• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.4
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• pp.1463-1480
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• 2014

It is well known that sparse code is effective for feature extraction of face recognition, especially sparse mode can be learned in the kernel space, and obtain better performance. Some recent algorithms made use of single kernel in the sparse mode, but this didn't make full use of the kernel information. The key issue is how to select the suitable kernel weights, and combine the selected kernels. In this paper, we propose a novel multiple kernel sparse representation based classification for face recognition (MKSRC), which performs sparse code and dictionary learning in the multiple kernel space. Initially, several possible kernels are combined and the sparse coefficient is computed, then the kernel weights can be obtained by the sparse coefficient. Finally convergence makes the kernel weights optimal. The experiments results show that our algorithm outperforms other state-of-the-art algorithms and demonstrate the promising performance of the proposed algorithms.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.35-51
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• 1993

This paper concerns collocation methods for integro-differential equations in which memory kernels have a singularity at t = 0. There has been extensive research in recent years on Volterra integral and integro-differential equations for physical systems with memory effects in which the stabilty and asymtotic stability of solutionsl have been the main interest. We will study a class of hereditary equations with singular kernels which interpolate between well known model equations as the order of singularity varies. We are also concerned with the smoothing effect of singular kernels, but we use energy methods and our results involve fractional time in fixed spatial norms. Galerkin methods for our models was studied and existence, uniqueness and stability results was obtained in [4]. Our major goal is to study collocation methods.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.277-303
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• 2021

Under the rough kernels Ω belonging to the block spaces B0,qr (Sn-1) or the radial Grafakos-Stefanov kernels W����(Sn-1) for some r, �� > 1 and q ≤ 0, the boundedness and continuity were proved for two classes of rough maximal singular integrals and maximal operators associated to polynomial mappings on the Triebel-Lizorkin spaces and Besov spaces, complementing some recent boundedness and continuity results in [27, 28], in which the authors established the corresponding results under the conditions that the rough kernels belong to the function class L(log L)α(Sn-1) or the Grafakos-Stefanov class ����(Sn-1) for some α ∈ [0, 1] and �� ∈ (2, ∞).

• Current Research on Agriculture and Life Sciences
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• v.1
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• pp.19-26
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• 1983

To investigate the influences of morphological features and the chemical compound of rice grain on the crack of rice kernels, rice was cultivated under the different method of fertilizer application and was harvested at optimal and late stage to the crack features of kernels of cracked and healthy grains. The results are summarized as follows ; The occurrence of cracked kernel was more severe in "Samgang-byeo" than in "Nagdong-byeo" and the rice harvested at the late stage was more cracked kernel than that of optimal harvest. The application of silicate fertilizer in addition to the N.P.K. fertilizer resulted in the decrease of cracked kernels. The grain weight, the grain volume (length ${\times}$ width ${\times}$ thickness), grain length and grain length/grain width etc. of the cracked kernels were larger than those of the healthy grains. The long "Samgang-byeo", having the long grain Shape, which has larger ratio of grain length/grain width than that of "Nagdong-byeo", shows higher rate of cracked kernels. The grain of "Samgang-byeo" which is easily cracked relatively it contains lower silica and higher phosphorus while "Nagdong-byeo" shows the opposite results. The ratio of silica/phosphorus in the grain was low in "Samgang-byeo" but it was high in "Nagdong-byeo". The ratio of silica/phosphorus in rice grain was increased by the application of silicate fertilizer in addition with N.P.K. fertilizers.

• Korean Journal of Digital Imaging in Medicine
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• v.9 no.1
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• pp.21-30
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• 2007

Our objective was to evaluate the CT attenuation coefficient and noise of spatial domain filtering as an alternative to additional image reconstruction using different kernels in abdominal CT. Derived from thin collimated source images was generated using abdomen B10 (very smooth), B20 (smooth), B30 (medium smooth), B40 (medium), B50 (medium sharp), B60 (sharp), B70 (very sharp) and B80 (ultra sharp) kernels. Quantitative CT coefficient and noise measurements provided comparable HU (hounsfield) units in this respect. CT attenuation coefficient (mean HU) values in the abdominal were 60.4$\sim$62.2 HU and noise (7.6$\sim$63.8 HU) in the liver parenchyma. In the stomach a mean (CT attenuation coefficient) of -2.2$\sim$0.8 HU and noise (10.1$\sim$82.4 HU) was measured. Image reconstructed with a convolution kernel led to an increase in noise, whereas the results for CT attenuation coefficient were comparable. Image medications of image sharpness and noise eliminate the need for reconstruction using different kernels in the future. CT images increase the diagnostic accuracy may be controlled by adjusting CT various kernels, which should be adjusted to take into account the kernels of the CT undergoing the examination.

• East Asian mathematical journal
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• v.34 no.1
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• pp.69-84
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• 2018

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source for each independent kernels h and g with respect to Volterra terms. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.101-112
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• 2010

Using some interesting convolution, we find kernels recovering the given function f. By a slight change of this convolution, we obtain an identity filter related to the Fourier series in the discrete time domain. We also introduce some techniques to decompose an impulse into several dilated pieces in the discrete domain. The detail examples deal with specific constructions of those decompositions. Also we obtain localized moving averages from a decomposition of an impulse to make hybrid Bollinger bands, that might give various strategies for stock traders.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.771-788
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• 2015

In this note we consider the parametric Marcinkiewicz integrals with mixed homogeneity along polynomials compound curves. Under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the $L^p$ bounds of such operators are given by an extrapolation argument. Some previous results are greatly extended and improved.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.645-658
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• 2008

In this paper, left-regular maps on d-algebras are defined. These mappings show behaviors reminiscent of homomorphisms on d-algebras which have been studied elsewhere. In particular for these mappings kernels, annihilators and co-annihilators are defined and some of their properties are investigated, especially in the setting of positive implicative d-algebras.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.125-138
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• 2018

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.