• 제목/요약/키워드: Gamma function

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Integral operators that preserve the subordination

  • Bulboaca, Teodor
    • 대한수학회보
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    • 제34권4호
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    • pp.627-636
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    • 1997
  • Let $H(U)$ be the space of all analytic functions in the unit disk $U$ and let $K \subset H(U)$. For the operator $A_{\beta,\gamma} : K \longrightarrow H(U)$ defined by $$ A_{\beta,\gamma}(f)(z) = [\frac{z^\gamma}{\beta + \gamma} \int_{0}^{z} f^\beta (t)t^{\gamma-1} dt]^{1/\beta} $$ and $\beta,\gamma \in C$, we determined conditions on g(z), $\beta and \gamma$ such that $$ z[\frac{z}{f(z)]^\beta \prec z[\frac{z}{g(z)]^\beta implies z[\frac{z}{A_{\beta,\gamma}(f)(z)]^\beta \prec z[\frac{z}{A_{\beta,\gamma}(g)(z)]^\beta $$ and we presented some particular cases of our main result.

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THE ARCHES CLUSTER MASS FUNCTION

  • Kim, Sung-Soo S.;Figer, Donald F.;Kudritzki, Rolf P.;Naharro, F.
    • 천문학회지
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    • 제40권4호
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    • pp.153-155
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    • 2007
  • We have analyzed H and $K_s$-band images of the Arches cluster obtained using the NIRC2 instrument on Keck with the laser guide star adaptive optics (LGS AO) system. With the help of the LGS AO system, we were able to obtain the deepest ever photometry for this cluster and its neighborhood, and derive the background-subtracted present-day mass function (PDMF) down to $1.3M_{\bigodot}$ for the 5"-9" annulus of the cluster. We find that the previously reported turnover at $6M_{\bigodot}$ is simply due to a local bump in the mass function (MF), and that the MF continues to increase down to our 50 % completeness limit ($1.3M_{\bigodot}$) with a power-law exponent of ${\Gamma}$ = -0.91 for the mass range of 1.3 < M/$M_{\bigodot}$ < 50. Our numerical calculations for the evolution of the Arches cluster show that the ${\Gamma}$ values for our annulus increase by 0.1-0.2 during the lifetime of the cluster, and thus suggest that the Arches cluster initially had ${\Gamma}$ of $-1.0{\sim}-1.1$, which is only slightly shallower than the Salpeter value.

Ti-(44-54)at.%Al 열처리 주조합금의 미세조직과 인장특성에 관한 연구 (A Study on the Microstructures and Tensile Properties of Heat-Treated Cast Ti-(44-54)at.%Al Alloys)

  • 정재영
    • 한국주조공학회지
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    • 제37권6호
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    • pp.199-206
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    • 2017
  • In this study, the variations of microstructures and tensile properties of Ti-(44-54)at.%Al binary alloys were investigated. The heat-treated microstructure depended greatly on their solidification structure and annealing temperature. We measured the variations of volume fractions of primary and secondary lamellar structure as a function of the heat treatment temperature in a Ti-47at.%Al alloy. The variation of ductility as a function of Al content was in good agreement with the change of fracture mode in the tensile fracture surface. It can be inferred that the variations of yield stress and hardness of ${\gamma}$ phase in a single ${\gamma}$-phase field region are enhanced by anti-site defects created by deviations from the stoichiometric composition. In a Ti-47at.%Al alloy within the (${\alpha}_2+{\gamma}$) two-phase field, the yield stress tended to be the maximum at a near equal volume fraction of lamellar and ${\gamma}$ grains. The ductility depended sensitively on the overall grain size and Al content. The calculation of fracture strain using Chan's model indicated that the change of ductility as a function of annealing temperature was primarily determined by the variations in the overall grain size and lamellar volume fraction.

Ion-induced secondary electron emission coefficient and work function for MgO thin film with $O_2$ plasma treatment

  • Jung, J.C.;Jeong, H.S.;Lee, J.H.;Oh, J.S.;Park, W.B.;Lim, J.Y.;Cho, J.W.;Choi, E.H.
    • 한국정보디스플레이학회:학술대회논문집
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    • 한국정보디스플레이학회 2004년도 Asia Display / IMID 04
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    • pp.525-528
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    • 2004
  • The ion-induced secondary electron emission coefficient ${\gamma}$ and work function for MgO thin film with $O_2$ plasma treatment has been investigated by ${\gamma}$ -FIB (focused ion beam) system. The MgO thin film deposited from sintered material with $O_2$ plasma treatment is found to have higher ${\gamma}$ and lower work function than those without $O_2$ plasma treatment. The energy of various ions used has been ranged from 100eV to 200eV throughout this experiment. It is found that the highest secondary electron emission coefficient ${\gamma}$ has been achieved for 10 minutes of $O_2$ plasma treatment under RF power of 50W.

