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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
1981, Springer series in information sciences, ISBN 9780387101590, Volume 2, x, 248
Book
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
IEICE transactions on information and systems, ISSN 0916-8532, 07/2020, Volume E103.D, Issue 7, pp. 1777 - 1781
Faster R-CNN uses a region proposal network which consists of a single scale convolution filter and fully connected networks to localize detected regions.... 
Convolution
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
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
1981, Springer series in information sciences, ISBN 9780387101590, Volume 2, x, 248
Book
2012, Annals of mathematics studies, ISBN 0691153310, Volume 180, vi, 203
Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin... 
Sequences (Mathematics) | Convolutions (Mathematics) | Mellin transform | Mathematics | Statistics
Book
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
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
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
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
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
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
Abstract and applied analysis, ISSN 1687-0409, 2019, Volume 2019, pp. 1 - 9
We introduce the two-dimensional quaternion linear canonical transform (QLCT), which is a generalization of the classical linear canonical transform (LCT) in... 
Quaternions | Theorems | Convolution
Journal Article
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