• Journal of the Korea Institute of Information Security & Cryptology
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• v.19 no.2
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• pp.23-30
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• 2009

Recently, rotation symmetric Boolean functions have attracted attention since they are suitable for fast evaluation and show good cryptographic properties. For example, important problems in coding theory were settled by searching the desired functions in the rotation symmetric function space. Moreover, they are applied to designing fast hashing algorithms. On the other hand, for some homogeneous rotation symmetric quadratic functions of simple structure, the exact formulas for their Hamming weights and nonlinearity were found[2,8]. Very recently, more formulations were carried out for much broader class of the functions[6]. In this paper, we make a further improvement by deriving the formula for the Hamming weight of quadratic rotation symmetric functions containing linear terms.

• KIPS Transactions on Software and Data Engineering
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• v.4 no.10
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• pp.431-438
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• 2015

In this paper we address the symmetric-invariant problem in boundary image matching. Supporting symmetric transformation is an important factor in boundary image matching to get more intuitive and more accurate matching results. However, the previous boundary image matching handled rotation transformation only without considering symmetric transformation. In this paper, we propose symmetric-invariant boundary image matching which supports the symmetric transformation as well as the rotation transformation. For this, we define the concept of image symmetry and formally prove that rotation-invariant matching of using a symmetric image always returns the same result for every symmetric angle. For efficient symmetric transformation, we also present how to efficiently extract the symmetric time-series from an image boundary. Finally, we formally prove that our symmetric-invariant matching produces the same result for two approaches: one is using the time-series extracted from the symmetric image; another is using the time-series directly obtained from the original image time-series by symmetric transformation. Experimental results show that the proposed symmetric-invariant boundary image matching obtains more accurate and intuitive results than the previous rotation-invariant boundary image matching. These results mean that our symmetric-invariant solution is an excellent approach that solves the image symmetry problem in time-series domain.

• Bulletin of the Korean Chemical Society
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• v.4 no.5
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• pp.228-230
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• 1983

Molecular reorientation of oblate symmetric top molecules with internal rotation is investigated theoretically and an analytic expression for the overall reorientational correlation time in terms of the internal angular momentum correlation time is derived. This expression is quite different from the expression for prolate symmetric top molecules but reduces to the same expression in the spherical top limit. Fast internal rotation is treated by a modified version of the extended rotational diffusion while the bulky symmetric top mainbody is treated by the rotational diffusion model.

• Bulletin of the Korean Chemical Society
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• v.14 no.1
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• pp.110-112
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• 1993

Molecular reorientation of oblate symmetric top molecules in the presence of internal rotation is investigated and an analytic expression for the overall reorientational correlation time is obtained. The overall reorientation of the symmetric top is treated by the anisotropic rotational diffusion and the internal rotation is analyzed by employing a model which describes jumps between several discrete states with different lifetimes. The lifetimes thus obtained can be compared with the internal angular momentum correlation time which appears when the internal rotation is treated by a modified extended rotational diffusion model.

• Bulletin of the Korean Chemical Society
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• v.10 no.5
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• pp.430-433
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• 1989

Molecular reorientation of oblate symmetric top molecules in the presence of internal rotation is investigated and an analytic expression for the spin-rotational relaxation rate of a nucleus attached to the internal rotor is obtained as a function of the internal angular momentum correlation time. The overall reorientation of the symmetric top is treated by the anisotropic rotational diffusion and the internal rotation is assumed to undergo modified extended rotational diffusion. The result is compared with the previous work for the prolate symmetric top molecule and it is shown that both results reduce to the same expression in the spherical top limit.

• Bulletin of the Korean Chemical Society
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• v.15 no.3
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• pp.228-236
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• 1994

The effect of the vibration mode coupling induced by the vibration-rotation interaction on total energy was investigated for the states with zero total angular momentum(J=0) in a quasilinear symmetric triatomic molecule of $AB_2$ type using a model potential function with a slight potential barrier to linearity. It is found that the coupling energy becomes larger for the levels of bend and asymmetric stretch modes and smaller for symmetric stretch mode as the excitation of the vibrational modes occurs. The results for the real molecule of $CH_2^+$, which is quasilinear, generally agree with the results for the model potential function in that common mode selective dependence of coupling energy is exhibited in both cases. The differences between the results for the model and real potential function in H-C-H system are analyzed and explained in terms of heavy mixing of the symmetric stretch and bend mode in excited vibrational states of the real molecule of $CH_2^+$. It is shown that the vibrational mode coupling in the potential energy function is primarily responsible for the broken nodal structure and chaotic behavior in highly excited levels of $CH_2^+$ for J= 0.

• Steel and Composite Structures
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• v.26 no.6
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• pp.663-672
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• 2018

This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.

• Bulletin of the Korean Chemical Society
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• v.27 no.4
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• pp.515-518
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• 2006

It is explicitly shown that a supersymmetry structure exists in the spectrum of a rigid symmetric top rotor in the molecule-fixed frame. Using projection operators constructed from the time-reversal symmetry of the rotor, the full rotor Hamiltonian is separated into two parts, i.e., the bosonic and fermionic components. The construction, without ambiguity, suggests that the rotor has a supersymmetry in it. This supersymmetry is mathematically equivalent to that of the free rotor on a plane recently noted by Rau.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.14 no.6
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• pp.599-605
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• 2003

A dual-mode asymmetric canonical filter is widely used in an input demultiplexer for satellite transponder. This paper deals with a simple synthesis method fur an asymmetric canonical filter. The coupling matrix of an asymmetric canonical filter is obtained by applying plane rotation technique to the coupling matrix of a symmetric canonical filter. This paper gives a list of pivots and rotation angles to obtain the coupling matrix of asymmetric canonical structure filters. The coupling matrix of 8th and 10th order asymmetric canonical filter is obtained by this proposed method. It is shown that the frequency response of asymmetric canonical filter is identical to that of symmetric canonical filter.

• Journal of Sensor Science and Technology
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• v.19 no.1
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• pp.62-66
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• 2010

We have proposed and demonstrated a rotation angle sensor based on the stress -optic effect of a fused fiber coupler whose transmission spectrum is altered by the torsional stress. The peak of transmission spectrum was shifted to longer wavelength region with rotation of the coupler. The rotation angle sensor revealed reproducibility and symmetric behavior with respect to the rotation direction. The sensitivity of the sensor was 0.367 [nm/degee].