• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.229-246
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• 2024

We consider the delay differential equations $$b(z)w(z+1)+c(z)w(z-1)+a(z)\frac{w'(z)}{w^k(z)}=\frac{P(z, w(z))}{Q(z, w(z))}$$, where k ∈ {1, 2}, a(z), b(z) ≢ 0, c(z) ≢ 0 are rational functions, and P(z, w(z)) and Q(z, w(z)) are polynomials in w(z) with rational coefficients satisfying certain natural conditions regarding their roots. It is shown that if this equation has a non-rational meromorphic solution w with hyper-order ρ2(w) < 1, then either deg_w(P) = deg_w(Q) + 1 ≤ 3 or max{deg_w(P), deg_w(Q)} ≤ 1. In addition, it is shown that in the case max{deg_w(P), deg_w(Q)} = 0 the equations above can have such a solution, with an additional zero density requirement, only if the coefficients of the equation satisfy certain strict conditions.

• Korean Journal of Materials Research
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• v.3 no.6
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• pp.661-667
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• 1993

Effects of $SiH_4//WF_6$(=R) ratio on the electrical properties of W films such as resistvity, contact resistance, junction leakage current in the selective W CVD technology for contact barrier metal were investigated with the emphasis on the role of $\alpha$-W Resistivity of W increases with increasing R, which is primarily due to the phase transformation from $\alpha$-W to , $\alpha$-W. $\alpha$-W found in the SiH4 reduced CVD W film is stabilized by Si incorporated into the W film rather than by oxygen. $\alpha$-W is found in the W film deposited on the Si substrate for high R, while $\alpha$-W is not found in the W film deposited on the TiN substrate even for high R. Also junction leakages increase with increasing R, which is caused not only by the vertical Si consumption but also the lateral Si consumption.

• Wind and Structures
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• v.26 no.5
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• pp.293-304
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• 2018

A numerical study is conducted on the flow characteristics of a rectangular cylinder (chord-to-width ratio C/W = 2 - 10) mounted close to a rigid wall at gap-to-width ratios G/W = 0.25 - 6.25. The effects of G/W and C/W on the Strouhal number, vortex structure, and time-mean drag and lift forces are examined. The results reveal that both G/W and C/W have strong influences on vortex structure, which significantly affects the forces on the cylinder. An increase in G/W leads to four different flow regimes, namely no vortex street flow (G/W < 0.75), single-row vortex street flow ($0.75{\leq}G/W{\leq}1.25$), inverted two-row vortex street flow ($1.25<G/W{\leq}2.5$), and two-row vortex street flow (G/W > 2.5). Both Strouhal number and time-mean drag are more sensitive to C/W than to G/W. For a given G/W, Strouhal number grows with C/W while time-mean drag decays with C/W, the growth and decay being large between C/W = 2 and 4. The time-mean drag is largest in the single-row vortex street regime, contributed by a large pressure on the front surface, regardless of C/W. A higher C/W, in general, leads to a higher time-mean lift. The maximum time-mean lift occurs for C/W = 10 at G/W = 0.75, while the minimum time-mean lift appears for C/W = 2 at the same G/W. The impact of C/W on the time-mean lift is more substantial in single-row vortex regime. The effect of G/W on the time-mean lift is larger at a larger C/W.

• Nuclear Engineering and Technology
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• v.54 no.12
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• pp.4491-4498
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• 2022

The thermal stress between W plasma-facing material (PFM) and Cu heat sink in fusion reactors can be significantly reduced by using a W-Cu functionally graded material (W-Cu FGM) interlayer. However, there is still considerable stress at the joining interface between W and W-Cu FGM in the W/W-Cu FGM/Cu portions. In this work, we fabricate W skeletons with continuous gradients in porosity by a modified sedimentation method. Sintering densification behavior and pore characteristics of the sedimented W skeletons at different sintering temperatures were investigated. After Cu infiltration, the final W-Cu FGM was obtained. The results indicate that the pore size and porosity in the W skeleton decrease gradually with the increase of sintering temperature, but the increase of skeleton sintering temperature does not reduce the gradient range of composition distribution of the final prepared W-Cu FGM. And W-Cu FGM with composition distribution from pure W to W-20.5wt.% Cu layer across the section was successfully obtained. The thickness of the pure W layer is about one-fifth of the whole sample thickness. In addition, the prepared W-Cu FGM has a relative density of 94.5 % and thermal conductivity of 185 W/(m·K). The W-Cu FGM prepared in this work may provide a good solution to alleviate the thermal stress between W PFM and Cu heat sink in the fusion reactors.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1327-1338
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• 2015

In this paper, we introduce and study the w-weak global dimension w-w.gl.dim(R) of a commutative ring R. As an application, it is shown that an integral domain R is a $Pr\ddot{u}fer$ v-multiplication domain if and only if w-w.gl.dim(R) ${\leq}1$. We also show that there is a large class of domains in which Hilbert's syzygy Theorem for the w-weak global dimension does not hold. Namely, we prove that if R is an integral domain (but not a field) for which the polynomial ring R[x] is w-coherent, then w-w.gl.dim(R[x]) = w-w.gl.dim(R).

