Results 291 to 300 of about 1,210,874 (307)

On Convoluted Numbers and Sums

The American Mathematical Monthly, 1967
(1967). On Convoluted Numbers and Sums. The American Mathematical Monthly: Vol. 74, No. 3, pp. 235-246.
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Evaluation of the convolution sums ∑l+36m=n σ(l)σ(m) and ∑4l+9m=n σ(l)σ(m)

, 2015
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 determine the number of representations of a positive integer by the forms $x_{1}^{2}+x_{1}x_{2}+x_{2}^
Dongxi Ye
semanticscholar   +1 more source

Evaluation of the convolution sums ∑l+20m=n σ(l)σ(m), ∑4l+5m=n σ(l)σ(m) and ∑2l+5m=n σ(l)σ(m)

, 2014
The theory of quasimodular forms is used to evaluate the convolution sums $$\sum_{l+20m=n}\sigma(l)\sigma(m), \quad \sum_{4l+5m=n}\sigma(l)\sigma(m) \quad \mbox {and} \sum_{2l+5m=n}\sigma(l)\sigma(m)$$ for all positive integers n.
S. Cooper, Dongxi Ye
semanticscholar   +1 more source

EVALUATION OF THE CONVOLUTION SUMS ∑i+3j=nσ(i)σ3(j) AND ∑3i+j=nσ(i)σ3(j)

, 2014
In this paper, the convolution sums ∑i+3j=nσ(i)σ3(j) and ∑3i+j=nσ(i)σ3(j) are evaluated for all n ∈ ℕ, which answers an open problem given by Huard, Ou, Spearman and Williams.
Olivia X. M. Yao, Ernest X. W. Xia
semanticscholar   +1 more source

Sum-product decoding of convolutional codes

2009 Fourth International Workshop on Signal Design and its Applications in Communications, 2009
This article proposes two methods to improve the sum-product soft-in/soft-out decoding performance of convolutional codes. The first method is to transform a parity check equation in such a way as to remove cycles of length four in a Tanner graph of a convolutional code, and performs sum-product algorithm (SPA) with the transformed parity check ...
Yuuichi Ogawa, Toshiyuki Shohon, Haruo Ogiwara   +2 more
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Computing the convolution and the Minkowski sum of surfaces

Proceedings of the 21st Spring Conference on Computer Graphics, 2005
In many applications, such as NC tool path generation and robot motion planning, it is required to compute the Minkowski sum of two objects. Generally the Minkowski sum of two rational surfaces cannot be expressed in rational form. In this paper we show that for LN spline surfaces (surfaces with a linear field of normal vectors) a closed form ...
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EVALUATION OF THE CONVOLUTION SUMS ∑l+15m=nσ(l)σ(m) AND ∑3l+5m=nσ(l)σ(m) AND AN APPLICATION

, 2013
We evaluate the convolution sums ∑l,m∈ℕ,l+15m=nσ(l)σ(m) and ∑l,m∈ℕ,3l+5m=nσ(l)σ(m) for all n ∈ ℕ using the theory of quasimodular forms and use these convolution sums to determine the number of representations of a positive integer n by the form We also ...
B. Ramakrishnan, B. Sahu
semanticscholar   +1 more source

A property of convolution sum for divisor functions

AIP Conference Proceedings, 2012
In this article, we shall give a generalization of the formula Σk = 1N−1σ1(2nk)σ3(2n(N−k)).
Daeyeoul Kim, Aeran Kim
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Evaluate the Convolution Integral and Convolution Sum Use Compact Formula

2011 7th International Conference on Wireless Communications, Networking and Mobile Computing, 2011
Abstract: Convolution integral and convolution summation play an important role in the analysis of the linear time invariant systems. At present, many text books have published in my home country or foreign country , especially the ?sSignals and Systems?t all discuss the methods by use of the graph to determine the up limit, low limit and the interval ...
De-yong Yu, Bin Ren
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Subconvexity for twisted L-functions over number fields via shifted convolution sums

Acta Mathematica Hungarica, 2017
P. Maga
semanticscholar   +2 more sources