• Korean Journal of Mathematics
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• v.19 no.4
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• pp.343-349
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• 2011

Let D be an integral domain, $D^w$ be the $w$-integral closure of D, X be an indeterminate over D, and $N_v=\{f{\in}D[X]{\mid}c(f)_v=D\}$. In this paper, we introduce the concept of $t$-locally APVD. We show that D is a $t$-locally APVD and a UMT-domain if and only if D is a $t$-locally APVD and $D^w$ is a $PvMD$, if and only if D[X] is a $t$-locally APVD, if and only if $D[X]_{N_v}$ is a locally APVD.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.409-445
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• 2016

The class $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ defined in the domain ${\mid}z{\mid}$ < 1 satisfying $Re\;e^{i{\phi}}\((1-{\alpha}+2{\gamma})(f/z)^{\delta}+\({\alpha}-3{\gamma}+{\gamma}\[1-1/{\delta})(zf^{\prime}/f)+1/{\delta}\(1+zf^{\prime\prime}/f^{\prime}\)\]\)(f/z)^{\delta}(zf^{\prime}/f)-{\beta}\)$ > 0, with the conditions ${\alpha}{\geq}0$, ${\beta}$ < 1, ${\gamma}{\geq}0$, ${\delta}$ > 0 and ${\phi}{\in}{\mathbb{R}}$ generalizes a particular case of the largest subclass of univalent functions, namely the class of $Bazilevi{\check{c}}$ functions. Moreover, for 0 < ${\delta}{\leq}{\frac{1}{(1-{\zeta})}}$, $0{\leq}{\zeta}$ < 1, the class $C_{\delta}({\zeta})$ be the subclass of normalized analytic functions such that $Re(1/{\delta}(1+zf^{\prime\prime}/f^{\prime})+1-1/{\delta})(zf^{\prime}/f))$ > ${\zeta}$, ${\mid}z{\mid}$<1. In the present work, the sucient conditions on ${\lambda}(t)$ are investigated, so that the non-linear integral transform $V^{\delta}_{\lambda}(f)(z)=\({\large{\int}_{0}^{1}}{\lambda}(t)(f(tz)/t)^{\delta}dt\)^{1/{\delta}}$, ${\mid}z{\mid}$ < 1, carries the fuctions from $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ into $C_{\delta}({\zeta})$. Several interesting applications are provided for special choices of ${\lambda}(t)$. These results are useful in the attempt to generalize the two most important extremal problems in this direction using duality techniques and provide scope for further research.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.745-756
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• 2019

We obtain Lipschitz type characterization and double integral characterization for Fock-type spaces with the norm $${\parallel}f{\parallel}^p_{F^p_{m,{\alpha},t}}\;=\;{\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{C}}^n}}\;{\left|{f(z){e^{-{\alpha}}{\mid}z{\mid}^m}}\right|^p}\;{\frac{dV(z)}{(1+{\mid}z{\mid})^t}}$$, where ${\alpha}>0$, $t{\in}{\mathbb{R}}$, and $m{\in}\mathbb{N}$. The results of this paper are the extensions of the classical weighted Fock space $F^p_{2,{\alpha},t}$.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.503-514
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• 2017

For real parameters ${\alpha}$ and ${\beta}$ such that ${\alpha}$ < 1 < ${\beta}$, we denote by $\mathcal{P}({\alpha},{\beta})$ the class of analytic functions p, which satisfy p(0) = 1 and ${\alpha}$ < ${\Re}\{p(z)\}$ < ${\beta}$ in ${\mathbb{D}}$, where ${\mathbb{D}}$ denotes the open unit disk. Let ${\mathcal{A}}$ be the class of analytic functions in ${\mathbb{D}}$ such that f(0) = 0 = f'(0) - 1. For $f{\in}{\mathcal{A}}$, ${\mu}{\in}{\mathbb{C}}{\backslash}\{0\}$ and ${\nu}{\in}{\mathbb{C}}$, let $I_{{\mu},{\nu}:{\mathcal{A}}{\rightarrow}{\mathcal{A}}$ be an integral operator defined by $$I_{{\mu},{\nu}[f](z)}=\({\frac{{\mu}+{\nu}}{z^{\nu}}}{\int}^z_0f^{\mu}(t)t^{{\nu}-1}dt\)^{1/{\mu}}$$. In this paper, we find some sufficient conditions on functions to be in the class $\mathcal{P}({\alpha},{\beta})$. One of these results is applied to the integral operator $I_{{\mu},{\nu}}$ of two classes of starlike functions which are related to the class $\mathcal{P}({\alpha},{\beta})$.