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.509-525
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• 2014

Let R be a commutative ring with identity. An R-module M is said to be w-projective if $Ext\frac{1}{R}$(M,N) is GV-torsion for any torsion-free w-module N. In this paper, we define a ring R to be w-semi-hereditary if every finite type ideal of R is w-projective. To characterize w-semi-hereditary rings, we introduce the concept of w-injective modules and study some basic properties of w-injective modules. Using these concepts, we show that R is w-semi-hereditary if and only if the total quotient ring T(R) of R is a von Neumann regular ring and $R_m$ is a valuation domain for any maximal w-ideal m of R. It is also shown that a connected ring R is w-semi-hereditary if and only if R is a Pr$\ddot{u}$fer v-multiplication domain.

• Journal of the Korea Organic Resources Recycling Association
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• v.6 no.2
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• pp.45-57
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• 1998

The object of this experiment was to determine the optimum mixing ratio of paper mill sludge and sewage sludge with woodchips as a bulking agent. The bulking agent was mixed with the mixture of paper mill sludge and sewage sludge(2:1 by dried weight) at the rates of 0(W-0), 20(W-20), 33(W-33), and 50(W-50)% on volume basis, and then the mixtures were composted by forced aerated static pile. The changes of physicochemical properties of the mixtures were measured during the composting in order to evaluate the maturity of composts. The temperatures of W-30 and W-50 treatments increased rapidly as soon as the composting started, and reached $60^{\circ}C$ in the fifth day of composting. Reduction of hot water soluble C/N ratio of W-33 and W-50 treatments showed faster than that of W-0 and W-20 treatments at early stage of the composting. The contents of hot water soluble $NO_3{^-}-N$ showed little change in the early stage of the composting in all treatments, but increased rapidly after 20 days of the composting, and the contents of W-0 among all treatments were lower than the others. The G.I. values of W-50 treatment were over 80 before 20 days after starting the composting, those of W-0 treatment were over 80 after 30 days. As a result of evaluation of compost, W-33 and W-50 treatments were found very reasonable at the mixing ratio of a bulking agent. But it is very difficult to aerate compost pile for W-50 treatment than W-33 treatment due to intensified fluctuation of temperature. Considering cost, availability of a bulking agent, and productivity of compost, W-33 treatments more efficient than W-50 treatment.

• Journal of the Korean Society of Food Science and Nutrition
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• v.19 no.6
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• pp.612-616
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• 1990

The addition of water into oil phase containing hydrophobic emulsifier while stirring forms W/O emulsions. When dispersed phase increase up to a certain extent, phase inversion into O/W emulsions occurs and just before phase inversion O/W/O emulsions exist in a mixed state with W/O emulsions. Thus this experiment was carried out to examine O/W/O emulsions formation in W/O emulsions. The viscosity of sample emulsions(water phase： $H_2O$, oil phase : TGCR-containing olive oil) was measured at the shear rate of 1.92 to 384 per second and at temperature of 25$\pm$0.1$^{\circ}C$, and the development of O/W/O emulsions evaluated from the difference between theoretical and measured values by substituting measured value for Mooney's equation. The formation of O/W/O emulsions tended to be high in sample emulsions just before phase inversion and increase with decreasing TGCR concentrations. This result suggests that high viscosity observed right before phase inversion may also be caused by the formation of O/W/O emulsions.

• Journal of the Korean Society of Food Science and Nutrition
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• v.24 no.6
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• pp.901-905
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• 1995

Three flavonoid compounds, astragalin(1), isoquercitrin(2) and quercetin $3-O-{\beta}-D-xylopyranosyl(1-2)-{\beta}-D-glucopyranoside(3)$ isolated from the leaves of Eucommia ulmoides were identified and quantified by HPLC. All flavonoids were well separated on a ${\mu}-Bondapak\;C_{18}$ column with a mobile phase composed of THF-dioxane-MeOH-HOAc-5% $H_3PO_4-H_2O$(145 : 125 : 50 : 20 : 2 : 658). The contents of compound 1 in the methanol extract and n-butanol fraction were 0.09%(w/w) and 0.46%(w/w), of compound 2 were 0.08%(w/w) and 0.48%(w/w), and of compound 3 were 0.40%(w/w) and 1.22%(w/w), respectively.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1351-1365
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• 2020

Let S and T be w-linked extension domains of a domain R with S ⊆ T. In this paper, we define what satisfying the w_R-GD property for S ⊆ T means and what being w_R- or w-GD domains for T means. Then some sufficient conditions are given for the w_R-GD property and w_R-GD domains. For example, if T is w_R-integral over S and S is integrally closed, then the w_R-GD property holds. It is also given that S is a w_R-GD domain if and only if S ⊆ T satisfies the w_R-GD property for each w_R-linked valuation overring T of S, if and only if S ⊆ (S[u])_w satisfies the w_R-GD property for each element u in the quotient field of S, if and only if S_𝔪 is a GD domain for each maximal w_R-ideal 𝔪 of S. Then we focus on discussing the relationship among GD domains, w-GD domains, w_R-GD domains, Prüfer domains, PνMDs and Pw_RMDs, and also provide some relevant counterexamples. As an application, we give a new characterization of Pw_RMDs. We show that S is a Pw_RMD if and only if S is a w_R-GD domain and every w_R-linked overring of S that satisfies the w_R-GD property is w_R-flat over S. Furthermore, examples are provided to show these two conditions are necessary for Pw_RMDs.