• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.38C no.2
• /
• pp.208-212
• /
• 2013

Due to the singularity of the within-class scatter, linear discriminant analysis (LDA) becomes ill-posed for small sample size (SSS) problems. An extension of LDA, the null space-based LDA (NLDA) provides good discriminant performances for SSS problems. In this paper, by applying the Lagrange technique, the procedure of transforming the problem of finding the feature extractor of NLDA into a linear equation problem is derived.

• Journal of Applied and Pure Mathematics
• /
• v.6 no.3_4
• /
• pp.141-154
• /
• 2024

This article offers a thorough exploration of a modified Black-Scholes model featuring two assets. The determination of option prices is accomplished through the Black-Scholes partial differential equation, leveraging the variational iteration method. This approach represents a semi-analytical technique that incorporates the use of Lagrange multipliers. The Lagrange multiplier emerges as a beacon of efficiency, adeptly streamlining the computational intricacies, and elevating the model's efficacy to unprecedented heights. For better understanding of the presented system, a graphical and tabular interpretation is presented with the help of Maple software.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.1
• /
• pp.35-43
• /
• 1996

A computer program for automatic deriving the symbolic equations of motion for robots using the programming language MATHEMATICA has been developed. The program, developed based on the Lagrange formalism, is applicable to the closed chain robots as well as the open chain robots. The closed chains are virtually cut open, and the kinematics and dynamics of the virtual open chain robot are analyzed. The constraints are applied to the virtually cut joints. As a result, the spatial closed chain robot can be considered as a tree structured open chain robot with kinematic constraints. The topology of tree structured open chain robot is described by a FATHER array. The FATHER array of a link indicates the link that is connected in the direction of base link. The constraints are represented by Lagrange multipliers. The parallel robot, DELTA, having three-dimensional closed chains is modeled and simulated to illustrate the approach.

• Computers and Concrete
• /
• v.16 no.3
• /
• pp.429-448
• /
• 2015

The dams are huge structures storing a large amount of water and failures of them cause especially irreparable loss of lives during the earthquakes. They are named as a group of structures subjected to fluid-structure interaction. So, the response of the fluid and its hydrodynamic pressures on the dam should be reflected more accurately in the structural analyses to determine the real behavior as soon as possible. Different mathematical and analytical modelling approaches can be used to calculate the water hydrodynamic pressure effect on the dam body. In this paper, it is aimed to determine the dynamic response of concrete gravity dams using different water modelling approaches such as Westergaard, Lagrange and Euler. For this purpose, Sariyar concrete gravity dam located on the Sakarya River, which is 120km to the northeast of Ankara, is selected as a case study. Firstly, the main principals and basic formulation of all approaches are given. After, the finite element models of the dam are constituted considering dam-reservoir-foundation interaction using ANSYS software. To determine the structural response of the dam, the linear transient analyses are performed using 1992 Erzincan earthquake ground motion record. In the analyses, element matrices are computed using the Gauss numerical integration technique. The Newmark method is used in the solution of the equation of motions. Rayleigh damping is considered. At the end of the analyses, dynamic characteristics, maximum displacements, maximum-minimum principal stresses and maximum-minimum principal strains are attained and compared with each other for Westergaard, Lagrange and Euler approaches.

• Journal of Advanced Marine Engineering and Technology
• /
• v.27 no.7
• /
• pp.862-871
• /
• 2003

In this paper, we addressed a modeling for the magnetic levitation stage. This planar magnetic levitator employs four permanent magnet liner motors. Each motor generates vertical force for suspension against gravity, as well as horizontal force for propulsion. Therefore. this stage can generate six degrees of freedom motion by the combination of forces. We derived a mechanical dynamics equation using Lagrangian method and electromechanical dynamics equation by using Co-energy method. Based on the derived dynamics, we can analyze the stage motion that is subject to the input currents and forces.

• Journal of the Korean Mathematical Society
• /
• v.47 no.1
• /
• pp.83-100
• /
• 2010

In this article, an optimal control problem associated with convection-diffusion equation is considered. Using Lagrange multiplier, the optimality system is obtained. The derived optimal system becomes coupled, non-symmetric partial differential equations. For discretizations and implementations, the finite element multigrid V-cycle is employed. The convergence analysis of finite element multigrid methods for the derived optimal system is shown. Some numerical simulations are performed.

• Honam Mathematical Journal
• /
• v.41 no.2
• /
• pp.369-380
• /
• 2019

Inspired by the problem of finding hyperelastic curves in a Riemannian manifold, we present a study on the variational problem of a hyperelastic curve in Lie group. In a Riemannian manifold, we reorganize the characterization of the hyperelastic curve with appropriate constraints. By using this equilibrium equation, we derive an Euler-Lagrange equation for the hyperelastic energy functional defined in a Lie group G equipped with bi-invariant Riemannian metric. Then, we give a solution of this equation for a null hyperelastic Lie quadratic when Lie group G is SO(3).

• Communications of Mathematical Education
• /
• v.29 no.4
• /
• pp.699-722
• /
• 2015

Based on Lagrange's general theory of algebraic equations, by applying the solution of the equation using the relationship between roots and coefficients to the high school 1st grade class, the purpose of this study is to recognize the significance of symmetry associated with the solution of the equation. Symmetry is the core idea of Lagrange's general theory of algebraic equations, and the relationship between roots and coefficients is an important means in the solution. Through the lesson, students recognized the significance of learning about the relationship between roots and coefficients, and understanded the idea of symmetry and were interested in new solutions. These studies gives not only the local experience of solutions of the equations dealing in school mathematics, but the systematics experience of general theory of algebraic equations by the didactical organization, and should be understood the connections between knowledges related to the solutions of the equation in a viewpoint of the mathematical history.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.13 no.4
• /
• pp.315-321
• /
• 2009

In this paper, a level set based energy functional is proposed, the minimization of which results in simultaneous reference background image modeling and foreground segmentation. Due to the mutual constraint of the two processes, a good estimate of the background can be obtained with a small number of frames, and due to the use of the level set, an Euler-Lagrange equation that directly solves the problem can be derived.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1993.10a
• /
• pp.175-180
• /
• 1993

A new method for the vibration analysis of arbitrarily-shaped beams is proposed on the assumption of imaginary seperation of the beams into prismatic beams and the remaining portions. The stiffness and mass of the beams are devided into two portions according to the seperation. Applying the mode shapes of prismatic beams and Lagrange's equations give new characteristics equation. This equation has a low dimension of matrix with the coupling terms showing the effect of remaining portions on the vibration of arbitrarily-shaped beams