• 전자공학회논문지B
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• 제33B권12호
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• pp.84-94
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• 1996

In this work, a fuzzy petri net model for modeling a general form of fuzzy production system which consists of chaining fuzzy production rules and so requires multistage reasoning process is presented. For the obtained fuzzy petri net model, the net will be transformed into some matrices, and also be systematically led to an algebraic form of a state equation. Since it is fond that the approximate reasoning process in fuzzy systems corresponds to the dynamic behavior of the fuzzy petri net, it is further shown that the multistage reasoning process can be carried out by executing the state equation.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.467-474
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• 2004

We prove the generalized Hyers-Ulam-Rassias stability of a partitioned functional equation. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with partitioned functional equations in Banach algebras.

• International Journal of Aeronautical and Space Sciences
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• 제3권2호
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• pp.46-58
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• 2002

An inverse method is introduced to construct benchmark problems for the numerical solution of initial value problems. Benchmark problems constructed through this method have a known exact solution, even though analytical solutions are generally not obtainable. The solution is constructed such that it lies near a given approximate numerical solution, and therefore the special case solution can be generated in a versatile and physically meaningful fashion and can serve as a benchmark problem to validate approximate solution methods. A smooth interpolation of the approximate solution is forced to exactly satisfy the differential equation by analytically deriving a small forcing function to absorb all of the errors in the interpolated approximate solution. A multi-variable orthogonal function expansion method and computer symbol manipulation are successfully used for this process. Using this special case exact solution, it is possible to directly investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for a given code and a given problem. Under the assumption that the original differential equation is well-posed with respect to the small perturbations, we thereby obtain valuable information about the optimal choice of the tuning parameters and the achievable accuracy of the numerical solution. Illustrative examples show the utility of this method not only for the ordinary differential equations (ODEs) but for the partial differential equations (PDEs).

• 대한수학회논문집
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• 제39권3호
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• pp.731-737
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• 2024

In this paper, we study the Hyers-Ulam stability of the classical iterative functional equation fⁿ(x) = x, the Babbage equation, using strictly monotonic approximate solutions on a real interval.

• 대한수학회보
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• 제52권4호
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• pp.1059-1068
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• 2015

The paper is devoted to studying a fourth-order degenerate parabolic equation, which arises in fluid, phase transformation and biology. Based on the existence and uniqueness of one semi-discrete problem, two types of approximate solutions are introduced. By establishing some necessary uniform estimates for those approximate solutions, the existence and uniqueness of the corresponding parabolic problem are obtained. Moreover, the long time asymptotic behavior is established by the entropy functional method.

• 대한기계학회논문집
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• 제5권3호
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• pp.183-192
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• 1981

The present study gives an apprximate equation of circular cylindrical shell on the basis of Flugges's exact theory. The longitudinal bending moment .MU.$\_$x/ and circumferential strain .epsilon.$\_$.theta. are assumed to be small to be small and have been neglected. The governing equation of the cylindrical shell, which is generaly presented as 8th order partial differential equation, is reduced into a 4th order partial differential equation for axial coordinate. To verify the validity and accuracy of this approximate theory, the cantilever cylindrical shell subjected to a concentrated load is analyzed. The maximum errors of longitudinal stress and deflection are about 10 percent compared with the analysis by flugge's theory and are about 15 percent with experimental results.

• 한국군사과학기술학회지
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• 제5권3호
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• pp.23-32
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• 2002

We predict the erosion rate of unknown cannon tubes by substituting measured values of the standard cannon, 155㎜ Howitzer M185 and ballistic data for the erosion equation. We know ten measured erosion values of the standard cannon at every 400 rounds. An approximate formula is derived to interpolate six values up to 2,000 rounds. Numerical example is presented and its results are analyzed. The new erosion equation is also suggested. This equation produces more accurate cannon tube erosion rate than the Rauf Imam's empirical approaches. Computer simulations are presented.

• 한국소음진동공학회논문집
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• 제21권6호
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• pp.553-561
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• 2011

A theoretical approach is carried out to predict the quality factors of flexible modes of a microcantilever on a squeeze-film. The frequency response function of an inertially-excited microcantilever beam is derived using an Euler-Bernoulli beam theory. The external force due to squeeze-film phenomenon is developed from the Reynolds equation. Slip boundary conditions are employed at the interfaces between the fluid and the structure to consider the gas rarefaction effect, and pressure boundary condition at both ends of fluid analysis region is enhanced to increase the exactness of predicted quality factors. To the end, an approximate equation is derived for the first bending mode of the microcantilever. Using the approximate equation, the quality factors of the second and third bending modes are calculated and compared with experimental results of previously reported work. The comparison shows the feasibility of the current approach.

• Tribology and Lubricants
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• 제10권1호
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• pp.35-45
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• 1994

The thermohydrodynamic analysis of tilting pad thrust bearing is studied with the consideration of elastic effect of pad. Reynolds equation, deflection equation and energy equation are solved simultaneously with the boundary conditions. Reynolds equation is modified as the approximate form. Pads are supported by the line pivot and the point pivot respectively. Pads are considered as the flat planes. Effects of pad thickness on the performance of thrust bearing are emphasized and the performances of rigid pad and elastic pad are compared. Effects of inlet temperature on performances of the bearing are compared. Dynamic characteristics of both pad supported by line and point pivot are compared.

• 대한수학회지
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• 제26권2호
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• pp.203-213
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• 1989