• 대한수학회지
• /
• 제49권2호
• /
• pp.251-263
• /
• 2012

A CW complex B is said to be I-trivial if there does not exist a $\mathbb{Z}_2$-map from $S^{i-1}$ to S(${\alpha}$) for any vector bundle ${\alpha}$ over B a any integer i with i > dim ${\alpha}$. In this paper, we consider the question of determining whether $\Sigma^k\mathbb{R}P^n$ is I-trivial or not, and to this question we give complete answers when k $\neq$ 1, 3, 8 and partial answers when k = 1, 3, 8. A CW complex B is I-trivial if it is "W-trivial", that is, if for every vector bundle over B, all the Stiefel-Whitney classes vanish. We find, as a result, that $\Sigma^k\mathbb{R}P^n$ is a counterexample to the converse of th statement when k = 2, 4 or 8 and n $\geq$ 2k.

• 대한수학회지
• /
• 제41권1호
• /
• pp.209-229
• /
• 2004

Let $\Sigma_{$\mid$\alpha$\mid$=m}\;s_{\alpha}z^{\alpha},\;z\;{\in}\;{\mathbb{C}}^n$ be a unimodular m-homogeneous polynomial in n variables (i.e. $$\mid$s_{\alpha}$\mid$\;=\;1$ for all multi indices $\alpha$), and let $R\;{\subset}\;{\mathbb{C}}^n$ be a (bounded complete) Reinhardt domain. We give lower bounds for the maximum modules $sup_{z\;{\in}\;R\;$\mid$\Sigma_{$\mid$\alpha$\mid$=m}\;s_{\alpha}z^{\alpha}$\mid$$, and upper estimates for the average of these maximum moduli taken over all possible m-homogeneous Bernoulli polynomials (i.e. $s_{\alpha}\;=\;{\pm}1$ for all multi indices $\alpha$). Examples show that for a fixed degree m our estimates, for rather large classes of domains R, are asymptotically optimal in the dimension n.

• 한국항해항만학회:학술대회논문집
• /
• 한국항해항만학회 2006년도 International Symposium on GPS/GNSS Vol.1
• /
• pp.9-14
• /
• 2006

This paper develops a complete methodology for the mitigation of ionosphere spatial anomalies by GBAS systems fielded in the Conterminous U.S. (CONUS). It defines an ionosphere anomaly threat model based on validated observations of unusual ionosphere events in CONUS impacting GBAS sites in the form of a linear ‘wave front’ of constant slope and velocity. It then develops a simulation-based methodology for selecting the worst-case ionosphere wave front impact impacting two satellites simultaneously for a given GBAS site and satellite geometry, taking into account the mitigating effects of code-carrier divergence monitoring within the GBAS ground station. The resulting maximum ionosphere error in vertical position (MIEV) is calculated and compared to a unique vertical alert limit, or $VAL_{H2,I}$, that applies to the special situation of worst-case ionosphere gradients. If MIEV exceeds $VAL_{H2,I}$ for one or more otherwise-usable subset geometries (i.e., geometries for which the 'normal' vertical protection level, or $VPL_{H0}$, is less than the 'normal' VAL), the broadcast ${\sigma}_{pr_{-}gnd}$ and/or ${\sigma}_{vig}$ must be increased such that all such potentially-threatening geometries have VPL$_{H0}$ > VAL and thus become unavailable. In addition to surveying all aspects of the methods used to generate the required ${\sigma}_{pr_{-}gnd}$ and ${\sigma}_{vig}$ inflation factors for CONUS GBAS sites, related methods for deriving similar results for GBAS sites outside CONUS are suggested.

• 한국수학사학회지
• /
• 제16권1호
• /
• pp.63-72
• /
• 2003

This paper is a sequel to [11]. We introduce $\sigma$-coherent frames, stably countably approximating frames and strongly Lindelof frames, and show that a stably countably approximating frame is a strongly Lindelof frame. We also show that a complete chain in a Lindelof frame if and only if it is a strongly Lindelof frame by using the concept of strong convergence of filters. Finally, using the concepts of super compact frames and filter compact frames, we introduce an example of a strongly Lindelof frame which is not a stably countably approximating frame.

• 대한수학회보
• /
• 제30권2호
• /
• pp.179-185
• /
• 1993

In this article S is a topologically complete subspace of $R^{1}$i.e., the relativized topology on S may be metrized so as to make S complete. B(S) is the Borel .sigma.-field of S. For .GAMMA. one takes a set of measurable monotone (increasing or dereasing) functions on S into itself. Make the assumption of pp. There exists $x_{0}$ and a positive integer $n_{0}$ such that (Fig.) It is then shown that there exists a unique inveriant probability to which $p^{(n)}$ (x,dy) converges exponentially fast in a metric (stronger than the Kolmogorov distance); this convergence is uniform for all x .mem. S. This generalizes an earlier result of Bhattacharya and Lee (1988) who considered monotone nondecreasing maps on S.

