• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.19-35
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• 2018

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [30] and the second Appell function [6], we introduce here the incomplete Lauricella functions ${\gamma}^{(n)}_A$ and ${\Gamma}^{(n)}_A$ of n variables. We then systematically investigate several properties of each of these incomplete Lauricella functions including, for example, their various integral representations, finite summation formulas, transformation and derivative formulas, and so on. We provide relevant connections of some of the special cases of the main results presented here with known identities. Several potential areas of application of the incomplete hypergeometric functions in one and more variables are also pointed out.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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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.

• East Asian mathematical journal
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• v.16 no.1
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• pp.1-7
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• 2000

• Journal of Radiation Protection and Research
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• v.35 no.2
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• pp.85-90
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• 2010

In the present work, peak relative efficiency for the energy was obtained and response function was worked out. This study was carried out using the high resolution high efficiency HPGe detector(diameter 78.7 mm, length 86.5 mm) and NaI(Tl) detector for anti-compton. The anti-coincidence of the signals from the two detectors could be used to lessen the Compton effect signal; thus, the $\gamma$-ray energy resolution could be improved. The $\gamma$-ray spectrum was measured at $55^{\circ}$ to the direction of the incident proton beam. Reaction spectrum was obtained from the $^{23}Na$(p, $\gamma$)$^{24}Mg$ reaction at $E_p$ = 1424 keV and $^{27}Al$(p, $\gamma$)$^{28}Si$ reaction at $E_p$ = 992 keV. To accelerate the incident proton which creates the (p, $\gamma$) capture reaction, the 3 MeV Pelletron accelerator at the Tokyo Institute of Technology was used. Response function was worked out by a noble technique. We worked out a response function from 1.2 to 9.4 MeV at intervals of 0.75 MeV.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.691-700
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• 1998

Simulation algorithms for one-sided and two-sided trun-cated gamma distributions are proposed. These algorithms suggest the optimal choice of derived functions. Some results of simulation are given. Finally an application with real data is presented.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.365-374
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• 2013

Let $k=\mathbb{F}_q(T)$ be a rational function field over the finite field $\mathbb{F}_q$, where q is a power of an odd prime number, and $\mathbb{A}=\mathbb{F}_q[T]$. Let ${\gamma}$ be a generator of $\mathbb{F}^*_q$. Let $\mathcal{H}_n$ be the subset of $\mathbb{A}$ consisting of monic square-free polynomials of degree n. In this paper we obtain an asymptotic formula for the mean value of $L(1,{\chi}_{\gamma}{\small{D}})$ and calculate the average value of the ideal class number $h_{\gamma}\small{D}$ when the average is taken over $D{\in}\mathcal{H}_{2g+2}$.

• Honam Mathematical Journal
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• v.35 no.3
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• pp.373-379
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• 2013

In contrast with numerous identities involving the binomial coefficients and the Stirling numbers of the first and second kinds, a few identities involving the Eulerian numbers have been known. The objective of this note is to present certain interesting and (presumably) new identities involving the Eulerian numbers by mainly making use of Worpitzky's identity.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.155-159
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• 2009

Using the Binet's formula, we show that the quotient related ratio $l_{1(x)}\;\neq\;0$ for the eventually periodic continued fraction x. Using this ratio, we also show that the derivative of the Minkowski question mark function at the simple periodic continued fraction is infinite or 0. In particular, $l_1({[\bar{1}]})$ = 2 log $\gamma$ where $\gamma$ is the golden mean $(1+\sqrt{5})/2$ and the derivative of the Minkowski question mark function at the simple periodic continued fraction $[\bar{1}]$ is infinite.

• International Journal of Reliability and Applications
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• v.16 no.2
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• pp.81-98
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• 2015

The Exponentiated Gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called kumaraswamy Exponentiated Gamma (KEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the KEG distribution is provided. We derive the $r^{th}$ moment and moment generating function of this distribution. Moreover, we discuss the maximum likelihood estimation of the distribution parameters. Finally, an application to real data sets is illustrated.

