• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.141-152
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• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.

• 충청수학회지
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• 제35권1호
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• pp.53-67
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• 2022

Nonlinear system of initial value problems involving R-L fractional derivative is studied. Monotone iterative technique coupled with lower and upper solutions is developed for the problem. It is successfully applied to study qualitative properties of solutions of nonlinear system of initial value problem when the function on the right hand side is nondecreasing.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.215-222
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• 2000

A multigrid algorithm is developed for solving the one- dimensional initial boundary value problem. The numerical solutions of linear and nonlinear Burgers; equation for various initial conditions are studied. The stability conditions are derived by Von -Neumann analysis . Numerical results are presented.

• 대한수학회지
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• 제53권5호
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• pp.1133-1148
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• 2016

In this paper, we first discuss a representation of solutions to the initial value problem and the initial-boundary value problem for discrete evolution equations $${\sum\limits^l_{n=0}}c_n{\partial}^n_tu(x,t)-{\rho}(x){\Delta}_{\omega}u(x,t)=H(x,t)$$, defined on networks, i.e. on weighted graphs. Secondly, we show that the weight of each link of networks can be uniquely identified by using their Dirichlet data and Neumann data on the boundary, under a monotonicity condition on their weights.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1995년도 제2회 단조심포지엄 단조기술의 진보
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• pp.64-73
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• 1995

The forging limit curves of sintered porous metals have been calculated, in terms of the two principal strains, by the Lee-Kuhn initial imperfection model. The various yield functions for porous metal have been applied to the initial imperfection model. When the value of initial imperfection ratio equals the value of initial relative density of the sintered porous metals, the calculation values are in good agreement with the measured data. The slopes of the forging limit curves are about 0.5 as in the case of non-porous metals.

• 대한치과보철학회지
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• 제43권5호
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• pp.671-683
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• 2005

Statement of problem: The most commonly reported problem associated with dental implant restoration is the loosening of the screws. Purpose: This study compared the efficacy of an implant system incorporating an anti-rotational locking sleeve(Anti-Rotating Inner Post Screw System(ARIPS-system)) with other, traditional implant systems as a means of minimizing vibration loosening. Materials and methods: Three implant systems were examined; the conventional external hex type, the ARIPS-system, and the internal taper type implant system 30 specimens(10 samples per group)were fabricated and each abutment screw was secured to the implant future with 32Ncm of torque force and loosening torque was measured using a Torque Gauge. The procedure was repeated 3 times, recording initial loosening torque each time. The re-tightened abutment screw was subjected to a cyclic load having a maximum forte of 200N and minimum of 20N at 2Hz over a period of 12,600 cycles. after which the loosening torque was measured. Measured values were calaulated for statistical analysis. Analysis of measured value was performed by 3 methods: (i) as a percentage average of the initial 3 loosening-torque values(initial loosening value) to the tightening torque of 32Ncm, (ii) as a percentage of the loosening torque value after a load of 200N(experimental value) to the initial loosening value, and (iii) as a percentage of the experimental value to the 32Ncm of tightening torque. The analyses shows the amount of initial loosening at the screw, loosening by repetitive load and the the final loosening value. Results: The results of this study were as follows (1) Percentage of initial loosening value to tightening-torque was increased in order of external hex, ARIPS-system and internal taper and all values between each groups showed statistical significance (p<0.05). (2) Percentage of experimental value to initial loosening value was increased in order of external hex, ARIPS-system and internal taper. Value of internal taper showed significant difference with those of external hex and ARIPS-system (p<0.05). (3) Percentage of experimental value to tightening torque was increased in order of external hex, ARIPS-system and internal taper and all values between each groups showed statistical significance (p<0.05). Conclusion: The results of the analysis of the final loosening level value, which are closely correlated to clinical use, show that the ARIPS-system can be a useful means of minimizing abutment screw loosening when compared to the external hex type system. Although further clinical studies need to be made, the ARIPS-system should be considered to maximize the long-term success of the implant prosthesis.

• 대한수학회보
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• 제50권3호
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• pp.811-821
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• 2013

We study the initial value problem of the exponential wave equation in $\math{R}^{n+1}$ for small initial data. We shows, in the case of $n=1$, the global existence of solution by applying the formulation of first order quasilinear hyperbolic system which is weakly linearly degenerate. When $n{\geq}2$, a vector field method is applied to show the stability of a trivial solution ${\phi}=0$.

• East Asian mathematical journal
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• 제35권1호
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• pp.1-7
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• 2019

We consider the initial value problem of the Schrodinger equation for an interesting Cauchy-Euler type operator ${\mathfrak{R}}$ on ${\mathbb{C}}^n$ that is an analogue of the harmonic oscillator in ${\mathbb{R}}^n$. We get an appropriate $L^1-L^{\infty}$ dispersive estimate for the solution of the initial value problem.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.450-455
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• 1993

Guidance commands for attitude controlled missiles inevitably take the form of attitude angle commands. On the other hand, many guidance laws compute the accelerations required to achieve their goals. Therefore some integrators must be in use for the attitude controlled missiles to implement the guidance laws. Naturally, the use of the integrator raises the problem of choosing a proper initial value. In this paper, we compute the integrator initial value which minimizes the terminal miss and show that if the total flight time of the mission is long enough, the "optimal" initial value becomes some multiple of the initial heading error or of the given impact angle to the target. We demonstrate the validity of the analysis by showing some linear and nonlinear simulation results.n results.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2000년도 추계학술대회 학술발표 논문집
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• pp.168-171
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• 2000

This paper is concerned with fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in E$\_$N/ We study continuously initial observability for the following fuzzy system. x(t)=a(t)x(t)+f(t,x(t)), x(0)=x$\_$0/, y(t)=$\_$${\alpha}$/∏(x(t)), where a: [0, T]\longrightarrowE$\_$N/ is fuzzy coefficient, initial value x$\_$0/$\in$E$\_$N/ and nonlinear funtion f: [0, T]${\times}$E$\_$N/\longrightarrowE$\_$N/ satisfies a Lipschitz condition. Given fuzzy mapping ∏: C([0, T]: E$\_$N/)\longrightarrowY and Y is an another E$\_$N/.