• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.559-581
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• 2021

In this paper, we establish the existence of solutions and the approximate controllability for the semilinear neutral differential control system under natural assumptions such as the local Lipschitz continuity of nonlinear term. First, we deal with the regularity of solutions of the neutral control system using fractional powers of operators. We also consider the approximate controllability for the semilinear neutral control equation, with a control part in place of a forcing term, using conditions for the range of the controller without the inequality condition as in previous results.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.183-200
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• 2012

In the present paper, we consider the condition that is a geodesic equation on a Finsler space with an (${\alpha},\;{\beta}$)-metric. Next we find the conditions that are equations of geodesic on the Finsler space with an approximate infinite series (${\alpha},\;{\beta}$)-metric.

• Coupled systems mechanics
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• v.1 no.2
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Honam Mathematical Journal
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• v.28 no.1
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• pp.113-124
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• 2006

In this article, we show that for an approximate derivation on a Banach *-algebra, there exist a unique derivation near the an approximate derivation and for an approximate derivation on a $C^*$-algebra, there exist a unique derivation near the approximate derivation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.9 s.240
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• pp.1270-1275
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• 2005

Rolling process to fabricate a strip with even thickness is significant to enhance the quality of the strip. The thickness of a strip can be effectively controlled by pair-cross mills. However, pair-cross mill generates thrust in the axial direction of roller and causes skewness, deflection, twist and even accidental roll chock failure. Therefore, accurate estimation of the thrust of the pair-cross mill during rolling process is necessary to monitor the failure of roll and the quality of products. An empirical equation given by Mitsubishi Heavy Industry (MHI) is hitherto employed, where the thrust is expressed in terms of rolling force, reduction ratio and crossed angle. However it turns out that the MHI empirical equation provides somehow inaccurate and unsuitable thrust in practical rolling processes. Moreover, we learn that three parameters involved in MHI equation are coupled each other. In this paper, axiomatic design principle is employed to select appropriate parameters involved in approximate equation in order to make parameters uncoupled. A quadratic equation using response surface method with new parameters is suggested. The accuracy of the approximate model is examined by comparing with real experimental data.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.159-175
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• 2006

This paper is a survey on the Hyers-Ulam-Rassias stability of the Jensen functional equation in $C^*$-algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. Its content is divided into the following sections: 1. Introduction and preliminaries. 2. Approximate isomorphisms in $C^*$-algebras. 3. Approximate isomorphisms in Lie $C^*$-algebras. 4. Approximate isomorphisms in $JC^*$-algebras. 5. Stability of derivations on a $C^*$-algebra. 6. Stability of derivations on a Lie $C^*$-algebra. 7. Stability of derivations on a $JC^*$-algebra.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.639-650
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• 2018

Finding a solution for the Legendre equation is difficult. Especially if it is as a part of the Laplace equation solving in the electric fields. In this paper, first a problem of the generalized differential transform method (GDTM) is solved by the Sturm-Liouville equation, then the Legendre equation is solved by using it. To continue, the approximate solution is compared with the nth-degree Legendre polynomial for obtaining the inner and outer potential of a sphere. This approximate is more accurate than the previous solutions, and is closer to an ideal potential in the intervals.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1601-1606
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• 1991

We present an algorithm to approximate the Voronoi diagrams of 2D objects bounded by algebraic curves. Since the bisector curve for two algebraic curves of degree d can have a very high algebraic degree of 2 * d$^{4}$, it is very difficult to compute the exact algebraic curve equation of Voronoi edge. Thus, we suggest a simple polygonal approximation method. We first approximate each object by a simple polygon and compute a simplified polygonal Voronoi diagram for the approximating polygons. Finally, we approximate each monotone polygonal chain of Voronoi edges with Bezier cubic curve segments using least-square curve fitting.

• Journal of the Korean Chemical Society
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• v.53 no.6
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• pp.663-670
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• 2009

Performing random number simulations, we obtained an approximate distribution of the number of ways arranging molecules in a binary lattice solution of nonrandom mixing with a specific interaction. From the distribution an approximate equation of excess Gibbs energy for a binary lattice solution was derived. Using the equation, liquid-vapor equilibrium at constant pressure for 15 binary solutions were calculated and compared with the result from Wilson equation, Van Laar equation and Redlich-Kister equation.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2002.10b
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• pp.231-232
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• 2002

Various methods that utilize erosion rate measurement of standard cannon, 155mm Howitzer M185, as reference, are being used to calculate erosion rate of an interested unknown cannon tubes. We know ten measured erosion values of the standard cannon from 391 rounds to 4.000. An approximate function fitting these value s is derived. The new erosion equation is also suggested and computer simulations arc presented.