• 대한수학회논문집
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• 제17권4호
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• pp.731-740
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• 2002

We derive the generalized Hermite interpolation by using the contour integral and extend the generalized Hermite interpolation to obtain the sampling expansion involving derivatives for band-limited functions f, that is, f is an entire function satisfying the following growth condition ｜f(ｚ)｜$\leq$ A exp($\sigma$｜y｜) for some A, $\sigma$ > 0 and any ｚ=$\varkappa$ + iy∈C.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.105-115
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• 2021

Generalized pseudo-differential operators (PDO) involving fractional Fourier transform associate with the symbol a(x, y) whose derivatives satisfy certain growth condition is defined. The product of two generalized pseudo-differential operators is shown to be a generalized pseudo-differential operator.

• Bulletin of the Korean Chemical Society
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• 제31권10호
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• pp.2934-2938
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• 2010

Some open tubular (OT) molecule imprinted polymer (MIP) silica capillary columns with templates of camphor derivatives such as 10-camphorsulfonic acid (10-CSA), 10-camphorsulfonamide (10-CS) and camphor-p-tosyl hydrazone (CTH) have been successfully prepared by the prior generalized preparation protocol. The three MIP thin layers of different templates showed quite different morphologies. The chiral selectivity of each MIP column for the template enantiomers was optimized by changing eluent composition and pH. The optimization conditions were found to be different for the three MIPs. This work suggests prospective successful extension of the generalized preparation protocol for OT-MIP silica capillary columns toward templates of a variety of chemical groups.

• 호남수학학술지
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• 제40권1호
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• pp.199-210
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• 2018

In this paper we obtain some formulae for several sums of generalized Fibonacci numbers $U_n$ and generalized Lucas numbers $V_n$ and their dual forms $G_n$ and $H_n$ by using extensions of an interesting identity by A. R. Amini for Fibonacci numbers to these four kinds of generalizations and their first and second derivatives.

• 대한수학회논문집
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• 제32권3호
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• pp.677-688
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• 2017

The composition of Jacobi type finite classes of the classical orthogonal polynomials with two generalized Riemann-Liouville fractional derivatives are considered. The outcomes are expressed in terms of generalized Wright function or generalized hypergeometric function. Similar composition formulas are also obtained by considering the generalized Riemann-Liouville and $Erd{\acute{e}}yi-Kober$ fractional integral operators.

• 대한수학회지
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• 제58권3호
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• pp.609-631
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• 2021

Let C[0, T] denote a generalized analogue of Wiener space, the space of real-valued continuous functions on the interval [0, T]. Define $Z_{\vec{e},n}$ : C[0, T] → ℝⁿ⁺¹ by $$Z_{\vec{e},n}(x)=\(x(0),\;{\int}_0^T\;e_1(t)dx(t),{\cdots},\;{\int}_0^T\;e_n(t)dx(t)\)$$, where e₁,…, e_n are of bounded variations on [0, T]. In this paper we derive a simple evaluation formula for Radon-Nikodym derivatives similar to the conditional expectations of functions on C[0, T] with the conditioning function $Z_{\vec{e},n}$ which has an initial weight and a kind of drift. As applications of the formula, we evaluate the Radon-Nikodym derivatives of various functions on C[0, T] which are of interested in Feynman integration theory and quantum mechanics. This work generalizes and simplifies the existing results, that is, the simple formulas with the conditioning functions related to the partitions of time interval [0, T].

• Journal of Mechanical Science and Technology
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• 제17권4호
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• pp.538-544
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• 2003

Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical approaches such as the Lagrange multiplier's method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba proposed explicit equations of motion for constrained systems based on Gauss's principle and elementary linear algebra without any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme, which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples.

• Korean Journal of Mathematics
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• 제31권1호
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• pp.49-54
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• 2023

In this paper, we obtain some results concerning the location of zeros of generalized derivatives of polynomials which are analogous to those for the ordinary derivative of polynomials.

• 대한수학회논문집
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• 제33권2호
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권3호
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• pp.157-175
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• 2019

In this paper we define higher-order Stieltjes derivatives, and using Schaefer's fixed point theorem we investigate the existence of solutions for a class of differential equations involving second-order Stieltjes derivatives with two-point boundary conditions. The equations include ordinary and impulsive differential equations, and difference equations.