• Title/Summary/Keyword: k-gamma function

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SEVERAL RESULTS ASSOCIATED WITH THE RIEMANN ZETA FUNCTION

  • Choi, Junesang
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.3
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    • pp.467-480
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    • 2009
  • In 1859, Bernhard Riemann, in his epoch-making memoir, extended the Euler zeta function $\zeta$(s) (s > 1; $s{\in}\mathbb{R}$) to the Riemann zeta function $\zeta$(s) ($\Re$(s) > 1; $s{\in}\mathbb{C}$) to investigate the pattern of the primes. Sine the time of Euler and then Riemann, the Riemann zeta function $\zeta$(s) has involved and appeared in a variety of mathematical research subjects as well as the function itself has been being broadly and deeply researched. Among those things, we choose to make a further investigation of the following subjects: Evaluation of $\zeta$(2k) ($k {\in}\mathbb{N}$); Approximate functional equations for $\zeta$(s); Series involving the Riemann zeta function.

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A GENERALIZATION OF LIOUVILLE′S THEOREM ON INTEGRATION IN FINITE TERMS

  • Utsanee, Leerawat;Vichian, Laohakosol
    • Journal of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.13-30
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    • 2002
  • A generalization of Liouville's theorem on integration in finite terms, by enlarging the class of fields to an extension called Ei-Gamma extension is established. This extension includes the $\varepsilon$L-elementary extension of Singer, Saunders and Caviness and contains the Gamma function.

MULTIPLICITY AND STABILITY OF SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS HAVING NOT NON-NEGATIVE MASS

  • Kim, Wan-Se;Ko, Bong-Soo
    • Journal of the Korean Mathematical Society
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    • v.37 no.1
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    • pp.85-109
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    • 2000
  • In this paper, the multiplicity, stability and the structure of classical solutions of semilinear elliptic equations of the form (equation omitted) will be discussed. Here $\Omega$ is a smooth and bounded domain in $R^{n}$ (n $\geq$ 1), f(x,u) = │u│$^{\alpha}$/sgn(u)-h(x), 0 < $\alpha$ < 1, (n $\geq$ 1) and h is a ${\gamma}$- Holder continuous function on $\Omega$ for some 0 < ${\gamma}$ < 1.a}$ < 1.

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Effects of Molybdenum on the Microstructure of Austempered Ductile Iron (오스템퍼드 구상흑연주철의 미세조직에 미치는 Mo의 영향)

  • Lee, Kil-Hong;Park, Yun-Woo
    • Journal of Korea Foundry Society
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    • v.14 no.1
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    • pp.35-44
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    • 1994
  • Mechanical properties of austempered ductile iron can be guaranteed if a good knowledge of its metallugical structure is obtained. In this paper, the effects of small Mo additions to austempered ductile iron on its metallurgical structures as a function of section size are examined. From the results, it is found that ${\gamma}-pool$ region and segregation of Mo in ${\gamma}-pool$ region are increased with increase in the section size.

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Inhomogeneous Poisson Intensity Estimation via Information Projections onto Wavelet Subspaces

  • Kim, Woo-Chul;Koo, Ja-Yong
    • Journal of the Korean Statistical Society
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    • v.31 no.3
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    • pp.343-357
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    • 2002
  • This paper proposes a method for producing smooth and positive estimates of the intensity function of an inhomogeneous Poisson process based on the shrinkage of wavelet coefficients of the observed counts. The information projection is used in conjunction with the level-dependent thresholds to yield smooth and positive estimates. This work is motivated by and demonstrated within the context of a problem involving gamma-ray burst data in astronomy. Simulation results are also presented in order to show the performance of the information projection estimators.

