• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2004년도 추계학술대회 논문집
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• pp.958-964
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• 2004

Most of people who are engaged in research and development find it difficult to solve the engineering problems creatively due to the lack of ideas. There are two famous methods for inventive problem solving: ＆apos;Brainstorming＆apos; and ＆apos;TRIZ＆apos;. Brainstorming is the most popular tool until now to find a creative solution and TRIZ is not so popular yet but leads us to a very useful and clear solution. These two methods whose goals are the same usually take quite different routes to the final solution; Those routes have their own unique advantages and disadvantages. In this paper, a creative problem solving method optimized by correlating Brainstorming and TRIZ is proposed. And this method demonstrates how rough initial ideas can be quickly refined and how a problem can be solved correctly.

• 대한수학회보
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• 제55권3호
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• pp.899-911
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• 2018

In this paper, we consider the second-order nonlinear differential equation with the nonlocal boundary conditions. We first reformulate this boundary value problem as a fixed point problem for a Fredholm integral equation operator, and then present a result on the existence and uniqueness of the solution by using the contraction mapping theorem. Furthermore, we establish a sufficient condition on the functions ${\mu}$ and $h_i$, i = 1, 2 that guarantee a unique solution for this nonlocal problem in a Hilbert space. Also, accurate analytic solutions in series forms for this boundary value problems are obtained by the Adomian decomposition method (ADM).

• Journal of Advanced Marine Engineering and Technology
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• 제27권6호
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• pp.783-789
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• 2003

An experimental method to investigate the fracture strength and fracture toughness for the silicon nitrides sintered at various sintering temperature is established. The erosion rate for these materials in the various concentration of NaOH solution is also investigated. In result, the fracture strength of Si3N4 is decreased with the increase of sintering temperature. On the other hand, the fracture toughness KIC is increased with the increase of sintering temperature. The erosion rate of silicon nitride in the NaOH solution depend largely on the grain size and the concentration of NaOH solution. The erosion rate of silicon nitride sintered at $1800^{\circ}C$ was much higher than that at $1950^{\circ}C$. These results are due to the unique columnar structure of silicon nitride.

• 호남수학학술지
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• 제30권1호
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• pp.197-203
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• 2008

We show the existence of the unique solution of the following system of the nonlinear wave equations with Dirichlet boundary conditions and periodic conditions under some conditions $U_{tt}-U_{xx}+av^+=s{\phi}_{00}+f$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, ${\upsilon}_{tt}-{\upsilon}_{xx}+bu^+=t{\phi}_{00}+g$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, where $u^+$ = max{u, 0}, s, t ${\in}$ R, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}$ of the wave operator. We first show that the system has a positive solution or a negative solution depending on the sand t, and then prove the uniqueness theorem by the contraction mapping principle on the Banach space.

• 한국CDE학회논문집
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• 제8권4호
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• pp.278-288
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• 2003

Presented in this paper is a numerical method for calculating the intersection points between Z-map vectors and the tool swept surface for circularly moving filleted-end mills. In numerically controlled(NC) machining simulation for large moulds and dies, a workpiece is frequently approximated as a set of z-axis aligned vectors, called Z-map vectors, and then the machining processes can be simulated through updating the Z-map with the intersection points. Circular motions are typically used for machining the free-form surfaces. For fast computation, we express each of intersection points with a single-variable non-linear equation and calculate the candidate interval in which the unique solution exists. Then, we prove the existence of a solution and its uniqueness in this candidate interval. Based on these properties, we can effectively apply numerical methods to finally calculate the solution of the nonlinear equation within a given precision. Experimental results are given for the case of a TV monitor and the hood of a car.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.1031-1049
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• 2012

In this paper, a class of impulsive fuzzy bi-directional associative memory (BAM) neural networks with distributed delays and variable coefficients are considered. Using Lyapunov functional method and fixed point theorem, we derived some sufficient conditions for the existence and globally exponential stability of unique periodic solution of the networks. The results obtained are new and extend the previous known results. In addition, an example is given to show the effectiveness of our results obtained.

• 대한수학회보
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• 제57권3호
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• pp.677-690
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• 2020

In this article, we study a reaction-diffusion system with homogeneous Dirichlet boundary conditions, which describing a three-species food chain model. Under some conditions, the predator-prey subsystem (u₁ ≡ 0) has a unique positive solution (${\bar{u_2}}$, ${\bar{u_3}}$). By using the birth rate of the prey r1 as a bifurcation parameter, a connected set of positive solutions of our system bifurcating from semi-trivial solution set (r₁, (0, ${\bar{u_2}}$, ${\bar{u_3}}$)) is obtained. Results are obtained by the use of degree theory in cones and sub and super solution techniques.

• 대한수학회보
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• 제57권1호
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• pp.219-244
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• 2020

In this paper, we approximate the solution of the coupled nonlinear Schrödinger equations by using a fully discrete finite element scheme based on the standard Galerkin method in space and implicit midpoint discretization in time. The proposed scheme guarantees the conservation of the total mass and the energy. First, a priori error estimates for the fully discrete Galerkin method is derived. Second, the existence of the approximated solution is proved by virtue of the Brouwer fixed point theorem. Moreover, the uniqueness of the solution is shown. Finally, convergence orders of the fully discrete Crank-Nicolson scheme are discussed. The end of the paper is devoted to some numerical experiments.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.475-487
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• 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.

• 대한안전경영과학회지
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• 제6권3호
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• pp.287-302
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• 2004

Most of people who are engaged in research and development find it difficult to solve the engineering problems creatively due to the lack of ideas. There are two famous methods for inventive problem solving' 'Brainstorming' and 'TRIZ'. Brainstorming is the most popular tool until now to find a creative solution and TRIZ is not so popular yet but leads us to a very useful and clear solution. These two methods whose goals are the same usually take quite different routes to the final solution; Those routes have their own unique advantages and disadvantages. In this paper, a creative problem solving method optimized by correlating Brainstorming and TRIZ is proposed. And this method demonstrates how rough initial ideas can be quickly refined and how a problem can be solved correctly.