• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1147-1165
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• 2010

In this paper we compare a torsion free sheaf F on $P^N$ and the free vector bundle $\oplus^n_{i=1}O_{P^N}(b_i)$ having same rank and splitting type. We show that the first one has always "less" global sections, while it has a higher second Chern class. In both cases bounds for the difference are found in terms of the maximal free subsheaves of F. As a consequence we obtain a direct, easy and more general proof of the "Horrocks' splitting criterion", also holding for torsion free sheaves, and lower bounds for the Chern classes $c_i$(F(t)) of twists of F, only depending on some numerical invariants of F. Especially, we prove for rank n torsion free sheaves on $P^N$, whose splitting type has no gap (i.e., $b_i{\geq}b_{i+1}{\geq}b_i-1$ 1 for every i = 1,$\ldots$,n-1), the following formula for the discriminant: $$\Delta(F):=2_{nc_2}-(n-1)c^2_1\geq-\frac{1}{12}n^2(n^2-1)$$. Finally in the case of rank n reflexive sheaves we obtain polynomial upper bounds for the absolute value of the higher Chern classes $c_3$(F(t)),$\ldots$,$c_n$(F(t)) for the dimension of the cohomology modules $H^iF(t)$ and for the Castelnuovo-Mumford regularity of F; these polynomial bounds only depend only on $c_1(F)$, $c_2(F)$, the splitting type of F and t.

• Journal of Sericultural and Entomological Science
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• v.31 no.1
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• pp.20-24
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• 1989

The purpose of this experiment was to obtain the basic information on heterosis and inbreeding depression of quantitative characters in the silkworm by diallel crosses of seven varieties differing widely in each character. Period of 5th instar cocoon weight, cocoon layer weight, cocoon layer ratio, boiling off ratio, raw silk percent, bave length, bave weight, bave size, weight of first molting larva and fourth molting larva were investigated. The results obtained were summarized as follows : The degrees of positive heterosis of cocoon weight and cocoon layer weight were higher. Period of 5th instar and boiling off ratio were negative heterosis. In F1 generation, cocoon weight and bave weight showed positive heterobeltiosis, while fifth instar-period, cocoon layer ratio and boiling off ratio showed negative heterobeltiosis in the F1 and F2 generation. Inbreeding depression was observed in cocoon layer ratio and boiling off ratio.

• MALSORI
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• no.63
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• pp.47-66
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• 2007

This study aims at exploring the degree of phonetic similarity between Korean and Japanese vowels in terms of acoustic features by performing the speech production test on Korean speakers and Japanese speakers. For this purpose, the speech of 16 Japanese speakers for Japanese speech data, and the speech of 16 Korean speakers for Korean speech data were utilized. The findings in assessing the degree of the similarity of the 7 nearest equivalents of the Korean and Japanese vowels are as follows: First, Korean /i/ and /e/ turned out to display no significant differences in terms of F1 and F2 with their counterparts, Japanese /i/ and /e/, and the distribution of F1 and F2 of Korean /i/ and /e/ in the distributional map completely overlapped with Japanese /i/ and /e/. Accordingly, Korean /i/ and /e/ were believed to be "identical." Second, Korean /a/, /o/, and /i/ displayed a significant difference in either F1 or F2, but showed a great similarity in distribution of F1 and F2 with Japanese /a/, /o/, and /m/ respectively. Korean /a/ /o/, and /i/, therefore, were categorized as very similar to Japanese vowels. Third, Korean /u/, which has the counterpart /m/ in Japanese, showed a significant difference in both F1 and F2, and only half of the distribution overlapped. Thus, Korean /u/ was analyzed as being a moderately similar vowel to Japanese vowels. Fourth, Korean /${\wedge}$/ did not have a close counterpart in Japanese, and was classified as "the least similar vowel."

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.157-163
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• 1997

Based on a n-regular polygon $P_n$, we show that $r_n = 1/(2 \sum^{[(n-4)/4]+1}_{j=0}{cos 2j\pi/n)}$ is the ratio of contractions $f_i(1 \leq i \leq n)$ at each vertex of $P_n$ yielding a symmetric gasket $G_n$ associated with the just-touching I.F.S. $g_n = {f_i $\mid$ 1 \leq i \leq n}$. Moreover we see that for any odd n, the ratio $r_n$ is still valid for just-touching I.F.S $H_n = {f_i \circ R $\mid$ 1 \leq i \leq n}$ yielding another symmetric gasket $H_n$ where R is the $\pi/n$-rotation with respect to the center of $P_n$.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.1-3
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• 1998

Let f : X longrightarrow Y be quasi-open. We show that: (1) If A $\subset$ X is open, f│A is quasi-open, (2) f : X longrightarrow f(X) is quasi-open. (3) And let $f_{\alpha}/,:X_{\alpha}$, longrightarrow $Y_{\alpha}$ be quasi-open. Then $\Pi f_{\alpha}, : \Pi X_{\alpha}$ longrightarrow $\Pi Y_{\alpha}$/ defined by {$x_{\alpha}$} longrightarrow {$f_{\alpha},({\chi}_{\alpha}$)}, is quasi-open. (4) Lastly, if $f_{i}: X_{i}$ longrightarrow Y are quasi-open, i = 1,2, then F: $X_1 \bigoplus X_2$ longrightarrow Y, defined by $F({\chi})=f_i({\chi})$, ${\chi} \in X_i$, is also quasi-open.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.679-690
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• 2005

