• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.249-259
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• 2022

Let 𝓐 be a unital C^*-algebra. Then it follows that $\sum\limits_{i=1}^{n}(a_ia^*_i)^{\frac{1}{2}}{\leq}\sqrt{n}\(\sum\limits_{i=1}^{n}a_ia^*_i\)^{\frac{1}{2}}$, ∀n ∈ ℕ, ∀a₁, …, a_n ∈ 𝓐. By modifications of arguments of Botelho-Andrade, Casazza, Cheng, and Tran given in 2019, for certain n-tuple x = (a₁, …, a_n) ∈ 𝓐ⁿ, we give a method to compute a positive element c_x in the C^*-algebra 𝓐 such that the equality $$\sum\limits_{i=1}^{n}(a_ia^*_i)^{\frac{1}{2}}=c_x\sqrt{n}\(\sum\limits_{i=1}^{n}a_ia^*_i\)^{\frac{1}{2}}$$ holds. We give an application for the integral of Kasparov. We also derive a formula for the exact constant for the continuous ℓ₁ - ℓ₂ inequality.

• Journal of environmental and Sanitary engineering
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• v.15 no.3
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• pp.23-23
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• 2000

In this study, to determine the optimum fermentation process for the feed production of food wastes and estimate the practical value of fermented feed using kudzu creeper and sawdust as bulking agent. This study considered initial C/N ratio control as the fermentation process variables. The results are summarized as follows. Minimum water contents of byproducts in the fermentation feed production showed 3994(kudzu), 37%( sawdust) at the C/N ratio 25 and 45%(kudzu, sawdust) at the C/N ratio 35. Temperature variations in the fermentation feed production at the C/n ratio 25 indicated 68'C(kudzu), 70'C (sawdust).Optimum condition of consists of fermentation process of water content, C/N ratio and permeability (porous structure of the mixture). For optimum fermentation of gravitationally, dewatered garbage, the proper mixing ratios of kudzu(moisture contents : 17.3%) and sawdust(moisture contents : 13.2%) were 41% and 39%, respectively Major biological reaction in the aerobic fermentation feed production occurred during 12~14hrs

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.525-534
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• 2019

Let $P(G,{\lambda})$ denote the number of proper vertex colorings of G with ${\lambda}$ colors. The chromatic polynomial $P(C_n,{\lambda})$ for the cycle graph $C_n$ is well-known as $$P(C_n,{\lambda})=({\lambda}-1)^n+(-1)^n({\lambda}-1)$$ for all positive integers $n{\geq}1$. Also its inductive proof is widely well-known by the deletion-contraction recurrence. In this paper, we give this inductive proof again and three other proofs of this formula of the chromatic polynomial for the cycle graph $C_n$.

• Journal of the Korean Chemical Society
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• v.15 no.5
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• pp.228-235
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• 1971

The solubilities of n-butyl bromide in nitrobenzene and in 1,2,4-trichlorobenzene have been measured at $19^{\circ},\;25^{\circ},\;and\;40^{\circ}C$ in the presence and absence of gallium bromide. When gallium bromide does not exist in the system, the solubility of n-butyl bromide in nitrobenzene is greater than in 1,2,4-trichlorobenzene, indicating a stronger interaction of n-butyl bromide with nitrobenzene than with 1,2,4-trichlorobenzene. In the presence of gallium bromide, complex of n-butyl bromide with gallium bromide, 1:1 complex, $n-C_4H_9Br{\cdot}GaBr_3$, is formed in the solution. The instability constant K of the complex was evaluated. $n-C_4H_9Br{\cdot}GaBr_3{\rightleftharpoons}n-C_4H_9Br+\frac{1}{2}Ga_2Br_6$ The changes of enthalpy, free energy and entropy for the dissociation of the complex were also calculated.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.10 no.4
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• pp.318-323
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• 2000

The intercalated compounds of alkylsulfonates into hydrated zinc were synthesized. From the high temperature powder X-ray diffraction (HTXRD), FT-IR, and molecular size, the temperature dependence of orientation for the intercalated alkylsulfonates were determined. In the temperatures range 1, alkylsulfonates were intercalated into hexa aqua zinc layer with the bilayer structure of $32.9^{\circ}$angle for ${Zn(H_2O_4]^{2+}[C_nH_{2n+1}SO_3]_2\;^-$. In the temperatures range 2, alkylsulfonates were intercalated into tetra aqua zinc layer with the bilayer structure of $55.2^{\circ}$angle for ${Zn(C_nH_{2n+1}SO_3)_2$. In the temperatures range 3, alkylsulfonates were directly bonded to zinc ion with the bilayer structure of $76.5^{\circ}$angle for ${Zn(C_nH_{2n+1}SO_3)_2$.