Effect of Corn Extracts on Mouse IL-2 Cytokine Production by Peritoneal Macrophage and the Ratio of IFN-${\gamma}$, IL-10 Cytokine (옥수수 추출물의 경구 투여가 사이토카인 IL-2 생성과 IFN-${\gamma}$와 IL-10 Ratio에 미치는 영향)

  • Ryu, Hye-Sook
    • The Korean Journal of Food And Nutrition
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    • v.25 no.2
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    • pp.362-367
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    • 2012
  • Corn has been used for a long time as a traditional remedy, as well as a food source. We previously reported that in vitro supplementation of corn water extracts enhanced the proliferation of splenocytes, compared to the control group. In this study, we examined the immunomodulative effect of a water extract of corn. Seven to eight weeks old mice(Balb/c) were fed an ad libitum chow diet, and were orally administrated a water extract of corn every other day, for four weeks, at two different concentrations(50 and 500 mg/kg B.W). Cytokine production(IL-2, IL-10 and IFN-${\gamma}$) by macrophages stimulated with LPS or not stimulated with LPS was detected by ELISA assay using the cytokine kit. In an ex vivo study, the cytokines IL-2, IL-10 and IFN-${\gamma}$ were detected at 500 mg/kg b.w. supplementation group with LPS stimulation in all cases. Also, the ratio of IFN-${\gamma}$ to IL-10 was in the range of 0~3 with mitogen stimulation, such as con A and LPS. In conclusion, this study suggests that in mice, corn extracts may enhance immune function by regulating the cytokine production(IL-2, IL-10 and IFN-${\gamma}$) of the activated macrophages.

Driving Forces for γ→ε Martensitic Transformation of Fe-Mn Alloys (Fe-Mn 합금의 γ→ε 마르텐사이트변태에 필요한 구동력)

  • Lee, Young-Kook;Choi, Chong-Sool
    • Journal of the Korean Society for Heat Treatment
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    • v.9 no.4
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    • pp.243-251
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    • 1996
  • Dilatometric experiment and thermodynamic calculation have been performed to determine $M_s$, $A_s$ and driving forces for ${\gamma}{\rightarrow}{\varepsilon}$ martensitic transformation of Fe-Mn alloys. The transformation temperatures($M_s$, $A_s$, $T_o) were decreased with increasing manganese content and were newly formulated as a function of manganese content. Driving force for ${\gamma}{\rightarrow}{\varepsilon}$ martensitic transformation was increased from -75J/mole to -105J/mole with increasing manganese content from 15wt.% to 25wt.%. Transformation temperature hysteresis($A_s-M_s$) was also increased from 50K to 80K with increasing mangenese content from 15wt.% to 25wt.%. The small driving force(-75J/mole~-105J/mole) and small ${\Delta}T$(50K~80K) for ${\gamma}{\rightarrow}{\varepsilon}$ martensitic transformation indicated that Fe-Mn alloys behave like thermoelastic martensitic alloys : We would like to call them semi-thermoelastic martensitic alloys.

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Retrospective Observation of Liver Function Parameters for 101 Patients Using Herbal Drugs for One Month (1개월 이상 한약을 복용한 101명의 간기능 검사에 대한 후향적 관찰)

  • Kim, Dong-Min;Kim, Hyee-Kwon;Cho, Seong-Yeun;Kim, Yong-Suk;Nam, Sang-Soo
    • The Journal of Korean Medicine
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    • v.31 no.2
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    • pp.149-157
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    • 2010
  • Objective: The purpose of this study was to investigate the level of safety on liver functions when Korean herbal medicine was taken internally. Method: 101 inpatients who took Korean herbal medicine were enrolled and liver function test (aspartic aminotransferase, alanine aminotransferase, alkaline phosphatase, total bilirubin, gamma glutamyltranspeptidase, albumin, lactate dehydrogenase) was performed on admission and 1 month later. Results: In 101 patients, alkaline phosphatase and gamma glutamyltranspeptidase decreased significantly compared with the value taken on admission (p<0.05) but aspartic aminotransferase, alanine aminotransferase, total bilirubin, albumin, and lactate dehydrogenase were not significantly changed (p>0.05). In the patients who took Scutellaria baicalensis (n=34), alkaline phosphatase decreased and albumin increased significantly (p<0.05). Among the patients who took Atractylodes macrocephala (n=29), alkaline phosphatase decreased significantly (p<0.05). In the patients who took Glycyrrhiza uralensis or Paeonia lactiflora, liver function parameters were not significantly changed (p>0.05). On admission 11 patients had abnormal liver function and 2 patients had liver injury while 7 patients had abnormal liver function and 2 patients showed liver injury 1 month later. Conclusions: This study suggests that prescribed Korean herbal medicine does not injure liver function.