Let K be a commutative ring with unity, R a prime K-algebra of characteristic different from 2, d a non-zero derivation of R, I a non-zero right ideal of R, f($x_1,{\cdots},\;x_n$) a multilinear polynomial in n non-commuting variables over K, a $\in$ R. Supppose that, for any $x_1,{\cdots},\;x_n\;\in\;I,\;a[d(f(x_1,{\cdots},\;x_n)),\;f(x_1,{\cdots},\;x_n)]$ = 0. If $[f(x_1,{\cdots},\;x_n),\;x_{n+1}]x_{n+2}$ is not an identity for I and $$S_4(I,\;I,\;I,\;I)\;I\;\neq\;0$$, then aI = ad(I) = 0.

• The KIPS Transactions:PartA
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• v.12A no.5 s.95
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• pp.413-420
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• 2005

The Newton-Raphson iterative algorithm for finding a floating point reciprocal square mot calculates it by performing a fixed number of multiplications. In this paper, a variable latency Newton-Raphson's reciprocal square root algorithm is proposed that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the rediprocal square root of a floating point number F, the algorithm repeats the following operations: '$X_{i+1}=\frac{{X_i}(3-e_r-{FX_i}^2)}{2}$, $i\in{0,1,2,{\ldots}n-1}$' with the initial value is '$X_0=\frac{1}{\sqrt{F}}{\pm}e_0$'. 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 28 for the single precision floating point, and 58 for the double precision floating point. Let '$X_i=\frac{1}{\sqrt{F}}{\pm}e_i$, there is '$X_{i+1}=\frac{1}{\sqrt{F}}-e_{i+1}$, where '$e_{i+1}{<}\frac{3{\sqrt{F}}{{e_i}^2}}{2}{\mp}\frac{{Fe_i}^3}{2}+2e_r$'. If '$|\frac{\sqrt{3-e_r-{FX_i}^2}}{2}-1|<2^{\frac{\sqrt{-p}{2}}}$' is true, '$e_{i+1}<8e_r$' is less than the smallest number which is representable by floating point number. So, $X_{i+1}$ is approximate to '$\frac{1}{\sqrt{F}}$. 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 square root tables ($X_0=\frac{1}{\sqrt{F}}{\pm}e_0$) 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 square root unit. Also, it can be used to construct optimized approximate reciprocal square root 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.

• Journal of the Korean Mathematical Society
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• v.15 no.1
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• pp.59-61
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• 1978

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be i.i.d. uniform (0,1) random variables. Let $f_n(x)$ denote the probability density function (p.d.f.) of $T_n={\sum}^n_{i=1}X_i$. Consider a set S(x ; ${\delta}$) of lattice points defined by S(x ; ${\delta}$) = $x{\mid}x={\delta}+j$, j=0, 1, ${\cdots}$, n-1, $0{\leq}{\delta}{\leq}1$} The lattice distribution induced by the p.d.f. of $T_n$ is defined as follow: (1) $f_n^{(\delta)}(x)=\{f_n(x)\;if\;x{\in}S(x;{\delta})\\0\;otherwise.$. In this paper we show that $f_n{^{(\delta)}}(x)$ is a probability function thus we obtain a family of lattice distributions {$f_n{^{(\delta)}}(x)$ : $0{\leq}{\delta}{\leq}1$}, that the mean and variance of the lattice distributions are independent of ${\delta}$.

• The Journal of Natural Sciences
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• v.11 no.1
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• pp.15-17
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• 1999

Let {f(n)} be an increasing sequence such that f(n)>0 for each n and f(n)$\rightarrow$$\infty$. Let {X$_n$,n$\geq1$} be a sequence of pairwise independent random variables. In this paper we give sufficient conditions on {X$_n$,n$\geq1$} such that $sum_{i=1}^n$(X$_i$-EX$_i$)/f(n) converges to zero almost surely.

• Korean Journal of Microbiology
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• v.18 no.3
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• pp.133-147
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• 1980

Washed mycelia of Aspergillus nidulans FGSC159 were incubated in CMC minimal liquid medium and the culture filtrate which contained induced extracellular cellulase was fractionated by a three-step procedure including chromatography on Bio-Gel P-150, chromatography on DEAE-Sephadex A-50 and chromatography on Sephadex G-100. Three CMCase components ; F-I-Ia, F-I-Ib and F-II-Ia were prepared. No enzyme activity toward avicel could be detected in these components. Similarly, there was no ${\beta}-glucosidase$ activity. pH-optima of the three components were all 5.0 in acetate buffer. Temperature-optima for the activities of F-I-Ia, F-Ib and F-II-Ia were $45^{\circ}C,\;40^{\circ}C\;and\;50^{\circ}C$, respectively. F-II-Ia was shown to be more thermostable than the other two components. F-II-Ia was proved to have quite a different substrate specificity and action property and action property from those of F-I-Ia and F-I-Ib by product analysis on liquid chromatography.