• Korean Journal of Mathematics
• /
• 제22권1호
• /
• pp.37-43
• /
• 2014

In this paper, we show that for any ${\sigma}$-complete Boolean subalgebra $\mathcal{M}$ of $\mathcal{R}(X)$ containing $Z(X)^{\sharp}$, the Stone-space $S(\mathcal{M})$ of $\mathcal{M}$ is a basically diconnected cover of ${\beta}X$ and that the subspace {${\alpha}{\mid}{\alpha}$ is a fixed $\mathcal{M}$-ultrafilter} of the Stone-space $S(\mathcal{M})$ is the the minimal basically disconnected cover of X if and only if it is a basically disconnected space and $\mathcal{M}{\subseteq}\{\Lambda_X(A){\mid}A{\in}Z({\Lambda}X)^{\sharp}\}$.

• Kyungpook Mathematical Journal
• /
• 제48권2호
• /
• pp.195-206
• /
• 2008

The purpose of this note is to compare the rings of continuous functions, integer-valued or real-valued, in pointfree topology with those in classical topology. To this end, it first characterizes the Boolean frames (= complete Boolean algebras) whose function rings are isomorphic to a classical one and then employs this to exhibit a large class of frames for which the functions rings are not of this kind. An interesting feature of the considerations involved here is the use made of nonmeasurable cardinals. In addition, the integer-valued function rings for Boolean frames are described in terms of internal lattice-ordered ring properties.

• 한국생명과학회:학술대회논문집
• /
• 한국생명과학회 2000년도 제28회 학술심포지엄
• /
• pp.3-8
• /
• 2000

The complete genome sequence of a Gram-positive bacterium .Bacillus subtilis has recently been reported and it is now clear that more than 50% of its ORFs have no known function (1). To study the global gene expression in B. subtilis at single gene resolution, we have tested the glass DNA microarrays in a step-wise fashion. As a preliminary experiment, we have created arrays of PCR products for 14 ORF whose transcription patterns have been well established through transcriptional mapping analysis. We measured changes in mRNA transcript levels between early exponential and stationary phase by hybridizing fluorescently labeled cDNA (with Cy3-UTP and Cy5-UTP) onto the array. We then compared the microarray data to confirm that the transcription patterns of these genes are well consistent with the known Northern analysis data. Since the preliminary test has been successful, we scaled up the experiments to ${\sim}$94% of the 4,100 annotated ORFs for the complete genome sequence of B. subtilis. Using this whole genomic microarray, we searched genes that are catabolite-repressive and those that are under the control of ${\sigma}^{Y}$, one of the functionally unknown ECF sigma factors. From these results, we here report that we have established DNA microarray techniques that are applicable for the whole genome of B. subtilis.

• 대한수학회지
• /
• 제47권5호
• /
• pp.967-983
• /
• 2010

Let M be an n-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant $-{\kappa}^2$. Using the cone total curvature TC($\Gamma$) of a graph $\Gamma$ which was introduced by Gulliver and Yamada [8], we prove that the density at any point of a soap film-like surface $\Sigma$ spanning a graph $\Gamma\;\subset\;M$ is less than or equal to $\frac{1}{2\pi}\{TC(\Gamma)-{\kappa}^2Area(p{\times}\Gamma)\}$. From this density estimate we obtain the regularity theorems for soap film-like surfaces spanning graphs with small total curvature. In particular, when n = 3, this density estimate implies that if $TC(\Gamma)$ < $3.649{\pi}\;+\;{\kappa}^2\inf\limits_{p{\in}F}Area(p{\times}{\Gamma})$, then the only possible singularities of a piecewise smooth (M, 0, $\delta$)-minimizing set $\Sigma$ are the Y-singularity cone. In a manifold with sectional curvature bounded above by $b^2$ and diameter bounded by $\pi$/b, we obtain similar results for any soap film-like surfaces spanning a graph with the corresponding bound on cone total curvature.

• KCI Concrete Journal
• /
• 제12권2호
• /
• pp.85-93
• /
• 2000

Potentially significant mechanical improvements in tension can be achieved by the incorporation of randomly distributed, short discrete fibers in concrete. The improvements due to the incorporation fibers significantly influence the composite stress - strain ($\sigma$-$\varepsilon$) characteristics. In general incorporating fibers in a plain concrete has relatively small effect on its precracking behavior. It, however, alters its post-cracking behavior quite significantly, resulting in greatly improved ductility, crack controls, and energy absorption capacity (or toughness). Therefore, a thorough understanding the complete tensile stress - strain ($\sigma$-$\varepsilon$) response of fiber reinforced concrete is necessary for proper analysis while using structural components made with fiber reinforced concrete. Direct tensile stress applied to a specimen is in principle the simplest configuration for determining the tensile response of concrete. However, problems associated with testing brittle materials in tension include (i) the problem related to gripping of the specimen and (ii) the problem of ensuring centric loading. Routinely, indirect tension tests for plain concrete, flexural and split-cylinder tests, have been used as simpler alternatives to direct uniaxial tension test. They are assumed to suitable for fiber reinforced concrete since typically such composites comprise 98% by volume of plain concrete. Clearly since the post-cracking characteristics are significantly influenced by the reinforcing parameters and interface characteristics, it would be fundamentally incorrect to use indirect tensile tests for determining the tensile properties of fiber reinforced concrete. The present investigation represents a systematic look at the failure and toughening mechanisms and macroscopic stress - strain ($\sigma$-$\varepsilon$) characteristics of fiber reinforced concrete in the uniaxial tension test. Results from an experimental parametric study involving used fiber quantity, type, and mechanical properties in the uniaxial tension test are presented and discussed.