• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.157-165
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• 2010

Let (M,p) be a germ of a $C^{\infty}$ CR manifold of CR dimension n and CR codimension d. Suppose (M,p) admits a $C^{\infty}$ contraction at p. In this paper, we show that (M,p) is CR equivalent to a generic submanifold in $\mathbb{C}^{n+d}$ defined by a vector valued weighted homogeneous polynomial.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.215-219
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• 1995

The most fundamental examples of (combinatorial) geometries are projective geometries PG(n - 1,q) of dimension n - 1, representable over GF(q), where q is a prime power. Every upper interval of a projective geometry is a projective geometry. The Whitney numbers of the second kind are Gaussian coefficients. Every flat of a projective geometry is modular, so the projective geometry is supersolvable in the sense of Stanley [6].

• Journal of the Korean Mathematical Society
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• v.40 no.4
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• pp.667-680
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• 2003

The mirror conjecture means originally the deep relation between complex and symplectic geometry in Calabi-Yau manifolds. Recently, this conjecture is posed beyond Calabi-Yau, and even to, open manifolds (e.g. $A_{n}$ singularities and its resolution) is discussed. While if we treat open manifolds, we can't avoid the boundary (in our case, CR manifolds). Therefore we pose the more precise conjecture (mirror symmetry with boundaries). Namely, in mirror symmetry, for boundaries, what kind of structure should correspond\ulcorner For this problem, the $A_{n}$ case is studied.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1145-1155
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• 2019

Let f be a transcendental meromorphic function, defined in the complex plane $\mathbb{C}$. In this paper, we give a quantitative estimations of the characteristic function T(r, f) in terms of the counting function of a homogeneous differential polynomial generated by f. Our result improves and generalizes some recent results.

• Asian-Australasian Journal of Animal Sciences
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• v.30 no.10
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• pp.1382-1387
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• 2017

Objective: During the last decade, genetic evaluation of dairy cows using longitudinal data (test day milk yield or 305-day milk yield) using random regression method has been officially adopted in several countries. The objectives of this study were to estimate covariance functions for genetic and permanent environmental effects and to obtain genetic parameters of 305-day milk yield over seven parities. Methods: Data including 60,279 total 305-day milk yield of 17,309 Iranian Holstein dairy cows in 7 parities calved between 20 to 140 months between 2004 and 2011. Residual variances were modeled by homogeneous and step functions with 7 and 10 classes. Results: The results showed that a third order polynomial for additive genetic and permanent environmental effects plus a step function with 10 classes for the residual variance was the most adequate and parsimonious model to describe the covariance structure of the data. Heritability estimates obtained by this model varied from 0.17 to 0.28. The performance of this model was better than repeatability model. Moreover, 10 classes of residual variance produce the more accurate result than 7 classes or homogeneous residual effect. Conclusion: A quadratic Legendre polynomial for additive genetic and permanent environmental effects with 10 step function residual classes are sufficient to produce a parsimonious model that explained the change in 305-day milk yield over consecutive parities of Iranian Holstein cows.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.187-204
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• 2018

Let $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}\;R_{\alpha}$ be a graded integral domain, H be the set of nonzero homogeneous elements of R, and ${\star}$ be a semistar operation on R. The purpose of this paper is to study the properties of $quasi-Pr{\ddot{u}}fer$ and UMt-domains of graded integral domains. For this reason we study the graded analogue of ${\star}-quasi-Pr{\ddot{u}}fer$ domains called $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. We study several ring-theoretic properties of $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. As an application we give new characterizations of UMt-domains. In particular it is shown that R is a $gr-t-quasi-Pr{\ddot{u}}fer$ domain if and only if R is a UMt-domain if and only if RP is a $quasi-Pr{\ddot{u}}fer$ domain for each homogeneous maximal t-ideal P of R. We also show that R is a UMt-domain if and only if H is a t-splitting set in R[X] if and only if each prime t-ideal Q in R[X] such that $Q{\cap}H ={\emptyset}$ is a maximal t-ideal.

• Journal of Korean Society for Geospatial Information Science
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• v.22 no.3
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• pp.121-128
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• 2014

This study investigated the accuracy of DEM generated by heterogeneous stereo satellite images based on RPC. Heterogeneous sensor images with different spatial resolution are SPOT-5 panchromatic and IKONOS images. For the accuracy evaluation of the DEM, we compared the DEMs generated from two kinds of sensors and that produced using homogeneous SPOT-5 and IKONOS stereo images. As results of the evaluation, accuracy of 3D positioning by heterogeneous images was substantially similar to that of homogeneous stereo images for exact conjugate points. But, in terms of quality of the DEM, DEM generated by heterogeneous sensor showed a lower accuracy about twice in RMSE and about 3 times in LE90 than that of homogeneous sensors. As a result, DEM can be generated by using heterogenous satellite imagery. But if we use a stereo image with different spatial resolution, the performance of image matching was very important factor for the production of high-quality DEM.

• Steel and Composite Structures
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• v.9 no.5
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• pp.473-497
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• 2009

For the spatially coupled free vibration analysis of composite box beams resting on elastic foundation under the axial force, the exact solutions are presented by using the power series method based on the homogeneous form of simultaneous ordinary differential equations. The general vibrational theory for the composite box beam with arbitrary lamination is developed by introducing Vlasov°Øs assumption. Next, the equations of motion and force-displacement relationships are derived from the energy principle and explicit expressions for displacement parameters are presented based on power series expansions of displacement components. Finally, the dynamic stiffness matrix is calculated using force-displacement relationships. In addition, the finite element model based on the classical Hermitian interpolation polynomial is presented. To show the performances of the proposed dynamic stiffness matrix of composite box beam, the numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and the results from other researchers. Particularly, the effects of the fiber orientation, the axial force, the elastic foundation, and the boundary condition on the vibrational behavior of composite box beam are investigated parametrically. Also the emphasis is given in showing the phenomenon of vibration mode change.

• Journal of Mechanical Science and Technology
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• v.17 no.12
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• pp.1922-1927
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• 2003

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6$\^$th/ order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhoff-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.7
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• pp.859-866
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• 2003

The Lagrangian dispserion of fluid particles in inhomogeneous turbulence is investigated by a direct numerical simulation of turbulent channel flow. Fluid particle velocity and acceleration along a particle trajectory are computed by employing several interpolation schemes such as linear interpolation, high-order Lagrange polynomial interpolation and the Hermite interpolation schemes. The performances of the schemes are evaluated through comparison of errors in computed particle positions, velocities and accelerations against spectral interpolation. Adopting the four-point Hermite interpolation in the homogeneous directions and Chebyshev polynomials in the wall-normal direction appears to produce most reliable Lagrangian statistics including acceleration correlations with a reasonable amount of computational overhead.