• Journal of the Korean Mathematical Society
• /
• v.47 no.1
• /
• pp.215-222
• /
• 2010

A T$_1$ topological space X is called an almost GP-space if every dense G$_{\delta}$-set of X has nonempty interior. The behaviour of almost GP-spaces under taking subspaces and superspaces, images and preimages and products is studied. If each dense G$_{\delta}$-set of an almost GP-space X has dense interior in X, then X is called a GID-space. In this paper, some interesting properties of GID-spaces are investigated. We will generalize some theorems that hold in almost P-spaces.

• Journal of applied mathematics & informatics
• /
• v.42 no.1
• /
• pp.189-197
• /
• 2024

The purpose of this paper is to introduce and study the new class of spaces called the fuzzy 𝛽-Volterra spaces with the help of fuzzy β-dense and fuzzy 𝛽-G_𝛿 sets. Examples are given to illustrate the concept. Some interesting characterizations of the fuzzy 𝛽-Volterra spaces are established in this paper.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.26 no.2D
• /
• pp.285-292
• /
• 2006

The objective of this study is to introduce the development of the first Korean full-scale APT(Accelerated Pavement Tester) and to compare the performances of general dense grade asphalt mixture and modified asphalt mixtures as the first running of the tester. The tests evaluated the rutting resistance for dense grade mixture and three different modified asphalt mixture under three different temperature conditions (25-30, 40, $50^{\circ}C$). The results of the testing were compared with the laboratory test results. Results of the tests indicated that the all the modified asphalt sections showed higher rutting resistance than the dense grade section. Especially, the difference was more noticeable at higher temperature condition. Additionally, $G^*/sin{\delta}$ is found out to be an important factor for permanent deformation prediction whereas the resilient modulus was not.

• 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.

• Communications of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.905-913
• /
• 2022

We characterize metrizability and submetrizability for point-open, open-point and bi-point-open topologies on C(X, Y), where C(X, Y) denotes the set of all continuous functions from space X to Y ; X is a completely regular space and Y is a locally convex space.

• Journal of the Chungcheong Mathematical Society
• /
• v.1 no.1
• /
• pp.71-76
• /
• 1988

For each continuous convex function ${\phi}$ defined on an open convex subset $A_{\phi}$ of a Banach space X, if we define a positively homogeneous sublinear functional ${\sigma}_x$ on X by ${\sigma}_x(y)=\sup{\lbrace}f(y)\;:\;f{\in}{\partial}{\phi}(x){\rbrace}$, where ${\partial}{\phi}(x)$ is a subdifferential of ${\phi}$ at x, then we get the following characterization theorem of Gateaux differentiability (weak Asplund) sapce. THEOREM. For every ${\phi}$ above, $D_{\phi}={\lbrace}x{\in}A\;:\;\sup_{||u||=1}\;{\sigma}_x(u)+{\sigma}_x(-u)=0{\rbrace}$ contains dense (dense $G_{\delta}$) subset of $A_{\phi}$ if and only if X is a Gateaux differentiability (weak Asplund) space.

• Proceedings of the Korean Powder Metallurgy Institute Conference
• /
• 2006.09b
• /
• pp.950-951
• /
• 2006

[ $Mg_{55}Y_{15}Cu_{30}$ ] metallic glass powders were prepared by the mechanical alloying of pure Mg, Y, and Cu after 10 h of milling. The thermal stability of these $Mg_{55}Y_{15}Cu_{30}$ amorphous powders was investigated using the differential scanning calorimeter (DSC). $T_g$, $T_x$, and ${\Delta}T_x$ are 442 K, 478 K, and 36 K, respectively. The as-milled $Mg_{55}Y_{15}Cu_{30}$ powders were then consolidated by vacuum hot pressing into disk compacts with a diameter and thickness of 10 mm and 1 mm, respectively. This yielded bulk $Mg_{55}Y_{15}Cu_{30}$ metallic glass with nanocrystalline precipitates homogeneously embedded in a highly dense glassy matrix. The pressure applied during consolidation can enhance thermal stability and prolong the existence of amorphous phase within $Mg_{55}Y_{15}Cu_{30}$ powders.

• International Journal of Highway Engineering
• /
• v.2 no.3
• /
• pp.129-144
• /
• 2000

This paper presents the characteristics of viscoelastic properties and fatigue performance of SBS modified asphalt mixtures depending on the aggregate gradation. Dynamic shear rheometer (DSR) and uniaxial tensile creep tests are performed to analyze the thermomechanical behavior of asphalt binders and mixtures, respectively. Uniaxial tensile fatigue tests for seven different asphalt mixtures are conducted to evaluate the effects of aggregate gradations and SBS modifier on the fatigue performance of the mixtures. DSR and uniaxial tensile creep tests results show that the SBS modified asphalt mixtures have better rutting resistance than the unmodified mixtures at high temperatures regardless of the aggregate gradations used. Fatigue factor $G^*sin\delta$ in Superpave binder specification may not be adequate for evaluating the fatigue Performance of asphalt mixtures. It is observed from uniaxial tensile fatigue tests that SBS modified asphalt mixtures compared to unmodified mixtures have ten times longer fatigue lives regardless of the aggregate gradations(dense, SMA, and Superpave gradations) used in the mixtures. The better fatigue performance of the SBS modified mixtures is observed even after long-term aging process. The effect of aggregate gradations on the fatigue performance is not as significant as the SBS modifier. The cellulose fiber added in the SMA mixture has negligible effects on the viscoelastic Properties and fatigue performance of the mixture, but is effective in reducing draindown. Although the SBS modified asphalt binder is used, it may be necessary to add the cellulose fiber into the SMA mixture to prevent the draindown.

• Journal of Powder Materials
• /
• v.12 no.6 s.53
• /
• pp.422-427
• /
• 2005

The $Al_2O_3$ with various phases were prepared by simple ex-situ hydrolysis and spark plasma sintering (SPS) process of Al powder. The nano bayerite $(\beta-Al(OH)_3)$ phase was derived by hydrolysis of commercial powder of Al with micrometer size, whereas the bohemite (AlO(OH)) phase was obtained by hydrolysis of nano Al powder synthesized by pulsed wire evaporation (PWE) method. Compaction as well as dehydration of both nano bayerite and bohemite was carried out simultaneously by SPS method, which is used to fabricate dense powder compacts with a rapid heating rate of $100^{\circ}C$ per min. under the pressure of 50MPa. After compaction treatment in the temperature ranges from $100^{\circ}C\;to\; 1100^{\circ}C$, the bayerite and bohemite phases change into various alumina phases depending on the compaction temperatures. The bayerite shows phase transition of $Al(OH)_3{\to}{\eta}-Al_2O_3{\to}{\theta}-Al_2O_3{\to}\alpha-Al_2O_3$ sequences. On the other hand, the bohemite experiences the phase transition from AlO(OH) to ${\gamma}-Al_2O_3\;at\;350^{\circ}C.$ It shows AlO(OH) ${\gamma}-Al_2O_3{\to}{\delta}-Al_2O_3{\to}{\alpha}-Al_2O_3$ sequences. The ${\gamma}-Al_2O_3$ compacted at $550^{\circ}C$ shows a high surface area $(138m^2/g)$.