• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.2
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• pp.140-147
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• 1987

In this paper, seven-order elliptic low-pass passive network is synthesized by using doublyterminated ladder network is directly transformed into the active network which has the advantage of low sensitivity and can be realized conveniently. The circuit simulation results of passive network and active network synthesized with FDNR and Leap-frog technique are compared, and it is proved that the two rest work has the same characteristics.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1693-1710
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• 2013

In this paper, we consider the biharmonic elliptic systems of the form $$\{{\Delta}^2u=F_u(u,v)+{\lambda}{\mid}u{\mid}^{q-2}u,\;x{\in}{\Omega},\\{\Delta}^2v=F_v(u,v)+{\delta}{\mid}v{\mid}^{q-2}v,\;x{\in}{\Omega},\\u=\frac{{\partial}u}{{\partial}n}=0,\; v=\frac{{\partial}v}{{\partial}n}=0,\;x{\in}{\partial}{\Omega},$$, where ${\Omega}{\subset}\mathbb{R}^N$ is a bounded domain with smooth boundary ${\partial}{\Omega}$, ${\Delta}^2$ is the biharmonic operator, $N{\geq}5$, $2{\leq}q$ < $2^*$, $2^*=\frac{2N}{N-4}$ denotes the critical Sobolev exponent, $F{\in}C^1(\mathbb{R}^2,\mathbb{R}^+)$ is homogeneous function of degree $2^*$. By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on ${\lambda}$ and ${\delta}$.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.969-980
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• 2011

In this paper, our main purpose is to consider the quasilinear elliptic equation $$div(|{\nabla}u|^{p-2}{\nabla}u)=(p-1)f(u)$$ on a bounded smooth domain ${\Omega}\;{\subset}\;R^N$, where p > 1, N > 1 and f is a smooth, increasing function in [0, ${\infty}$). We get some estimates of a solution u satisfying $u(x){\rightarrow}{\infty}$ as $d(x,\;{\partial}{\Omega}){\rightarrow}0$ under different conditions on f.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.3 no.1
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• pp.11-25
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• 1991

The steady, incompressible developing 3-dimensional turblent flow in a square sectioned curved duct has been investigated by using partially-parabolic equation and Finite Analytic Method. The calculation of turbulent flow field is performed using 2-equation K-$\epsilon$ turbulence model, modified wall function, simpler algorithm and numerically generated body fitted coordinates. Iso-mean velocity contours at the various sections are compared with the existing experimental data and elliptic solutions by other authors. In the region of $0^{\circ}<{\theta}<71^{\circ}$, present results agree with the experimental data much better than the elliptic solution for the similar number of grid points. Furthermore, for the same tolerance, the present solution converges four times faster than the elliptic solution.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.857-867
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• 2019

Suppose that G = (V, E) is a connected locally finite graph with the vertex set V and the edge set E. Let ${\Omega}{\subset}V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph G $$\{-{\Delta}_{pu}={\lambda}K(x){\mid}u{\mid}^{p-2}u+f(x,u),\;x{\in}{\Omega}^{\circ},\\u=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}^{\circ}$ and ${\partial}{\Omega}$ denote the interior and the boundary of ${\Omega}$, respectively, ${\Delta}_p$ is the discrete p-Laplacian, K(x) is a given function which may change sign, ${\lambda}$ is the eigenvalue parameter and f(x, u) has exponential growth. We prove the existence and monotonicity of the principal eigenvalue of the corresponding eigenvalue problem. Furthermore, we also obtain the existence of a positive solution by using variational methods.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.1
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• pp.74-82
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• 1986

The elliptic functions have a set of zeros on the jw axis. In acitve realization we decompose a function into product of biquads. In this paper, a simple method of pole-zero pairing is proposed for the enhancement of overall dynamic range. Secondly, the optimum sequencing of individual biquads is developed and it is demonstrated that the commonly accepted sequencing technique does not hold in the case of elliptic functions. This work is an approximation for Leuder's(1970)method.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.113-131
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• 2024

In this paper we give conditions for the existence of, and describe the asymtotic behavior of, radial positive solutions of the nonlinear elliptic equation of Emden-Fowler type with convection term ∆_p u + 𝛼|u|^q-1u + 𝛽x.∇(|u|^q-1u) = 0 for x ∈ ℝ^N, where p > 2, q > 1, N ≥ 1, 𝛼 > 0, 𝛽 > 0 and ∆_p is the p-Laplacian operator. In particular, we determine ${\lim}_{r{\rightarrow}}{\infty}\,r^{\frac{p}{q+1-p}}\,u(r)$ when $\frac{{\alpha}}{{\beta}}$ > N > p and $q\,{\geq}\,{\frac{N(p-1)+p}{N-p}}$.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.1-9
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• 1997

We obtained some class fields associated to an order R of a function field and evaluated the valuation of the invariant $\xi (c)$ for an invertible ideal c of R.

• Journal of Astronomy and Space Sciences
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• v.25 no.3
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• pp.255-266
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• 2008

The current paper presents application of a new analytic solution in general relative motion to spacecraft formation flying in an elliptic orbit. The calculus of variations is used to analytically find optimal trajectories and controls for the given problem. The inverse of the fundamental matrix associated with the dynamic equations is not required for the solution in the current study. It is verified that the optimal thrust vector is a function of the fundamental matrix of the given state equations. The cost function and the state vector during the reconfiguration can be analytically obtained as well. The results predict the form of optimal solutions in advance without having to solve the problem. Numerical simulation shows the brevity and the accuracy of the general analytic solutions developed in the current paper.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.807-819
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• 2008

We prove that for any continuous function f on the s-harmonic (1{\infty})$ boundary of a complete Riemannian manifold M, there exists a solution, which is a limit of a sequence of bounded energy finite solutions in the sense of supremum norm, for a certain elliptic operator A on M whose boundary value at each s-harmonic boundary point coincides with that of f. If $E_1,\;E_2,...,E_{\iota}$ are s-nonparabolic ends of M, then we also prove that there is a one to one correspondence between the set of bounded energy finite solutions for A on M and the Cartesian product of the sets of bounded energy finite solutions for A on $E_i$ which vanish at the boundary ${\partial}E_{\iota}\;for\;{\iota}=1,2,...,{\iota}$