ}W$) < D ($N70{\sim}80^{\circ}W{\cdot}N60{\sim}70^{\circ}W{\cdot}N60{\sim}70^{\circ}E{\cdot}N50{\sim}60^{\circ}E{\cdot}N40{\sim}50^{\circ}E{\cdot}N0{\sim}10^{\circ}W$) < C ($N20{\sim}30^{\circ}W{\cdot}N10{\sim}20^{\circ}W$) < B ($N0{\sim}10^{\circ}E{\cdot}N30{\sim}40^{\circ}E$) < A ($N20{\sim}30^{\circ}E{\cdot}N10{\sim}20^{\circ}E$). Especially the forms of graph gradually transition from a uniform distribution to an exponential one. Lastly, the values of the six parameters for fault-segment length were divided into five groups. Among the six parameters, mean length and length of the longest fault segment decrease in the order of group III ($N10^{\circ}W{\sim}N20^{\circ}E$) > IV ($N20{\sim}60^{\circ}E$) > II ($N10{\sim}60^{\circ}W$) > I ($N60{\sim}90^{\circ}W$) > V ($N60{\sim}90^{\circ}E$). Frequency, longest length, total length, mean length and density of fault segments, belonging to group V, show the lowest values. The above order of arrangement among five groups suggests the interrelationship with the relative formation ages of fault segments.

• Journal of Life Science
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• v.19 no.6
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• pp.765-769
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• 2009

Recent studies have reported that the distribution of HPV-16 sequence variation differs geographically, and more specifically that HPV-16 E6/E7 intratypic variants might carry a high risk for development of ICC (invasive cervical cancer) and CIN (cervical intraepithelial neoplasia) in a given population. To investigate the genetic diversities of HPV-16 E6/E7 oncogene by region, we collected nineteen HPV-16 isolates from sexually high-risk women in Busan, and analyzed the HPV-16 E6/E7 coding regions (nt 34 to 880) with HPV-16 E6/E7 specific PCR amplification. At the nucleotide levet eleven variants of the E6 genes and nine variants of the E7 genes were identified as follows: E6 T178G (n=l1), E6 T178A (n=l), E6 T350G (n=3), E6 A442C (n=2), E6 AI04T, E6 All1G, E6 C116T, E6 G145T, E6 T183G, E6 C335T, E6 G522C and E7 A647G (n=12), E7 A645C, E7 A777C, E7 G663A, E7 T732C, E7 T760C, E7 A775T, E7 T789C and E7 T795G, respectively. At the amino acid levet the isolated HPV-16 E6 and E7 genes showed eleven E6 variants: E6 D25E (n=12), E6 L83V (n=4), E6 E113D (n=2), E6 MIL, E6 Q3R, E6 P5S, E6 Q14H, E6 D25N, E6 127R, E6 H78Y, E6 C140S and three E7 variants: N29S (n=12), L28F, T72S. HPV16 E6 L83V, the dominant variant in the Caucasian population, showed relatively low frequencies in our study population. We elucidated that the dominant HPV-16 E6/E7 variants were HPV-16 E6 D25E (63.2%) and HPV-16 E7 N29S (63.2%), which were phylogenetically included in Asian lineage. Further study is needed to evaluate the risk of cervical cancer related HPV-16 E6/E7 intratypic variants in the Korean population.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.881-889
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• 1994

Let ($X, \Beta, \mu$) be a measure space with the $\sigma$-algebra $\Beta$ and the probability measure $\mu$. Throughouth this article set equalities and inclusions are understood as being so modulo measure zero sets. A transformation T defined on a probability space X is said to be measure preserving if $\mu(T^{-1}E) = \mu(E)$ for $E \in B$. It is said to be ergodic if $\mu(E) = 0$ or i whenever $T^{-1}E = E$ for $E \in B$. Consider the sequence ${x, Tx, T^2x,...}$ for $x \in X$. One may ask the following questions: What is the relative frequency of the points $T^nx$ which visit the set E\ulcorner Birkhoff Ergodic Theorem states that for an ergodic transformation T the time average $lim_{n \to \infty}(1/N)\sum^{N-1}_{n=0}{f(T^nx)}$ equals for almost every x the space average $(1/\mu(X)) \int_X f(x)d\mu(x)$. In the special case when f is the characteristic function $\chi E$ of a set E and T is ergodic we have the following formula for the frequency of visits of T-iterates to E : $$ lim_{N \to \infty} \frac{$\mid${n : T^n x \in E, 0 \leq n $\mid$}{N} = \mu(E) $$ for almost all $x \in X$ where $$\mid$\cdot$\mid$$ denotes cardinality of a set. For the details, see [8], [10].

