Results 201 to 210 of about 40,198 (236)
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Oscillatory Singular Integrals with Rough Kernel
1995This paper is devoted to the study on the L p -boundedness for the oscillatory singular integral defined by $$ Tf(x) = p.v.\int_{\mathbb{R}^n } {e^{iP(x,y)} } K(x - y)f(y)dy, $$ where P(x,y) is a real polynomial on ℝ n × ℝ n , and \( K(x) = \frac{{h(\mid x\mid \Omega (x)}} {{\mid x\mid ^n }} \) with Ω ∈ Llog + L(S n−1) and h ∈ BV(ℝ+) (i.e.
Yinsheng Jiang, Shanzhen Lu
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Rough bilinear fractional integrals with variable kernels
Frontiers of Mathematics in China, 2010The authors show in the paper that the bilinear operator \[ \tilde B_{\Omega,\alpha}(f,g)(x)= \int_{\mathbb R^n} f(x+y)g(x-y)\frac{\Omega(x,y')}{|y|^{n-\alpha}} dy \] where ...
Chen, Jiecheng, Fan, Dashan
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Rough Cluster Algorithm Based on Kernel Function
2008By means of analyzing kernel clustering algorithm and rough set theory, a novel clustering algorithm, rough kernel k-means clustering algorithm, was proposed for clustering analysis. Through using Mercer kernel functions, samples in the original space were mapped into a highdimensional feature space, which the difference among these samples in sample ...
Tao Zhou +4 more
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On Singular Integral Operators with Rough Kernel Along Surface
Integral Equations and Operator Theory, 2010Let \(\Omega\) be a homogeneous function of degree 0 on \(\mathbb{R}^n\), with \(\Omega \in L^1(S^{n-1})\) and \( \int \Omega (y') d\sigma (y')=0. \) Suppose that \(\Phi\) is a nonnegative (or nonpositive) and monotonic \(C^1\) function on \((0, \infty)\) such that \( \varphi (t) := \frac{\Phi(t)}{t \Phi'(t)} \) is bounded.
Ding, Yong +2 more
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On Marcinkiewicz Integral Operators with Rough Kernels
Integral Equations and Operator Theory, 2005This paper is devoted to the study on the L p -mapping properties of Marcinkiewicz integral operators with rough kernels along “polynomial curves” on $$\mathbb{R}^n .$$ The
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Singular Integrals along Surfaces of Revolution with Rough Kernels
SUT Journal of Mathematics, 2003Let \(n\geq 2\) and \(S^{n-1}\) be the unit sphere in \(\mathbb{R}^n\) equipped with the normalized Lebesgue measure \(d\sigma\). Suppose that \(\Omega\) is a homogeneous function of degree zero on \(\mathbb{R}^n\) that satisfies \(\Omega\in B_q^{0,0}(S^{n-1})\) and \(\int_{S^{n-1}} \Omega (x)d\sigma=0\), where \(B_q^{0,0}\) is a certain block space ...
Al-Qassem, Hussain, Pan, Yibiao
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A roughness-penalty view of kernel smoothing
Statistics & Probability Letters, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Applications of Boolean Kernels in Rough Sets
2014Rough Sets (RS) and Support Vector Machine (SVM) are the two big and independent research areas in AI. Originally, rough set theory is dealing with the concept approximation problem under uncertainty. The basic idea of RS is related to lower and upper approximations, and it can be applied in classification problem.
Sinh Hoa Nguyen, Hung Son Nguyen
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Parabolic singular integrals with rough kernels and extrapolation
SCIENTIA SINICA Mathematica, 2014This paper is devoted to studying the parabolic singular integrals with rough kernels both on the unit sphere and in the radial direction, as well as the corresponding maximal singular integrals. By the estimates of Fourier transforms, the Littlewood-Paley theory and the extrapolation arguments, under the rather weak size conditions, which are the best
Feng LIU, HuoXiong WU
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Rough Kernel Clustering Algorithm with Adaptive Parameters
2011Through analyzing kernel clustering algorithm and rough set theory, a novel clustering algorithm, Rough kernel k-means clustering algorithm with adaptive parameters, is proposed for clustering analysis in this paper. By using Mercer kernel functions, we can map the data in the original space to a highdimensional feature space, in which we can use rough
Tao Zhou +4 more
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