• East Asian mathematical journal
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• v.18 no.1
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• pp.75-84
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• 2002

The third important Euler-Mascheroni constant $\gamma$, like $\pi$ and e, is involved in representations, evaluations, and purely relationships among other mathematical constants and functions, in various ways. The main object of this note is to summarize some known series representaions for $\gamma$ with comments for their proofs, and to point out that one of those series representaions for $\gamma$ seems to be incorrectly recorded. A brief historical comment for $\gamma$ is also provided.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.131-136
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• 2016

The main object of this paper is to present two general integral formulas whose integrands are the integrand given in the integral formula (3) and a finite product of the generalized Bessel function of the first kind.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.177-195
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• 2021

In this paper, we introduce the modification of a generalized (Ψ, L)-weak contraction and we prove some coincidence point results for self-mappings G, T and S, and some fixed point results for some maps by using a (c)-comparison function and a comparison function in the sense of a b-metric space.

• Membrane Journal
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• v.14 no.4
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• pp.304-311
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• 2004

The poly(1-trimethylsilyl-1-propyne) (PTMSP) and silica-filled PTMSP membranes were prepared by casting from a toluene solution on porous polyetherimide (PEI). FT-IR spectrum, GPC and SEM pictures have been taken to characterize the membranes. The particle size of membrane decreases as silica content of the membrane increases from 23 to 60 wt%, and a uniform distribution of the silica is observed. The separation properties of the gas mixture (32 mol% $H_2$/ 68 mol% $N_2$) through the composite membranes were studies as a function of pressure and percentage of silica. Selectivity values of $H_2$/$N_2$ increased as the pressure of permeation cell and silica content of the membrane increased. The real separation factor($\alpha$), head separation factor($\beta$), and tail separation factor((equation omitted)) of PTMSP-PEI composite membrane were 2.28, 1.58, and 1.44 respectively at $\Delta$P 30 psi and $25^{\circ}C$. $\alpha$, $\beta$, and (equation omitted) of PTMSP-Silica-PEI composite membrane for 60 wt% silica were 3.34, 1.95, 1.72 at $\Delta$P 30 psi and $25^{\circ}C$.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.583-611
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• 1998

We consider a general class of real-valued Levy processes {X(t), $t\geq0$}, and obtain suitable large deviation results for the empiricals L(t, A) defined by $t^{-1}{\int^t}_01_A$(X(s)ds for t > 0 and a Borel subset A of R. These results are used to obtain the asymptotic behavior of P{Z(t) < a}, where Z(t) = $sup_{u\leqt}\midx(u)\mid$ as $t\longrightarrow\infty$, in terms of the rate function in the large deviation principle. A subclass of these processes is the Feller class: there exist nonrandom functions b(t) and a(t) > 0 such that {(X(t) - b(t))/a(t) : t > 0} is stochastically compact, i.e., each sequence has a weakly convergent subsequence with a nondegenerate limit. The stable processes are in this class, but it is much larger. We consider processes in this class for which b(t) may be taken to be zero. For any t > 0, we consider the renormalized process ${X(u\psi(t))/a(\psi(t)),u\geq0}$, where $\psi$(t) = $t(log log t)^{-1}$, and obtain large deviation probability estimates for $L_{t}(A)$ := $(log log t)^{-1}$${\int_{0}}^{loglogt}1_A$$(X(u\psi(t))/a(\psi(t)))dv$. It turns out that the upper and lower bounds are sharp and depend on the entire compact set of limit laws of {X(t)/a(t)}. The results extend to random walks in the Feller class as well. Earlier results of this nature were obtained by Donsker and Varadhan for symmetric stable processes and by Jain for random walks in the domain of attraction of a stable law.

• Horticulture, Environment, and Biotechnology : HEB
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• v.59 no.6
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• pp.815-826
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• 2018

The intense drought affecting olive production in Northern Chile underscores the need to research non-traditional irrigation strategies to obtain the best crop performance. Accordingly, this study aimed to obtain preliminary data to guide future research on this topic. Different water replenishment levels on crop evapotranspiration ($ET_c$ ; 13.5, 27.0, 40.5, and 54%) were established in a young orchard, cv. Arbequina, from the end of fruit drop (EFD) to full bloom in the next season. We evaluated the influence of plant water status (${\Psi}_{stem}$ ) and crop load, considered as function of fruit number divided by trunk cross-sectional area, on reproductive and productive variables using multiple linear regressions. Our results show that crop load and ${\Psi}_{stem}$ measured from EFD to harvest affected yield components. Nevertheless, ${\Psi}_{stem}$ had the strongest influence on fruit size, pulp development, oil accumulation, and yield. Oil content and yield were reduced by 54% and 50% for each MPa, respectively, from ${\Psi}_{stem\;EFD-H}$ -1.8 MPa, an effect that intensified as crop load increased. During the period of flower development (September-November), the number of flowers per inflorescence and percentage of perfect flowers were reduced when ${\Psi}_{stem}$ was less than -2.0 MPa. These preliminary results showed that bud differentiation, inflorescence and flower formation are highly sensitive to water deficit.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.413-431
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• 2012

Let $C^r[0,t]$ be the function space of the vector-valued continuous paths $x:[0,t]{\rightarrow}\mathbb{R}^r$ and define $X_t:C^r[0,t]{\rightarrow}\mathbb{R}^{(n+1)r}$ and $Y_t:C^r[0,t]{\rightarrow}\mathbb{R}^{nr}$ by $X_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}),\;x(t_n))$ and $Y_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}))$, respectively, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n=t$. In the present paper, using two simple formulas for the conditional expectations over $C^r[0,t]$ with the conditioning functions $X_t$ and $Y_t$, we establish evaluation formulas for the analogue of the conditional analytic Fourier-Feynman transform for the function of the form $${\exp}\{{\int_o}^t{\theta}(s,\;x(s))\;d{\eta}(s)\}{\psi}(x(t)),\;x{\in}C^r[0,t]$$ where ${\eta}$ is a complex Borel measure on [0, t] and both ${\theta}(s,{\cdot})$ and ${\psi}$ are the Fourier-Stieltjes transforms of the complex Borel measures on $\mathbb{R}^r$.

• 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.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.541-547
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• 2009

We consider distribution, reliability and moment of ratio in two independent beta random variables X and Y, and reliability and $K^{th}$ moment of ratio are represented by a mathematical generalized hypergeometric function. We introduce an approximate maximum likelihood estimate(AML) of reliability and right-tail probability in the beta distribution.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.591-599
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• 2013

A large number of sequences of polynomials and numbers have arisen in mathematics. Some of them, for example, Bernoulli polynomials and numbers, have been investigated deeply and widely. Here we aim at presenting certain interesting and (potentially) useful identities involving mainly in the second-order Eulerian numbers and Stirling polynomials, which seem to have not been given so much attention.