• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.47-52
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• 1996

We consider the third order linear homogeneous differential equation L$_3$(y) = y(equation omitted) ＋ P($\chi$)y' ＋ Q($\chi$)y = 0 (E) P($\chi$) $\geq$ 0, Q($\chi$) ＞ 0 and P($\chi$)/Q($\chi$) is nondecreasing on [${\alpha}$, $\infty$) for some real number ${\alpha}$. (1) In this paper we discuss the distribution of zeros of solutions and a condition of oscillatory for equation (E).(omitted)

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.143-154
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• 2003

A finite group G is called (l, m, n)-generated, if it is a quotient group of the triangle group T(l, m, n) = 〈$\chi$, y, z│$\chi$$\^$l/ = y$\^$m/ = z$^n$ = $\chi$yz = 1〉. In [19], the question of finding all triples (l, m, n) such that non-abelian finite simple group are (l, m, n)-generated was posed. In this paper we partially answer this question for the sporadic group Ru. In fact, we prove that if p, q and r are prime divisors of │Ru│, where p < q < r and$.$(p, q) $\neq$ (2, 3), then Ru is (p, q, r)-generated.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2095-2105
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• 2015

Given c, a positive integer, we set. $$M(f,c):=\frac{2}{{\phi}(f)}\sum_{{\chi}{\in}X^-_f}{\chi}(c)|L(1,{\chi})|^2$$, where $X^-_f$ is the set of the $\phi$(f)/2 odd Dirichlet characters mod f > 2, with gcd(f, c) = 1. We point out several mistakes in recently published papers and we give explicit closed formulas for the f's such that their prime divisors are all equal to ${\pm}1$ modulo c. As a Corollary, we obtain closed formulas for M(f, c) for c $\in$ {1, 2, 3, 4, 5, 6, 8, 10}. We also discuss the case of twisted quadratic moments for primitive characters.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.413-424
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• 2023

The main purpose of this paper is to show that over a large class of bounded domains Ω ⊂ ℂ², for 1 < p < ∞, the Bergman projection 𝓟 is bounded from L^p(Ω, dV ) to the Bergman space A^p(Ω); from L^∞(Ω) to the holomorphic Bloch space BlHol(Ω); and from L¹(Ω, P(z, z)dV) to the holomorphic Besov space Besov(Ω), where P(ζ, z) is the Bergman kernel for Ω.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.483-492
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• 2004

Let : [0, 1] $\times$ [0, $\infty$) $\longrightarrow$ [0, $\infty$) be continuous and a ${\in}$ C([0, 1], [0, $\infty$)),and let ${\xi}_{i}$ $\in$ (0, 1) with 0 < {\xi}$_1$ < ${\xi}_2$ < … < ${\xi}_{m-2}$ < 1, $a_{i}$, $b_{i}$ ${\in}$ [0, $\infty$) with 0 < $\Sigma_{i=1}$ /$^{m-2}$ $a_{i}$ < 1 and $\Sigma_{i=1}$$^{m-2}$ < l. This paper is concerned with the following m-point boundary value problem: $\chi$″(t)＋a(t) (t.$\chi$(t))＝0,t ${\in}$(0,1), $\chi$'(0)＝$\Sigma_{i=1}$ $^{m-2}$ /$b_{i}$$\chi$'(${\xi}_{i}$),$\chi$(1)＝$\Sigma_{i=1}$$^{m-2}$$a_{i}$$\chi$(${\xi}_{i}$). The existence, multiplicity and uniqueness of positive solutions of this problem are discussed with the help of two fixed point theorems in cones, respectively.

