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International Journal of Number Theory, ISSN 1793-0421, 02/2015, Volume 11, Issue 1, pp. 171 - 183
In this work, we evaluate the convolutions ∑l+36m=n σ(l)σ(m) and ∑4l+9m=n σ(l)σ(m) for all positive n. As an application, these evaluations are used to... 
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 09/2014, Volume 10, Issue 6, pp. 1421 - 1430
In this paper, the convolution sum ∑i+25j=n σ(i)σ(j) is evaluated for all n ∈ ℕ based on some identities due to Berndt, Lemire and Williams. 
Journal Article
Journal of theoretical probability, ISSN 0894-9840, 09/2020, Volume 33, Issue 3, pp. 1493 - 1505
Journal Article
INDIANA UNIVERSITY MATHEMATICS JOURNAL, ISSN 0022-2518, 2019, Volume 68, Issue 4, pp. 1199 - 1215
A Herglotz function is a holomorphic map from the open complex unit disk into the closed complex right half plane. A classical Herglotz function has an... 
MATHEMATICS | CONVOLUTION
Journal Article
1982, 2nd corr. and updated ed. --, Springer series in information sciences, ISBN 9780387118253, Volume 2, cm. --
Book
Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 08/2017, Volume 2017, Issue 729, pp. 119 - 149
It is a classical result in complex analysis that the class of functions that arise as the Cauchy transform of probability measures may be characterized... 
MATHEMATICS | CONVOLUTION
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 12/2018, Volume 2046, Issue 1
The main purpose of this paper is to present three new convolutions for the offset linear canonical transform, with the Hermite weights, and to illustrated... 
Convolution
Journal Article
Sbornik. Mathematics, ISSN 1064-5616, 08/2019, Volume 210, Issue 8
The paper is concerned with convolution operators in \(\mathbb R^d\), whose kernels are in \(L_q\), which act from \(L_p\) into \(L_s\), where... 
Convolution
Journal Article
P-adic numbers, ultrametric analysis, and applications, ISSN 2070-0466, 04/2020, Volume 12, Issue 2, pp. 90 - 111
Journal Article
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2018, Volume 11211, pp. 3 - 19
Conference Proceeding
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2017, Volume 39, Issue 6, pp. A3089 - A3106
We present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using... 
Fredholm convolution integral | Convolution | Fourier extension | Toeplitz matrix | Volterra convolution integral | Fast Fourier transform | MATHEMATICS, APPLIED | APPROXIMATION | convolution | fast Fourier transform | MATHEMATICS AND COMPUTING
Journal Article
IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 08/2013, Volume 35, Issue 8, pp. 1872 - 1886
A wavelet scattering network computes a translation invariant image representation which is stable to deformations and preserves high-frequency information for... 
Fourier transforms | Convolution | Scattering | deformations | Computer architecture | Classification | convolution networks | wavelets | Wavelet coefficients | invariants | MODELS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Wavelet transforms | Usage | Kernel functions | Image processing | Gaussian processes | Innovations | Fourier transformations
Journal Article
1982, 2nd ed. --, Mathematics and its applications. East European series, ISBN 9027714096, Volume 2., xvii, 332
Book
IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 04/2018, Volume 40, Issue 4, pp. 834 - 848
Journal Article
Bolletino dell Unione Matematica Italiana, ISSN 1972-6724, 06/2017, Volume 10, Issue 2, pp. 241 - 269
Journal Article
IEEE signal processing letters, ISSN 1558-2361, 2016, Volume 23, Issue 10, pp. 1499 - 1503
Face detection and alignment in unconstrained environment are challenging due to various poses, illuminations, and occlusions. Recent studies show that deep... 
Training | Convolution | Detectors | Computer architecture | Cascaded convolutional neural network (CNN) | Benchmark testing | Face | Face detection | face alignment | face detection | ENGINEERING, ELECTRICAL & ELECTRONIC
Journal Article
Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 07/2020, Volume 26, Issue 2, pp. 399 - 416
Journal Article
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