• 대한전자공학회논문지
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• 제25권5호
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• pp.550-558
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• 1988

This paper presents laplacian pyramid vector quantization (LPVQ) approach in which a vector quantizer is used to encode a series of quasi-bandpassed images generated by the laplacian pyramid processing. Performance of the LPVQ is compared to those of DCT domain methods at the same bit rate via computer simulations. Experimental results show that the PSNR's (peak signal-to-noise ratio) for the LPVQ are almost the same as those of the DCT based methods. However, subjective study indicates the LPVQ obtains slightly higher scores than the DCT based techniques.

• Journal of the Korean Statistical Society
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• 제22권2호
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• pp.259-269
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• 1993

A moving average model, LMA(q) and an autoregressive-moving average model, NLARMA(p, q), with Laplacian marginal distribution are constructed and their properties are discussed; Their autocorrelation structures are completely analogus to those of Gaussian process and they are partially time reversible in the third order moments. Finally, we study the mixing property of NLARMA process.

• 대한수학회논문집
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• 제26권4호
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• pp.591-601
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• 2011

In this paper, we deal with the discrete p-Laplacian operators with a potential term having the smallest nonnegative eigenvalue. Such operators are classified as its smallest eigenvalue is positive or zero. We discuss differences between them such as an existence of solutions of p-Laplacian equations on networks and properties of the energy functional. Also, we give some examples of Poisson equations which suggest a difference between linear types and nonlinear types. Finally, we study characteristics of the set of a potential those involving operator has the smallest positive eigenvalue.

• 대한수학회논문집
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• 제12권2호
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• pp.325-332
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• 1997

Let $Z = X \times Y$ where X and Y are complex manifolds. We suppose that projection $\pi$ on the second factor is a Riemannian submersion, that TX is perpendicular to TY, and that the metrics on Z and on Y are Hermetian; we do not assume Z is a Riemannian product. We study when the pull-back of an eigenfunction of the complex Laplacian on Y is an eigenfunction of the complex Laplacian on Z.

• 대한수학회논문집
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• 제28권3호
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• pp.501-509
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• 2013

In this paper we give a definition of the Hodge type Laplacian ${\Delta}$ on a non-commutative manifold which is the smooth dense subalgebra of a $C^*$-algebra. We prove that the Laplacian on a quantum Heisenberg manifold is an elliptic operator in the sense that $({\Delta}+1)^{-1}$ is compact.

• 대한수학회지
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• 제61권3호
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• pp.445-459
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• 2024

In this paper, by establishing the direct method of moving planes for the fractional Laplacian system with positive-negative mixed powers, we obtain the radial symmetry and monotonicity of the positive solutions for the fractional Laplacian systems with positive-negative mixed powers in the whole space. We also give two special cases.

• 대한수학회보
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• 제37권4호
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• pp.721-727
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• 2000

We study some spectral properties of the $\rho-Laplacian$ on quaternionic Kaehler manifolds.

• 대한수학회논문집
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• 제12권2호
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• pp.333-346
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• 1997

The purposer of this paper is to study the spectrum of the Laplacian and the cosymplectic conformal curvature tensor of cosymplectic manifold.

• 대한수학회보
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• 제47권2호
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• pp.355-367
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• 2010

In this paper, the existence of periodic solutions is obtained for a kind of p-Laplacian systems by the minimax methods in critical point theory. Moreover, the existence of infinite periodic solutions is also obtained.

• Kyungpook Mathematical Journal
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• 제50권1호
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• pp.109-116
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• 2010

In this paper, we study the signless Laplacian spectral radius of bicyclic graphs with given number of pendant vertices and characterize the extremal graphs.