• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2004.10a
• /
• pp.225-228
• /
• 2004

The generalized knapsack problem, or gknap is the combinatorial optimization problem of optimizing a nonnegative linear functional over the integral hull of the intersection of a polynomially separable 0 - 1 polytope and a knapsack constraint. Among many potential applications, the knapsack, the restricted shortest path, and the restricted spanning tree problem are such examples. We prove via the ellipsoid method the equivalence between the fully polynomial approximability and a certain pseudo-polynomial separability of the gknap polytope.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2003.11a
• /
• pp.93-96
• /
• 2003

The generalized knapsack problem, or gknap is the combinatorial optimization problem of optimizing a nonnegative linear functional over the integral hull of the intersection of a polynomially separable 0 - 1 polytope and a knapsack constraint. Among many potential applications, the knapsack, the restricted shortest path, and the restricted spanning tree problem are such examples. We establish some necessary and sufficient conditions for a gknap to admit a fully polynomial approximation scheme, or FPTAS, To do so, we recapture the scaling and approximate binary search techniques in the framework of gknap. This also enables us to find a condition that a gknap does not have an FP-TAS. This condition is more general than the strong NP-hardness.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.28 no.4
• /
• pp.191-198
• /
• 2003

The generalized knapsack problem or gknap is the combinatorial optimization problem of optimizing a nonnegative linear function over the integral hull of the intersection of a polynomially separable 0-1 polytope and a knapsack constraint. The knapsack, the restricted shortest path, and the constrained spanning tree problem are a partial list of gknap. More interesting1y, all the problem that are known to have a fully polynomial approximation scheme, or FPTAS are gknap. We establish some necessary and sufficient conditions for a gknap to admit an FPTAS. To do so, we recapture the standard scaling and approximate binary search techniques in the framework of gknap. This also enables us to find a weaker sufficient condition than the strong NP-hardness that a gknap does not have an FPTAS. Finally, we apply the conditions to explore the fully polynomial approximability of the constrained spanning problem whose fully polynomial approximability is still open.

• Communications of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.1269-1284
• /
• 2022

This paper is concerned with the following Schrödinger-Poisson system $$\{\begin{array}{lll}-{\Delta}u+V(x)u+K(x){\phi}u=a(x){\mid}u{\mid}^{p-2}u&&\text{ in }{\mathbb{R}}^3,\\-{\Delta}{\phi}=K(x)u^2&&\text{ in }{\mathbb{R}}^3,\end{array}$$ where 4 < p < 6. For the case that K is nonnegative, V and a are indefinite, we prove the above problem possesses one ground state sign-changing solution with exactly two nodal domains by constraint variational method and quantitative deformation lemma. Moreover, we show that the energy of sign-changing solutions is larger than that of the ground state solutions. The novelty of this paper is that the potential a is indefinite and allowed to vanish at infinity. In this sense, we complement the existing results obtained by Batista and Furtado [5].

• Analytical Science and Technology
• /
• v.20 no.6
• /
• pp.502-507
• /
• 2007

X-ray diffraction method has been widely used for qualitative and quantitative analysis of a mixture of materials since every crystalline material gives a unique X-ray diffraction pattern independently of others, with the intensity of each pattern proportional to that material's concentration in a mixture. For determination of mixing ratios, extracting source spectra correctly is important and crucial. Based on the source spectra extracted, a regression model with non-negativity constraint is applied for determining mixing ratios. In some mixtures, however, X-ray diffraction spectrum has sharp and narrow peaks, which may result in partial negative source spectrum from independent component analysis. We propose several procedures of extracting non-negative source spectra and determining mixing ratios. The proposed method is validated with experimental data on powder mixtures.

• Journal of Korea Multimedia Society
• /
• v.18 no.12
• /
• pp.1439-1444
• /
• 2015

Measuring spectral reflectance can be regarded as obtaining inherent color parameters, and spectral reflectance has been used in image processing. Model-based spectrum recovering, one of the method for obtaining spectral reflectance, uses ordinary camera with multiple illuminations. Conventional model-based methods allow to recover spectral reflectance efficiently by using only a few parameters, however it requires some parameters such as power spectrum of illuminations and spectrum sensitivity of camera. In this paper, we propose an enhanced model-based spectrum recovering method without pre-measured parameters: power spectrum of illuminations and spectrum sensitivity of camera. Instead of measuring each parameters, spectral reflectance can be efficiently recovered by estimating and using the spectrum characteristic matrix which contains spectrum parameters: basis function, power spectrum of illumination, and spectrum sensitivity of camera. The spectrum characteristic matrix can be easily estimated using captured images from scenes with color checker under multiple illuminations. Additionally, we suggest fast recovering method preserving positive constraint of spectrum by nonnegative basis function of spectral reflectance. Results of our method showed accurately reconstructed spectral reflectance and fast constrained estimation with unmeasured camera and illumination. As our method could be conducted conveniently, measuring spectral reflectance is expected to be widely used.