• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.13-16
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• 1998

For continuous maps f of the circle to itself, we show that (1) every $\omega$-limit point is recurrent (or almost periodic) if and only if every $\omega$-limit set is minimal, (2) every $\omega$-limit set is almost periodic, then every $\omega$-limit set contains only one minimal set.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.703-713
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• 2012

In this paper we study ${\omega}$-limit sets and attraction of non-autonomous discrete dynamical systems. We introduce some basic concepts such as ${\omega}$-limit set and attraction for non-autonomous discrete system. We study fundamental properties of ${\omega}$-limit sets and discuss the relationship between ${\omega}$-limit sets and attraction for non-autonomous discrete dynamical systems.

• Nuclear Engineering and Technology
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• v.5 no.1
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• pp.30-37
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• 1973

The Nishitani's equations for impedance of anodic oxide films have been derived based on a p-i-n model under the assumption of $\omega$$\varepsilon$$\rho$$_{ο}$<<4$\pi$<<$\omega$$\varepsilon$$\rho$$_{\omega}$, where $\omega$ is angular frequency, $\varepsilon$ is dielectric constant, and $\rho$$_{ο}$ and $\rho$$_{\omega}$ are the resistivity of the interface region and the intrisic region of the anodic oxide film, respectively. Since it is not possible to evaluate all parameters in the equations, however, any clear physical picture cannot be obtained from the equations. Therefore, the equations are modified under the assumption of $\omega$$\tau$$_{\omega}$>>1 and In(1+$\omega$$^2$$\tau$$_{ο}$$^2$)<<1, where $\tau$$_{\omega}$=$\varepsilon$$\rho$$_{\omega}$(4$\pi$) and $\tau$$_{ο}$=$\varepsilon$$\rho$$_{ο}$/(4$\pi$). The modified equations are then used to explain the change in the frequency characteristics of anodic oxide films when they are heated. The change in impedance of anodic oxide films when they are heated is attributed mainly to the increase in the diffusion layer and to the decrease in the resistivity of anodic oxide films.s.

• The Pure and Applied Mathematics
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• v.19 no.1
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• pp.23-35
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• 2012

Given a set ${\Omega}$ and the notion of bipolar valued fuzzy sets, the concept of a bipolar ${\Omega}$-fuzzy sub-semigroup in semigroups is introduced, and related properties are investigated. Using bipolar ${\Omega}$-fuzzy sub-semigroups, bipolar fuzzy sub-semigroups are constructed. Conversely, bipolar ${\Omega}$-fuzzy sub-semigroups are established by using bipolar fuzzy sub-semigroups. A characterizations of a bipolar ${\Omega}$-fuzzy sub-semigroup is provided, and normal bipolar ${\Omega}$-fuzzy sub-semigroups are discussed. How the homomorphic images and inverse images of bipolar ${\Omega}$-fuzzy sub-semigroups become bipolar ${\Omega}$-fuzzy sub-semigroups are considered.

• Journal of Sensor Science and Technology
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• v.11 no.6
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• pp.358-364
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• 2002

In this paper, we used U.V.(wavelength, 355nm) laser for adjusting Pt thin films temperature sensor to $100{\Omega}$ at $0^{\circ}C$. Internationally, A-class tolerance of temperature sensor is $0.06{\Omega}$ at $0^{\circ}C$. This is under value of $0.15^{\circ}C$, actually, so high-fine trimming technology is essential to this process. The width of trimmed lines was about $10{\mu}m$ and the best trimming of Pt thin films of $1{\sim}1.5{\mu}m$ was carried out with power : 35mW, rep. rate frequency : 200Hz and bite size : $1.5{\mu}m$. And using photolithography process, 96 resistors were fabricated in $2"{\times}2"$ substrate as the proportion of $79{\sim}90{\Omega}$ and $91{\sim}102{\Omega}$ is 42.7% and 57.3%, respectively. As result of trimming resistors to the target value of $109.73{\Omega}$ at $25^{\circ}C$, 82.3% of resistors had the tolerance within ${\pm}0.30{\Omega}$ and the others(17.7%) were within ${\pm}0.06{\Omega}$ of A-class tolerance.

• Journal of Nutrition and Health
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• v.31 no.5
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• pp.897-905
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• 1998

Docosahexaenoic acid(DHA), a $\omega$3 series fatty acid and arachidonic acid(AA). a $\omega$6 series fatty acid were found in relatively high concentrations in the phospholipids(PLs) of cell membranes of nerve tissues, and they can be affected by various factors. The present study examined the effects of dietary $\omega$6 and $\omega$3 fatty acid composition on P/M/S and on $\omega$3/$\omega$6 fatty acid ratios in brain PLs of 2nd generation rats. The expeimental diets consisted of 10% fat(by wt), which were computer- searched mixed oil('M') with P/M/S ratio, 1 : 1.4 : 1 and $\omega$6/$\omega$3 ratio, 6 : 1 and safflower oil('S') poor in $\omega$3 fatty acids. The experimental diets were started 3-4 wks prior to conception. During the lactation period, the feeding mothers were switched 1 wk after birth and provided the pups for 2 wks with milk which had compositions different from that of their natural mother. The same diet as their mothers was provided from weaning to 9 wks of age. The 'M'and 'S' rats were again subdivided into MM, MS, SS, SM rats according to diet which their lactating mothers were fed from the begining of the experiment. The relative percentage of P/M/S fatty acids in brain PLs in all experimental groups converged to a very similar value at 9 wks of age, indicating the existence of a control mechanism for the degree of fatty acids, unsaturation. The $\omega$3/$\omega$6 fatty acid ratios of brain PLs converged to about 1.0 in MM & SM groups and to 0.7 in SS & MS groups, suggesting also the existence of some balance between $\omega$3 and $\omega$6 fatty acids in developing rat brain. The concentrations of $\omega$3 fatty acids, especially DHA, in the SM group were increased and became similar to those in MM group at 9 wks of age. The increase in DHA of brain PLs was counterbalanced b)r a decrease in 22 5$\omega$6. Therefore, the ratios of 22 : 6$\omega$6/22 : 5$\omega$6 were higher in both MM & SM groups than those of SS & MS groups at 9 wak of age. Although dietary $\omega$3 and $\omega$6 fatty acids affected 22 : 6$\omega$S and 22 : 5$\omega$6 contained in rat brain PLs reciprocally, the relative percentage of AA did not appear to be significantly influenced by the diet in all groups at 9 wks of age, suggesting that a mechanism for the maintenance of a certain level of AA in brain PLs exists. In conclusion, the $\omega$3/$\omega$6 fatty acid and 22 : 6$\omega$3/22 : 5$\omega$6 ratios, but not P/M/S ratio, of rat brain PLs were affected by the postnatal dietary changes. Futher studies are required to clarify the mechanism(S) of ensuring a certain level of DHA and of maintaining a similar level of AA in rat brain PLs after. weaning(9 wk) regardless of prenatal and postnatal dietary changes. (Korean J Nutrition 31(5) : 897-905, 1998)

