• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.635-648
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• 2015

We consider a weakly coupled system of singularly perturbed convection-diffusion equations with discontinuous source term. The diffusion term of each equation is associated with a small positive parameter of different magnitude. Presence of discontinuity and different parameters creates boundary and weak interior layers that overlap and interact. A numerical method is constructed for this problem which involves an appropriate piecewise uniform Shishkin mesh. The numerical approximations are proved to converge to the continuous solutions uniformly with respect to the singular perturbation parameters. Numerical results are presented which illustrates the theoretical results.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.495-508
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• 2016

A singularly perturbed reaction-diffusion fourth-order ordinary differential equation(ODE) with discontinuous source term is considered. Due to the discontinuity, interior layers also exist. The considered problem is converted into a system of weakly coupled system of two second-order ODEs, one without parameter and another with parameter ε multiplying highest derivatives and suitable boundary conditions. In this paper a computational method for solving this system is presented. A zero-order asymptotic approximation expansion is applied in the second equation. Then, the resulting equation is solved by the numerical method which is constructed. This involves non-overlapping Schwarz method using Shishkin mesh. The computation shows quick convergence and results presented numerically support the theoretical results.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.330-333
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• 2002

This study Presents improvement of Precision in the non-contacted laser application measuring techniques. The phase map of deformation obtained by phase shifting method in Electronic Speckle Pattern Interferometry displays the wrapped image by the arctangent function, which is a characteristic of 4-step phase shifting method. To obtain deformation distribution from the results, the wrapped phase map is processed by an unwrapping method. But a previous method cannot apply discontinuous object as like plate with a circular hole to obtain precious deformation distribution To solve this problem, new algorithm is developed and the result is compared with previous method.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.12 s.177
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• pp.198-204
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• 2005

For precise micro V-grooving, ultrasonic elliptical vibration cutting (UEVC) is proposed using two parallel piezoelectric actuators, which are energized by sinusoidal voltages with a phase difference of 90 degrees. Experimental setup is composed of stacked PZT actuators, a single crystal diamond cutting tool, and a precision motorized xyz stage. It is found that the chip formed in the process of UEVC is discontinuous because of the periodic contacts and non-contacts occurring between the tool and workpiece. It is experimentally observed that the cutting force in the process of UEVC significantly reduces compared to the ordinary non-vibration cutting. In addition, the creation of burr during UEVC is significantly suppressed, which is attributable to the decrease in the specific cutting energy.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.625-628
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• 2005

For precise micro-grooving and surface machining, ultrasonic cyclic elliptical cutting is proposed using two parallel piezoelectric actuators. The piezoelectric actuators are energized by sinusoidal voltages of varying phase which is essenstial to generating elliptical cutting. Experimental setup is composed of ultrasonic motor, single crystal diamond cutting tool, and precise motorized xyz stage. It is confirmed experimentally that the cutting performance, in terms of the cutting force, the burr formation, and the discontinuous chip formation is improved remarkably by applying ultrasonic elliptical vibration cutting.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.267-280
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• 2009

In this paper we investigate a simple two-level additive Schwarz preconditioner for the P1 symmetric interior penalty Galerkin method of the Poisson equation on rectangular meshes. The construction is based on the decomposition of the global space of piecewise linear polynomials into the sum of local subspaces, each of which corresponds to an element of the underlying mesh, and the global coarse subspace consisting of piecewise constants. This preconditioner is a direct combination of the block Jacobi iteration and the cell-centered finite difference method, and thus very easy to implement. Explicit upper and lower bounds for the maximum and minimum eigenvalues of the preconditioned matrix system are derived and confirmed by some numerical experiments.

• The Journal of the Acoustical Society of Korea
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• v.14 no.3
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• pp.114-121
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• 1995

Outdoor experimental study is presented the insertion loss caused by barrier considering discontinuous ground condition. Measurements ware made in 1/3 octave band over the frequency range 315 Hz~3150 Hz with the various geometry of the source, receiver and barriers. The frequency range of the interference pattern depends on the phase difference between path from the edge of barrier to receiver, and hence on the acoustical properties of the ground on the receiver side of the barrier. The insertion loss by barrier, in addition to diffraction, is shown to be dependent on the ground characteristic.

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.89-93
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• 1985

One of the most important problems in automatic continuity theory is to solve the question of continuity of an algebra homomorphism from a Banach algebra into a semisimple Banach algebra with dense range. Many results on this subject are obtained imposing some conditions on the domains or the ranges of homomorphisms. For most recent results and references in automatic continuity theory one may refer to [1], [4] and [5]. In this note we study some properties of homomorphisms from $C^{*}$-algebras into Banach algebras. It is shown that the range of an isomorphism from a $C^{*}$-algebra into a Banach algebra contains no non zero element of the radical of B. Using this result we show that the same holds for a continuous homomorphism, hence a Banach algebra which is the image of a $C^{*}$-algebra under a continuous homomorphism is necessarily semisimple. Thus if there is a homomorphism from a $C^{*}$-algebra onto a non-semisimple Banach algebra it must be discontinuous. Also it follows that every non zero homomorphism from a $C^{*}$-algebra into a radical algebra is discontinuous. Then we make a brief observation on the behavior of quasinilpotent element of noncommutative $C^{*}$-algebras in relation with continuous homomorphisms.momorphisms.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1869-1889
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• 2018

We are concerned with the following fractional p-Laplacian inclusion: $$(-{\Delta})^s_pu+V(x){\mid}u{\mid}^{p-2}u{\in}{\lambda}[{\underline{f}}(x,u(x)),\;{\bar{f}}(s,u(x))]$$ in ${\mathbb{R}}^N$, where $(-{\Delta})^s_p$ is the fractional p-Laplacian operator, 0 < s < 1 < p < $+{\infty}$, sp < N, and $f:{\mathbb{R}}^N{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is measurable with respect to each variable separately. We show that our problem with the discontinuous nonlinearity f admits at least one or two nontrivial weak solutions. In order to do this, the main tool is the Berkovits-Tienari degree theory for weakly upper semicontinuous set-valued operators. In addition, our main assertions continue to hold when $(-{\Delta})^s_pu$ is replaced by any non-local integro-differential operator.

• Korean Journal of Cognitive Science
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• v.4 no.2
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• pp.115-143
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• 1994

In this paper,I present an extended two-level model using LR parsing techniques.The LR-based two-level model not only guarantees effcient morphological processing but also achieves a higher degree of descriptive adequacy than Koskenniemi's original model.The two-level model is augmented with an independent morphosyntactic module based on feature-based CF word grammar.By adopting a CF word grammar,our model is capable of dealing with complex words with discontinuous dependencies without having duplicate lexicons.It is shown how LR predictions manifested in the parsing table can help the morphological processor to minimize the dictionary lookup process.