• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.689-702
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• 2019

Let 𝓐 and 𝓑 be real (or complex) algebras. We investigate the stability of a sequence F = {f₀, f₁, ⋯, f_n, ⋯ } of mappings from 𝓐 into 𝓑 satisfying the higher functional equation: $$f_n(x+y+zw)=f_n(x)+f_n(y)+\;{\normalsize\sum\limits_{\tiny{i+j=n \atop i{\leq}j}}}\;[f_i(z)f_j(w)+c_{ij}f_i(w)f_j(z)]$$ for each n = 0, 1, ⋯ and all x, y, z, w ∈ 𝓐, where $$c_{ij}=\left\{1{\text{ if }}i{\neq}j,\\0{\text{ if }}i=j.\right.$$.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.475-484
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• 2005

Let W(t) be a Wiener path, let $\xi\;:\;[0,\;{\infty})\;\to\;\mathbb{R}$ be a continuous and increasing function satisfying $\xi$(0) > 0, let $$T_{/xi}=inf\{t{\geq}0\;:\;W(t){\geq}\xi(t)\}$$ be the first-passage time of W over $\xi$, and let F denote the distribution function of $T_{\xi}$. Then the first passage problem has a unique continuous solution as following $$F(t)=u(t)+{\sum_{n=1}^\infty}\int_0^t\;H_n(t,s)u(s)ds$$, where $$u(t)=2\Psi(\xi(t)/\sqrt{t})\;and\;H_1(t,s)=d\Phi\;(\{\xi(t)-\xi(s)\}/\sqrt{t-s})/ds\;for\;0\;{\leq}\;s.

• Journal of the Korean institute of surface engineering
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• v.22 no.1
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• pp.17-25
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• 1989

The structural Charactesties and adhesion of chemically vapor deposited TiN film on stain less steels have been investated as functions of deposition temperature, surface roughness of sub state, and types of substrates. The grain zine and the lattice parameter of TiN film decreased with decreasing roughness of substates. The(200) preferred orientation was developed dominatly and the lattlice parameter decreased as temperature intereased reardless of the surdless roughnessand type of the substrates used. The surface morphology of TiN film changed from bushed crystal to a plate and then to pyamidal dense crystals with an increase in the deposition temperature. The adhesion of TiN films increased with coating thinkness and decreased with surface roughness in general. The calculations using a Bejamin & Weaver's model have been compard. Maximum valuse of adhesion energy calculated using Laguier's model were W304=331Jm-2,w410=113Jm-2,andW430=107jm-2

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.697-705
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• 2014

For a complex measure ${\mu}$ on B and $f{\in}L^2_a(B)$, the Toeplitz operator $T_{\mu}$ on $L^2_a(B,dv)$ with symbol ${\mu}$ is formally defined by $T_{\mu}(f)(w)=\int_{B}f(w)\bar{K(z,w)}d{\mu}(w)$. We will investigate properties of the Toeplitz operator $T_{\mu}$ with symbol ${\mu}$. We define the Toeplitz type operator $T^r_{\psi}$ with symbol ${\psi}$, $$T^r_{\psi}f(z)=c_r\int_{B}\frac{(1-{\parallel}w{\parallel}^2)^r}{(1-{\langle}z,w{\rangle})^{n+r+1}}{\psi}(w)f(w)d{\nu}(w)$$. We will also investigate properties of the Toeplitz type operator with symbol ${\psi}$.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.30 no.4
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• pp.543-549
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• 1997

The problems in the existing modeling rules for fishing nets, especially in the Tauti's rule which had been used most commonly, were investigated and it was found that the rules could not give a good similarity between the prototype and model nets because they din neither analyze the flow resistance of nets accurately nor decide the ratio of flow velocity between the two nets properly. Thus, the modeling rule was newly derived by regarding the nets as holey structures sucking water into their mouth and then filtering water through their meshes as in the previous paper. The similarity conditions obtained, between the two nets distinguished by subscript 1 and 2, are as follows; $$\frac{d_2}{d_1}=\sqrt{\frac{l_2}{l_1}},\;\frac{N_2}{N_1}=(\frac{d_1}{d_2})^{1.5}\frac{L_2}{L_1},\;\varphi_1=\varphi_2,\;\frac{d_{r2}}{d_{r1}}=\sqrt{\frac{L_2{(\rho_{r1}-\rho_{w1})}}{{L_1{(\rho_{r2}-\rho_{w2})}}$$ $$\frac{N_{a2}}{N_{a1}}=\frac{W_{a1}}{W_{a2}}(\frac{L_2}{L_1})^2,\;\nu_1=\nu_2\;and\;\frac{R_2}{R_1}=(\frac{L_2}{L_1})^2$$, where L is the length of nettings, d the diameter of netting twines, 2l the mesh size, $2\varphi$ the angle between two adjacent bars, N the number of meshes at the sides of nettings, $d_r$, the diameter of ropes, $\rho_r$, the specific gravity of ropes, $W_a$ the weight in water of one piece of float or sinker, $N_a$ the number of floats or sinkers, $\nu$ the flow velocity, and R the flow resistance of net. In the case where the model experiments aim at investigating the influence of weight in water of nettings on their shapes in nets subjected to the water flow of very low velocity, however, the following condition is added; $$\frac{\rho_2-\rho_{w2}}{\rho_1-\rho_{w1}}=\frac{d_1}{d_2}$$ where $\rho$ is the specific gravity of netting twines.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1905-1914
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• 2013

