• International Journal of Computer Science & Network Security
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• v.24 no.1
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• pp.85-94
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• 2024

In this paper, we present the very first time the generalized notion of (α, β, γ, δ) - convex (concave) function in mixed kind, which is the generalization of (α, β) - convex (concave) functions in 1^st and 2^nd kind, (s, r) - convex (concave) functions in mixed kind, s - convex (concave) functions in 1^st and 2^nd kind, p - convex (concave) functions, quasi convex(concave) functions and the class of convex (concave) functions. We would like to state the well-known Ostrowski inequality via SVN-Riemann Integrals for (α, β, γ, δ) - convex (concave) function in mixed kind. Moreover we establish some SVN-Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are (α, β, γ, δ)-convex (concave) functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases with respect to convexity of function.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.137-146
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• 2013

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the log-sine and log-cosine integrals have been evaluated, in the existing literature on the subject, in many different ways. The main object of this paper is to present explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta function.

• YAKHAK HOEJI
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• v.46 no.4
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• pp.258-264
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• 2002

Zinc plays an important role in immunobiological responses, while excessive zinc attenuates immune functions in a dose-dependent manner. Zinc excess has been reported to increase levels of plasma prostaglandin E$_2$ (PGE$_2$), which is known to inhibit production of Th (helper T) 1-associated cytokines and to induce inflammatory responses. Thus, this study was investigated the effects of indomethacin, a potent inhibitor of PGE$_2$ synthesis, on the proinflammatory cytokine and lymphokine production in ICR mice exposed to excessive zinc. Indomethacin at doses of 5 mg/kg was administered i.p. 30 minutes before zinc chloride (Zn) 30 mg/kg orally daily for 10 days. Excessive Zn remarkedly increased tumor necrosis factor (TNF)-$\alpha$ and interleukin (IL)-1$\beta$ levels in both serum and splenic supernatants compared with those in controls, while indomethacin significantly reduced the excessive Zn-induced levels of IL-1$\beta$. In serum, excessive Zn significantly decreased the levels of IL-2 and interferon (IFN)-${\gamma}$ compared with those in controls, whereas indomethacin significantly enhanced the excessive Zn-decreased levels of IFN-${\gamma}$ but did not affect the Zn-decreased levels of serum IL-2. In splenic supernatants, All of excessive Zn, indomethacin, and combination of Zn and indomethacin significantly enhanced IL-2 levels compared with those in controls, but indomethacin didn't affect the Zn-induced production of IL-2. These data, therefore, suggest that indomethacin significantly attenuated the in vivo and ex vivo IL-1$\beta$ production increased by excessive zinc and remarkedly enhanced the in vivo excessive zinc-suppressed production of IFN-${\gamma}$ but not IL-2.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.137-145
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• 2012

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_B$.

• Honam Mathematical Journal
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• v.34 no.4
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• pp.473-482
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• 2012

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeo-metric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_C$.

• Honam Mathematical Journal
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• v.34 no.1
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• pp.113-124
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• 2012

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_A$.

• JSTS:Journal of Semiconductor Technology and Science
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• v.10 no.4
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• pp.251-259
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• 2010

We proposed a tail function parameter extraction procedure for the establishment of a robust ion implantation database. We showed that, for the expression of ion implantation profiles, there are many local minimum values set for the third and fourth moment parameters of $\gamma$ and $\beta$ for the Pearson function that comprises the standard dual Pearson and tail functions. We proposed the use of a joined tail function as a mediate function to extract $\gamma$ and $\beta$, and demonstrated that this enables us to extract the parameters uniquely. Other parameters associated with channeling phenomena can also be simply and uniquely extracted by our procedure.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.835-850
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• 2017

A remarkably large number of special functions (such as the Gamma and Beta functions, the Gauss hypergeometric function, and so on) have been investigated by many authors. Motivated the works of both works of both Burchnall and Chaundy and Chaundy and very recently, Brychkov and Saad gave interesting generalizations of Appell type functions. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present some new differential formulas for the generalized Appell's type functions ${\kappa}_i$, $i=1,2,{\ldots},18$ by considering the product of two $_4F_3$ functions.

• Microbiology and Biotechnology Letters
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• v.37 no.2
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• pp.160-169
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• 2009

Poly-$\gamma$-glutamic acid ($\gamma$-PGA) was mixed natural flora of Bacillus subtilis, contaminated from cooked soybeans. Also, it was performed to find out the antiallergic activity by using NC/Nga mice, in vitro. The $\gamma$-PGA (PGA-HM : PGA-high molecular weight), Molecular weight 300 kDa, was decomposed and made PGA-LM (PGA-low molecular weight) which has molecular weight below 30 kDa by sonication. Therefore, it was same result between PGA-HM and PGA-LM, and reported PGA-LM as basic result. We found that PGA-LM contains antiallergic efficacy that inhibit B cells and Th2 cells activation from isolated CD4+T cells in NC/Nga atopic dermatitis model mice, and not show a cytotoxicity in the hFCs. To investigate the effects of these PGA-LM in vitro, isolation of splenic B cell and CD4+ T cells in atopic dermatitis mice were used. To elucidate the role of PGA-LM in anti-CD40+ interleukin-4 (IL-4)-mediated B-cell activation, showed that the capacity of B cells to expression IL-$1\beta$, IL-6, and TNF-$\alpha$ mRNA down-regulated, and IL-10 mRNA up-regulation by PGA-LM treatment, but it had no effect on TGF-$\beta$ expression. In addition to CD4+IFN-$\gamma$+ and CD4+CD25+foxp3+, the functions of PGA-LM in the development of the CD4+CD25+foxp3+ and CD4+IFN-$\gamma$+cells, the phenotype and functions of PGA-LM induced CD4+CD25+foxp3+, and CD4+IFN-$\gamma$+cells in CD4+T cells. These results suggested that PGA-LM could change cytokine production and generate CD4+CD25+foxp3+ Tregs in NC/Nga mice, and may be effective for immunotherapy in patients with AD.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1285-1301
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• 2018

This paper is devoted to the study of $Tur{\acute{a}}n$-type inequalities for some well-known special functions such as Gauss hypergeometric functions, generalized complete elliptic integrals and confluent hypergeometric functions which are derived by using a new form of the Cauchy-Bunyakovsky-Schwarz inequality. We also apply these inequalities for some sample of interest such as incomplete beta function, incomplete gamma function, elliptic integrals and modified Bessel functions to obtain their corresponding $Tur{\acute{a}}n$-type inequalities.