• Pediatric Gastroenterology, Hepatology & Nutrition
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• v.16 no.2
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• pp.123-126
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• 2013

$M\acute{e}n\acute{e}$trier's disease is a rare protein-losing gastropathy characterized by hypertrophic gastric fold, foveolar hyperplasia, and hypoproteinemia with resulting peripheral edema. It is clinically evident as nonspecific gastrointestinal symptoms, including abdominal discomfort, nausea and vomiting, abdominal pain, weight loss, diarrhea, and edema. Pediatric $M\acute{e}n\acute{e}$trier's disease usually has an insidious onset and progressive, chronic clinical course and it spontaneously resolves in weeks or months. The pathogenesis of $M\acute{e}n\acute{e}$trier's disease is not clearly understood. $M\acute{e}n\acute{e}$trier's disease is thought to be associated with some gastric infections. But the cause of $M\acute{e}n\acute{e}$trier's disease is unknown, an association with cytomegalovirus (CMV) and Helicobacter pylori has been suggested. In Korea, We present the first a case of pediatric $M\acute{e}n\acute{e}$trier's disease with positive evidence of CMV and H. pylori.

• Fisheries and Aquatic Sciences
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• v.13 no.2
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• pp.118-126
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• 2010

A feeding trial was conducted to investigate the effects of different levels of dietary n-3 highly unsaturated fatty acids (HUFA) (1.1-5.6%) and vitamin E (70 and 400 mg/kg) on the growth and body composition of juvenile rockfish. Six isonitrogenous (45% crude protein) and isolipidic (17% crude lipid) diets were formulated to contain graded levels of n-3 HUFA and vitamin E. Diets 1, 2 and 3 consist of 400 mg vitamin E/kg diet with graded levels of 1.1, 3.0, and 5.6% n-3 HUFA, respectively. Graded levels of n-3 HUFA (1.1, 3.0, and 4.0%) were added in diets 4, 5 and 6, respectively, containing 70 mg vitamin E/kg diet each. At the end of feeding trial, growth performance of rockfish was affected by neither dietary n-3 HUFA nor vitamin E levels. Feed efficiency and hepatosomatic index were slightly decreased (P<0.05) with increment of dietary n-3 HUFA at each dietary vitamin E level. Dietary vitamin E and n-3 HUFA levels did not affect proximate composition and vitamin E concentration in the dorsal muscle of rockfish. Liver moisture and crude protein contents positively related to dietary n-3 HUFA levels. Liver lipid content and hematocrit value were significantly decreased (P<0.05) by increasing dietary n-3 HUFA levels. Eicosapentaenoic acid (20:5n-3; EPA) and docosahexaenoic acid (22:6n-3; DHA) concentrations in the dorsal muscle significantly correlated to dietary n-3 HUFA levels, except for fish fed the diet 6 containing 4% n-3 HUFA and 70 mg vitamin E/kg diet. EPA concentration in the dorsal muscle of fish fed the diet 6 was significantly lower than that of fish fed the diets 2, 3 and 5. The present findings suggest that feeding of diets containing excessive n-3 HUFA level with varying addition of vitamin E may alter fatty acid composition in the dorsal muscle, but do not affect growth of juvenile rockfish.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.503-510
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• 2004

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation $Tx_i\;=\;y_i,\;for\;i\;=\;1,\;2,\;\cdots,\;n$. In this paper the following is proved: Let H be a Hilbert space and L be a commutative subspace lattice on H. Let H and y be vectors in H. Let $M_x\;=\;\{{\sum{n}{i=1}}\;{\alpha}_iE_ix\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}\;and\;M_y\;=\;\{{\sum{n}{i=1}}\;{\alpha}_iE_iy\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}. Then the following are equivalent. (1) There exists an operator A in AlgL such that Ax = y, Af = 0 for all f in ${\overline{M_x}}^{\bot}$, AE = EA for all $E\;{\in}\;L\;and\;A^{*}\;=\;A$. (2) $sup\;\{\frac{{\parallel}{{\Sigma}_{i=1}}^{n}\;{\alpha}_iE_iy{\parallel}}{{\parallel}{{\Sigma}_{i=1}}^{n}\;{\alpha}_iE_iy{\parallel}}\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}\;<\;{\infty},\;{\overline{M_u}}\;{\subset}{\overline{M_x}}$ and < Ex, y >=< Ey, x > for all E in L.