• The Korean Journal of Ceramics
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• v.5 no.4
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• pp.317-323
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• 1999

Si3N4-TiC composites have been known as electrically conductive ceramics. $Si_3N_4-TiC$ composites with 2 wt% $Al_2O_3$ and 4 wt% $Y_2O_3$ were hot pressed in $N_2$ environment. The mechanical properties including hardness, fracture toughness, and flexural strength and tribological properties were investigated as a function of TiC content. $Si_3N_4-40$ vol% TiC composite was hot pressed at $1,750^{\circ}C$, $1,800^{\circ}C$, and $1,850^{\circ}C$ for 1, 3 and 5 hours in $N_2$ gas. Mechanical and tribolgical properties depended on microstructures, which were controlled by hte TiC content, hot press temperature, and hot press holding time. However, mechanical properties and tribological behaviors were degraded by the chemical reaction between TiC and N. The chemically reacted products such as TiCN, SiC, and $SiO_2$ were detered by the X-ray diffraction analysis.

• Journal of Power System Engineering
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• v.18 no.1
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• pp.51-56
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• 2014

In this paper, the performance of the $CO_2-C_2H_6-N_2$ cascade liquefaction cycle with respect to temperature differences in the LNG heat exchangers is analyzed theoretically using HYSYS software and then compared the COP(coefficient of performance) of the cascade liquefaction cycles using $C_3H_8-C_2H_4-C_1H_4$ and $CO_2-N_2O-N_2$. In comparison of COP of three cycles, the cascade liquefaction cycles using $C_3H_8-C_2H_4-C_1H_4$ showed the highest COP. And the liquefaction cycle using $CO_2-C_2H_6-N_2$ and $CO_2-N_2O-N_2$ presented the second and third highest COP, respectively. In case of COP, the $C_3H_8-C_2H_4-C_1H_4$ cascade liquefaction cycle yields better COP. But, in terms of the environment and maintain, it is confirmed that the cascade liquefaction cycle using $CO_2-C_2H_6-N_2$ provides favorable characteristics.

• Journal of the Korean Ceramic Society
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• v.36 no.10
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• pp.1007-1015
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• 1999

The Si3N4 composites reinforced with carbon-coated SiC whiskers were fabricated by hot-pressing at 180$0^{\circ}C$ for 2 hours to examine the effects of carbon-coated whiskers on the mechanical properties of SiC whisker reinforced Si3N4 composites. The flexural strength of the Si3N4 composites and Si3N4 monolith respectively. The weak interfacial bond between carbon-coated SiC whiskers and Si3N4 matrix which enhances the crack deflection and whisker pull-out could contribute to the improvement of mechanical properties of the composites.

• Journal of the Korean Ceramic Society
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• v.31 no.1
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• pp.25-30
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• 1994

W-Ti-C-N based multiphase hard materials have been prepared from WC/TiN powder mixture. By sintering at and above 190$0^{\circ}C$, the two phases of powder mixture has transformed into intermixed W, W2C and Ti(C, N) phases. For the temperature range between 180$0^{\circ}C$ and 210$0^{\circ}C$, the sintered or hot pressed samples show maximum density and hardness. The seems that metallic W grains enhance the fracture toughness of materials. The wear resistance of the material is found to increase with increasing hardness.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.13-30
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• 2010

Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by $x_0\;{\in}\;C$ arbitrarily chosen, $x_{n+1}\;=\;{\alpha}_n{\gamma}f(W_nx_n)+{\beta}_nx_n+((1-{\beta}_n)I-{\alpha}_nA)W_nP_C(I-s_nB)x_n$, ${\forall}_n\;{\geq}\;0$, where $\gamma$ > 0, B : C $\rightarrow$ H is a $\beta$-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient $\alpha$ (0 < $\alpha$ < 1), $P_C$ is a projection of H onto C, A is a strongly positive linear bounded operator on H and $W_n$ is the W-mapping generated by a finite family of nonexpansive mappings $T_1$, $T_2$, ${\ldots}$, $T_N$ and {$\lambda_{n,1}$}, {$\lambda_{n,2}$}, ${\ldots}$, {$\lambda_{n,N}$}. Nonexpansivity of each $T_i$ ensures the nonexpansivity of $W_n$. We prove that the sequence {$x_n$} generated by the above iterative algorithm converges strongly to a common fixed point $q\;{\in}\;F$ := $\bigcap^N_{i=1}F(T_i)\;\bigcap\;VI(C,\;B)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)q,\;p\;-\;q{\rangle}\;{\leq}\;0$ for all $p\;{\in}\;F$. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.