• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.809-817
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• 1998

We investigate when the product of two smooth manifolds admits a weakly Lagrangian embedding. Prove that, if $M^m$ and $N^n$ are smooth manifolds such that M admits a weakly Lagrangian embedding into ${\mathbb}C^m$ whose normal bundle has a nowhere vanishing section and N admits a weakly Lagrangian immersion into ${\mathbb}C^n$, then $M \times N$ admits a weakly Lagrangian embedding into ${\mathbb}C^{m+n}$. As a corollary, we obtain that $S^m {\times} S^n$ admits a weakly Lagrangian embedding into ${\mathbb}C^{m+n}$ if n=1,3. We investigate the problem of whether $S^m{\times}S^n$ in general admits a weakly Lagrangian embedding into ${\mathbb} C^{m+n}$.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.3
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• pp.29-38
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• 1990

A totally, new approach of Lagrangian formulation named 'Pseudo Lagrangian Formulation(PLF)' for large deformation analysis of continue and structures by the finite of element method has been presented, and the efficiency and accuracy of nonlinear analysis beam element formulated by PLF has been discussed by solving several numerical examples. In PLF, the deformation of a body is maeasured by assigning a nonphysical 'Pseudo' configuration as reference. The Lagrangian deformation and the finite element mapping of the traditonal Lagrangian approaches are then carried out directly at the same time, The result of numerical tests shows superior performance of PLF to the traditional Lagrangian methods, Applications of PLF to small and finite deformation problems indicate that PLF not only serves as an alternative but has certain implementational advantages over total or updated Lagrangian formulations.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.149-159
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• 2009

In this paper, we introduce some approximate optimal solutions and an augmented Lagrangian function in nonlinear programming, establish dual function and dual problem based on the augmented Lagrangian function, discuss the relationship between the approximate optimal solutions of augmented Lagrangian problem and that of primal problem, obtain approximate KKT necessary optimality condition of the augmented Lagrangian problem, prove that the approximate stationary points of augmented Lagrangian problem converge to that of the original problem. Our results improve and generalize some known results.

• 한국연소학회:학술대회논문집
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• 2002.06a
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• pp.113-122
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• 2002

The purpose of this study is to verify that the modified Lagrangian model can predict temperature, flow and scalar fields in the high temperature recirculation region of swirling confined diffusion flame. In the meantime numerical results from EBU and Equilibrium PDF models as well as experimental results are compared with those from the modified Lagrangian model. Adaption of three different turbulent models were accompanied with this procedure. Look-up table of the ignition characteristic time scale which is one of important factors of the Lagrangian model was referred to the 11-step reduced mechanism. Eventually, results with the Lagrangian model show a good accordance with experimental results, which shows the validity of this model. Results from Chen's model differ from those of the others. Numerical results of ${\widetilde{k}$ show significant deviation from experimental results for three models.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.489-501
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• 2016

In this paper, we study the rigidity under $K{\ddot{a}}hler$ deformation of the complex structure of odd Lagrangian Grassmannians, i.e., the Lagrangian case $Gr_{\omega}$(n, 2n+1) of odd symplectic Grassmannians. To obtain the global deformation rigidity of the odd Lagrangian Grassmannian, we use results about the automorphism group of this manifold, the Lie algebra of infinitesimal automorphisms of the affine cone of the variety of minimal rational tangents and its prolongations.

• 한국연소학회:학술대회논문집
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• 2012.11a
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• pp.195-198
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• 2012

Numerical simulation is performed to evaluate the conditional moment closure (CMC) models for spray development, ignition, and turbulent combustion for the Engine Combustion Network (ECN) test cases. The CMC model is implemented in the open source code, OpenFOAM, to provide conditional flame structures through the solution of Eulerian as well as Lagrangian conditional transport equations. In spite of more accurate treatment of the convective term, Eulerian CMC provides similar ignition delays and lift-off lengths with Lagrangian CMC.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.799-808
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• 1999

We investigate when the .product of two smooth manifolds admits a weakly Lagrangian embedding. Assume M, N are oriented smooth manifolds of dimension m and n,. respectively, which admit weakly Lagrangian immersions into $C^m$ and $C^n$. If m and n are odd, then $M\;{\times}\;N$ admits a weakly Lagrangian embedding into $C^{m+n}$ In the case when m is odd and n is even, we assume further that $\chi$(N) is an even integer. Then $M\;{\times}\;N$ admits a weakly Lagrangian embedding into $C^{m+n}$. As a corollary, we obtain the result that $S^n_1\;{\times}\;S^n_2\;{\times}\;...{\times}\;S^n_k$, $\kappa$>1, admits a weakly Lagrang.ian embedding into $C^n_1+^n_2+...+^n_k$ if and only if some ni is odd.

• Journal of the Society of Naval Architects of Korea
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• v.41 no.1
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• pp.23-30
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• 2004

In the Lagrangian vortex particle method based on the vorticity-velocity formulation for solving the incompressible Navier-Stokes equations, a numerical scheme for calculating pressure fields is presented. Implementation of the numerical method is directly connected with the well-established surface panel methods, just by dealing with the dynamic coupling among vorticity field. Assuming the vorticity and the velocity fields are to be calculated in time domain analysis, the pressure calculation for a complete set of solution at present time step is performed in a similar way to the one used in the Eulerian description. For a validation of the present method, we illustrate the early development of the viscous flow about an impulsive started circular cylinder for Reynolds number 550. The comparative study with the Eulerian finite Volume method provides an extensive understanding and application of the mesh-free Lagrangian vortex methods for numerical simulation of viscous flows around arbitrary bodies of general shape.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.789-804
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• 2019

In this paper, we prove that a link which has an almost positive diagram with a certain condition is Lagrangian fillable.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.6
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• pp.755-760
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• 2010

In general, Lagrangian method for discrete optimization is a kind of technique to easily manage constraints. It is traditionally used for finding upper bounds in the branch-and-bound method. In this paper, we propose a new Lagrangian search method for the 0-1 knapsack problem with multiple constraints. A novel feature of the proposed method different from existing Lagrangian approaches is that it can find high-quality lower bounds, i.e., feasible solutions, efficiently based on a new property of Lagrangian vector. We show the performance improvement of the proposed Lagrangian method over existing ones through experiments on well-known large scale benchmark data.