• Journal of Mechanical Science and Technology
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• v.18 no.3
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• pp.357-369
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• 2004

The purposes of the paper are to analyze the fracture phenomenon by delamination and cracking when the encapsulant of plastic IC package with polyimide coating shows viscoelastic behavior under hygrothermal loading in the IR soldering process and to suggest more reliable design conditions by the approaches of stress analysis and fracture mechanics. The model is the plastic SOJ package with the polyimide coating surrounding chip and dimpled diepad. On the package without cracks, the optimum position and thickness of polyimide coating to decrease the maximum differences of strains at the bonding surfaces of parts of the package are studied. For the model delaminated fully between the chip and the dimpled diepad, C(t)-integral values are calculated for the various design variables. Finally, the optimal values of design variables to depress the delamination and crack growth in the plastic IC package are obtained.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.695-706
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• 1996

In the control system $ \dot{x} = f(t,x(t)) + g(t,x(t))\dot{u}, x(0) = \bar{x}, t \in [0,T], $ this paper shows that the map from u with $L^1(m)$-topology to $x_u$ with $L^1(\mu)$-topology is Lipschitz continuous where f is $C^1$, $\mu$ is the Stieltjes measure derived from the function g which is not smooth in the variable t and $x_u$ is the solution of the above system corresponding to u under the assumption that $\dot{u}$ is bounded.

• Journal of Welding and Joining
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• v.16 no.4
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• pp.83-91
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• 1998

Cracking problems which high temperature plant components suffer during long-term service, occur very often at welded locations. The crack occurs due to accumulated creep damage near fusion line or at heat affected zone (HAZ). However, most of the studies on creep crack growth behavior have been performed with matrix metal not wit welded metal due to the difficulty of interpreting the test results. In this study, creep crack growth rates were measured with C(T) specimens whose cracks were formed along the fusion line or HAZ. The measured crack growth rates were characterized by {TEX}$C_{t}${/TEX}-parameter derived for elastic-primary-secondary creeping material. Since contribution of primary creep was significant for the tested 1Cr-0.5Mo steel, its effect was carefully studied. Effects of crack tip plasticity and material aging were also discussed.

• Proceedings of the Korean Nuclear Society Conference
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• 2001.05a
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• pp.235.2-235
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• 2001

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.301-314
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• 1992

In this paper, motivated by [1] and [7] we give a sequential definition of conditional Wiener integral and then use this definition to evaluate conditional Wiener integral of several functions on C [0, T]. The sequential definition is defined as the limit of a sequence of finite dimensional Lebesgue integrals. Thus the evaluation of conditional Wiener integrals involves no integrals in function space [cf, 5].

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.93-111
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• 2004

In this paper, we use a generalized Brownian motion process to define a generalized Feynman integral and a generalized Fourier-Feynman transform. We also define the concepts of the multiple Lp analytic generalized Fourier-Feynman transform and the generalized convolution product of functional on function space $C_{a,\;b}[0,\;T]$. We then verify the existence of the multiple $L_{p}$ analytic generalized Fourier-Feynman transform for functional on function space that belong to a Banach algebra $S({L_{a,\;b}}^{2}[0, T])$. Finally we establish some relationships between the multiple $L_{p}$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $S({L_{a,\;b}}^{2}[0, T])$.