• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.1 s.256
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• pp.40-50
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• 2007

The present contribution describes the application of elliptic-blending second moment closure to predict the gas cooling process of turbulent super-critical carbon dioxide flow in a square cross-sectioned duct. The gas cooling process under super-critical state experiences a drastic change in thermodynamic and transport properties. Redistributive terms in the Reynolds stress and turbulent heat flux equations are modeled by an elliptic-blending second moment closure in order to represent strongly non-homogeneous effects produced by the presence of walls. The main feature of Durbin's elliptic relaxation second moment closure that accounts for the nonlocal character of pressure-velocity gradient correlation and the near-wall inhomogeneity guaranteed by the elliptic blending second moment closure.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.533-540
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• 2012

We consider the multiplicity of the solutions for the elliptic boundary value problem with $C^1$ nonlinear term decaying at the origin. We get a theorem which shows the existence of the nontrivial solution for the elliptic problem with $C^1$ nonlinear term decaying at the origin. We obtain this result by reducing the elliptic problem with the $C^1$ nonlinear term to the el-liptic problem with bounded nonlinear term and then approaching the variational method and using the mountain pass geometry for the reduced the elliptic problem with bounded nonlinear term.

• Journal of Integrative Natural Science
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• v.7 no.4
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• pp.273-277
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• 2014

In this article, we consider a singular and a degenerate elliptic operators in a divergence form. The singularities exist on a part of boundary, and comparable to the logarithmic distance function or its inverse. If we assume that the operator can be treated in a pointwise sense than distribution sense, with this operator we obtain a priori Harnack continuity near the boundary. In the proof we transform the singular elliptic operator to uniformly bounded elliptic operator with unbounded first order terms. We study this type of estimations considering a De Giorgi conjecture. In his conjecture, he proposed a certain ellipticity condition to guarantee a continuity of a solution.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.12
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• pp.45-50
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• 1994

The elliptic filters are optimal in the sense that the magnitude characteristic exhibits the steepest slope at the cutoff frequency. The other characteristics such as delay and step response, however, are rather undesirable. In this paper, the modified elliptic low-pass filter function is proposed. The modified elliptic function possesses progressively diminishing ripples in both passband and stopband, and the lower pole-Q, values when compared to the elliptic counterparts, thus producting the flatter delay characteristics and improved time-domain performances. And it is realizable in the doubley-terminated ladder structures for the order n even or odd, thus lending themselves amaenable to high-quality active RC or switched capacitor filters through the simulation techniques.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.721-733
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• 2000

A paeabolic-elliptic system modelling chemotaxis is analysed. We study the behavior of solutions, especially the finite-time blowup of nonradial dolutions, to parabolic-elliptic system of n(n 2).

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.591-600
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• 2015

By linking theorem, we prove the existence of nontrivial solutions for the elliptic system with jumping nonlinearity and growth nonlinearity and Dirichlet boundary condition.

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.181-188
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• 2009

In this article we consider nontrivial solutions of an elliptic system in the bounded smooth domain with homogeneous Dirichlet data. We apply the linking theorem for showing the existence results that is obtained by Massa.

• Korean Journal of Mathematics
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• v.18 no.1
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• pp.53-61
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• 2010

In this work, we consider an elliptic system of three equations in dimension greater than one. We prove that the system has at least three nontrivial solutions by applying a linking theorem.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.301-310
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• 1999

This paper is concerned with the existence of positive solution of a semilinear elliptic equation with homogeneous Dirichlet boundary condition.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.425-441
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• 2013

In literature, several strong designated verifier signature (SDVS) schemes have been devised using elliptic curve bilinear pairing and map-topoint (MTP) hash function. The bilinear pairing requires a super-singular elliptic curve group having large number of elements and the relative computation cost of it is approximately two to three times higher than that of elliptic curve point multiplication, which indicates that bilinear pairing is an expensive operation. Moreover, the MTP function, which maps a user identity into an elliptic curve point, is more expensive than an elliptic curve scalar point multiplication. Hence, the SDVS schemes from bilinear pairing and MTP hash function are not efficient in real environments. Thus, a cost-efficient SDVS scheme using elliptic curve cryptography with pairingfree operation is proposed in this paper that instead of MTP hash function uses a general cryptographic hash function. The security analysis shows that our scheme is secure in the random oracle model with the hardness assumption of CDH problem. In addition, the formal security validation of the proposed scheme is done using AVISPA tool (Automated Validation of Internet Security Protocols and Applications) that demonstrated that our scheme is unforgeable against passive and active attacks. Our scheme also satisfies the different properties of an SDVS scheme including strongness, source hiding, non-transferability and unforgeability. The comparison of our scheme with others are given, which shows that it outperforms in terms of security, computation cost and bandwidth requirement.