• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.377-381
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• 2005

We present a convenient recursive formula for the sums of alternating harmonic series of odd order. The recursion is obtained by expanding in Fourier series certain elementary functions.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1261-1278
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• 2021

Recently, a new kind of multiple zeta value of level two T(k) (which is called multiple T-value) was introduced and studied by Kaneko and Tsumura. In this paper, we define a kind of alternating version of multiple T-values, and study several duality formulas of weighted sum formulas about alternating multiple T-values by using the methods of iterated integral representations and series representations. Some special values of alternating multiple T-values can also be obtained.

• 전기의세계
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• v.26 no.4
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• pp.41-53
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• 1977

With the equivalent series circuit analyzed aby revolving field theory and drawn by using the equivalent circuit constant ratios in capacitor motor with windings not in quadrature having space harmonics in its magnetic field (the above ratios are the equivalent circuit constants for the fundamental flux to the magnetizing reactance of the circuit), the equation for the alternating torque with twice line freequency in the motor is directly derived, and the alternating torque is measured with the self-made stator vibration angle amplitude measuring apparatus that is composed of a pickup, filter, photoelectric pickoff etc. The measured values satisfactorily compared with computed values. The properties of the alternating torque characteristics for respective harmonic fluxes and the r5esultant alternating torque characteristic, the effects of the alternating torque characteristics for respective harmonic fluxes on the resultant alternating torque characteristic, the effects of the variation in the motor constants and the equivalent circuit constant ratios for the fundamental flux on the alternating torque characteristics for respective harmonic fluxes and the resultant alternating torque characteristic, are made clear, applying the equation. There exist the optimum values of the motor constants and the equivalent circuit constant ratios for the fundamental flux for decreasing the alternating torque, and the value could be determined in design by the method presented in this paper.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.263-273
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• 2014

Ever since Euler solved the so-called Basler problem of ${\zeta}(2)=\sum_{n=1}^{\infty}1/n^2$, numerous evaluations of ${\zeta}(2n)$ ($n{\in}\mathbb{N}$) as well as ${\zeta}(2)$ have been presented. Very recently, Ritelli [61] used a double integral to evaluate ${\zeta}(2)$. Modifying mainly Ritelli's double integral, here, we aim at evaluating certain interesting alternating series.

• Macromolecular Research
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• v.11 no.6
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• pp.437-443
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• 2003

A series of alternating and alternating block copolycarbonates containing the constituent groups of polysulfone was synthesized through a multi-step solution condensation method. For the regulation of block length, monodisperse oligomers were prepared by using a large excess of the bisphenols and were subsequently incorporated into the copolymer chains. Separating the unreacted bisphenols from the oligomers by dissolution/precipitation steps took advantage of solubility differences. The structures of the monomers, oligomers, and copolymers were characterized and confirmed by GPC, NMR spectroscopy, mass spectrometry, and elemental analysis. Monodispersity of the oligomers, which is critical for control over the block length in the copolymers, was confirmed by GPC and mass spectrometry. Of the two constituent groups of the polysulfone, the sulfone linkage stiffens the polycarbonate copolymer chain, while the ether linkage softens it.

• Honam Mathematical Journal
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• v.38 no.2
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• pp.279-294
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• 2016

Half integer values of harmonic numbers and reciprocal binomial squared coeffients sums are investigated in this paper. Closed form representations and integral expressions are developed for the infiite series.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.789-797
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• 2017

The main purpose of this paper is to present closed integral form expressions for the Mathieu-type a-series and its associated alternating version whose terms contain a (p, q)-extended Gauss' hypergeometric function. Certain upper bounds for the two series are also given.

• Journal of Information Display
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• v.3 no.1
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• pp.1-5
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• 2002

A series of fully conjugated polymers containing new arylenevinylene units were synthesized and their light-emitting properties were investigated. A bisphosphonate containing tetraphenyl group was made to react with three different dialdehyde monomers to produce fully conjugated alternating copolymers. The photoluminescence (PL) and the electroluminescence (EL) peak wavelengths of the polymers were varied from 500 nm to 460 nm depending on the polymer structure. Single layer EL devices using the polymers as an emissive layer have been fabricated. The single layer EL devices became visible between 12-22 V and emitted blue light.

• 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.