• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.1-22
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• 2023

Let L(s, χ) be the Dirichlet L-series associated with an f-periodic complex function χ. Let P(X) ∈ ℂ[X]. We give an expression for ∑^f_n=1 χ(n)P(n) as a linear combination of the L(-n, χ)'s for 0 ≤ n < deg P(X). We deduce some consequences pertaining to the Chowla hypothesis implying that L(s, χ) > 0 for s > 0 for real Dirichlet characters χ. To date no extended numerical computation on this hypothesis is available. In fact by a result of R. C. Baker and H. L. Montgomery we know that it does not hold for almost all fundamental discriminants. Our present numerical computation shows that surprisingly it holds true for at least 65% of the real, even and primitive Dirichlet characters of conductors less than 10⁶. We also show that a generalized Chowla hypothesis holds true for at least 72% of the real, even and primitive Dirichlet characters of conductors less than 10⁶. Since checking this generalized Chowla's hypothesis is easy to program and relies only on exact computation with rational integers, we do think that it should be part of any numerical computation verifying that L(s, χ) > 0 for s > 0 for real Dirichlet characters χ. To date, this verification for real, even and primitive Dirichlet characters has been done only for conductors less than 2·10⁵.

• Korean Journal of Food Science and Technology
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• v.23 no.5
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• pp.561-567
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• 1991

This study was designed to investigate the productivity of L-methionine by the method of protoplast fusion between Brevibacterium flavum ATCC 14067 and Corynebacterium glutamicm ATCC 13032, and then L-methionine production was performed to continuous fermentation using the immobilized fusant cells. Mutants B. flavum K 104($thr\;met\;Km^{r}\;Et^{r}\;Sm^{r}\;Tm^{r}\;as\;genetic\;marker$) and C. glutamicum B 70($thr\;Hos\;Km^{r}\;Et^{r}\;Sm^{r}\;Tm^{r}as\;genetic\;marker$) were isolated by MNNG treatment. On the other hand, protoplast of mutants were formed to treat with lysis solution containing $500{\mu}g/ml$ of lysozyme. The ratios of protoplast formation and regeneration were 99% and $64{\sim}66%$ respectively. Fusion frequency between B. flavum K 104 and C. glutamicum B 70 showed the $3.5{\times}10^{5}$ in the 35% polyethylene glycol(PEG6000) containing 3% PVP solution. The productivity of L-methionine by fusant BFCG 37 immobilized with sodium alginate was 0.89 g/l the batch fermentation and was $18.75mg/^{1}hr\;^{1}$ on the continuous fermentation at $30^{\circ}C$ for 72 hr.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.347-349
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• 1995

In this paper a central limit theorem on $L^P(R)$ for $1{\leq}p<{\infty}$ is obtained with an example when ${X_n}$ is a sequence of independent, identically distributed random variables on $L^P(R)$.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1285-1301
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• 2018

In this paper, we mainly consider the determinantal representations of the unique solution and the general solution to the restricted system of quaternion matrix equations $$\{{A_1X=C_1\\XB_2=C_2,}\;{{\mathcal{R}}_r(X){\subseteq}T_1,\;{\mathcal{N}}_r(X){\supseteq}S_1$$, respectively. As an application, we show the determinantal representations of the general solution to the restricted quaternion matrix equation $$AX+Y B=E,\;{\mathcal{R}}_r(X){\subseteq}T_1,\;{\mathcal{N}}_(X){\supseteq}S_1,\;{\mathcal{R}}_l(Y){\subseteq}T_2,\;{\mathcal{N}}_l (Y){\supseteq}S_2$$. The findings of this paper extend some known results in the literature.

• Journal of Astronomy and Space Sciences
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• v.9 no.1
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• pp.11-29
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• 1992

In 1963, Toomre built up classes of mass models for the highly flattened galaxies which have free parameters n, $a_n$ and $C_n$. In order to keep the universal dimension, we adopt parameters $b_n({C_n}^2={a_n}^{2n}+^2{b_n}^2/(n-1)!)$ insteal of $C_n$. Series of the normalized Toomre's mass models (G = $V_{max}$ =$R_{max}$ = 1, n = 1 to 7) are derived and the normalized parameters $a_n$ and $b_n$ are determined by the iteration method. Replacing parameters $a_n$ and $b_n$ to ${a_n}^l(=a_nr_{max})$ and ${b_n}^l(=b_n\cdotV_{max}/r_{max})$, we can get the generalization of Toomre's mass model.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2000.07a
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• pp.726-729
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• 2000

Though L $a_{1+x}$S $r_{2-x}$M $n_2$ $O_{7}$ n=2 R-P phases have been well known to have CMR effect, it was generally believed that n=1 phase was insulating. But recently monolayered perovskite $Ca_{2-x}$L $n_{x}$Mn $O_4$phase has been reported to show magnetoresistance. In this study, layered perovskite $Ca_{2-x}$L $n_{x}$Mn $O_4$ (x=0, 0.5, Ln=Pr, Nd, Sm, Gd) phases were synthesized by solid state reaction and their structures were refined by Rietveld method. The space groups of $Ca_2$Mn $O_4$, N $d_{0.5}$C $a_{1.5}$Mn $O_4$phases were refined as C2cb and Fmmm, respectively.y.ely.y.y.y.y.y.y.