Let D be an integral domain with quotient field K, M a torsion-free D-module, X an indeterminate, and $N_v=\{f{\in}D[X]|c(f)_v=D\}$. Let $q(M)=M{\otimes}_D\;K$ and $M_{w_D}$={$x{\in}q(M)|xJ{\subseteq}M$ for a nonzero finitely generated ideal J of D with $J_v$ = D}. In this paper, we show that $M_{w_D}=M[X]_{N_v}{\cap}q(M)$ and $(M[X])_{w_{D[X]}}{\cap}q(M)[X]=M_{w_D}[X]=M[X]_{N_v}{\cap}q(M)[X]$. Using these results, we prove that M is a strong Mori D-module if and only if M[X] is a strong Mori D[X]-module if and only if $M[X]_{N_v}$ is a Noetherian $D[X]_{N_v}$-module. This is a generalization of the fact that D is a strong Mori domain if and only if D[X] is a strong Mori domain if and only if $D[X]_{N_v}$ is a Noetherian domain.

• Membrane and Water Treatment
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• v.10 no.5
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• pp.361-372
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• 2019

Effect of different alkane based solvents on the stability of emulsion liquid membrane was investigated using normal alkanes (n-hexane, n-heptane, n-octane and n-decane) under various operating parameters of surfactant concentration, emulsification time, internal phase concentration, volume ratio of internal phase to organic phase, volume ratio of emulsion phase to external phase and stirring speed. Results of stability revealed that emulsion liquid membrane containing n-octane as solvent and span-80 (5 % (w/w)) as emulsifying agent presented the highest amount of emulsion stability (the lowest breakage) compared with other solvents; however, operating parameters (surfactant concentration (5% (w/w)), emulsification time (6 min), internal phase concentration (0.05 M), volume ratio of internal phase to organic phase (1/1), volume ratio of emulsion phase to external phase (1/5) and stirring speed (300 rpm)) were also influential on improving the stability (about 0.2% breakage) and on achieving the most stable emulsion. The membrane with the highest stability was employed to extract acridine orange with various concentrations (10, 20 and 40 ppm) from water. The emulsion liquid membrane prepared with n-octane as the best solvent almost removed 99.5% of acridine orange from water. Also, the prepared liquid membrane eliminated completely (100%) other cationic dyes (methylene blue, methyl violet and crystal violet) from water demonstrating the efficacy of prepared emulsion liquid membrane in treatment of dye polluted waters.

• Korean Journal of Materials Research
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• v.3 no.5
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• pp.466-475
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• 1993

Adhesion of W to TiN which is used as a glue layer in the blanket tungsten process has been investigated using the pulling and scratch methods and analysed using surface roughness measurements by SEM and the reflectivity measurement, the stress measurement and the SIMS depth profiling Significant differences between the adhesion of the CVD tungsten film to the s-TiN and that to the a-TiN were found. It appeared that the fomer were better than the latter, which is due to the facts that the s-TiN film has a rougher surface and a lower stress level and a higher oxygen content than the a-TiN film. Also the ashesion strength was degreaded with increasing the TIN film thickness because of the increase of the TiN film stress.

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.5
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• pp.46-54
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• 1984

A silicon-gate n-well CMOS process with 3 $\mu$m gate length was developed and its possibility for the applications was discussed,. Threshold voltage was easily controlled by ion implantation and 3-$\mu$m gate length with 650 $\AA$ oxide shows ignorable short channel effect. Large value of Al-n+ contact resistance is one of the problems in fabrications of VLSI circuits. Transfer characteristics of CMOS inverter is fairly good and the propagation delay time per stage in ring oscillator with layout of (W/L) PMOS /(W/L) NMOS =(10/5)/(5/5) is about 3.4 nsec. catch-up occurs on substrate current of 3-5 mA in this process and critically dependent on the well doping density and nt-source to n-well space. Therefore, research, more on latch-up characteristics as a function of n-well profile and design rule, especially n+-source to n-well space, is required.

• Journal of the Korean Geotechnical Society
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• v.35 no.3
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• pp.5-16
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• 2019

With the recent concentration of urban populations, the constructions of large structures are increasing, along with the development of foundations for large structures. PHC Piles have been used in many structures ever since Japanese introduced the technology at the end of the 20th century. Recently, many studies on the use of the PHC Pile have been carried out as earth retaining using the merits of PHC piles. In this study, static axial compression tests were conducted on the PHC-W piles constructed as column-type in building underground additional wall using the PHC-W earth retaining wall. The end bearing capacity of pile was calculated using the axial load transfer measurement that was obtained from the static axial compression test result. Since end bearing capacity of the PHC-W pile embedded in weathered rock showed a different behaviour from the conventional PHC pile, the calculation method of end bearing capacity for column-type PHC-W piles would be proposed. The unit ultimate end bearing equation proposed for single and group PHC-W pile embedded in weathered rock is $q_b=13.3N_b$ and $q_b=6.8N_b$.