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항해단(沆瀣丹)이 아토피 피부염 환자 단핵세포의 Cytokine 분비능에 미치는 영향 (Effects of Hanghaedan on the Cytokine Secretory Function of Monocytes of Atopic Dermatitis Patients)

  • 이진용;김우연
    • 대한한방소아과학회지
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    • 제21권2호
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    • pp.169-184
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    • 2007
  • Objetives The late research tendency on atopic dermatitis is mainly focused on the experiment of unbalance of cytokine released from T cell subtype. Merhods As there's no experiment with herbal medicine using Hanghaedan(HHD), we isolated and cultured monocytes of atopic dermatitis pateints (AD) peripheral blood, for knowing the influence of HHD on the secretory function of IL-4, IL-5, $IFN-{\gamma}$. Results 1. In AD group, HHD exhibits statistically significant inhibitory effect on IL-4(p<0.05). 2. In AD group, HHD exhibits statistically significant inhibitory effect on IL-5(p<0.05). 3. In AD group, HHD exhibits statistically significant inhibitory effect on $IFN-{\gamma}$ (p<0.01). 4. Sample group comparing with the cytokine concentration rate value of AD patients and that of NAD patients IL-4 of AD patients exhibits statistically significant decrease(p<0.05). 5. In AD group, there is no significant relation between serum IgE and cytokines. 6. In AD group, there is no significant relation between total eosinophil and IL-5. Conclusions Effects of Hanghaedan on the cytokine(IL-4, IL-5, $IFN-{\gamma}$) secretory function of monocytes of atopic dermatitis patients is recognized.

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Computer-Aided Alloy Design of Insert Metal for Transient Liquid Phase Bonding of High Aluminum Ni-base Superalloys

  • Nishimotd, Kazutoshi;Saida, Kazuyoshi
    • 대한용접접합학회:학술대회논문집
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    • 대한용접접합학회 2002년도 Proceedings of the International Welding/Joining Conference-Korea
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    • pp.803-808
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    • 2002
  • A computer-aided alloy-designing technique to develop the insert metal for transient liquid phase (TLP) bonding was applied to high aluminum Ni-base superalloys. The main procedure of a mathematical programming method was to obtain the optimal chemical composition through rationally compromising the plural objective performances of insert metal by a grid-search which involved data estimation from the limited experimental data using interpolation method. The objective function Z which was introduced as an index of bonding performance of insert metal involved the melting point, hardness (strength), formability of brittle phases and void ratio (bonding defects) in bond layer as the evaluating factors. The contour maps of objective function Z were also obtained applying the interpolation method. The compositions of Ni-3.0%Cr-4.0%B-0.5%Ce (for ${\gamma}$/${\gamma}$/${\beta}$ type alloy) and Ni3.5%Cr-3.5%B-3%Ti (for ${\gamma}$/${\gamma}$ type alloy) which optimized the objective function were determined as insert metal. SEM observations revealed that the microstructure in bond layers using the newly developed insert metals indicated quite sound morphologies without forming microconstituents and voids. The creep rupture properties of both joints were much improved compared to a commercial insert metal of MBF-80 (Ni-15.5%Cr-3.7%B), and were fairly comparable to those of base metals.

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ON A NEW CLASS OF DOUBLE INTEGRALS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTION 3F2

