• The Pure and Applied Mathematics
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• v.10 no.4
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• pp.207-215
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• 2003

Let R be a prime ring with characteristic different from two and let $\theta,\varphi,\sigma,\tau$ be the automorphisms of R. Let d : $R{\rightarrow}R$ be a nonzero ($\theta,\varphi$)-derivation. We prove the following results: (i) if $a{\in}R$ and [d(R), a]$_{{\theta}o{\sigma},{\varphi}o{\tau}}$=0, then $\sigma(a)\;+\;\tau(a)\;\in\;Z$, the center of R, (ii) if $d([R,a]_{\sigma,\;\tau)\;=\;0,\;then\;\sigma(a)\;+\;\tau(a)\;\in\;Z$, (iii) if $[ad(x),\;x]_{\sigma,\;\tau}\;=\;0;for\;all\;x\;\in\;RE$, then a = 0 or R is commutative.

• International Journal of Air-Conditioning and Refrigeration
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• v.9 no.3
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• pp.1-9
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• 2001

In this study, condensation heat transfer coefficients (HTCs) of nonazeotropic refrigerant mixtures of HFC32/HFC 134a and HCFC123 at various compositions were measured on a horizontal smooth tube. All data were taken at the vapor temperature of 39$^{\circ}C$ with a wall subcooling of 3~8K. Test results showed that HTCs of tested mixtures were 11.0~85.0% lowed than the ideal values calculated by the mass fraction weighting of the HTCs of the pure components. Thermal resistance due to the diffusion vapor film was partly responsible for the significant reduction of HTCs with these nonazeotropic mixtures. The measured data were compared against thc predicted ones by Colburn and Drew's film model and a good agreement was observed within a deviation of 15%.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.167-172
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• 1994

For a given $C^{*}$-dynamical system (A, G, .alpha.) with a G-simple $C^{*}$-algebra A (that is A has no proper .alpha.-invariant ideal) many authors have studied the simplicity of a $C^{*}$-crossed product A $x_{\alpha{r}}$ G. In [1] topological freeness of an action is shown to guarantee the simplicity of the reduced $C^{*}$-crossed product A $x_{\alpha{r}}$ G when A is G-simple. In this paper we investigate the pure infiniteness of a simple $C^{*}$-crossed product A $x_{\alpha}$ G of a purely infinite simple $C^{*}$-algebra A and a topologically free action .alpha. of a finite group G, and find a sufficient condition in terms of the action on the spectrum of the multiplier algebra M(A) of A. Showing this we also prove that some extension of a topologically free action is still topologically free.

• The Pure and Applied Mathematics
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• v.1 no.1
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• pp.1-6
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• 1994

In this paper, some properties for a PI-ring satisfying the descending chain condition on essential left ideals are studied: Let R be a ring with a polynomial identity satisfying the descending chain condition on essential ideals. Then all minimal prime ideals in R are maximal ideals. Moreover, if R has only finitely many minimal prime ideals, then R is left and right Artinian. Consequently, if every primeideal of R is finitely generated as a left ideal, then R is left and right Artinian. A finitely generated PI-algebra over a commutative Noetherian ring satisfying the descending chain condition on essential left ideals is a finite module over its center.(omitted)

• Structural Engineering and Mechanics
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• v.42 no.3
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• pp.313-334
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• 2012

This paper examines the problem of a penny-shaped crack in a thermoporoelastic body. On the basis of the recently developed general solutions for thermoporoelasticity, appropriate potentials are suggested and the governing equations are solved in view of the similarity to those for pure elasticity. Exact and closed form fundamental solutions are expressed in terms of elementary functions. The singularity behavior is then discussed. The present solutions are compared with those in literature and an excellent agreement is achieved. Numerical calculations are performed to show the influence of the material parameters upon the distribution of the thermoporoelastic field. Due to its ideal property, the present solution is a natural benchmark to various numerical codes and simplified analyses.

