• Journal of The Korean Astronomical Society
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• v.47 no.2
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• pp.77-86
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• 2014

Using a cosmological ${\Lambda}CDM$ simulation, we analyze the differences between the widely-used spin parameters suggested by Peebles and Bullock. The dimensionless spin parameter ${\lambda}$ proposed by Peebles is theoretically well-justified but includes an annoying term, the potential energy, which cannot be directly obtained from observations and is computationally expensive to calculate in numerical simulations. The Bullock's spin parameter ${\lambda}^{\prime}$ avoids this problem assuming the isothermal density profile of a virialized halo in the Newtonian potential model. However, we find that there exists a substantial discrepancy between ${\lambda}$ and ${\lambda}^{\prime}$ depending on the adopted potential model (Newtonian or Plummer) to calculate the halo total energy and that their redshift evolutions differ to each other significantly. Therefore, we introduce a new spin parameter, ${\lambda}^{\prime\prime}$, which is simply designed to roughly recover the value of ${\lambda}$ but to use the same halo quantities as used in ${\lambda}^{\prime}$. If the Plummer potential is adopted, the ${\lambda}^{\prime\prime}$ is related to the Bullock's definition as ${\lambda}^{\prime\prime}=0.80{\times}(1+z)^{-1/12}{\lambda}^{\prime}$. Hence, the new spin parameter ${\lambda}^{\prime\prime}$ distribution becomes consistent with a log-normal distribution frequently seen for the ${\lambda}^{\prime}$ while its mean value is much closer to that of ${\lambda}$. On the other hand, in case of the Newtonian potential model, we obtain the relation of ${\lambda}^{\prime\prime}=(1+z)^{-1/8}{\lambda}^{\prime}$; there is no significant difference at z = 0 as found by others but ${\lambda}^{\prime}$ becomes more overestimated than ${\lambda}$ or ${\lambda}^{\prime\prime}$ at higher redshifts. We also investigate the dependence of halo spin parameters on halo mass and redshift. We clearly show that although the ${\lambda}^{\prime}$ for small-mass halos with $M_h$ < $2{\times}10^{12}M_{\odot}$ seems redshift independent after z = 1, all the spin parameters explored, on the whole, show a stronger correlation with the increasing halo mass at higher redshifts.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.957-965
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• 2018

We study the class $C{\mathcal{V}} ({\Omega})$ of analytic functions f in the unit disk ${\mathbb{D}}=\{z{\in}{\mathbb{C}}$ : ${\mid}z{\mid}$ < 1} of the form $f(z)=z+{\sum}_{n=2}^{\infty}a_nz^n$ satisfying $$1+\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}{\in}{\Omega},\;z{\in}{\mathbb{D}}$$, where ${\Omega}$ is a convex and proper subdomain of $\mathbb{C}$ with $1{\in}{\Omega}$. Let ${\phi}_{\Omega}$ be the unique conformal mapping of $\mathbb{D}$ onto ${\Omega}$ with ${\phi}_{\Omega}(0)=1$ and ${\phi}^{\prime}_{\Omega}(0)$ > 0 and $$k_{\Omega}(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\exp}\({\displaystyle\smashmargin{2}{\int\nolimits_{0}}^t}{\zeta}^{-1}({\phi}_{\Omega}({\zeta})-1)d{\zeta}\)dt$$. Let $z_0,z_1{\in}{\mathbb{D}}$ with $z_0{\neq}z_1$. As the first result in this paper we show that the region of variability $\{{\log}\;f^{\prime}(z_1)-{\log}\;f^{\prime}(z_0)\;:\;f{\in}C{\mathcal{V}}({\Omega})\}$ coincides wth the set $\{{\log}\;k^{\prime}_{\Omega}(z_1z)-{\log}\;k^{\prime}_{\Omega}(z_0z)\;:\;{\mid}z{\mid}{\leq}1\}$. The second result deals with the case when ${\Omega}$ is the right half plane ${\mathbb{H}}=\{{\omega}{\in}{\mathbb{C}}$ : Re ${\omega}$ > 0}. In this case $CV({\Omega})$ is identical with the usual normalized class of convex univalent functions on $\mathbb{D}$. And we derive the sharp upper bound for ${\mid}{\log}\;f^{\prime}(z_1)-{\log}\;f^{\prime}(z_0){\mid}$, $f{\in}C{\mathcal{V}}(\mathbb{H})$. The third result concerns how far two functions in $C{\mathcal{V}}({\Omega})$ are from each other. Furthermore we determine all extremal functions explicitly.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.15-23
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• 2009