• Bulletin of the Korean Chemical Society
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• v.21 no.10
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• pp.951-952
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• 2000

Acylation of an intermediate tetrahydroxoplatinum(IV) complex, $[Pt(OH)_4(dach)]$ (dach = $trans-(\pm)-12-di-aminocyclohexane)$, with one or two kinds of carboxylic anhydrides in stepwise manner afforded various car-boxylatoplatinum(IV) complexes, $[Pt(O_2CR)\chi(OR’)4-\chi(dach)]$ (R = $(CH_2)_3CH_3$ or $C(CH_3)_3$, R’ = H or $OCCH_3$, and $\chi$ = 1-4) with a wide range of lipophilicity. The title complexes were subjected to bioassay using the murine leukemia L1210 cell line, and in particular, their in vivo oral antitumor activity was attempted to correlate with their lipophilicity and water solubility. The most orally active complex exhibited intermediate lipophilicity and water solubility, but it has been found that an exact relationship between the lipophilicity and oral anticancer activity could not be established, since the lipophilicity of the complexes is not the sole parameter to determine the oral activity. One of the important intermediate complexes partially substituted was subjected to X-ray anal-ysis for positit of the substituted group: $[Pt(OPiv)_3(OH)(dach)]$ crystallizes in the tetragonal sys-tem, space group $P42_1c$ with a = 21.161(3) $\AA$, b = 21.161(6) $\AA$, c = 12.816(3) $\AA$, $\alpha=\beta=$ r $=90^{\circ}$, V = 5739(2) $\AA^3$ and Z = 8.

• Magazine of the Korean Society of Agricultural Engineers
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• v.43 no.3
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• pp.85-93
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• 2001

In this study, a computer program considering shape imperfections of arch under dynamic loading was developed. The shape imperfection of arch was assumed as higher degree polynomial expressed as $\omega$$_{i}$ = $\omega$$_{o}$ (1-(2$\chi$/L)$^{m}$ )$^n$and sinusoidal curve such as $\omega$$_{i}$ = $\omega$$_{o}$ sin(η$\pi$$\chi$/L). In finite element formulation, the material nonlinear behavior was assumed the elasto-viscoplastic model highly corresponding to the real behavior of the material and the geometrically nonlinear behavior was modeled using Lagrangian description of motion. Also, the behavior of steel was modeled by applying yield criteria of Von Mises. The developed program was applied to the analysis of the dynamic behavior for the clamped beam subjected to the concentrated load at midspan and the results were compared with those from other research to investigate accuracy of the presented finite element program. In numerical examples, the shape imperfections of L/500, L/1,000 and L/2,000 were considered and the modes of shape imperfections of the symmetric and antisymmetric were adopted. The effects of the shape imperfections on the dynamic behavior of arch were conspicuous and results of analysis indicate that the reasonable values of arch rise to arch span ratio ranged between 0.1 and 0.3.

• Journal of Microbiology and Biotechnology
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• v.29 no.5
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• pp.721-730
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• 2019

The probiotic Lactobacillus acidophilus KBL409 was encapsulated with alginate (Al) and alginate-chitosan (Al/Chi) through extrusion method. The sizes and zeta potentials of microspheres were measured to confirm encapsulation. To evaluate the protective effect of microspheres against gastrointestinal fluids, all the samples were exposed to simulated gastric fluids (SGFs, pH 1.5) at $37^{\circ}C$ for 1 or 2 h, followed by incubation with simulated intestinal fluids (SIFs, pH 6.5) for 2 h. The mucoadhesive ability of microspheres was evaluated using the intestinal epithelial cell line HT29-MTX. To extend the shelf-life of probiotics, lyoprotectants such as disaccharide and polysaccharide were mixed with free or encapsulated cells during the freeze-drying process. The size of the microspheres demonstrated a narrow distribution, while the zeta potentials of Al and Al/Chi-microspheres were $-17.9{\pm}2.3$ and $20.4{\pm}2.6mV$, respectively. Among all the samples, Al/Chi-encapsulated cells showed the highest survival rate even after exposure to SGF and SIF. The mucoadhesive abilities of Al and Al/Chi-microspheres were higher than 94%, whereas the free L. acidophilus showed 88.1% mucoadhesion. Ten percent of sucrose showed over 80% survival rate in free or encapsulated cells. Therefore, L. acidophilus encapsulated with Al and Al/Chi-microspheres showed higher survival rates after exposure to the gastrointestinal tract and better mucoadhesive abilities than the free cells. Also, sucrose showed the highest protective effect of L. acidophilus during the freeze-drying process.

