• Bulletin of the Korean Mathematical Society
• /
• v.40 no.1
• /
• pp.29-51
• /
• 2003

In this paper we construct a natural filtration associated to the plethysm $S_{r}(\wedge^2 \varphi)$ over arbitrary commutative ring R. Let $\phi$ : G longrightarrow F be a morphism of finite free R-modules. We construct the natural filtration of $S_{r}(\wedge^2 \varphi)$ as a $GL(F){\times}GL(G)$- complex such that its associated graded complex is ${\Sigma}_{{\lambda}{\in}{\Omega}_{\gamma}}=L_{2{\lambda}{\varphi}$, where ${{\Omega}_{\gamma}}^{-}$ is a set of partitions such that $│\wedge│\;=;{\gamma}\;and\;2{\wedge}$ is a partition of which i-th term is $2{\wedge}_{i}$. Specializing our result, we obtain the filtrations of $S_{r}(\wedge^2 F)\;and\;D_{r}(D_2G).

• Journal of the Korean Mathematical Society
• /
• v.56 no.3
• /
• pp.579-594
• /
• 2019

A colored space is a pair (X, r) of a set X and a function r whose domain is $\(^X_2\)$. Let (X, r) be a finite colored space and $Y,\;Z{\subseteq}X$. We shall write $Y{\simeq}_rZ$ if there exists a bijection $f:Y{\rightarrow}Z$ such that r(U) = r(f(U)) for each $U{\in}\({^Y_2}\)$ where $f(U)=\{f(u){\mid}u{\in}U\}$. We denote the numbers of equivalence classes with respect to ${\simeq}_r$ contained in $\(^X_i\)$ by $a_i(r)$. In this paper we prove that $a_2(r){\leq}a_3(r)$ when $5{\leq}{\mid}X{\mid}$, and show what happens when equality holds.

• Membrane Journal
• /
• v.11 no.4
• /
• pp.143-151
• /
• 2001

We have fabricated mixed-ionic conducting membranes, L $a_{0.6}$S $r_{0.4}$ $Co_{0.2}$F $e_{0.8}$ $O_{3-}$$\delta$/ and L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ by the solid state method. Ceramic membranes consisted of perovskite-type structures and exhibited high relative density, >95%. Especially, dense L $a_{0.6}$S $r_{0.4}$Co $O_{3-}$$\delta$/ layer was coated on the L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes by using screen printing technique in order to improve oxygen ion flux. We measured oxygen ion flux on uncoated L $a_{0.6}$S $r_{0.4}$ $Co_{0.2}$F $e_{0.8}$ $O_{3-}$$\delta$/, uncoated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/, and coated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes. The L $a_{0.6}$S $r_{0.4}$ $Co_{0.2}$F $e_{0.8}$ $O_{3-}$$\delta$/ membranes showed the highest flux, 0.26 mL/min.$\textrm{cm}^2$ at 90$0^{\circ}C$, after steady state had been reached. The oxygen flux of coated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes showed higher value, 0.19 mL/min.$\textrm{cm}^2$ at 95$0^{\circ}C$. This flux was as much as 2 or 3 times higher than those of uncoated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes. 3-$\delta$/ membranes.X> 3-$\delta$/ membranes.membranes.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.9 no.2
• /
• pp.380-389
• /
• 2005

The Goldschmidt iterative algorithm for a floating point divide calculates it by performing a fixed number of multiplications. In this paper, a variable latency Goldschmidt's divide algorithm is proposed, that performs multiplications a variable number of times until the error becomes smaller than a given value. To calculate a floating point divide '$\frac{N}{F}$', multifly '$T=\frac{1}{F}+e_t$' to the denominator and the nominator, then it becomes ’$\frac{TN}{TF}=\frac{N_0}{F_0}$'. And the algorithm repeats the following operations: ’$R_i=(2-e_r-F_i),\;N_{i+1}=N_i{\ast}R_i,\;F_{i+1}=F_i{\ast}R_i$, i$\in${0,1,...n-1}'. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than ‘$e_r=2^{-p}$'. The value of p is 29 for the single precision floating point, and 59 for the double precision floating point. Let ’$F_i=1+e_i$', there is $F_{i+1}=1-e_{i+1},\;e_{i+1}',\;where\;e_{i+1}, If '$[F_i-1]<2^{\frac{-p+3}{2}}$ is true, ’$e_{i+1}<16e_r$' is less than the smallest number which is representable by floating point number. So, ‘$N_{i+1}$ is approximate to ‘$\frac{N}{F}$'. 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 tables ($T=\frac{1}{F}+e_t$) with varying sizes. 1'he 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 divider. Also, it can be used to construct optimized approximate reciprocal 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 Digital Imaging in Medicine
• /
• v.9 no.1
• /
• pp.37-43
• /
• 2007

1. Purpose : This study is to present effective exposure conditions to acquire the best image of simple abdomen in Film Screen (F.S) system and Computed Radiography (C.R) system. 2. Method : In the F.S system, while an exposure condition was fixed as 70kVp, images of a patients simple abdomen were taken under the different mAs exposure conditions. Among these images, the best one was chosen by radiologists and radiological technologists. In the C.R system, the best image of the same patient was acquired with the same method from the F.S system. Both characteristic curves from F.S system and C.R system were analyzed. 3. Results : In the F.S system, the best exposure condition of simple abdomen was 70kVp and 20mAs. In the CR system, with the fixed condition at 70kVp, the image densities of human organs, such as liver, kidney, spleen, psoas muscle, lumbar spine body and iliac crest, were almost same despite different environments (3.2mAs, 8mAs, 12mAs, 16mAs and 20mAs). However, when the exposure conditions were over or under (below) 12mAs, the images between the abdominal wall and the directly exposed part became blurred because the gap of density was decreased. In the C.R system, while the volume of mAs was decreased, an artifact of quantum mottle was increased. 4. Conclusion : This study shows that the exposure condition in the C.R system can be reduced 40% than in the F.S system. This paper concluded that when the exposure conditions are set in CR environment, after the analysis of equipment character, such as image processing system(EDR : Exposure Data Recognition processing), PACS and so on, the high quality of image with maximum information can be acquired with a minimum exposure dose.