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.207-222
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• 2011

Let R be a commutative ring and let M be a GV -torsionfree R-module. Then M is said to be a $\omega$-module if $Ext_R^1$(R/J, M) = 0 for any J $\in$ GV (R), and the w-envelope of M is defined by $M_{\omega}$ = {x $\in$ E(M) | Jx $\subseteq$ M for some J $\in$ GV (R)}. In this paper, $\omega$-modules over commutative rings are considered, and the theory of $\omega$-operations is developed for arbitrary commutative rings. As applications, we give some characterizations of $\omega$-Noetherian rings and Krull rings.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1169-1182
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• 2011

In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form $$-div(h(x){\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+b(x){\mid}u{\mid}^{p-2}u=f(x,\;u),\;p{\geq}2$$ in an unbounded domain ${\Omega}{\subset}\mathbb{R}^N$, $N{\geq}3$, with sufficiently smooth bounded boundary ${\partial}{\Omega}$, where $h(x){\in}L_{loc}^1(\overline{\Omega})$, $\overline{\Omega}={\Omega}{\cup}{\partial}{\Omega}$, $h(x){\geq}1$ for all $x{\in}{\Omega}$. The proof of main results rely essentially on the arguments of variational method.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1051-1066
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• 2013

By utilizing known characterizations of ${\omega}$-Noetherian rings in terms of injective modules, we give more characterizations of ${\omega}$-Noetherian rings. More precisely, we show that a commutative ring R is ${\omega}$-Noetherian if and only if the direct limit of GV -torsion-free injective R-modules is injective; if and only if every R-module has a GV -torsion-free injective (pre)cover; if and only if the direct sum of injective envelopes of ${\omega}$-simple R-modules is injective; if and only if the essential extension of the direct sum of GV -torsion-free injective R-modules is the direct sum of GV -torsion-free injective R-modules; if and only if every $\mathfrak{F}_{w,f}(R)$-injective ${\omega}$-module is injective; if and only if every GV-torsion-free R-module admits an $i$-decomposition.

• Applied Biological Chemistry
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• v.41 no.7
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• pp.533-538
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• 1998

In order to gain fundamental information on the utilization of lipids as energy source in mud-skipper, muscle lipids and their fatty acid composition were investigated with respect to life cycle-maturation (Aug), before-hibernation (Nov), and after-hibernation (Apr). Crude and neutral lipid were found to decrease from 1.2, 68.3% (Aug) via 0.7, 53.8% (Nov) to 0.4, 42.6% (Apr), respectively, whilst phospholipids and glycolipids increased from 29.5 and 2.2% (Aug) to 52.1 and 5.3% (Apr), respectively. In neutral lipids, TG contents gradually decreased from 53.8% (Aug) via 33.6% (Nov) to 23.1% (Apr), while FFA and sterol contents increased from 13.5 and 14.2% (Aug) to 22.3 and 24.5% (Apr), respectively. In phospholipids, PC content decreased from 61.2% (Aug) to 50.6% (Apr), while changes in PS and PE contents, as a whole, showed the opposite trends. In neutral lipids, the levels of some fatty acids such as 16:0, 16:1, 18:0, 18:1 and 20:5 $({\omega}3)$ were analyzed to be high, with the 20 : 5 being predominant, and the levels of saturated and monoene-acids gradually decreased, while polyene-acids increased in before and after hibernation. In before hibernation, 16:0, 16:1, 18:1 mainly decreased but 18:2, 18:3 $({\omega}3)$ and most of saturated and monoene acids such as 14:0, 14:1, 16:1, 18:0, 18:1 slightly decreased in after hibernation. From these findings, it was suggested that those fatty acids decreased during hibernation were used as a energy source, particularly 16:1 and 18:1 being most preferentially used. In phospholipids, the levels of 16:0, 18:0, 20:5 $({\omega}3)$, 22:5 $({\omega}3)$ and 22:6 $({\omega}3)$ were found to be high. Throughout the life cycle, the levels of monoene-acids in phospholipids stayed constant, whilst those of 18:2, 18:3 $({\omega}3)$ and saturated acids such as 16:0, 18:0 were found to be decreased gradually in before and after hibernation, whereas those for the high degree of polyene-acids such as 20:4 $({\omega}6)$, 20:5 $({\omega}3)$, 22:5 $({\omega}3)$, 22:6 $({\omega}3)$ increased, particularly 20:4 $({\omega}6)$, 20:5 $({\omega}3)$ being most increased.