Let D be an integral domain, P be a nonzero prime ideal of D, $\{P_{\alpha}{\mid}{\alpha}{\in}{\mathcal{A}}\}$ be a nonempty set of prime ideals of D, and $\{I_{\beta}{\mid}{\beta}{\in}{\mathcal{B}}\}$ be a nonempty family of ideals of D with ${\cap}_{{\beta}{\in}{\mathcal{B}}}I_{\beta}{\neq}(0)$. Consider the following conditions: (i) If $P{\subseteq}{\cup}_{{\alpha}{\in}{\mathcal{A}}}P_{\alpha}$, then $P=P_{\alpha}$ for some ${\alpha}{\in}{\mathcal{A}}$; (ii) If ${\cap}_{{\beta}{\in}{\mathcal{B}}}I_{\beta}{\subseteq}P$, then $I_{\beta}{\subseteq}P$ for some ${\beta}{\in}{\mathcal{B}}$. In this paper, we prove that D satisfies $(i){\Leftrightarrow}D$ is a generalized weakly factorial domain of ${\dim}(D)=1{\Rightarrow}D$ satisfies $(ii){\Leftrightarrow}D$ is a weakly Krull domain of dim(D) = 1. We also study the t-operation analogs of (i) and (ii).

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.445-460
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• 2022

In this paper, we studied on 𝛽-fuzzy filters of Stone almost distributive lattices. An isomorphism between the lattice of 𝛽-fuzzy filters of a Stone ADL A onto the lattice of fuzzy ideals of the set of all boosters of A is established. The fact that any 𝛽-fuzzy filter of A is an e-fuzzy filter of A is proved. We discuss on some properties of prime 𝛽-fuzzy filters and some topological concepts on the collection of prime 𝛽-fuzzy filters of a Stone ADL. Further we show that the collection 𝓣 = {X^𝛽(λ) : λ is a fuzzy ideal of A} is a topology on 𝓕Spec_𝛽(A) where X^𝛽(λ) = {𝜇 ∈ 𝓕Spec_𝛽(A) : λ ⊈ 𝜇}.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.139-144
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• 2000

The generalized noncommutative torus $T_{\rho}^d$ of rank m was defined in [2]. Assume that for the completely irrational noncommutative subtorus $A_{\rho}$ of rank m of $T_{\rho}^d$ there is no integer q > 1 such that $tr(K_0(A_{\rho}))=\frac{1}{q}{\cdot}tr(K_0(A_{\rho^{\prime}}))$ for $A_{\rho^{\prime}}$ a completely irrational noncommutative torus of rank m. All $C^*$-algebras ${\Gamma}({\eta})$ of sections of locally trivial $C^*$-algebra bundles ${\eta}$ over $M=\prod_{i=1}^{e}S^{2k_i}{\times}\prod_{i=1}^{s}S^{2n_i+1}$, $\prod_{i=1}^{s}\mathbb{PR}_{2n_i}$, or $\prod_{i=1}^{s}L_{k_i}(n_i)$ with fibres $T_{\rho}^d{\otimes}M_c(\mathbb{C})$ were constructed in [6, 7, 8]. We prove that ${\Gamma}({\eta}){\otimes}M_{p^{\infty}}$ is isomorphic to $C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C}){\otimes}M_{p^{\infty}}$ if and only if the set of prime factors of cd is a subset of the set of prime factors of p, that $\mathcal{O}_{2u}{\otimes}{\Gamma}({\eta})$ is isomorphic to $\mathcal{O}_{2u}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if and only if cd and 2u - 1 are relatively prime, and that $\mathcal{O}_{\infty}{\otimes}{\Gamma}({\eta})$ is not isomorphic to $\mathcal{O}_{\infty}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if cd > 1 when no non-trivial matrix algebra can be ${\Gamma}({\eta})$.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.869-915
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• 2019