• Communications of the Korean Mathematical Society
• /
• v.20 no.4
• /
• pp.645-648
• /
• 2005

Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that $K\;{\otimes}_F\;L\;=\; N_1\;{\oplus}N_2\;{\oplus}{\cdots}{\oplus}N_k$ with corresponding primitive idempotents $e_1,\;e_2,{\cdots},e_k$, where Ni's are fields. Then G acts on $\{e_1,\;e_2,{\cdots},e_k\}$ transitively and $Gal(N_1/K)\;{\cong}\;\{\sigma\;{\in}\;G\;/\;{\sigma}(e_1)\;=\;e_1\}$. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = $K\;{\otimes}_F\;R$, and suppose there are only finitely many prime ideals $Q_1,\;Q_2,{\cdots},Q_k$ of T with $Q_i\;{\cap}\;R\;=\;P$. Then G acts transitively on $\{Q_1,\;Q_2,{\cdots},Q_k\},\;and\;Gal(qf(T/Q_1)/qf(R/P))\;{\cong}\;\{\sigma{\in}\;G/\;{\sigma}-(Q_1)\;=\;Q_1\}$ where qf($T/Q_1$) is the quotient field of $T/Q_1$.

• Proceedings of the Korea Association of Crystal Growth Conference
• /
• 1998.09a
• /
• pp.3-7
• /
• 1998

The rare-earth ions (R3+, R=Nd, Er) doped CaF2 layers have been grown on CaF2(111) substrate by molecular beam epitaxy. The epitaxial relationship and the crystallinity of CaF2:R3+ layers depending on the concentration of R3+ were studied by reflection high-energy electron diffraction (RHEED). In aspect of application as buffer layer in semiconductor-related hybrid structure, the lattice displacement between CaF2:R3+ layers and CaF2(111) substrate was investigated by X-ray rocking curve analysis.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.2
• /
• pp.439-450
• /
• 2019

Let R be a ring with unity. Given modules $M_R$ and $_RN$, $M_R$ is said to be absolutely $_RN$-pure if $M{\otimes}N{\rightarrow}L{\otimes}N$ is a monomorphism for every extension $L_R$ of $M_R$. For a module $M_R$, the subpurity domain of $M_R$ is defined to be the collection of all modules $_RN$ such that $M_R$ is absolutely $_RN$-pure. Clearly $M_R$ is absolutely $_RF$-pure for every flat module $_RF$, and that $M_R$ is FP-injective if the subpurity domain of M is the entire class of left modules. As an opposite of FP-injective modules, $M_R$ is said to be a test for flatness by subpurity (or t.f.b.s. for short) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. Every ring has a right t.f.b.s. module. $R_R$ is t.f.b.s. and every finitely generated right ideal is finitely presented if and only if R is right semihereditary. A domain R is $Pr{\ddot{u}}fer$ if and only if R is t.f.b.s. The rings whose simple right modules are t.f.b.s. or injective are completely characterized. Some necessary conditions for the rings whose right modules are t.f.b.s. or injective are obtained.

• Bulletin of the Korean Mathematical Society
• /
• v.20 no.1
• /
• pp.31-36
• /
• 1983

Let R be a commutative ring with 1, and A a unitary commutative R-algebra. By a derivation module of A, we mean a pair (M, d), where M is an A-module and d: A.rarw.M and R-derivation, i.e., d is an R-linear mapping such that d(ab)=a)db)+b(da). A derivation module homomorphism f:(M,d).rarw.(N, .delta.) is an A-homomorphism f:M.rarw.N such that f.d=.delta.. A derivation module of A, (U, d), there exists a unique derivation module homomorphism f:(U, d).rarw.(M,.delta.). In fact, a universal derivation module of A exists in the category of derivation modules of A, and is unique up to unique derivation module isomorphisms [2, pp. 101]. When (U,d) is a universal derivation module of R-algebra A, the A-module U is denoted by U(A/R). For out convenience, U(A/R) will also be called a universal derivation module of A, and d the R-derivation corresponding to U(A/R).

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.1
• /
• pp.149-157
• /
• 2003

Let M be an exponentially bounded o-minimal expansion of the standard structure R = (R ,＋,.,<) of the field of real numbers. We prove that if r is a non-negative integer, then every definable $C^{r}$ manifold is affine. Let f : X ${\longrightarrow}$ Y be a definable $C^1$ map between definable $C^1$ manifolds. We show that the set S of critical points of f and f(S) are definable and dim f(S) < dim Y. Moreover we prove that if 1 < s < ${\gamma}$ < $\infty$, then every definable $C^{s}$ manifold admits a unique definable $C^{r}$ manifold structure up to definable $C^{r}$ diffeomorphism.