scholarly journals Multivariate integration for analytic functions with Gaussian kernels

2016 ◽  
Vol 86 (304) ◽  
pp. 829-853 ◽  
Author(s):  
Frances Y. Kuo ◽  
Ian H. Sloan ◽  
Henryk Woźniakowski
Keyword(s):  
Analytic Functions ◽  
Multivariate Integration ◽  
Gaussian Kernels

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

A NEW SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY OPOOLA DIFFERENTIAL OPERATOR

2020 ◽  
Vol 9 (8) ◽  
pp. 5343-5348 ◽  
Author(s):  
T. G. Shaba ◽  
A. A. Ibrahim ◽  
M. F. Oyedotun
Keyword(s):  
Differential Operator ◽  
Analytic Functions

ON MONOTONIC AND ANALYTIC FUNCTIONS IN C ∞

1997 ◽  
Vol 23 (2) ◽  
pp. 697
Author(s):  
Cater
Keyword(s):  
Analytic Functions

scholarly journals Superpixel Segmentation Based on Anisotropic Edge Strength

2019 ◽  
Vol 5 (6) ◽  
pp. 57 ◽  
Author(s):  
Gang Wang ◽  
Bernard De Baets
Keyword(s):  
Distance Measure ◽  
Saliency Detection ◽  
Experimental Results ◽  
Segmentation Method ◽  
Superpixel Segmentation ◽  
Gaussian Kernels ◽  
First Derivative ◽  
Edge Strength

Superpixel segmentation can benefit from the use of an appropriate method to measure edge strength. In this paper, we present such a method based on the first derivative of anisotropic Gaussian kernels. The kernels can capture the position, direction, prominence, and scale of the edge to be detected. We incorporate the anisotropic edge strength into the distance measure between neighboring superpixels, thereby improving the performance of an existing graph-based superpixel segmentation method. Experimental results validate the superiority of our method in generating superpixels over the competing methods. It is also illustrated that the proposed superpixel segmentation method can facilitate subsequent saliency detection.

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