Let H be a Krull monoid with class group G such that every class contains a prime divisor. Then every nonunit $a{\in}H$ can be written as a finite product of irreducible elements. If $a=u_1{\cdot}\;{\ldots}\;{\cdot}u_k$ with irreducibles $u_1,{\ldots},u_k{\in}H$, then k is called the length of the factorization and the set L(a) of all possible k is the set of lengths of a. It is well-known that the system ${\mathcal{L}}(H)=\{{\mathcal{L}}(a){\mid}a{\in}H\}$ depends only on the class group G. We study the inverse question asking whether the system ${\mathcal{L}}(H)$ is characteristic for the class group. Let H' be a further Krull monoid with class group G' such that every class contains a prime divisor and suppose that ${\mathcal{L}}(H)={\mathcal{L}}(H^{\prime})$. We show that, if one of the groups G and G' is finite and has rank at most two, then G and G' are isomorphic (apart from two well-known exceptions).

• Asian-Australasian Journal of Animal Sciences
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• v.13 no.6
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• pp.733-738
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• 2000

The objective of this study was to describe the nature of the inheritance of jumping as a behavioral trait and to analyze quantitatively the jumping height as a measure of vigor in two subspecies of mice. Two subspecies of mice, Yonakuni wild mouse (Y) and $CF_{{\sharp}1}$ laboratory mouse (C), were used as the parental types. Reciprocal mating between these two subspecies was made to produce subsequently the first and second generations. The first generation was $F_1$ (YC) resulting from $Y\;male{\times}C\;female$, and $F_1{^\prime}$ (CY) from $C\;male{\times}Y\;female$. The second generation $F_2$ (YCYC) was from mating $F_1{\times}F_1$ and $F_2{^\prime}$ (CYCY) from $F_1{^\prime}{\times}F_1{^\prime}$. Individuals were treated with a set of direct current shock apparatus at six weeks of age to evoke jumping. The results showed that the ratio between jumping and non jumping mice (J: NJ) for C was 0%:100% (0:1), which means that all C did not jump throughout the experiment, whereas Y was 68%:32% (2:1); and the $F_1$ and $F_2$ showed 65%:35% (2:1) and 51%:49% (1:1), respectively. All $F_1{^\prime}$ and $F_2{^\prime}$ individuals jumped as indicated by the ratio 100%:0% (1:0) for both these two genetic groups. Of the jumped mice, average height of the first three jumping observed for pooled sexes in Y, $F_1$, $F_2$, $F_1{^\prime}$ and $F_2{^\prime}$ were 19.3 cm, 19.3 cm, 18.0 cm, 19.9 cm and 16.4 cm, respectively. The distribution of jumping height showed a tendency to be a normal distribution. The jumping activity and jumping height may be affected by some major genes and polygenes, respectively.

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.75-82
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• 2001

In this paper, we show the existence of open subsets U of $S^3$ which admit a C-transformation onto the interior of $B^3$. Let U be an open set which is homeomorphic to the interior of $B^3$. Then, we prove that if U has a pseudo general polyhedral prime end structure then U admits a C-transformation.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1159-1180
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• 2019

In this article, we present the notion of e-fuzzy filters in an MS-Algebra and characterize in terms of equivalent conditions. The concept of D-fuzzy filters is studied and the set of equivalent conditions under which every e-fuzzy filter is an D-fuzzy filter are observed. Moreover we study some properties of the space of all prime e-fuzzy filters of an MS-algebra.

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.39-44
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• 1988

In 1940, B. H. Neumann, working with a system more general than a near-field, proved that the additive group of such a system (and of a near-field) is commutative. The algebraic structure he used is known as a Neumann system (N-system). Here, the prime N-systems are classified and for each possible characteristic, examples of N-systems which are neither near-fields nor rings are given. It is also shown that a necessary condition for the set of all odd polynomials over GF(p) to be an N-system is that p is a Fermat prime.