• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.31-35
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• 2022

In the note, by virtue of Abel's theorem and Abel's limit theorem in the theory of power series, the author provides three proofs for a sum of an alternating series involving central binomial numbers.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.504-512
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• 1994

A simple proof for the random central limit theorem is given for a family of stationary linear lattice processes, which belogn to a class of 2 dimensional random fields, applying the Beveridge and Nelson decomposition in time series context. The result is an extension of Fakhre-Zakeri and Fershidi (1993) dealing with the linear process in time series to the case of the linear lattice process with 2 dimensional indices.

• The Pure and Applied Mathematics
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• v.29 no.2
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• pp.171-177
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• 2022

The aim of this note is to establish two known sums involving central binomial coefficients via a hypergeometric series approach. As an application, we discover two new closed-form evaluations of generalized hypergeometric function.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.503-503
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• 1994

• Bulletin of the Korean Chemical Society
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• v.4 no.3
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• pp.143-148
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• 1983

Two series of thermotropic compounds were prepared and their thermal and liquid crystal properties were examined by differential scanning calorimetry and on the hot-stage of a cross-polarizing microscope. The first series of the compounds has two terminal mesogenic units based on unsubstituted and substituted p-(phenoxycarbonyl) phenyl ethers bracketing a central decamethylene spacer, and the second has 4-(p-phenylphenoxycarbonyl) phenyl ether moiety as the two terminal mesogenic units and central polymethylene spacers of varying lengths. A thermodynamic analysis of the phase transitions was made and explained in relation to structures and thermotropic behavior of the compounds.

• Proceedings of the Korean Society of Applied Pharmacology
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• 1997.04a
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• pp.73-73
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• 1997

A series of 4-phenyl-1-(indoline-5-sulfonyl)-2-imidazolone derivatives has been synthesized starting from 2-bromoacetophenone. Reaction of 2-aminoacetophenone obtained from 2-bromoacetophenon by Delepin synthesis and potassium cyanate affords 1,3-dihydro-4-phenyl-2-imidazolone. This key intermediate was treated with sodium hydride and N-trifluoroacetyl-indoline-5-sulfonylchloride, and trifluoroacetyl group was deprotected to give 4-Phenyl-1-(indoline-5-sulfonyl)-2-imidazolone. Various substituents were introduced on the nitrogen of indoline. Antitumor activity of this series of compound was evaluated by MTT method. Nearly all of the compounds showed broad-spectrum activity.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.169-187
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• 2022

There have been provided a surprisingly large number of summation formulae for generalized hypergeometric functions and series incorporating a variety of elementary and special functions in their various combinations. In this paper, we aim to consider certain generalized hypergeometric function ₃F₂ with particular arguments, through which a number of summation formulas for _p+1F_p(1) are provided. We then establish a power series whose coefficients are involved in generalized hypergeometric functions with unit argument. Also, we demonstrate that the generalized hypergeometric functions with unit argument mentioned before may be expressed in terms of Bell polynomials. Further, we explore several special instances of our primary identities, among numerous others, and raise a problem that naturally emerges throughout the course of this investigation.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.225-242
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• 2017

A family of $Ap{\acute{e}}ry$-like series involving reciprocals of central binomial coefficients is studied and it is shown that they represent transcendental numbers. The structure of such series is further examined in terms of finite combinations of logarithms and arctangents with arguments and coefficients belonging to a suitable algebraic extension of rationals. Monotonicity of certain quotients of weighted binomial sums which arise in the study of competitive cheap talk models is established with the help of a continuous extension of the discrete model at hand. The monotonic behavior of such quotients turns out to have important applications in game theory.

• Journal of Power Electronics
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• v.16 no.3
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• pp.960-969
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• 2016

High-power three-level voltage-source converters are widely utilized in high-performance AC drive systems. In several ultra-power instances, the harmonics on the grid side should be reduced through multiple rectifications. A combined harmonic elimination method that includes a dual primary-side series-connected winding transformer and selective harmonic elimination pulse-width modulation is proposed to eliminate low-order current harmonics on the primary and secondary sides of transformers. Through an analysis of the harmonic influence caused by dead time and DC magnetic bias, a synthetic compensation control strategy is presented to minimize the grid-side harmonics in the dual primary side series-connected winding transformer application. Both simulation and experimental results demonstrate that the proposed control strategy can significantly reduce the converter input current harmonics and eliminates the DC magnetic bias in the transformer.

• Bulletin of the Korean Chemical Society
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• v.6 no.1
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• pp.40-45
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• 1985

The thermal and optical properties of two new series of thermotropic, liquid crystalline compounds were studied by differential scanning calorimetry and on the hot-stage of a polarizing microscope. The first series contained two identical mesogenic units, 4-(p-phenylbenzoyloxy) benzoate moieties, at both ends of the polymethylene spacer of varying lengths and the second series, mesogenic units with different substituents and the hexamethylene group as the central spacer. A thermodynamic analysis of the phase transitions of the compounds was made and the results were discussed in relation to their chemical structures.