• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.329-338
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• 2014

In this paper, we study the method of upper and lower solutions and develop the generalized quasilinearization technique for the existence and approximation of solutions to some three-point nonlocal boundary value problems associated with higher order fractional differential equations of the type $$^c{\mathcal{D}}^q_{0+}u(t)+f(t,u(t))=0,\;t{\in}(0,1)$$ $$u^{\prime}(0)={\gamma}u^{\prime}({\eta}),\;u^{\prime\prime}(0)=0,\;u^{\prime\prime\prime}(0)=0,{\ldots},u^{(n-1)}(0)=0,\;u(1)={\delta}u({\eta})$$, where, n-1 < q < n, $n({\geq}3){\in}\mathbb{N}$, 0 < ${\eta},{\gamma},{\delta}$ < 1 and $^c\mathcal{D}^q_{0+}$ is the Caputo fractional derivative of order q. The nonlinear function f is assumed to be continuous.

• Journal of Industrial Technology
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• v.21 no.B
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• pp.331-339
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• 2001

Zero to tension fatigue tests and strain controlled fatigue tests were carried out to find how initial strain induced martensite, ${\alpha}^{\prime}$ affects low and high cycle fatigue behavior and fatigue crack growth mechanisms. Microscopic study and phase analysis were carried out with TEM, SEM, EDAX, Optical Microscope, Ferriscope, and X-ray diffractometry. The amount of Initial ${\alpha}^{\prime}$ was controlled from 0% to 33% by controlling the temperatures for cold working and heat treatment. Lower contents of initial ${\alpha}^{\prime}$ showed higher fatigue resistance in low cycle fatigue but lower fatigue resistance in high cycle fatigue because it is ascribed to the more transformation of ${\alpha}^{\prime}$ martensite during low cycle fatigue and higher ductility. In high cycle fatigue, fatigue life is attributed to the strength and phase transformation of austenite into ${\alpha}^{\prime}$ during fatigue was negligible. ${\gamma}$ boundary, ${\gamma}/twin$ boundary, and ${\gamma}/{\alpha}^{\prime}$ boundary were found to be the preferred site of fatigue crack initiation.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1051-1060
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• 2009

In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact $T_1$-subspace. We also study the zero-divisor graph $\Gamma_I$(R) with respect to the completely semiprime ideal I of N. We show that ${\Gamma}_{\mathbb{P}}$ (R), where $\mathbb{P}$ is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph ${\Gamma}_{\mathbb{P}}$ (R).

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.269-284
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• 2016

In this paper, we firstly use Krasnosel'skii fixed point theorem to investigate positive solutions for the following three-point boundary value problems for p-Laplacian with a parameter $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+{\lambda}f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕ_p(s) = |s|^p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1), λ > 0 is a parameter. Then we use Leggett-Williams fixed point theorem to study the existence of three positive solutions for the fractional boundary value problem $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕ_p(s) = |s|^p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1).

• Kyungpook Mathematical Journal
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• v.27 no.2
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• pp.191-195
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• 1987

In this note we introduce the concept of a lower radical for ${\Gamma}$-rings. As an application we also characterise the prime radical introduced by Barnes [1] as a lower radical. Furthermore it is shown that the prime radical can also be determined by the class of all semiprime ${\Gamma}$-rings.

• Journal of Korea Foundry Society
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• v.36 no.5
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• pp.159-166
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• 2016

The microstructural evolution of a cast Ni base superalloy, IN738LC, has been investigated after long term exposure at several temperatures. Most of the fine secondary ${\gamma}^{\prime}$ particles resolved after 2000 hour exposure at $816^{\circ}C$. At higher temperatures of $871^{\circ}C$ and $927^{\circ}C$, secondary ${\gamma}^{\prime}$ resolved after 1000 hours of exposure, and cuboidal primary ${\gamma}^{\prime}$ grew with exposure time. During the thermal exposure, ${\sigma}$ phase formed at all tested temperatures, and ${\eta}$ phase was observed around interdendritic regions due to carbide degeneration. The influence of microstructural evolution during thermal exposure on the mechanical properties has been analyzed. The effects of ${\gamma}^{\prime}$ particle growth are more pronounced on the high temperature creep properties than on the room temperature tensile properties.

• Journal of the Korean Society for Heat Treatment
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• v.21 no.5
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• pp.251-258
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• 2008

A transmission electron microscope investigation has been performed on the morphology of dislocations in deformed ${\gamma}^{\prime}-Ni_3(Al,Ti)$ alloys containing fine dispersion of disordered ${\gamma}$ particles. Superlattice dislocations dissociate into fourfold Shockley partial dislocations in a uniform supersaturated solid solution of the ${\gamma}^{\prime}$ phase. Dislocations are attracted into the disordered ${\gamma}$ phase and dissociate further in the particles. At any stage of aging, dislocations cut through the particles and the Orowan bypassing process does not occur even in the over-aged stage of this alloy system. The work necessary to pull the dislocation away from the disordered particles into the ordered matrix should mainly contribute to increase the strength of the ${\gamma}^{\prime}$ phase containing fine dispersion of the disordered ${\gamma}$ phase.