• Ocean and Polar Research
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• v.26 no.4
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• pp.567-579
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• 2004

To investigate the spatial distribution and community structure of heterotrophic protists, we collected water samples at 23 stations of central Barents Sea in August, 2003. This study area was divided into three area with physico-chemical and chi-a distribution characteristics: Area I of warm Atlantic water mass, Area III of cold Arctic water mass and Area II of mixed water mass. Chl-a concentration ranged from 0.18 to $1.04{\mu}g\;l^{-1}$ and was highest in Area I. The nano-sized chi-a accounted fur more than 80% of the total chi-a biomass in this study area. The contribution of nano-sized chi-a to total chi-a was higher in Area I than in Area II. Communities of heterotrophic protists were classified into three groups such as heterotrophic nanoflagellates (HNF), ciliates and heterotrophic dinoflagellates (HDF). During the study periods, carbon biomass of heterotrophic protists range from 11.3 to $38.7{\mu}gC\;l^{-1}$ (average $21.0{\mu}gC\;l^{-1}$), and were highest in Area I and were lowest in Area III. The biomass of ciliates ranged from 4.2 to $19.3{\mu}gC\;l^{-1}$ and contributed 31.5-66.9% (average 48.1%) to the biomass of heterotrophic protists. Ciliates to heterotrophic protists biomass accounted fur more than 50% in Area I. Heterotrophic dinoflagellates biomass ranged from 5.7 to $18.4{\mu}gC\;l^{-1}$ and contributed 27.1 to 56.3% (average 42.8%) of heterotrophic protists. Heterotrophic dinoflakellates to heterotrophic protists biomass accounted fur about 50% in Area III. Heterotrophic nanoflageltate biomass ranged from 0.5 to $3.4{\mu}gC\;l^{-1}$ and contributed 3.2 to 19.6% (average 9.2%) of heterotrophic protists. Heterotrophic nanoflagellates to heterotrophic protists biomass accounted fur more than 10% in Area III. These results indicate that the relative importance and structure of heterotrophic protists may vary according to water mass. Heterotrophic protists and phytoplankton biomass showed strong positive correlation in the study area The results suggest that heterotrophic protists are important consumers of phytoplankton, and protists might play a pivotal role in organic carbon cycling In the pelagic ecosystem of this study area during the study period.

• Journal of the Korean Magnetics Society
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• v.14 no.6
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• pp.219-223
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• 2004

L $i_{0.5}$F $e_{2.5-{\chi}}$R $h_{\chi}$ $O_4$ ($\chi$ = 0.25, 0.50, 0.75, 1.00) has been prepared by solid state reaction. Crystallographic and magnetic properties were investigated by Mossbauer spectroscopy, SQUID magnetometry, and x-ray diffraction. The crystal structure is found to be a cubic spinel structure with space group Fd3m for all the samples. The lattice constant $a_{0}$ increases from 8.3365 $\AA$ to 8.3932 $\AA$ with increasing Rh concentration $\chi$. The migration of Li ion has been confirmed by x-ray patterns and the results of applied field Mossbauer analysis. The temperature dependence of the absorption area of each site was analyzed with the Debye model for the recoil-free fraction. The Debye temperature for the octahedral sites is almost as large as for the tetrahedral sites, thereby suggesting similar inter-atomic binding forces for the octahedral and the tetrahedral sites. The saturated magnetic moment and the Mossbauer spectra taken at 4.2 K under the applied field (6 T) show that the spin structure of L $i_{0.5}$F $e_{2.5-{\chi}}$R $h_{\chi}$ $O_4$ is compatible with the collinear Neel Model.