• The Korean Journal of Physiology
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• v.8 no.2
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• pp.19-31
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• 1974

In oder to study the correlation between daily urinary output of sodium chloride and blood pressure, twenty four hour urine samples were collected from 224 cases (70 male and 154 female) of healthy Koreans whose age varied from 18 to 70 years old. The volume and concentration of sodium, chloride and potassium and total nitrogen were measured, along with the resting blood pressure. Results obtained are summarized as follows; 1. Daily urinary output was increased as a function of age. However, daily urinary output per unit sulface area was maintained at approximately 800 to 900 $ml/m^2$ in all age groups of male and it increased as a function of age in female groups. There was no significant difference between male and female. 2. The daily urinary sodium concentration was decreased gradually acceding to age in both sexes. Daily excretion of sodium was constant regardless of age in both sexes but especially high in 25-39 year female age group, which was slightly greater in males than in females. 3. The daily urinary chloride concentration was at approximately 250 meq/L in all age groups of male and which decreased as a function of age in females. 4. Hence the daily urinary output of sodium chloride was constant in all age groups of males which increased as a function of age in female groups. However, daily excretion of sodium chloride per unit sulface area was maintained at approximately 11 $gm/m^2$ in males and which increased as a function of age in females. 5. The daily urinary excretion of potassium was constant regardless of age in both sexes. 6. Urinary K/Na ratio was maintained at approximately 0.27 in males and 0.33 in females. 7. The daily urinary output of total nitrogen amount was approximately $8{\sim}10$ gm in males and $7{\sim}9$ gm in females. However, daily urinary output of nitrogen per unit sulface area was constant regardless of age in both sexes. 8. The systolic blood pressure was increased gradually according to the age in both sexes and was higher for males than females under 40 years of age. However, there was no significant difference between both sexes in ages over 40 years. 9. Quantitative comparisons indicated that daily urinary output and sodium chloride excretion are higher while daily potassium output, nitrogen excretion and urinary K/Na ratio are significantly lower among Koreans than a among Occidentals. These findings suggest that average Koreans live on low-protein and high-salt diet throughout their livers. Statistical result obtained may he summarized as follows; 10. The relation between blood pressure and sodium concentration of urine. The correlation between systolic blood pressure and sodium concentration was negatively associated for both sexes and the correlation coefficient was significant for females $({\gamma}_1=-.19<-{\gamma}_{152},\;_{0.05}=-0.159)$ and it was not significant for males $({\gamma}_1=-.19>-{\gamma}_{68},\;_{0.05}=-0.232)$ tut may be due to the sample size for males. The correlation between diastolic blood Pressure and sodium concentration was negatively associated for both sexes and the correlation coefficient was significant for males $({\gamma}_1=-.37<-{\gamma}_{68},\;0.05=-0.232)$ and the relation was not significant for females $({\gamma}_1=-.11>-{\gamma}_{152},\;_{0.05}=-0.159)$. 11. The relation between blood pressure and daily urinary sodium chloride excretion. The association between systolic blood pressure and sodium chloride excretion was positively correlated for both sexes and the relation was significant for females $({\gamma}_1=.20>{\gamma}_{152},\;_{0.05}= 0.159)$ and it was insignificant for males $({\gamma}_1=.09<{\gamma}_{68},\;_{0.05}=0.232)$, The relation between diastolic blood pressure and sodium chloride excretion was positively associated and insignificant for both sexes males $({\gamma}_1=.17<{\gamma}_{68},\;_{0.05}=0.232)$ and females $({\gamma}_1=.09<{\gamma}_{152},\;_{0.05}=0. 159)$. 12. The relation between daily urinary nitrogen excretion and sodium chloride excretion. The association between daily nitrogen excretion and sodium chloride excretion was positively significant for both sexes, males $({\gamma}_1=.31>{\gamma}\;_{68},\;_{0.05}=0.232)$ and females $({\gamma}_1=.36>{\gamma}_{-152},\;_{0.05}=0.159)$.