• 충청수학회지
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• 제31권3호
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• pp.287-308
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• 2018

This paper deals with blow-up phenomena for an initial boundary value problem of a quasilinear parabolic equation with time-dependent coefficient in a bounded star-shaped region under nonlinear boundary flux. Using the auxiliary function method and differential inequality technique, we establish some conditions on time-dependent coefficient and nonlinear functions for which the solution u(x, t) exists globally or blows up at some finite time $t^*$. Moreover, some upper and lower bounds for $t^*$ are derived in higher dimensional spaces. Some examples are presented to illustrate applications of our results.

• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.677-688
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• 2018

In this paper, we introduce and investigate a new subclass of bi-univalent functions defined by $S{\breve{a}}l{\breve{a}}gean$ q-calculus operator in the open disk ${\mathbb{U}}$. For functions belonging to the subclass, we obtain estimates on the first two Taylor-Maclaurin coefficients ${\mid}a_2{\mid}$ and ${\mid}a_3{\mid}$. Some consequences of the main results are also observed.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.887-902
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• 2021

In this paper, we have introduced a generalized class Sⁱ_H (m, n, 𝛾, 𝜙, 𝜓; 𝛼), i ∈ {0, 1} of harmonic univalent functions in unit disc 𝕌, a sufficient coefficient condition for the normalized harmonic function in this class is obtained. It is also shown that this coefficient condition is necessary for its subclass 𝒯 Sⁱ_H (m, n, 𝛾, 𝜙, 𝜓; 𝛼). We further obtained extreme points, bounds and a covering result for the class 𝒯 Sⁱ_H (m, n, 𝛾, 𝜙, 𝜓; 𝛼). Also, show that this class is closed under convolution and convex combination. While proving our results, certain conditions related to the coefficients of 𝜙 and 𝜓 are considered, which lead to various well-known results.

• 대한수학회보
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• 제57권4호
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• pp.839-850
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• 2020

For functions f(z) = z + a₂z² + a₃z³ + ⋯ belonging to particular classes, this paper finds sharp bounds for the initial coefficients a₂, a₃, a₄, as well as the sharp estimate for the second order Hankel determinant H₂(2) = a₂a₄ - a₂³. Two classes are treated: first is the class consisting of f(z) = z + a₂z² + a₃z³ + ⋯ in the unit disk 𝔻 satisfying $$\|\(\frac{z}{f(z)}\)^{1+{\alpha}}\;f^{\prime}(z)-1\|<{\lambda},\;0<{\alpha}<1,\;0<{\lambda}{\leq}1.$$ The second class consists of Bazilevič functions f(z) = z+a₂z²+a₃z³+⋯ in 𝔻 satisfying $$Re\{\(\frac{f(z)}{z}\)^{{\alpha}-1}\;f^{\prime}(z)\}>0,\;{\alpha}>0.$$

• Journal of Advanced Marine Engineering and Technology
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• 제28권6호
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• pp.1026-1036
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• 2004

In this study, single-phase heat transfer experiments were conducted with Oblong Shell and Plate heat exchanger using water. An experimental water loop has been developed to measure the single-phase heat transfer coefficient and pressure drop in a vertical Oblong Shell and Plate heat exchanger. Downflow of hot water in one channel receives heat from the cold water upflow of water in the other channel. Similar to the case of a plate heat exchanger, even at a very low Reynolds number, the flow in the Oblong Shell and Plate heat exchanger remains turbulent. The present data show that the heat transfer coefficient and pressure drop increase with the Reynolds number. Based on the present data, empirical correlations of the heat transfer coefficient and pressure drop in terms of Nusselt number and friction factor were proposed. Also, performance prediction analyses for Oblong Shell and Plate heat exchanger were executed and compared with experiments. $\varepsilon$-NTU method was used in this prediction program. Independent variables are flow rates and inlet temperatures. Compared with experimental data, the accuracy of the program is within the error bounds of $\pm$5% in the heat transfer rate.