Coil-to-globule transition of thermo-responsive γ-substituted poly (ɛ-caprolactone) in water: A molecular dynamics simulation study

  • Koochaki, Amin;Moghbeli, Mohammad Reza;Nikkhah, Sousa Javan
    • Current Applied Physics
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    • v.18 no.11
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    • pp.1313-1319
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    • 2018
  • The coil-to-globule behavior of poly{${\gamma}$-2-[2-(2methoxyethoxy)ethoxy]ethoxy-3-caprolactone} (PMEEECL) as a ${\gamma}$-substituted poly (${\varepsilon}$-caprolactone) was investigated via atomistic molecular dynamics (MD) simulation. For this purpose, radius of gyration, end-to-end distance and radial distribution function of the chain in the presence of water were calculated. Consequently, the lower critical solution temperature (LCST) of PMEEECL chain at which the coil-to-globule transition takes place, was determined in each calculated parameter curve. The simulation results indicated that the LCST of PMEEECL was occurred at close to 320 K, which is in a good agreement with previous experimental results. Additionally, the appearance of sudden change in both Flory-Huggins interaction parameter (${\chi}$) and interaction energy between the PMEEECL chain and water molecules at about 320 K confirmed the calculated LCST result. The radial distribution function (RDF) results showed that the affinity of the PMEEECL side chain to water molecules is lower than its backbone.

Increased B cell-activating factor (BAFF) level in the sputum of children with asthma

  • Jee, Hye-Mi;Choi, Bong-Seok;Kim, Kyung-Won;Sohn, Myung-Hyun;Han, Man-Yong;Kim, Kyu-Earn
    • Clinical and Experimental Pediatrics
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    • v.53 no.8
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    • pp.795-800
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    • 2010
  • Purpose: B cell-activating factor (BAFF) is a tumor-necrosis factor (TNF) superfamily member best known for its role in the survival and maturation of B cells. BAFF activity is observed in naive cells as well as in effector/memory T cells. We aimed to explore whether BAFF in sputum is expressed at elevated levels in asthmatic airways and associated with eosinophilic inflammation, pulmonary function, and bronchial hyperresponsiveness in children. Methods: One hundred and fifty-four asthmatic children and 98 healthy children were enrolled in the study. Sputum supernatants were collected and sputum BAFF and eosinophil cationic protein (ECP) levels were measured. We performed pulmonary function tests and methacholine challenge tests, while measuring total eosinophil count, total serum IgE, and serum ECP in all subjects. Results: Asthmatic children had significantly higher levels of BAFF in induced sputum [26.50 (10.50-100.27) pg/mL] compared to healthy children [18.32 (7.68-44.63) pg/mL; $P$=0.011]. Sputum BAFF positively correlated with sputum eosinophils (${\gamma}$=0.406, $P$<0.001) and sputum ECP (${\gamma}$=0.789, $P$<0.001). Significant negative correlations were found between sputum BAFF and FEV1 (${\gamma}$=-0.291, $P$<0.001) or post-bronchodilator FEV1 (${\gamma}$=-0.334, $P$<0.001), whereas nonsignificant correlations were found between sputum BAFF and bronchial hyperresponsiveness, serum eosinophil count, and serum ECP. Conclusion: These findings suggest that BAFF may play a role in childhood asthma, and BAFF levels in sputum could be a supportive marker that represents airway inflammation, especially eosinophilic inflammation.