• 충청수학회지
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• 제25권2호
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• pp.331-339
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• 2012

In this paper, let Q be the real quaternion algebra which consists of all quaternionic numbers, and let G be the Lie group of all automorphisms of the algebra Q. Assume that g is an arbitrary given left invariant Riemannian metric on the Lie group G. Then, we obtain a necessary and sufficient condition for an automorphism of the group G to be harmonic.

• 한국기계가공학회지
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• 제12권5호
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• pp.57-66
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• 2013

This study investigates structural and vibration analyses due to the change of bolt Numbers on models 1 and 2 of flange couplings connected with both sides of axis. As maximum equivalent stresses of models 1 and 2 are 122.05 and 102.3 MPa respectively by the basis of bolt, these stresses are within the allowable stress of this model and the safety of bolt design is verified. As maximum equivalent stresses of models 1 and 2 are 196.2 and 196.4 MPa respectively by the basis of body, these stresses are within the allowable stress of this model and the safety of body design is verified. Through natural frequency analysis, maximum displacements of model 1 and 2 are shown at the frequencies of 6565.1 and 6614.9 Hz respectively. Maximum displacements in cases of models 1 and 2 are shown at harmonic frequencies of 7760 and 7840 Hz at real loading conditions. By putting these study results together, the durability of vibration at model 2 with bolt numbers of 8 becomes better than model 1 with bolt numbers of 6. These study results can be effectively utilized with the design on flange coupling by anticipating and investigating prevention and durability against its damage.

• Journal of Electrical Engineering and Technology
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• 제10권1호
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• pp.261-270
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• 2015

In this paper, the Optimal Harmonic Stepped Waveform (OHSW) method is proposed in order to eliminate the selective harmonic orders available at the output of cascaded multilevel inverter (CMLI) fed by solar photovoltaic (SPV). This technique is used to solve the harmonic elimination equations based on stepped waveform analysis in order to obtain the optimal switching angles which in turn reduce the Total Harmonic Distortion (THD). The OHSW method considers the output voltage waveform as four equal symmetries in each half cycle. In the proposed method, a solar fed fifteen level cascaded multilevel is considered where the magnitude of six numbers of harmonic orders is reduced. A programmable pulse generator is developed to carry the switching angles directly to the semiconductor switches obtained as a result of OHSW analysis. Simulations are carried out in MATLAB/Simulink in which a separate model is developed for solar photovoltaic which serves as the input for cascaded multilevel inverter. A 3kWp solar plant with multilevel inverter system is implemented in hardware to show the effectiveness of the proposed system. Based on the observation the OHSW method provides the reduced THD thereby improving power quality in renewable energy applications.

• 대한수학회지
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• 제59권6호
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• pp.1103-1137
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• 2022

Our motivation in this note is to find equal hyperharmonic numbers of different orders. In particular, we deal with the integerness property of the difference of hyperharmonic numbers. Inspired by finiteness results from arithmetic geometry, we see that, under some extra assumption, there are only finitely many pairs of orders for two hyperharmonic numbers of fixed indices to have a certain rational difference. Moreover, using analytic techniques, we get that almost all differences are not integers. On the contrary, we also obtain that there are infinitely many order values where the corresponding differences are integers.

• 대한수학회보
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• 제56권2호
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• pp.521-533
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• 2019

In this paper, we define a mean of two positive numbers called the k-golden mean and study some properties of it. Especially, we show that the 2-golden mean refines the harmonic and the geometric means. As an application, we define the k-golden ratio and give some properties of it as an generalization of the golden ratio. Furthermore, we define the matrix k-golden mean of two positive-definite matrices and give some properties of it. This is an improvement of Lim's results [2] for which the matrix golden mean.

• Journal of Photoscience
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• 제7권1호
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• pp.9-13
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• 2000

An alternately assembled polycation-anionic dye film was prepared on a precursor assembly of poly(allylamine)hydrochloride (PAH) and poly(sodium styrenesulfonate) (PSS) or of poly (djallyldimethyl)ammonium chloride (PDDA) and PSS. The (PAH/PSS) precursor assembly gave better adsorptivity to the anionic dye than the (PDDA/PSS) one. Four kinds of anionic dyes (EB-T, AR-17 AR-18, AR-27) with different numbers of sulfonate substituents were compared. The extent of dye assembling was higher for the dye with a smaller number of sufonate substituents. Second harmonic generation (SHG) was clearly observed from the films. The SHG signal and the absorption intensity correlated well up to four polycation/dye bilayers, while further assembly did not increase the SHG signal appreciably. Second order nonlinear coefficients for ten bilayer assemblies were the order of pm/V.

• 한국윤활학회:학술대회논문집
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• 한국윤활학회 1998년도 제28회 추계학술대회
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• pp.343-349
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• 1998

A modeling of machined geometry and cutting force was proposed for the case of round shape machining, and the effects of internally machined profile are analyzed and its realiability was verified by the experiments of roundness tester, especially in boring operation in lathe. Also, harmonic cutting force model was proposed with the parameter of specific cutting force, chip width and chip thickness, and in this study, we can see that bored workpiece profile was also mapped into cutting force signal with this model. In general, we can calculated the theoretical lobe profile with arbitrary multilobe. But in real experiments, the most frequently measured numbers are 3 and 5 lobe profile in experiments. With this results, we can predict that these results may be applied to round shape machining such as drilling, boring, ball screw and internal grinding operation with the same method.

• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.521-529
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• 2014

In this paper we derive some optimal convex combination bounds related to arithmetic mean. We find the greatest values ${\alpha}_1$ and ${\alpha}_2$ and the least values ${\beta}_1$ and ${\beta}_2$ such that the double inequalities $${\alpha}_1T(a,b)+(1-{\alpha}_1)H(a,b)<A(a,b)<{\beta}_1T(a,b)+(1-{\beta}_1)H(a,b)$$ and $${\alpha}_2T(a,b)+(1-{\alpha}_2)G(a,b)<A(a,b)<{\beta}_2T(a,b)+(1-{\beta}_2)G(a,b)$$ holds for all a,b > 0 with $a{\neq}b$. Here T(a,b), H(a,b), A(a,b) and G(a,b) denote the second Seiffert, harmonic, arithmetic and geometric means of two positive numbers a and b, respectively.

• 항공우주시스템공학회지
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• 제2권1호
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• pp.13-16
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• 2008

The line of sight(LOS) is affected by the vibration of spacecraft. It is necessary to predict the effect of disturbance on LOS stability. Reaction wheel assembly is anticipated to be the largest disturbance source on spacecraft. The disturbance which is occurred mainly due to the mass imbalance is analyzed with harmonic numbers. The accuracy and stability are verified by probability density function with dynamic equation of the satellite motion.

• 대한수학회논문집
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• 제17권1호
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• pp.165-173
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• 2002

We first review Ramaswami's find Apostol's identities involving the Zeta function in a rather detailed manner. We then present corrected, or generalized formulas, or a different method of proof for some of them. We also give closed-form evaluation of some series involving the Riemann Zeta function by an integral representation of ζ(s) and Apostol's identities given here.