• Journal of the Korean Mathematical Society
• /
• v.45 no.3
• /
• pp.835-840
• /
• 2008

The main result of this paper shows that every reciprocal Littlewood polynomial, one with {-1, 1} coefficients, of odd degree at least 7 has at least five unimodular roots, and every reciprocal Little-wood polynomial of even degree at least 14 has at least four unimodular roots, thus improving the result of Mukunda. We also give a sketch of alternative proof of the well-known theorem characterizing Pisot numbers whose minimal polynomials are in $$A_N=\{[{X^d+ \sum\limits^{d-1}_{k=0} a_k\;X^k{\in} \mathbb{Z}[X]\;:\;a_k={\pm}N,\;0{\leqslant}k{\leqslant}d-1}\}$$ for positive integer $N{\geqslant}2$.

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

• Communications of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.239-255
• /
• 2014

We develop a set of identities for Euler type sums. In particular we investigate products of shifted harmonic numbers of order two and reciprocal binomial coefficients.

• Communications for Statistical Applications and Methods
• /
• v.14 no.3
• /
• pp.667-677
• /
• 2007

In this paper, we propose a method for estimating the mean of a population which has a linear trend, when both n, the sample size, and k, the reciprocal of the sampling fraction, are odd numbers. The proposed method, not having the drawbacks of centered systematic sampling, centered modified sampling and centered balanced sampling, consists of selecting a sample by balanced systematic sampling and estimating the population mean by using interpolation. We compare the efficiency of the proposed method and existing methods under the criterion of the expected mean square error based on the infinite superpopulation model.

• Proceedings of the Korea Society of Poultry Science Conference
• /
• 2002.11a
• /
• pp.140-142
• /
• 2002

This study was conducted to obtain some genetic information for developing superior Korean native chickens. Heterosis and combining ability effects were estimated with 1,080 progenies of full diallel crosses of 3 strains in Korean Native Chicken. The traits of egg productivity were Investigated, and heterosis effect, general combining ability, specific combining ability and reciprocal effect were analyzed model I of the Griffing's method 1. The general performance were 147.0 days in age at first egg laying, 71.8 eggs in egg numbers to 270 days, 50.1g in egg weight at 270 days, 75.6 in egg shape index, 356$\mu\textrm{m}$ in egg shell thickness, and 4.27kg/$\textrm{cm}^2$ in egg shell strength, respectively. According to result, heterosis effect revealed comparatively high in age at first egg laying, egg numbers, egg weight, and egg shell strength. The effects estimated highly in general combining ability for age at first egg laying, egg numbers, egg weight, egg shape Index and egg shell thickness, and in specific combining ability were egg numbers, egg weight and egg shell thickness, and in reciprocal effects for egg numbers, egg shape index, and egg shell thickness. This result could be used for developing Korean native chicken.

• 제어로봇시스템학회:학술대회논문집
• /
• 2003.10a
• /
• pp.473-478
• /
• 2003

To detect motions of bodies, we have discussed them with two viewpoints; one is a detection algorithm, and another is the hardware implementation. The former is to find small terms expansions for sine/cosine functions. We researched Maclaurin and optimum expansions, and moreover to reduce hardware amounts, revised the expansions. The expansions don't include divide calculations, and the error is within 0.01%. As for the former problem, there is another approach also; that is the cordic method. The method is based on the rotation of a vector on the complex plain. It is simple iterations and don't require large logic. We examined the precision and convergence of the method on C-simulations, and implemented on HDL. The later problem is to make FPGA within small gates. We considered approaches to eliminate a divider and to reduce the bit number of arithmetic. We researched Newton-Raphson's method to get reciprocal numbers. The higher-order expression shows rapid convergence and doesn't be affected by the initial guess. It is an excellent algorithm. Using them, we wish to design a detector, and are developing it on a FPGA.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.11 no.1
• /
• pp.46-55
• /
• 2007

The Newton-Raphson's algorithm for finding a floating point reciprocal and inverse square root calculates the result by performing a fixed number of multiplications. In this paper, an improved Newton-Raphson's algorithm is proposed, that performs multiplications a variable number. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal and inverse square tables with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal and inverse square root unit. Also, it can be used to construct optimized approximate tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

• Korean Journal of Ichthyology
• /
• v.24 no.1
• /
• pp.1-10
• /
• 2012

Reciprocal hybrids between the mud loach ($Misgurnus$ $mizolepis$) and cyprinid loach ($M.$ $anguillicaudatus$) were produced by artificial fertilization. The chromosome number of mud loach was 2n=48, consisting of 12M+4SM+32A chromosomes. The cyprinid loach has 2n=50, consisting of 10M+4SM+36A chromosomes. The chromosome numbers of the diploid reciprocal hybrids were 2n=49, consisting of 11M+4SM+34A chromosomes. All the karyotypes documented in this study had the same arm number of 64. There was no evidence of chromosomal polymorphisms or sex-related heteromorphism. The cytogenetic traits of the hybrid genotypes were intermediate between those of the parent species. In all genotypes, the chromosomal NORs localized to the terminal short arms of the same metacentric chromosome pair. These results suggest that Robertsonian translocation occurred between metacentric chromosome 1 of mud loach and acrocentric chromosome of cyprinid loach.

• Korean Journal of Agricultural Science
• /
• v.10 no.1
• /
• pp.22-27
• /
• 1983

The community structure and dynamic succession of forest were determinated on the quadrat plot selected randomly at the Mt. Bomun. The polt size was $5{\times}5m$, and analysis of vegetation was adapted reciprocal averaging (RA) ordination method. 1. The numbers of shrub species were 45, and dominant species were Quercus aliena, Quercus serraia, and Rhododendron mucronulatum. 2. The succession of shrub stratum was determined through RA ordination method. It was assumed thet there were two main succession types: the one from Zanthoxylum community through Spiraea- Rubus community to Quercus community and the other from Stephanandra-Corylus community through Lespedeza community to Quercus community.

• Journal for History of Mathematics
• /
• v.31 no.2
• /
• pp.73-91
• /
• 2018

This study begins with the awareness of problem that the education of mathematics teachers has failed to link the limit and the infinite set conceptually. Thus, this study analyzes the historical and reciprocal development of the limit and the infinite set, and discusses how to improve the education of these concepts and their relation based on the outcome of this analysis. The results of the study confirm that the infinite set is the historical tool of linking the limit and the real numbers. Also, the result shows that the premise of 'the component of the straight line is a point.' had the fundamental role in the construction of the real numbers as an arithmetical continuum and that the moral certainty of this premise would be obtained through a thought experiment using an infinite set. Based on these findings, several proposals have been made regarding the teacher education of awakening someone to the fact that 'the theoretical foundation of the limit is the real numbers, and it is required to introduce an infinite set for dealing with the real numbers.' in this study. In particular, by presenting one method of constructing the real numbers as an arithmetical continuum based on a thought experiment about the component of the straight line, this study opens up the possibility of an education that could get the limit values psychologically connected to the infinite set in overcoming the epistemological obstacle related to the continuum concept.