• The Pure and Applied Mathematics
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• v.13 no.3 s.33
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• pp.189-195
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• 2006

Let R be a prime ring with characteristics not 2 and ${\sigma},\;{\tau},\;{\alpha},\;{\beta}$ be auto-morphisms of R. Suppose that $d_1$ is a (${\sigma},\;{\tau}$)-derivation and $d_2$ is a (${\alpha},\;{\beta}$)-derivation on R such that $d_{2}{\alpha}\;=\;{\alpha}d_2,\;d_2{\beta}\;=\;{\beta}d_2$. In this note it is shown that; (1) If $d_1d_2$(R) = 0 then $d_1$ = 0 or $d_2$ = 0. (2) If [$d_1(R),d_2(R)$] = 0 then R is commutative. (3) If($d_1(R),d_2(R)$) = 0 then R is commutative. (4) If $[d_1(R),d_2(R)]_{\sigma,\tau}$ = 0 then R is commutative.

• The Pure and Applied Mathematics
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• v.11 no.2
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• pp.117-125
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• 2004

Let T be an integral domain, M a nonzero maximal ideal of T, K = T/M, $\psi$: T \longrightarrow K the canonical map, D a proper subring of K, and R = $\psi^{-1}$(D) the pullback domain. Assume that for each $x \; \in T$, there is a $u \; \in T$ such that u is a unit in T and $ux \; \in R$, . In this paper, we show that R is a weakly Krull domain (resp., GWFD, AWFD, WFD) if and only if htM = 1, D is a field, and T is a weakly Krull domain (resp., GWFD, AWFD, WFD).

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.1-7
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• 2022

A mapping T : R → R (not necessarily additive) is called multiplicative left 𝛼-centralizer if T(xy) = T(x)𝛼(y) for all x, y ∈ R. A mapping F : R → R (not necessarily additive) is called multiplicative (generalized)(𝛼, 𝛽)-derivation if there exists a map (neither necessarily additive nor derivation) f : R → R such that F(xy) = F(x)𝛼(y) + 𝛽(x)f(y) for all x, y ∈ R, where 𝛼 and 𝛽 are automorphisms on R. The main purpose of this paper is to study some algebraic identities with multiplicative (generalized) (𝛼, 𝛽)-derivations and multiplicative left 𝛼-centralizer on the left ideal of a prime ring R.

• Tribology and Lubricants
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• v.39 no.6
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• pp.228-234
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• 2023

In this study, reciprocating wear tests are performed on AISI 52100 bearing steel to investigate its tribological behavior in a hexagonal boron nitride (h-BN) water solution. The h-BN-based aqueous lubricant is prepared using an atoxic procedure called ultrasonic sonication in pure water. Ball-on-flat reciprocating sliding experiments are conducted, where the ball is slewed on a fixed flat at 50-㎛ displacement. The lubricating behavior of h-BN is compared with that of deionized (DI) water. Results show that the friction coefficient is higher in h-BN testing than that in DI tests, but the results are equalized as the friction coefficient reaches a stable level. Scanning electron microscopic images reveal significant material loss in the center and mild abrasion on the edge of the wear scar in h-BN tests. However, these effects are minor in DI water situations. The results of energy-dispersive X-ray spectroscopy show that considerable oxidation occurs in the central zone of the wear scar in h-BN cases with strong adhesion and material removal. These findings reveal the importance of determining ideal circumstances that can tolerate material friction and wear.

• Journal of the Korean Applied Science and Technology
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• v.37 no.3
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• pp.438-447
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• 2020

The critical micelle concentration (CMC) values of the mixed surfactant systems and the solubilization conatant (K_s) values of 4-ethylaniline in those solutions were measured and analyzed by the UV-Vis method. As a result, the mixed surfactant systems of TTAB/LSB and TTAB/TX-100 did not deviate significantly from ideal mixed micellization. However, the mixed systems of SDS/LSB and SDS/TX-100 showed great negative deviations from ideal mixed model. These differences showed that the intensity of the interaction between two components in the mixed micelle was different for each mixed system and that these differences greatly influenced the solubilization of 4-ethylaniline by a mixed surfactant system. Among pure surfactants, an anionic surfactant such as SDS showed a greater K_s value than other ionic surfactants, and the K_s value by each surfactant system decreased in the order of SDS≫TTAB≧LSB>TX-100. In addition, the K_s values of all the mixed surfactant systems were higher than those of the pure surfactants constituting the mixed systems.