• YAKHAK HOEJI
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• v.1 no.1
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• pp.1-2
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• 1948

The finely powdered entire harbs of Polygala japonica Houttuyn, a drug known as Yong Shin-Cho in Korea, were boiled with methanol and from the filtered extract the methanol was distilled off under diminished pressure and the aqueous solution of the residue was evaporated to dryness after being mixed with ignited magnesia. The dried mass was boiled with absolute alcohol, the filtered clear liquid was evaporated to a small volume and the precipitate Saponin produced by mixing with ether was filtered off. When the filtrate was again evaporated to the thickness of a syrup and allowed to cool for a few days in an ice box, crystalls were separated out in about 5% yield, which formed colorless columns, M. P. 142.deg., from methanol and had the formula $C_{6}$ $H_{12}$ $O_{5}$. On heating it with acetic acid anhybride and sodium acetate, its tetraacetyl derivative $C_{6}$ $H_{8}$ $O_{5}$(C $H_{3}$CO)$_{4}$ was obtained and which formed colorless needles, M. P. 62-5.deg., from ethanol. Their melting points, results of elementar analysis and other characteristics agreed with that of Polygalitol and its derivative. Finally they were proved to be identical with Polygalitol and its derivative, respectively, through determination of mixed melting points with the samples. Polygalitol was isolated from several plants of genus polugala e. g. P. amara, P. vulgaris, P. teunifolia, P. senega etc. The authors added to them another instance of identifying Polygalitol from the plant of genus polygala.olygala.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.15-27
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• 2008

We present and discuss an algorithm for the numerical solution of initial value problems of the form $D_*^\alpha$y(t) = f(t, y(t)), y(0) = y0, where $D_*^\alpha$y is the derivative of y of order $\alpha$ in the sense of Caputo and 0<${\alpha}{\leq}1$. The algorithm is based on the fractional Euler's method which can be seen as a generalization of the classical Euler's method. Numerical examples are given and the results show that the present algorithm is very effective and convenient.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1141-1158
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• 2017

In this paper, we study the value distribution of the derivative of a Dirichlet L-function $L^{\prime}(s,{\chi})$ at the a-points ${\rho}_{a,{\chi}}={\beta}_{a,{\chi}}+i{\gamma}_{a,{\chi}}$ of $L^{\prime}(s,{\chi})$. We give an asymptotic formula for the sum $${\sum_{{\rho}_{a,{\chi}};0<{\gamma}_{a,{\chi}}{\leq}T}\;L^{\prime}({\rho}_{a,{\chi}},{\chi})X^{{\rho}_{a,{\chi}}}\;as\;T{\rightarrow}{\infty}$$, where X is a fixed positive number and ${\chi}$ is a primitive character mod q. This work continues the investigations of Fujii [4-6], $Garunk{\check{s}}tis$ & Steuding [8] and the authors [12].

• Kyungpook Mathematical Journal
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• v.64 no.3
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• pp.423-433
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• 2024

Let ζ^(k)(s) be the k-th derivative of the Riemann zeta function and a be a complex number. The solutions of ζ^(k)(s) = a are called a-points. In this paper, we give an asymptotic formula for the sum $$\sum_{1<{\gamma}_a^{(k)}, where j and k are non-negative integers and ρ^(k)_a denotes an a-point of the k-th derivative ζ^(k)(s) and γ^(k)_a = Im(ρ^(k)_a).

• Structural Engineering and Mechanics
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• v.36 no.1
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• pp.19-36
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• 2010

The load and resistance factors are generally obtained using the First Order Reliability Method (FORM), in which the design point should be determined and derivative-based iterations have to be used. In this paper, a simple method for estimating the load and resistance factors using the first four moments of the basic random variables is proposed and a simple formula for the target mean resistance is also proposed to avoid iteration computation. Unlike the currently used method, the load and resistance factors can be determined using the proposed method even when the probability density functions (PDFs) of the basic random variables are not available. Moreover, the proposed method does not need either the iterative computation of derivatives or any design points. Thus, the present method provides a more convenient and effective way to estimate the load and resistance factors in practical engineering. Numerical examples are presented to demonstrate the advantages of the proposed fourth moment method for determining the load and resistance factors.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.10a
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• pp.98-105
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• 1993

A method for shape design sensitivity analysis for axisymmetric shells of general shapes is developed. The basic approach is to divide the structures into many segments. For each of the segments, the formula for a shallow arch or shell can be applied and the results assembled. To interconnect those segments, the existing sensitivity formula, obtained for a variation only in the direction perpendicular to the plane on which the structure is mapped, has been extended to include a variation normal to the middle surface. The method follows the adjoint variable approach based on the material derivative concept as established in the literature. Numerical examples are taken to illustrate the method and the applicability to practical design problems.

• East Asian mathematical journal
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• v.18 no.1
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• pp.111-125
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• 2002

Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.

• East Asian mathematical journal
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• v.35 no.1
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• pp.23-30
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• 2019

Since Mittag-Leffler introduced the so-called Mittag-Leffler function, a number of its extensions have been investigated due mainly to their applications in a variety of research subjects. Shukla and Prajapati presented a lot of formulas involving a generalized Mittag-Leffler function in a systematic manner. Motivated mainly by Shukla and Prajapati's work, we aim to investigate a generalized multi-index Mittag-Leffler function and, among possible numerous formulas, choose to present several formulas involving this generalized multi-index Mittag-Leffler function such as a recurrence formula, derivative formula, three integral transformation formulas. The results presented here, being general, are pointed out to reduce to yield relatively simple formulas including known ones.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.613-635
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• 1998

In this note we reformulate the white noise calculus on the classical Wiener space (C', C). It is shown that most of the examples and operators can be redefined on C without difficulties except the Hida derivative. To overcome the difficulty, we find that it is sufficient to replace C by L$_2$[0,1] and reformulate the white noise on the modified abstract Wiener space (C', L$_2$[0, 1]). The generalized white noise functionals are then defined and studied through their linear functional forms. For applications, we reprove the Ito formula and give the existence theorem of one-side stochastic integrals with anticipating integrands.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.415-425
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• 2001

We consider the problem of determining conductivity of the medium from the measurements of the electric potential on the boundary and the corresponding current flux across the boundary. We give a formula for reconstructing the conductivity and its normal derivative at the point of the boundary simultaneously from the localized Diichlet to Neumann map around that point.