• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.61-69
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• 2008

For a real subextension of some cyclotomic function field with a non-cyclic Galois group order $l^2$, l being a prime different from the characteristic of function field, we compute the index of the Sinnott group of circular units.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.389-397
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• 2005

Let K be an absolutely real abelian number field with $G=Gal(K/{\mathbb{Q}})$. Let E be a subfield of K and ${\Delta}=Gal(K/E)$. Let $C_K$ and $C_E$ be the group of circular units of K and E respectively. In [G], Greither has shown that if G is cyclic then $C_K^{\Delta}=C_E$. In this paper we show that the same result holds in function field case.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.161-168
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• 1996

This paper describes a sampling method, which can be used instead of the simple random sampling without replacement(SRSWOR). This method, circular sampling, assumes that the sampling units of the population are arranged in circular format, and randomly selects as many as samples of contiguous units. Therefore this method gathers information quicker and easier than STSWOR. In certain circumstances, the reliability of this method is better than that of STSWOR. And of circular sampling would be applied to nonprobability could be determined. methods, the reliability of the sample results in terms of probability could be determined.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.623-631
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• 2001

Let $\kappa$ be a real abelian field of conductor f and $\kappa$(sub)$\infty$ = ∪(sub)n$\geq$0$\kappa$(sub)n be its Z(sub)p-extension for an odd prime p such that płf$\phi$(f). he aim of this paper is ot compute the cohomology groups of circular units. For m>n$\geq$0, let G(sub)m,n be the Galois group Gal($\kappa$(sub)m/$\kappa$(sub)n) and C(sub)m be the group of circular units of $\kappa$(sub)m. Let l be the number of prime ideals of $\kappa$ above p. Then, for mm>n$\geq$0, we have (1) C(sub)m(sup)G(sub)m,n = C(sub)n, (2) H(sup)i(G(sub)m,n, C(sub)m) = (Z/p(sup)m-n Z)(sup)l-1 if i is even, (3) H(sup)i(G(sub)m,n, C(sub)m) = (Z/P(sup)m-n Z)(sup l) if i is odd (※Equations, See Full-text).

• Journal of the Korean Society for Precision Engineering
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• v.12 no.2
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• pp.37-47
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• 1995

In recent years, it has been variously developed for testing the accuracy of circular motion of NC machine tools, for example Telescoping Ball Bar Method by Bryan, Circular test Method by Knapp and $r^{-{\theta} }$ Method by Tsutsumi etc., but these methods are all 2-dimentional measuring methods on plane. These simple methods of circular motion accuracy test of NC machine tools have been studied by many reserchers as above, but it is not yet settled in the code of measuring methods of motion errors of NC machine tools, because of errors of measuring units and sensors, and also especially the difficulties of centering of measuring units and the spindle of machining center. In this paper, in use of 2 rotary encoders and 1 magnetic type linear scale with resolution of 0.5 .mu. m, it has become possible for measuring of 3 dimentional space motion accuracy.

• Korean Journal of Mathematics
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• v.8 no.2
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• pp.173-180
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• 2000

Let $k$ be a real abelian field such that the conductor of every nontrivial character belonging to $k$ agrees with the conductor of $k$. Note that real quadratic fields satisfy this condition. For a prime $p$, let $k_{\infty}$ be the $\mathbb{Z}_p$-extension of $k$. The aim of this paper is to produce a set of generators of the Tate cohomology group $\hat{H}^{-1}$ of the circular units of $k_n$, the $nth$ layer of the $\mathbb{Z}_p$-extension of $k$, where $p$ is an odd prime. This result generalizes some earlier works which treated the case when $k$ is real quadratic field and used them to study ${\lambda}$-invariants of $k$.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.233-239
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• 2007

Let $\mathbb{A}=\mathbb{F}_q$[T] be the polynomial ring over a finite field $\mathbb{F}_q$[T] and K=$\mathbb{F}_q$(T) its field of fractions. Let ${\ell}$ be a fixed prime divisor of q-1. Let J be a finite set of monic irreducible polynomials $P{\in}{\mathbb{A}}$ with deg $P{\equiv}0$ (mod ${\ell})$. In this paper we define the group $C_K$ of circular units in K=k$(\{\sqrt[{\ell}]P\;:\;P{\in}J\})$ in the sense of Kucera [4] and compute the index of $C_K$ in the full unit group $O^*_K$.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1993.10a
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• pp.305-311
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• 1993

In recent years, it has been variously developed for testing the accuracy of circular motion of NC machine tools, for example Telescoping Ball Bar Method by Bryan,Circular Test Method by Knapp and r $_{- \theta}$ Mathod by Tsutsumi etc., but it is not yet settled in the code of measuring methods of motion errors of NC machine tools, because of errors of measuring units and sensors, and also especially the difficulties of centering of measuring units. In this paper, in use of magnetic type linear scale with resolution of 0.5 .mu. m and tick pulses come out from computer, it has become possible for detecting of linear displacement of radial errors and measuring of revolution angle of circular motion of NC machine tools.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.6
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• pp.1-7
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• 2001

It is very important to test circular motion accuracy of NC machine tools as it affects all other machines machined by them in industries. In this paper, it has become possible to detect errors of linear displacement of radial directions for circle tar motion accuracy test using newly assembled magnetic type of linear scale so called Magnescale ball-bar system. It has also organized computer program systems using tick pulses come out from computer for getting error motion data at colt start time interval in circular motion test on NC lathe. Error data gotten from test is expressed to plots and analysed to numerics by various statistical treatments.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.1144-1149
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• 2003

It is very important to measure circular motion accuracy of NC lathes it affects accuracy, performance, interchange ability and quality of machine parts machined by the NC lathes in industries. So, in this study, measuring units system to measure circular motion accuracy two axes circular motion accuracy of NC lathes was composed of two optical linear scales installed on the z and x-axes of work coordinate system on NC lathe and a computer inserted with PC counter card enables to obtain measuring data. Here, ATC(Automatic Tool Changer) and moving part of linear scales are fixed with magnet bases in order to measure circular motion accuracy of the ATC of NC lathe. And next, computer software was developed in order to measure the circular motion accuracy of NC lathe under resolution of 0.1 $\mu\textrm{m}$ using two linear scales, and also computer softwares were developed so that measuring data could be modeled on plots and be analyzed numerically,