• Korea-Australia Rheology Journal
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• v.16 no.2
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• pp.91-99
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• 2004

For the Rouse chain composed of infinite number of beads (continuous limit), conformational changes during the creep and creep recovery processes was recently analyzed to reveal the interplay among all Rouse eigenmodes under the constant stress condition (Watanabe and Inoue, Rheol. Acta, 2004). For completeness of the analysis of the Rouse model, this paper analyzes the conformational changes of the discrete Rouse chain having a finite number of beads (N = 3 and 4). The analysis demonstrates that the chain of finite N exhibits the affine deformation on imposition/removal of the stress and this deformation gives the instantaneous component of the recoverable compliance, $J_{R}$(0) = 1/(N-l)v $k_{B}$T with v and $k_{B}$ being the chain number density and Boltzmann constant, respectively. (This component vanishes for N\longrightarrow$\infty$.) For N = 2, it is known that the chain has only one internal eigenmode so that the affinely deformed conformation at the onset of the creep process does not change with time t and $J_{R}$(t) coincides with $J_{R}$(0) at any t (no transient increase of $J_{R}$(t)). However, for N$\geq$3, the chain has N-l eigenmodes (N-l$\geq$2), and this coincidence vanishes. For this case, the chain conformation changes with t to the non-affine conformation under steady flow, and this change is governed by the interplay of the Rouse eigenmodes (under the constant stress condition). This conformational change gives the non-instantaneous increase of $J_{R}$(t) with t, as also noted in the continuous limit (N\longrightarrow$\infty$).X>).TEX>).X>).

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.242-246
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• 2010

It is well-known that the space $E^n$ of fuzzy numbers(i.e., normal, upper-semicontinuous, compact-supported and convex fuzzy subsets)in the n-dimensional Euclidean space $R^n$ is separable but not complete with respect to the $L_p$-metric. In this paper, we introduce the space $F_p(R^n)$ that is separable and complete with respect to the $L_p$-metric. This will be accomplished by assuming p-th mean bounded condition instead of compact-supported condition and by removing convex condition.

• Journal of The Korean Society of Grassland and Forage Science
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• v.20 no.4
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• pp.285-294
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• 2000

To investigate the effect of Mycorrhiza (Glomus intradics) and Rhizobium inoculation on the N, P utilization and growth response of Alfalfa (Medicago saliva L.) and Perennial ryegrass (Lolium perenne L.) in mixed sward, four treatments (non-inoculation, Control; Mycorrhiza inoculation: M; Rhizobium inoculation, R and Mycorrhiza and Rhizobium inoculation, M+R) were applied. The associated analyses were canied out on the early vegetative growth stage (DAS 56, 56 days after seeding) and on the early flowering stage (DAS 126). The decreased rate of total N and P content in soil, with advancing plant growth, was relatively higher in the M and M + R treatment than control. The content of availabie phosphorus in soil at DAS 126 increased by about 34 and 38 % in M and M+R treatment compared to control (189.2 mg PzOskg DM), while non-significant changes was observed in R treatment. Total N uptake and P uptake in the control at DAS 126 were 44.71 and 3.52 mglplant in mixed sward, respectively. About 71, 98 and 197 % of increases in total N uptake and 70, 72 and 11 1 % of increases in total P uptake were estimated in M, R and M+R treatment. Comparing to control, total dry matter yield significantly increased by 27, 33 and 53 %, and crude protein yield also by 78, 83 and 204 %, respectively, in M, R and M+R treatment. The present data indicated that mycorrhiza orland rhizobium inoculation improved N, P utilization of both alfalfa and perennial ryegrass plants, and consequently increased total yield (especially by dual inoculation, M+R). (Key words : Alfalfa, Perennial ryegrass, Mycorrhiza, Rhizobium, N and P Utilization, Growth, Yield)

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.125-131
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• 1999

We obtain some sufficient conditions for oscillation of the neutral difference equation with positive and negative coefficients $${\Delta}(x_n-cx_{n-m})+px_{n-k}-qx_{n-l}=0$$, where ${\Delta}$ denotes the forward difference operator, m, k, l, are nonnegative integers, and $c{\in}[0,1),p,q{\in}\mathbb{R}^+$.