• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.475-487
• /
• 2009

This paper studies the iteration method of solving a type of second-order three-point boundary value problem with non-linear term f, which depends on the first order derivative. By using the upper and lower method, we obtain the sufficient conditions of the existence and uniqueness of solutions. Furthermore, the monotone iterative sequences generated by the method contribute to the minimum solution and the maximum solution. And the error estimate formula is also given under the condition of unique solution. We apply the solving process to a special boundary value problem, and the result is interesting.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.7 no.2 s.17
• /
• pp.57-64
• /
• 2004

A Requirement statement validation process is suggested which was established and applied to the rolling stock development project of the Korean Railway Research Institute. The validation process includes team organization, selection of validation criteria, development of validation template, education of team members, validation, construction of database and management of requirement change. Many defects in the specification of requirement were found to be associated with the problem of non-uniqueness, describing solution instead of problem, ambiguity and redundancy. This paper described detailed activities at each step of the validation process and lessons learned from these activities.

• Journal of Soil and Groundwater Environment
• /
• v.15 no.6
• /
• pp.46-52
• /
• 2010

Derivative analysis, based on the derivative of the drawdown as a function of time (i.e., rate of drawdown change), was applied to the evaluation of hydraulic parameters of the aquifer as an aid of the aquifer test interpretation based on the Theis solutions. Pumping tests were conducted at a coastal fractured aquifer in Muan county, Korea, of which the drawdown data, measured at the two observation wells, were used for derivative analysis. Wellbore storage and transition period were hard to identify at conventional log-log and semi long plots, but was easily recognized by distinctive curves of positive unit slope, hump and negative unit slope in the derivative plot. For the observation well of OW-2 at which wellbore storage and transition lasted over an hour, conventional aquifer analysis would suffer from the uniqueness problems and in further result in erroneous hydraulic parameters. Derivative analysis was found to be effective for distinguishing the drawdown data directly reflecting the aquifer property from those reflecting non aquifer effects such as wellbore storage and transition, which offers a unified methodology to yield correct hydraulic parameters from aquifer test data.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.637-669
• /
• 2024

The goal of this paper is to study decay properties of weak solutions to Cauchy problem of the non-stationary fractional Navier-Stokes equations. By using the Fourier splitting method, we give the time L²-decay rate of weak solutions, which reveals that L²-decay is generally determined by its linear generalized Stokes flow. In second part, we establish various decay results and the uniqueness of the two dimensional fractional Navier-Stokes flows. In the end of this article, as an appendix, the existence of global weak solutions is given by making use of Galerkin' method, weak and strong compact convergence theorems.

• Transactions on Control, Automation and Systems Engineering
• /
• v.4 no.2
• /
• pp.130-139
• /
• 2002

In this paper, at first, we investigate existing algorithms for finding the minimum infinity-norm solution of consistent linear equations and then propose a new algorithm. The proposed algorithm is intended to includes the advantages of computational efficiency as well as geometric explicitness. As a practical application example, optimum trajectory planning for redundant robot manipulators is considered. Also, an efficient approach avoiding discontinuity in trajectory is proposed by resolving the non-uniqueness problem of minimum infinity-norm solution. To be specific, the proposed method for checking possible discontinuity does not need any other algorithms in checking the possibility of discontinuity while previous work needs specially designed checking courses. To show the usefulness of the proposed techniques, an example calculating minimum infinity-norm solution for comparing the computational efficiency as well as the trajectory planning for a redundant robot manipulator are included.

• Journal of Korean Institute of Industrial Engineers
• /
• v.20 no.1
• /
• pp.99-112
• /
• 1994

This paper describe the development of a systematic method of slicing solid parts based on a data structure called Sliced Profile Data Structure(SPDS). SPDS is an augmented polygon data structure that allows multiple layers of sliced profiles to be connected together. The method consists of five steps: (1) Selection of slicing directions, (2) Determination of slicing levels, (3) Creation of sliced profiles, (4) Connection of sliced profiles, and (5) Refinement. The presented method is aimed at enhancing the applicability of CSG for manufacturing by overcoming the problem of non-uniqueness and global nature. The SPDS-based method of feature extraction is suitable for recognizing broad scope of features with detailed information. The method is also suitable for identifying the global relationships among features and is capable of incorporating the context dependency of feature extraction.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.28 no.1
• /
• pp.89-98
• /
• 2004

In this paper, we develope a dispersion model based on the Generalized Langevin Model. Thomson's well-mixed condition is the well known criterion to determine particle dispersion. But, it has 'non-uniqueness problem'. To resolve this, we adopt a turbulent model which is a new approach in this field of study. Our model was greatly simplified under the self-similarity condition, leaving model only two model constants $C_{0}$ and ${\gamma}$$_{5}$ that control the dispersion and spin which measures rotational property of the Lagrangian particle trajectory. We investigated the sign of spin as well as magnitude by using the Direct Numerical Simulation. Model calculations were performed on the neutrally stable boundary layer flow. We found that spin has weak effect on the particle dispersion but it shows the significant effect on the horizontal flux compared to the zero-spin model.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.33 no.5
• /
• pp.447-454
• /
• 2009

Rate-independent crystal plasticity model suffers from the non-uniqueness of activated slip systems and the determination of the shear slip rates on the active slip systems. In this paper, a time-integration algorithm which circumvents the problem of the multiplicity of the slip systems was developed and implemented into the user subroutine VUMAT of a commercial finite element program ABAQUS. The magnitude of the slip shears on the active slip systems in f.c.c Cu single crystal aligned with the specific crystallographic orientation was investigated to validate our solution procedure. Also, texture developments under various deformation modes such as simple compression, simple tension and plane strain compression were compared with the results of the rate-dependent model by using the rate-independent crystal plasticity model. The computation time employing the rate-independent model is much more reduced than the those of the rate-dependent model.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.11b
• /
• pp.1078-1082
• /
• 2001

An alternative formulation of the Helmholtz integral equation is derived to express the pressure field explicitly in terms of the velocity vector of a radiating surface. This formulation, derived for arbitrary sources, is similar in form to the Rayleigh's formula for planar sources. Because the pressure field is expressed explicitly as a surface integral of the particle velocity, which can be implemented numerically using standard Gaussian quadratures, there is no need to use Boundary element method to solve a set of simultaneous equations for the surface pressure at the discretized nodes. Furthermore the non-uniqueness problem inherent in methods based on Helmholtz integral equation is avoided. Validation of this formulation is demonstrated for some simple geometries.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.161-193
• /
• 2024

In this paper, we consider the asymptotic behavior of solutions for the partly dissipative reaction diffusion systems of the FitzHugh-Nagumo type with hereditary memory and a very large class of nonlinearities, which have no restriction on the upper growth of the nonlinearity. We first prove the existence and uniqueness of weak solutions to the initial boundary value problem for the above-mentioned model. Next, we investigate the existence of a uniform attractor of this problem, where the time-dependent forcing term h ∈ L²_b(ℝ; H^-1(ℝ^N)) is the only translation bounded instead of translation compact. Finally, we prove the regularity of the uniform attractor A, i.e., A is a bounded subset of H²(ℝ^N) × H¹(ℝ^N) × L²_µ(ℝ⁺, H²(ℝ^N)). The results in this paper will extend and improve some previously obtained results, which have not been studied before in the case of non-autonomous, exponential growth nonlinearity and contain memory kernels.