• 대한수학회지
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• 제45권6호
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• pp.1635-1646
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• 2008

Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.

• 대한수학회보
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• 제50권4호
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• pp.1243-1259
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• 2013

In this paper, we study the root system of rank 2 hyperbolic Kac-Moody algebras. We give some sufficient conditions for the existence of imaginary roots of square length $-2k(k{\in}\mathbb{Z}_{>0}$. We also give several relations between the integral points on the hyperbola $\mathfrak{h}$ to show that the value of the symmetric bilinear form of any two integral points depends only on the number of integral points between them. We also give some generalizations of Binet formula and Catalan's identity.

• 한국수학교육학회지시리즈A:수학교육
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• 제13권2호
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• pp.21-23
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• 1974

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권2호
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• pp.37-49
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• 1999

In this paper we develop a general Homotopy method called the Group Homotopy method to solve the symmetric eigenproblem. The Group Homotopy method overcomes notable drawbacks of the existing Homotopy method, namely, (i) the possibility of breakdown or having a slow rate of convergence in the presence of clustering of the eigenvalues and (ii) the absence of any definite criterion to choose a step size that guarantees the convergence of the method. On the other hand, We also have a good approximations of the largest eigenvalue of a Symmetric matrix from Lanczos algorithm. We apply it for the largest eigenproblem of a very large symmetric matrix with a good initial points.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1992년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 19-21 Oct. 1992
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• pp.212-217
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• 1992

In this paper, a two ports machine(TPM) model for discrete event dynamic systems(DEDS) is proposed. The proposed model is a finite state machine which has two inputs and two outputs. Inputs and outputs have two components, events and informations. TPM is different from other state machine models, since TPM has symmetric input and output. This symmetry enables the block diagram representation of the DEDS with TPM blocks, summing points, multiplying points, branch points, and connections. The graphical representation of DEDS is analogous to that of control system theory. TPM has a matrix representation of its transition and information map. This matrix representation simplifies the analysis of the DEDS.

• Kyungpook Mathematical Journal
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• 제53권2호
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• pp.295-306
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• 2013

First we present the explicit formula for the norm of a symmetric bilinear form on the 2-dimensional real predual of the Lorentz sequence space $d_*(1,w)^2$. Using this formula, we classify the extreme points of the unit ball of $\mathcal{L}_s(^2d_*(1,w)^2)$.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2003년도 추계학술대회논문집
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• pp.318-321
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• 2003

In order to generate the extrusion die surface of non-symmetric H- and U-shaped sections, an automatic surface construction method based on B-spline surface and scalar field theory is proposed in this study. The isothermal lines and stream lines designed in the scalar field are introduced to find the control points which are used in constructing B-spline surfaces. Intersected points between the isothermal lines and stream lines are used to construct B-spline surfaces. The inlet and outlet profiles are precisely described with B-spline curves by using the centripetal method for uniform parameterization. The extrusion die surface is generated by using the cubic curve interpolation in the u- and v-directions. A quantitative measure for the control of surface is suggested by introducing the tangential vectors at the inlet and outlet sections.

• Structural Engineering and Mechanics
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• 제34권3호
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• pp.319-334
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• 2010

The dynamic response of a finite Bernoulli-Euler beam resting on a tensionless Pasternak foundation and subjected to a concentrated harmonic load is investigated in this study. This load may be applied at the center of the beam, or it may be offset from the center. Since the elastic foundation is assumed to be tensionless, the beam may lift off the foundation, resulting in contact and non-contact regions in the system. An analytical/numerical solution is obtained from the governing equations of the contact and non-contact regions to determine the coordinates of the lift-off points. Although there is no nonlinear term in the equations, the problem appears to be nonlinear since the contact regions are not known in advance. Due to that nonlinearity, the essentials of the problem (the coordinates of the lift-off points) are calculated numerically using the Newton-Raphson technique. The results, which represent the symmetric and asymmetric responses of the beam, are presented graphically in this work. They illustrate the effects of the forcing frequency and the beam length on the extent of the contact regions and displacements.

• 대한수학회보
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• 제43권3호
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• pp.589-598
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• 2006

In the present investigation, sharp upper bounds of $|a3-{\mu}a^2_2|$ for functions $f(z)=z+a_2z^2+a_3z^3+...$ belonging to certain subclasses of starlike and convex functions with respect to symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szego inequalities for certain classes of functions defined through fractional derivatives are obtained.

• Korean Journal of Mathematics
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• 제24권2호
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• pp.139-168
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• 2016

In this work, we rst introduce a class of analytic functions involving the Dziok-Srivastava linear operator that generalizes the class of uniformly starlike functions with respect to symmetric points. We then establish the closure of certain well-known integral transforms under this analytic function class. This behaviour leads to various radius results for these integral transforms. Some of the interesting consequences of these results are outlined. Further, the lower bounds for the ratio between the functions f(z) in the class under discussion, their partial sums $f_m(z)$ and the corresponding derivative functions f'(z) and $f^{\prime}_m(z)$ are determined by using the coecient estimates.