• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권3호
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• pp.293-303
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• 2020

The present work aims to analyzed the transient thermoelastic stress analysis of a thin circular plate with uniform internal heat generation. Initially, the plate is characterized by a parabolic temperature distribution along the z-direction given by T = T₀(r, z) and perfectly insulated at the ends z = 0 and z = h. For times t > 0, the surface r = a is subjected to convection heat transfer with convection coefficient h_c and fluid temperature T_∞. The integral transform method used to obtain the analytical solution for temperature, displacement, and thermal stresses. The associated thermoelastic field is analyzed by making use of the temperature and thermoelastic displacement potential function. Numerical results are carried out with the help of computational software PTC Mathcad Prime-3.1 and shown in figures.

• 충청수학회지
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• 제22권4호
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• pp.743-748
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• 2009

In 1970, Fernique proved that there is a positive real number $\alpha$ such that $\int_{\mathbb{B}}\exp\{\alpha{\parallel}x{\parallel}^{2}\}dP(x)$ is finite where ($\mathbb{B},\;P$) is an abstract Wiener measure space and ${\parallel}\;{\cdot}\;{\parallel}$ is a measurable norm on ($\mathbb{B},\;P$) in [2, 3]. In this article, we investigate the existence of the integral $\int_{c}\exp\{\alpha(sup_t{\mid}x(t){\mid})^p\}dm_{\varphi}(x)$ where ($\mathcal{C}$, $m_{\varphi}$) is the analogue of Wiener measure space and p and $\alpha$ are both positive real numbers.

• 한국초전도ㆍ저온공학회논문지
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• 제3권2호
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• pp.77-83
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• 2001

The thermal characteristics of solid nitrogen are investigated by experiment and analysis for the purpose of evaluating its feasibility as a cooling medium for HTS (high T$_{c}$ superconductor) magnets. A cryostat to refrigerate a liquid-nitrogen container well below its freezing temperature with a 2-stage GM cryocooler is designed and constructed. The spatial distribution of temperature is measure as a function of time during the freezing and melting processes. from which the thermal diffusivity of solid nitrogen can be approximately calculated. the freezing process is formulated and solved by the integral method with an assumption of phase equilibrium at the solid-liquid interface and experimental observation. It may be concluded that the thermal diffusion in solid phase is much slower than in liquid and the degree of super-saturation is quite severe in the solidification of nitrogen.n.

• 대한수학회논문집
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• 제35권4호
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• pp.1123-1132
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• 2020

In the present paper, we define new class of functions T_α,β(λ; z) which is an extension of the classical Wright function and the Mittag-Leffler function. We show some mean value inequalities for the this function, such as Turán-type inequalities, Lazarević-type inequalities and Wilker-type inequalities. Moreover, integrals formula and integral inequality for the function T_α,β(λ; z) are presented.

• 대한수학회지
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• 제53권5호
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• pp.991-1017
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• 2016

In this paper we define a generalized analytic Fourier-Feynman transform associated with Gaussian process on the function space $C_{a,b}[0,T]$. We establish the existence of the generalized analytic Fourier-Feynman transform for certain bounded functionals on $C_{a,b}[0,T]$. We then proceed to establish a translation theorem for the generalized transform associated with Gaussian process.

• 한국해양공학회지
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• 제5권2호
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• pp.207-207
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• 1991

The crack length measurements by electrical potential(EP) method for 1% Cr-Mo-V and 12%Cr steel of 0.5T-CT specimen were performed at $500^{\circ}C, 600^{\circ}C 700^{\circ}C$, and an applicability of stress intensity factor($K_I$), net section stress($\sigma_{net}$), $C^*$-ingegral and $C_t$ parameter was studied to measure creep crack growth rate(da/dt) with side groove and without side groove under static and cyclic loading condition. The experimental result could be summarized as follows: 1) Crack measurement by EP method was available and coincided with the Johnson,s analytical equation. 2) da/dt by $K_I$ and $\sigma_{net}$ was not adequate because of the wide scatter band according to load and temperature, but $C^*$-integral, except for transition region, was adequate. 3) $C_t$ parameter showed the best fitted line through total creep region without relating with both temperature and load condition. 4) Under the cyclic loading condition, $C_t$ parameter was proper to extimate da/dt. And it was shown that da/dt for 1% Cr-Mo V steel under the static condition(R=1) was 1.16 times faster than the case under cyclic loading(R=0), and for 12% Cr steel, 1.43 times.

• 한국해양공학회지
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• 제5권2호
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• pp.67-75
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• 1991

The crack length measurements by electrical potential(EP) method for 1% Cr-Mo-V and 12%Cr steel of 0.5T-CT specimen were performed at $500^{\circ}C, 600^{\circ}C 700^{\circ}C$, and an applicability of stress intensity factor($K_I$), net section stress($\sigma_{net}$), $C^*$-ingegral and $C_t$ parameter was studied to measure creep crack growth rate(da/dt) with side groove and without side groove under static and cyclic loading condition. The experimental result could be summarized as follows: 1) Crack measurement by EP method was available and coincided with the Johnson, s analytical equation. 2) da/dt by $K_I$ and $\sigma_{net}$ was not adequate because of the wide scatter band according to load and temperature, but $C^*$-integral, except for transition region, was adequate. 3) $C_t$ parameter showed the best fitted line through total creep region without relating with both temperature and load condition. 4) Under the cyclic loading condition, $C_t$ parameter was proper to extimate da/dt. And it was shown that da/dt for 1% Cr-Mo V steel under the static condition(R=1) was 1.16 times faster than the case under cyclic loading(R=0), and for 12% Cr steel, 1.43 times.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.467-478
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• 2013

The purpose of the present paper is to establish some interesting results involving coefficient conditions, extreme points, distortion bounds and covering theorems for the classes $V_H({\beta})$ and $U_H({\beta})$. Further, various inclusion relations are also obtained for these classes. We also discuss a class preserving integral operator and show that these classes are closed under convolution and convex combinations.

• 대한수학회논문집
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• 제26권2호
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• pp.273-289
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• 2011

In this paper we dene the concept of a conditional generalized Fourier-Feynman transform on very general function space $C_{a,b}$[0, T]. We then establish the existence of the conditional generalized Fourier-Feynman transform for functionals in a Fresnel type class. We also obtain several results involving the conditional transform. Finally we present functionals to apply our results. The functionals arise naturally in Feynman integration theories and quantum mechanics.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 추계학술대회논문집A
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• pp.322-327
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• 2000

This paper investigates the time-dependent crack growth in X20CrMoV 12 1 steel weld joints. Crack growth test are carried out $545^{\circ}C$ on side-grooved 1/2T CT specimens under static loads. A simulated material is produced for the intercritical HAZ, where fracture normally occurs. Constitutive properties are obtained for the simulated HAZ material as well as for the base metal and weld metal. Finite element analyses of crack growth are performed on the models with and without a HAZ layer, using the experimental crack length-time history. The inclusion of HAZ layer increase the load line velocities significantly. The crack growth rates are correlated reasonably well with $C^*$. The smallest crack size for the validity of $C^*$ is found much smaller than the ASTM crack initiation size for 1T CT specimen of creep ductile materials.