• Journal of Radiation Protection and Research
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• v.43 no.2
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• pp.75-84
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• 2018

Background: Gamma-ray spectrometry helps in radiation shielding problems and different applications of radioisotopes. Experimental arrangements including broad beam geometries are widely used. The aim is to investigate and evaluate the ${\gamma}-ray$ spectra via attenuation by environmental materials. Materials and Methods: The photo peak to nominated parts in the ${\gamma}-ray$ spectra and the attenuation coefficients ${\mu}_b/{\rho}$ from broad beam geometries are measured for the materials water, soil, sand and cement at the energies 0.662, 1.25, and 1.332 MeV with a $3{^{\prime}^{\prime}}{\times}3{^{\prime}^{\prime}}$ NaI(Tl) detector. Results and Discussion: The ${\gamma}-ray$ spectra vary according to changes in the effective atomic number $Z_{eff}$ of the attenuator, the photon energy and the solid angle. The peak to total ratios are the most sensitive parts to variations in the experimental conditions and overturn in the region 0.663 MeV to 1.332 MeV. This is indicated as inversion trend. The results are discussed in view of $Z_{eff}$ and the experimental conditions. The intensity build-up is larger at the lower energy and larger scattering angles in agreement with Klein-Nishina formula and other results. The build-up factor B is$${\sim_=}$$1 at high ${\gamma}-energies$ and small scattering angles. Conclusion: The sensitivity to material characteristics decrease gradually from peak: to total, to Compton valley, to Compton plateau ratios. Rigorous collimation is necessary at small energies. Cement, of the largest $Z_{eff}$, is characterized by the maximum broad beam mass attenuation coefficients ${\mu}_b/{\rho}$. The obtained results provide information to decide for the suitable experimental set-up based on aim of the work.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.139-144
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• 2000

The generalized noncommutative torus $T_{\rho}^d$ of rank m was defined in [2]. Assume that for the completely irrational noncommutative subtorus $A_{\rho}$ of rank m of $T_{\rho}^d$ there is no integer q > 1 such that $tr(K_0(A_{\rho}))=\frac{1}{q}{\cdot}tr(K_0(A_{\rho^{\prime}}))$ for $A_{\rho^{\prime}}$ a completely irrational noncommutative torus of rank m. All $C^*$-algebras ${\Gamma}({\eta})$ of sections of locally trivial $C^*$-algebra bundles ${\eta}$ over $M=\prod_{i=1}^{e}S^{2k_i}{\times}\prod_{i=1}^{s}S^{2n_i+1}$, $\prod_{i=1}^{s}\mathbb{PR}_{2n_i}$, or $\prod_{i=1}^{s}L_{k_i}(n_i)$ with fibres $T_{\rho}^d{\otimes}M_c(\mathbb{C})$ were constructed in [6, 7, 8]. We prove that ${\Gamma}({\eta}){\otimes}M_{p^{\infty}}$ is isomorphic to $C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C}){\otimes}M_{p^{\infty}}$ if and only if the set of prime factors of cd is a subset of the set of prime factors of p, that $\mathcal{O}_{2u}{\otimes}{\Gamma}({\eta})$ is isomorphic to $\mathcal{O}_{2u}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if and only if cd and 2u - 1 are relatively prime, and that $\mathcal{O}_{\infty}{\otimes}{\Gamma}({\eta})$ is not isomorphic to $\mathcal{O}_{\infty}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if cd > 1 when no non-trivial matrix algebra can be ${\Gamma}({\eta})$.

• Korean Journal of Materials Research
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• v.25 no.11
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• pp.630-635
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• 2015

The fatigue strength of a nickel-base superalloy was studied. Stress-controlled fatigue tests were carried out at $700^{\circ}C$ and 5 Hz using triangular wave forms. In this study, two kinds of testing procedures were adopted. One is the conventional tension-zero fatigue test(R = 0). The other was a procedure in which the maximum stress was held at 1000 MPa and the minimum stress was diverse from zero to 1000 MPa at 24 and $700^{\circ}C$. The results of the fatigue tests at $700^{\circ}C$ indicate that the fracture mechanism changed according to both the mean stress and the stress range. At a higher stress range, ${\gamma}^{\prime}$ precipitates are sheared by a/2<110> dislocation pairs coupled by APB. Therefore, in a large stress range, the deformation occurred by shearing of ${\gamma}^{\prime}$ by a/2<110> dislocations, which brought about crystallographic shear fracture. As the stress range was decreased, the fracture mode gradually changed from crystallographic shear fracture to gradual growth of fatigue cracks. At an intermediate stress range, as it became more difficult for a/2<110> dislocation pairs to shear ${\gamma}^{\prime}$ particles, cracks started to propagate in the matrix, avoiding the harder ${\gamma}^{\prime}$ particles. High mean stress induced creep deformation, that is, ${\gamma}^{\prime}$ particles were sheared by {111}<112> slip systems, which led to the formation of stacking faults in the precipitates. Thus, the change in fracture mechanism brought about the inversion of the S-N curves.