• Title/Summary/Keyword: gamma and beta functions

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PRODUCT AND CONVOLUTION OF CERTAIN UNIVALENT FUNCTIONS

  • Jain, Naveen Kumar;Ravichandran, V.
    • Honam Mathematical Journal
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    • v.38 no.4
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    • pp.701-724
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    • 2016
  • For $f_i$ belonging to various subclasses of univalent functions, we investigate the product given by $h(z)=z{\prod_{i=1}^{n}}(f_i(z)/z)^{{\gamma}_i}$.The largest radius ${\rho}$ is determined such that $h({\rho}z)/{\rho}$ is starlike of order ${\beta}$, $0{\leq}{\beta}$ < 1 or to belong to other subclasses of univalent functions. We also determine the sharp radius of starlikeness of order ${\beta}$and other radius for the convolution f*g of two starlike functions f, g.

GENERATING FUNCTIONS FOR THE EXTENDED WRIGHT TYPE HYPERGEOMETRIC FUNCTION

  • Jana, Ranjan Kumar;Maheshwari, Bhumika;Shukla, Ajay Kumar
    • Communications of the Korean Mathematical Society
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    • v.32 no.1
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    • pp.75-84
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    • 2017
  • In recent years, several interesting families of generating functions for various classes of hypergeometric functions were investigated systematically. In the present paper, we introduce a new family of extended Wright type hypergeometric function and obtain several classes of generating relations for this extended Wright type hypergeometric function.

EFFECTS OF SEVERAL CYTOKINES ON THE FUNCTIONS OF FETAL RAT OSTEOBLAST-LIKE CELLS IN VITRO

  • Han, Hee-Sung;Kim, Jung-Keun;Chang, Young-IL
    • The korean journal of orthodontics
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    • v.25 no.6 s.53
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    • pp.689-696
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    • 1995
  • Effects of several cytokines($IL-1{\beta},\;TNF_{\alpha},\;and\;IFN_{\gamma}$) have been examined on fetal rat osteoblast-like cells. To investigate whether cytokines play direct causal roles in production of lysosomal enzyme, fetal rat osteoblast-like cells were treated with $IL-1{\beta},\;TNF_{\alpha},\;and\;IFN_{\gamma}$, respectively or combined. And acid phosphatase was determined by biochemical method. Alkaline phosphatase was assayed to determine the effects of $IL-1{\beta},\;TNF_{\alpha},\;and\;IFN_{\gamma}$ on the expression of this enzyme. And also experiment of calcified nodule formation was performed to assess the effects of cytokines on the bone-forming activity of osteoblast-like cells in vitro. Acid phosphatase activity was significantly increased by the addition of $IL-1{\beta}\;and\;TNF_{\alpha}$, whereas decreased by $IFN_{\gamma}$. However, no significant change:: in alkaline phosphatase activity was observed when the osteoblast-like cells were treated with $IL-1{\beta}\;and\;TNF_{\alpha}$. Interestingly, $IFN_{\gamma}$ showed stimulatory effect on alkaline phosphatase activity. The number of calcified nodules was decreased by treatment of cultures with 1 ng/ml $IL-1{\beta},\;20\;ng/ml\;TNF_{\alpha}$, and 500 u/ml $IFN_{\gamma}$ continuously for 21 days, while considerable number of calcified nodules were formed in control group of osteoblast-like cell in culture for 21 days. These results seem to suggest that cytokines may play crucial roles in bone remodeling through the direct action on the osteoblast-like cell.

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UPPER BOUND OF SECOND HANKEL DETERMINANT FOR A SUBCLASS OF BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER

  • Mustafa, Nizami
    • Communications of the Korean Mathematical Society
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    • v.34 no.3
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    • pp.783-797
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    • 2019
  • In this paper, we introduce and investigate a subclass ${\Im}_{\Sigma}({\alpha},{\beta},{\gamma})$ of analytic and bi-univalent functions of complex order in the open unit disk U in complex plane. Here, we obtain an upper bound for the second Hankel determinant of the functions belonging to this class. Moreover, several interesting conclusions of the results obtained here are also discussed.

AN APPLICATION OF FRACTIONAL DERIVATIVE OPERATOR TO A NEW CLASS OF ANALYTIC AND MULTIVALENT FUNCTIONS

  • Lee, S.K.;Joshi, S.B.
    • Korean Journal of Mathematics
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    • v.6 no.2
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    • pp.183-194
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    • 1998
  • Making use of a certain operator of fractional derivative, a new subclass $L_p({\alpha},{\beta},{\gamma},{\lambda})$) of analytic and p-valent functions is introduced in the present paper. Apart from various coefficient bounds, many interesting and useful properties of this class of functions are given, some of these properties involve, for example, linear combinations and modified Hadamard product of several functions belonging to the class introduced here.

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ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF GENERAL SUBCLASSES OF BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER INVOLVING SUBORDINATION

  • Altinkaya, Sahsene;Yalcin, Sibel
    • Honam Mathematical Journal
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    • v.40 no.3
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    • pp.391-400
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    • 2018
  • The object of this paper to construct a new class $$A^m_{{\mu},{\lambda},{\delta}}({\alpha},{\beta},{\gamma},t,{\Psi})$$ of bi-univalent functions of complex order defined in the open unit disc. The second and the third coefficients of the Taylor-Maclaurin series for functions in the new subclass are determined. Several special consequences of the results are also indicated.