• Journal of Mechanical Science and Technology
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• 제19권8호
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• pp.1632-1648
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• 2005

The effects of Reynolds number on the non-nulling calibration of a typical cone-type five-hole probe have been investigated for the representative Reynolds numbers in turbomachinery. The pitch and yaw angles are changed from - 35 degrees to 35 degrees with an angle interval of 5 degrees at six probe Reynolds numbers in range between $6.60{\times}10^3\;and\;3.17{\times}10^4$. The result shows that not only each calibration coefficient itself but also its Reynolds number dependency is affected significantly by the pitch and yaw angles. The Reynolds-number effects on the pitch- and yaw-angle coefficients are noticeable when the absolute values of the pitch and yaw angles are smaller than 20 degrees. The static-pressure coefficient is sensitive to the Reynolds number nearly all over the pitch- and yaw-angle range. The Reynolds-number effect on the total-pressure coefficient is found remarkable when the absolute values of the pitch and yaw angles are larger than 20 degrees. Through a typical non-nulling reduction procedure, actual reduced values of the pitch and yaw angles, static and total pressures, and velocity magnitude at each Reynolds number are obtained by employing the calibration coefficients at the highest Reynolds number ($Re=3.17{\times}10^4$) as input reference calibration data. As a result, it is found that each reduced value has its own unique trend depending on the pitch and yaw angles. Its general tendency is related closely to the variation of the corresponding calibration coefficient with the Reynolds number. Among the reduced values, the reduced total pressure suffers the most considerable deviation from the measured one and its dependency upon the pitch and yaw angles is most noticeable. In this study, the root-mean-square data as well as the upper and lower bounds of the reduced values are reported as a function of the Reynolds number. These data would be very useful in the estimation of the Reynolds-number effects on the non-nulling calibration.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.1424-1429
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• 2004

In this paper a mathematical framework for deriving acceleration bounds from given joint torque limits of multiple cooperating robots are described. Especially when the different frictional contacts for every contact are assumed and the torque limits are given in 2-norm sense, we show that the resultant geometrical configuration for the acceleration is composed of corresponding parts of ellipsoids. Since the frictional forces at the contacts are proportional to the normal squeezing forces, the key points of the work includes how to determine internal forces exerted by each robot in order not to cause slip at the contacts while the object is carried by external forces. A set of examples composed of two robot systems are shown with point-contact-with-friction model and insufficient or proper degree of freedom robots.

• 대한수학회보
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• 제43권3호
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• pp.589-598
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• 2006

In the present investigation, sharp upper bounds of $|a3-{\mu}a^2_2|$ for functions $f(z)=z+a_2z^2+a_3z^3+...$ belonging to certain subclasses of starlike and convex functions with respect to symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szego inequalities for certain classes of functions defined through fractional derivatives are obtained.

• Kyungpook Mathematical Journal
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• 제45권1호
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• pp.105-114
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• 2005

In this paper we investigate the growth of finite order solutions of the differential equation $f^{(k)}\;+\;A_{k-1}(Z)f^{(k-l)}\;+\;{\cdots}\;+\;A_1(z)f^{\prime}\;+\;A_0(z)f\;=\;F(z)$, where $A_0(z),\;{\cdots}\;,\;A_{k-1}(Z)\;and\;F(z)\;{\neq}\;0$ are entire functions. We find conditions on the coefficients which will guarantees the existence of an asymptotic value for a transcendental entire solution of finite order and its derivatives. We also estimate the lower bounds of order of solutions if one of the coefficient is dominant in the sense that has larger order than any other coefficients.

• 호남수학학술지
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• 제15권1호
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• pp.75-85
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• 1993

For A and B, $-1{\leq}B<A{\leq}1$, let P[A, B] be the class of functions p analytic in the unit disk E with P(0) = 1 and subordinate to $\frac{1+Az}{1+Bz}$. We introduce the class $T_{\alpha}[A,B]$ of functions $f:f(z)=z+\sum\limits_{n=2}^{{\infty}}a_nz^n$ which are analytic in E and for $z{\in}E$, ${\alpha}{\geq}0$, $[(1-{\alpha}){\frac{f(z)}{z}}+{\alpha}f^{\prime}(z)]{\in}P[A,B]$. It is shown that, for ${\alpha}{\geq}1$, $T_{\alpha}[A,B]$ consists entirely of univalent functions and the radius of univalence for $f{\in}T_{\alpha}[A,B]$, $0<{\alpha}<1$ is obtained. Coefficient bounds and some other properties of this class are studied. Some radii problems are also solved.