  • Kim, Insuk
    • 호남수학학술지
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    • 제40권4호
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    • pp.809-816
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    • 2018
  • The aim of this research paper is to evaluate fifty double integrals invoving generalized hypergeometric function (25 each) in the form of $${{\int}^1_0}{{\int}^1_0}\;x^{{\gamma}-1}y^{{\gamma}+c-1}(1-x)^{c-1}(1-y)^{c+{\ell}}(1-xy)^{{\delta}-2c-{\ell}-1}{\times}_3F_2\[{^{a,\;b,\;2c+{\ell}+1}_{\frac{1}{2}(a+b+i+1),\;2c+j}}\;;{\frac{(1-x)y}{1-xy}}\]dxdy$$ and $${{\int}^1_0}{{\int}^1_0}\;x^{{\gamma}-1}y^{{\gamma}+c+{\ell}}(1-x)^{c+{\ell}}(1-y)^{c-1}(1-xy)^{{\delta}-2c-{\ell}-1}{\times}_3F_2\[{^{a,\;b,\;2c+{\ell}+1}_{\frac{1}{2}(a+b+i+1),\;2c+j}}\;;{\frac{1-y}{1-xy}}\]dxdy$$ in the most general form for any ${\ell}{\in}{\mathbb{Z}}$ and i, j = 0, ${\pm}1$, ${\pm}2$. The results are derived with the help of generalization of Edwards's well known double integral due to Kim, et al. and generalized classical Watson's summation theorem obtained earlier by Lavoie, et al. More than one hundred ineteresting special cases have also been obtained.

MONOTONICITY PROPERTIES OF THE GENERALIZED STRUVE FUNCTIONS

  • Ali, Rosihan M.;Mondal, Saiful R.;Nisar, Kottakkaran S.
    • 대한수학회지
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    • 제54권2호
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    • pp.575-598
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    • 2017
  • This paper introduces and studies a generalization of the classical Struve function of order p given by $$_aS_{p,c}(x):=\sum\limits_{k=0}^{\infty}\frac{(-c)^k}{{\Gamma}(ak+p+\frac{3}{2}){\Gamma}(k+\frac{3}{2})}(\frac{x}{2})^{2k+p+1}$$. Representation formulae are derived for $_aS_{p,c}$. Further the function $_aS_{p,c}$ is shown to be a solution of an (a + 1)-order differential equation. Monotonicity and log-convexity properties for the generalized Struve function $_aS_{p,c}$ are investigated, particulary for the case c = -1. As a consequence, $Tur{\acute{a}}n$-type inequalities are established. For a = 2 and c = -1, dominant and subordinant functions are obtained for the Struve function $_2S_{p,-1}$.

PPARγ Physiology and Pathology in Gastrointestinal Epithelial Cells

  • Thompson, E. Aubrey
    • Molecules and Cells
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    • 제24권2호
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    • pp.167-176
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    • 2007
  • Peroxisome proliferator-activated receptor-gamma ($PPAR{\gamma}$) is expressed at very high levels in the gastrointestinal epithelium. Many of the functions of $PPAR{\gamma}$ in gastrointestinal epithelial cells have been elucidated in recent years, and a pattern is emerging which suggests that this receptor plays an important role in gastrointestinal physiology. There is also strong evidence that $PPAR{\gamma}$ is a colon cancer suppressor in pre-clinical rodent models of sporadic colon cancer, and there is considerable interest in exploitation of $PPAR{\gamma}$ agonists as prophylactic or chemopreventive agents in colon cancer. Studies in mice and in human colon cancer cell lines suggest several mechanisms that might account for the tumor suppressive effects of $PPAR{\gamma}$ agonists, although it is not in all cases clear whether these effects are altogether mediated by $PPAR{\gamma}$. Conversely, several reports suggest that $PPAR{\gamma}$ agonists may promote colon cancer under certain circumstances. This possibility warrants considerable attention since several million individuals with type II diabetes are currently taking $PPAR{\gamma}$ agonists. This review will focus on recent data related to four critical questions: what is the physiological function of $PPAR{\gamma}$ in gastrointestinal epithelial cells; how does $PPAR{\gamma}$ suppress colon carcinogenesis; is $PPAR{\gamma}$ a tumor promoter; and what is the future of $PPAR{\gamma}$ in colon cancer prevention?

CERTAIN CLASSES OF UNIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS

  • Lee, Sang-Keun
    • East Asian mathematical journal
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    • 제5권2호
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    • pp.135-150
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    • 1989
  • In this paper, we define new classes $S*({\alpha},{\beta},{\gamma})$ and $C*({\alpha},{\beta},{\gamma})$ of T, the class of analytic and univalent functions with negative coefficients. We have sharp results concerning coefficients, distortion of functions belonging to these classes along with a. representation formular for the function in $S*({\alpha},{\beta},{\gamma})$ and $C*({\alpha},{\beta},{\gamma})$. Furthermore, we improve the results of Libera for the class of starlike functions having negative coefficients.

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