• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.853-860
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• 2010

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}-3$ (mod 36).

• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.303-309
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• 2024

An imaginary bicyclic biquadratic number field K is a field of the form ${\mathbb{Q}}({\sqrt{-m}},{\sqrt{-n}})$ where m and n are squarefree positive integers. The ideal class number h_K of K is the order of the abelian group I_K/P_K, where I_K and P_K are the groups of fractional and principal fractional ideals in the ring of integers 𝒪_K of K, respectively. This provides a measure on how far is 𝒪_K from being a PID. We determine all imaginary bicyclic biquadratic number fields with class number 5. We show there are exactly 243 such fields.

• ETRI Journal
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• v.31 no.2
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• pp.140-150
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• 2009

Although mutation testing is potentially powerful, it is a computationally expensive testing method. To investigate how we can reduce the cost of object-oriented mutation testing, we have conducted empirical studies on class mutation operators. We applied class mutation operators to 866 classes contained in six open-source programs. An analysis of the number and the distribution of class mutants generated and preliminary data on the effectiveness of some operators are provided. Our study shows that the overall number of class mutants is smaller than for traditional mutants, which offers the possibility that class mutation can be made practically affordable.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.639-652
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• 2005

We find the class number of orders in a quaternion algebra over a dyadic local field.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.163-171
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• 2007

In this paper, we determine all subfields of cyclotomic function fields with divisor class number two. We also give the generators of such fields explicitly.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.595-599
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• 2011

We prove that for any positive integer $g{\geq}3$, there are ${\gg}q^{\frac{l}{2g}}$ real cyclotomic function fields whose conductor has degree ${\leq}l$ and ideal class number is divisible by $\frac{g}{gcd(2,g)}$.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.709-716
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• 1996

Nielsen coincidence theory is concerned with the determinatin of a lower bound of the minimal number MC[f,g] of coincidence points for all maps in the homotopy class of a given map (f,g) : X $\to$ Y. The Nielsen Nielsen number $N_R(f,g)$ (similar to [9]) is introduced in [3], which is a lower bound for the number of coincidence points in the relative homotopy class of (f,g) and $N_R(f,g) \geq N(f,g)$.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.217-228
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• 2009

In this paper, we consider a multi-class queueing system in which different classes of customers have different arrival rates, service rates and class-transition probabilities. We use the fast simulation method to estimate the overflow probability and the expected number of customers of each class at the first time the total number of customers hits a high level. We also discuss the overflow probabilities and the expected number of customers at different loads, respectively.

• The Korean Journal of Ecology
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• v.17 no.4
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• pp.453-461
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• 1994

Size class structure and vegetative growth of a perennial herb of the temperate deciduous forests, Symplocarpus renifolius Schott, were studied from 1991 to 1994 in Namhansansung, Kyonggi Province, Korea. The size class structures of leaf number and leaf area per individual followed bell-shape curve, i.e. frequency of middle class was relatively high. The leaf area increased from the late-March to mid-May. At the end of the growing season, leaf area(length X breadth) was proportional to biomass, especially aboveground biomass. The leaf number and leaf area per individual increased at the rate of 0.08 leaf/year and 9.7 $cm^2/year$, respectively. The size of the individuals in large-sized classes, in leaf number and leaf area, decreased in next year, while the size of the individuals in small-sized classes increased. Therefore, it was concluded that the size class structure of S. renifolius population was largely determined by the growth form.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.765-773
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• 2002

Let $textsc{k}$＝$F_{q}$(T) be a rational function field. Let $\ell$ be a prime number with ($\ell$, q-1) ＝ 1. Let K/$textsc{k}$ be an elmentary abelian $\ell$-extension which is contained in some cyclotomic function field. In this paper, we study the $\ell$-divisibility of ideal class number $h_{K}$ of K by using cyclotomic units.s.s.