Molecular cloning and characterization of novel human JNK2 (MAPK9) transcript variants that show different stimulation activities on AP-1

  • Wang, Pingzhang;Xiong, Ying;Ma, Chuan;Shi, Taiping;Ma, Dalong
    • BMB Reports
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    • v.43 no.11
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    • pp.738-743
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    • 2010
  • The c-Jun $NH_2$-terminal kinase (JNK) signaling pathway participates in many physiological functions. In the current study we reported the cloning and characterization of five novel JNK2 transcript variants, which were designated as $JNK2\alpha3$, $JNK2\alpha4$, $JNK2\beta3$, $JNK2\gamma1$ and $JNK2\gamma2$, respectively. Among them, $JNK2\alpha4$ and $JNK2\gamma2$ are potential non-coding RNA because they contain pre-mature stop codons. Both $JNK2\alpha3$ and $JNK2\beta3$ contain an intact kinase domain, and both encode a protein product of 46 kDa, the same as those of $JNK2\alpha1$ and $JNK2\beta1$. $JNK2\gamma1$ contains a disrupted kinase domain and it showed a disable function. When over-expressed in mammalian cells, $JNK2\alpha3$ showed higher activity on AP-1 than that of $JNK2\beta3$ and $JNK2\gamma1$. Furthermore, $JNK2\alpha3$ and $JNK2\beta3$ showed different levels of substrate phosphorylation, although they both could promote the proliferation of 293T cells. Our results further demonstrate that JNK2 isoforms preferentially target different substrates and may regulate the expression of various target genes.

Dynamic response of functionally gradient austenitic-ferritic steel composite panels under thermo-mechanical loadings

  • Isavand, S.;Bodaghi, M.;Shakeri, M.;Mohandesi, J. Aghazadeh
    • Steel and Composite Structures
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    • v.18 no.1
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    • pp.1-28
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    • 2015
  • In this paper, the dynamic response of functionally gradient steel (FGS) composite cylindrical panels in steady-state thermal environments subjected to impulsive loads is investigated for the first time. FGSs composed of graded ferritic and austenitic regions together with bainite and martensite intermediate layers are analyzed. Thermo-mechanical material properties of FGS composites are predicted according to the microhardness profile of FGS composites and approximated with appropriate functions. Based on the three-dimensional theory of thermo-elasticity, the governing equations of motionare derived in spatial and time domains. These equations are solved using the hybrid Fourier series expansion-Galerkin finite element method-Newmark approach for simply supported boundary conditions. The present solution is then applied to the thermo-elastic dynamic analysis of cylindrical panels with three different arrangements of material compositions of FGSs including ${\alpha}{\beta}{\gamma}M{\gamma}$, ${\alpha}{\beta}{\gamma}{\beta}{\alpha}$ and ${\gamma}{\beta}{\alpha}{\beta}{\gamma}$ composites. Benchmark results on the displacement and stress time-histories of FGS cylindrical panels in thermal environments under various pulse loads are presented and discussed in detail. Due to the absence of similar results in the specialized literature, this paper is likely to fill a gap in the state of the art of this problem, and provide pertinent results that are instrumental in the design of FGS structures under time-dependent mechanical loadings.

SOME INTEGRAL TRANSFORMS AND FRACTIONAL INTEGRAL FORMULAS FOR THE EXTENDED HYPERGEOMETRIC FUNCTIONS

  • Agarwal, Praveen;Choi, Junesang;Kachhia, Krunal B.;Prajapati, Jyotindra C.;Zhou, Hui
    • Communications of the Korean Mathematical Society
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    • v.31 no.3
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    • pp.591-601
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    • 2016
  • Integral transforms and fractional integral formulas involving well-known special functions are interesting in themselves and play important roles in their diverse applications. A large number of integral transforms and fractional integral formulas have been established by many authors. In this paper, we aim at establishing some (presumably) new integral transforms and fractional integral formulas for the generalized hypergeometric type function which has recently been introduced by Luo et al. [9]. Some interesting special cases of our main results are also considered.

AMPK γ is Required for Maintaining Epithelial Cell Structure and Polarity (AMPK γ 유전자의 표피세포극성 유지기능 규명)

  • Koh, Hyong-Jong
    • Journal of Life Science
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    • v.21 no.5
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    • pp.621-626
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    • 2011
  • AMP-activated protein kinase (AMPK), a heterotrimeric complex comprising a catalytic ${\alpha}$ subunit and regulatory ${\beta}$ and ${\gamma}$ subunits, has been primarily studied as a major metabolic regulator in various organisms, but recent genetic studies discover its novel physiological functions. The first animal model with no functional AMPK ${\gamma}$ subunit gene was generated by using Drosophila genetics. AMPK ${\gamma}$ flies demonstrated lethality with severe defects in cuticle formation. Further histological analysis found that deletion of AMPK ${\gamma}$ causes severe defects in cell polarity in embryo epithelia. The phosphorylation of nonmuscle myosin regulatory light chain (MRLC), a critical regulator of epithelial cell polarity, was also diminished in AMPK ${\gamma}$ embryo epithelia. These defects in AMPK ${\gamma}$ mutant epithelia were successfully restored by over-expression of AMPK ${\gamma}$. Collectively, these results suggested that AMPK ${\gamma}$ is a critical cell polarity regulator in metazoan development.