• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.385-401
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• 2021

We prove existence and regularity results of solutions for a class of nonlinear singular elliptic problems like $$\{-div\((a(x)+{\mid}u{\mid}^q){\nabla}u\)=\frac{f}{{\mid}u{\mid}^{\gamma}}{\text{ in }}{\Omega},\\{u=0\;on\;{\partial}{\Omega},$$ where Ω is a bounded open subset of ℝℕ(N ≥ 2), a(x) is a measurable nonnegative function, q, �� > 0 and the source f is a nonnegative (not identicaly zero) function belonging to Lm(Ω) for some m ≥ 1. Our results will depend on the summability of f and on the values of q, �� > 0.

• Transactions of Materials Processing
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• v.9 no.3
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• pp.304-312
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• 2000

An inverse finite element approach is employed to efficiently design the optimum blank shape and intermediate shapes from the desired final shape in multi-stage elliptic cup drawing processes. The multi-stage deep-drawing process is difficult to design with the conventional finite element analysis since the process is very complicate with the conventional finite element analysis since the process is very complicated with intermediate shapes and the numerical analysis undergoes the convergence problem even with tremendous computing time. The elliptic cup drawing process needs much effort to design sine it requires full three-dimensional analysis. The inverse analysis is able to omit all complicated and tedious analysis procedures for the optimum process design. In this paper, the finite element inverse analysis provides the thickness strain distribution of each intermediate shape through the multi-stage analysis. The multi-stage analysis deals with the convergence among intermediate shapes and the corresponding sliding constraint surfaces that are described by the analytic function of merged-arc type surfaces.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.159-166
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• 1999

For classical elliptic pseudodifferential operators $A({\lambda})$ of order $m$ > 0 with parameter ${\lambda}$ of weight ${\chi}$ > 0, it is known that $logDet_{\theta}A({\lambda})$ admits an asymptotic expansion as ${\theta}{\rightarrow}+{\infty}$. In this paper we show, with some assumptions, that the coefficients of ${\lambda}^-{\frac{n}{\chi}}$ can be expressed by the values of zeta functions at 0 for some elliptic ${\psi}$DO's on $M{\times}S^1{\times}{\cdots}{\times}S^1$ multiplied by $\frac{m}{c_{n-1}}$.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.11
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• pp.1476-1482
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• 2001

Turbulent boundary layer over a flat plate was disturbed by installing an elliptic cylinder with an axis ratio of AR=2. For comparison, the same experiment was carried out for a circular cylinder having the same vertical height. The surface pressure and the heat transfer coefficient on the flat plate were measured with varying the gap distance between the elliptic cylinder and the flat plate. The mean velocity and the turbulent intensity profile of the streamwise velocity component were measured using a hot-wire anemometry. As a result, the flow structure and the local heat transfer rate were modified by the interaction between the cylinder wake and the turbulent boundary layer as a function of the critical gap ratio where the regular vortices start to shed. For the elliptic cylinder, the critical gap ratio is increased and the surface pressure on the flat plate is recovered rapidly at downstream location, compared with the equivalent circular cylinder. The maximum heat transfer rate occurs at the gap ratio of G/B = 0.5, where the flow interaction between the lower shear layer of the cylinder wake and the turbulent boundary layer is strong.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.11 no.5
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• pp.315-322
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• 1986

In this paper, we have studied on the IIR digital filters design using Elliptic functions. In process of transformation to digital fouctions from analos Elliptic functions, Bilinear z transformation method has been silized. Designing of digital filter using the Bilinear z transformation the problems of aliasing can be avoidedm whereas the frequency distrotion is generated. The transformation form analog function to digital function is not equal in the region of the cut off frequency response caused by this effect. Avoiding the problem of this effect, we have used proewarping method. Finally, the magnitude characteristics of digital filters are compared with its of analog filters by computer simulation. The results have shown that the magnitude characteristics of digital filters by the prewarping method have made more remarkable improvement than its of analog filters.

• Journal of Biomedical Engineering Research
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• v.15 no.4
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• pp.447-454
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• 1994

A method has been proposed for the fully automatic detection of left ventricular endocardial boundary in 2D short axis echocardlogram using geometric model. The procedure has the following three distinct stages. First, the initial center is estimated by the initial center estimation algorithm which is applied to decimated image. Second, the center estimation algorithm is applied to original image and then best-fit elliptic model estimation is processed. Third, best-fit boundary is detected by the cost function which is based on the best-fit elliptic model. The proposed method shows effective result without manual intervention by a human operator.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1461-1484
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• 2021

We deal with the following elliptic equations: $\{-div({\varphi}^{\prime}(\left|{\nabla}z\right|^2){\nabla}z)+V(x)\left|z\right|^{{\alpha}-2}z={\lambda}{\rho}(x)\left|z\right|^{r-2}z+h(x,z),\\z(x){\rightarrow}0,\;as\;\left|x\right|{\rightarrow}{\infty},$ in ℝ^N , where N ≥ 2, 1 < p < q < N, 1 < α ≤ p^*q'/p', α < q, 1 < r < min{p, α}, φ(t) behaves like t^q/2 for small t and t^p/2 for large t, and p' and q' the conjugate exponents of p and q, respectively. Here, V : ℝ^N → (0, ∞) is a potential function and h : ℝ^N × ℝ → ℝ is a Carathéodory function. The present paper is devoted to the existence of at least two distinct nontrivial solutions to quasilinear elliptic problems of Schrödinger type, which provides a concave-convex nature to the problem. The primary tools are the well-known mountain pass theorem and a variant of Ekeland's variational principle.

• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.85-109
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• 2000

In this paper, the multiplicity, stability and the structure of classical solutions of semilinear elliptic equations of the form (equation omitted) will be discussed. Here $\Omega$ is a smooth and bounded domain in $R^{n}$ (n $\geq$ 1), f(x,u) = │u│$^{\alpha}$/sgn(u)-h(x), 0 < $\alpha$ < 1, (n $\geq$ 1) and h is a ${\gamma}$- Holder continuous function on $\Omega$ for some 0 < ${\gamma}$ < 1.a}$ < 1.

• Journal of Biomedical Engineering Research
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• v.10 no.2
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• pp.114-116
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• 1989

A method has been proposed for the fully automatic detection of left ventricular endocardial boundary in 2D short axis echocardiogram using geometric model. The procedure has the following three distinct stages. First, the initial center is estimated by the initial center estimation algorithm which is applied to decimated image. Second, the center estimation algorithm is applied to original image and then best-fit elliptic model estimation is processed. Third, best-fit boundary is detected by the cost function which is based on the best-fit elliptic model. The proposed method shows effective result without manual intervention by a human operator.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.67-73
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• 2002

In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$