• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.783-801
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• 2006

Let A be the mod p Steenrod algebra for p an arbitrary odd prime and S the sphere spectrum localized at p. In this paper, some useful propositions about the May spectral sequence are first given, and then, two new nontrivial homotopy elements ${\alpha}_1{\jmath}{\xi}_n\;(p{\geq}5,n\;{\geq}\;3)\;and\;{\gamma}_s{\alpha}_1{\jmath}{\xi}_n\;(p\;{\geq}\;7,\;n\;{\geq}\;4)$ are detected in the stable homotopy groups of spheres, where ${\xi}_n\;{\in}\;{\pi}_{p^nq+pq-2}M$ is obtained in [2]. The new ones are of degree 2(p - 1)($p^n+p+1$) - 4 and 2(p - 1)($p^n+sp^2$ + sp + (s - 1)) - 7 and are represented up to nonzero scalar by $b_0h_0h_n,\;b_0h_0h_n\tilde{\gamma}_s\;{\neq}\;0\;{\in}\;Ext^{*,*}_A^(Z_p,\;Z_p)$ in the Adams spectral sequence respectively, where $3\;{\leq}\;s\;<\;p-2$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.505-521
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• 2011

We present a duality between the category of compact Riemannian spin manifolds (equipped with a given spin bundle and charge conjugation) with isometries as morphisms and a suitable "metric" category of spectral triples over commutative pre-$C^*$-algebras. We also construct an embedding of a "quotient" of the category of spectral triples introduced in [5] into the latter metric category. Finally we discuss a further related duality in the case of orientation and spin-preserving maps between manifolds of fixed dimension.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.131-134
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• 2005

Conventional high order interpolation schemes are limitative in several aspects mainly because they need data of neighboring cells at the reconstruction step. However, discontinuous Galerkin method and spectral volume method, two high order flux schemes which will be analyzed and compared in this paper, have an important benefit that they are not necessary to determine the flow gradients from data of neighboring cells or elements. These two schemes construct polynomial of variables within a cell so that even near wall or discontinuity, the high order does not deteriorate.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.1066-1071
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• 2002

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide very accurate solutions, while reducing the number of degrees-of-freedom to resolve the computational and cost problems. Thus, in the present paper, the spectral element model is formulated for the axially moving Timoshenko beam under a uniform axial tension. The high accuracy of the present spectral element is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension on the vibration characteristics, the dispersion relation, and the stability of a moving Timoshenko beam are investigated, analytically and numerically.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.438-443
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• 1998

In this paper, the axial-bending coupled equations of motion for an elastic layered beam are derived. From this equation of motion, the spectral element is formulated for the vibration analysis by use of the spectral element method (SEM). The modal analysis methodology for the present coupled field equations of motion is then developed. As an illustrative example, a cantilevered beam is considered. The correctness of the equations of motion developed herein is verified by gradually reducing the thickness of upper elastic layer to converge to the single layered elastic beam solutions. Also, the accuracy of spectral element is confirmed by comparing its results with the result by modal analysis.

• Journal of Korean Society for Atmospheric Environment
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• v.9 no.3
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• pp.242-246
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• 1993

Theoretically, spectral method has the highest accuracy among present numerical methods, but it is generally difficult to apply to complex terrains because of complex boundary conditions. Recently, spectral-element method, basically divide the domain into a set of rectangular subdomain and solve the equation at each subdomain, has been introduced. However, boundary conditions become more complex and requires more computing time, thus spectral-element method is not powerful for all complex terrain problems. In this paper, potential flow theory was intorduced to solve the air flows and diffusion phenomenon in the presence of terrain obstacles. Using the velocity potential-stream line orthogonal coordinate space, the diffusion problems of hilly terrain by pseudospectral method were solved and compared those with no terrain real scale solutions.

• Journal of the Korean Graphic Arts Communication Society
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• v.22 no.1
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• pp.9-18
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• 2004

Recently as color image processing to be become independent have been desired at the light source in an image processing and it have been enlarged. An image processing of the light source which is become independent means an image processing which uses a spectral reflectance information. We improved it in the spectral reflectance estimation method which uses existing 3-band image in this research that the improvement of an identity color population generation method which uses the hue angle and the processing speed improvement and introduces a labelling method. The precision of a spectral reflectance estimation appeared to the ${\Delta}E^*_{ab}$ of an average 2.7 comparing with the measurement price. The practical use possibility came to be fast and appeared a processing speed compared with existing method.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.595-612
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• 2014

The spectral collocation method for a second order elliptic boundary value problem on a domain ${\Omega}$ with curved boundaries is studied using the Gordon and Hall transformation which enables us to have a transformed elliptic problem and a square domain S = [0, h] ${\times}$ [0, h], h > 0. The preconditioned system of the spectral collocation approximation based on Legendre-Gauss-Lobatto points by the matrix based on piecewise bilinear finite element discretizations is shown to have the high order accuracy of convergence and the efficiency of the finite element preconditioner.

• Journal of the Korean Magnetic Resonance Society
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• v.15 no.2
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• pp.157-174
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• 2011

Although the use of apodization functions in connection with postprocessing of a 2D NMR spectrum proves improved spectral quality, there is usually a trade-off between resolution enhancement and noise suppression due to a classical "uncertainty principle." In this study, therefore, a mathematical deconvolution technique called "Maximum Likelihood Deconvolution (MLD)" was adopted to achieve the spectral resolution and sensitivity enhancement simultaneously. The MLD technique greatly facilitates visualization and restoration of the genuine spectral information from complex 2D NMR spectra that would be problematic with the conventional apodization/FT processing. In particular, application of the MLD to the 2D-NOE spectrum would be very useful to derive the important proton connectivities, which are essential to achieve elucidating the 3D molecular structure.

• Proceedings of the KIEE Conference
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• 1999.11c
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• pp.748-750
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• 1999

In this study, a speech enhancement is presented based on the utilization of well-known auditory mechanism, noise masking. The speech enhancement approach adopted here is to derive an modifier that achieves audible noise suppression. This modification selectively affects the perceptually significant spectral values, and is therefore less prone to introduction of unwanted distortions than methods that affect the complete STSA and produces more enhanced results at low SNR as well as at high SNR. The speech enhancement method adopted here needs exact estimation of the minimum specteal value per critical band because it uses only the minimum spectral value per critical band. For this, the method adopted here uses the modified spectral subtraction that is more flexible than power spectral subtraction. So, the result in experiment represented better SNR than before.