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A Review: Construction of Statistical Distributions. [PDF]
Entropy (Basel)Fang KT, Lin YX, Deng YH.
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A MONOTONIC CONVOLUTION FOR MINKOWSKI SUMS
International Journal of Computational Geometry & Applications, 2007We present a monotonic convolution for planar regions A and B bounded by line and circular arc segments. The Minkowski sum equals the union of the cells with positive crossing numbers in the arrangement of the convolution, as is the case for the kinetic convolution.
Victor Milenkovic, Elisha Sacks
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A sharp discrete convolution sum estimate
Communications in Nonlinear Science and Numerical Simulation, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Martin Stynes, Dongling Wang
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SIAM Journal on Mathematical Analysis, 1972
Let $\Omega $ be an open set in $R_n $ and let $\mathcal{E}(\Omega )$ denote the space of infinitely differentiable functions on $\Omega $. Necessary and sufficient conditions are exhibited for a family $\{ \Omega _i \} _{i = 1}^N $ of open sets in $R_n$ and a family $\{ S_i \} _{i = 1}^N \subset \mathcal{E}'(R_n )$ in order that the convolution ...
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Let $\Omega $ be an open set in $R_n $ and let $\mathcal{E}(\Omega )$ denote the space of infinitely differentiable functions on $\Omega $. Necessary and sufficient conditions are exhibited for a family $\{ \Omega _i \} _{i = 1}^N $ of open sets in $R_n$ and a family $\{ S_i \} _{i = 1}^N \subset \mathcal{E}'(R_n )$ in order that the convolution ...
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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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Sums with convolutions of Dirichlet characters
manuscripta mathematica, 2010Let \(\chi_1\) and \(\chi_2\) be primitive Dirichlet characters with conductors \(q_1\) and \(q_2\), respectively, and let \[ S_{\chi_1,\chi_2}(X):=\sum_{ab\leq X}\chi_1(a)\chi_2(b). \] The authors prove that if \(X\geq q_2^{\frac 23}\geq q_1^{\frac 23}\) and \(\log X=q_2^{o(1)}\), then \[ \left| S_{\chi_1,\chi_2}(X)\right|\leq X^{\frac {13}{18}}q_1 ...
Banks, William D., Shparlinski, Igor E.
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Computing the convolution and the Minkowski sum of surfaces
Proceedings of the 21st Spring Conference on Computer Graphics, 2005In 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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Problem of Minimizing a Sum of Differences of Weighted Convolutions
Computational Mathematics and Mathematical Physics, 2020In this paper the problem of minimizing a sum of differences of weighted convolutions is formulated as the problem of optimal summing of elements of two sequences where indices play the role of variables. It is shown that the considered problem can be interpreted as the problem that minimizes the sum of squared distances between the elements of an ...
Kel'manov, A. V. +3 more
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The convolution sums of MacMahon’s q-series
The Ramanujan JournalIn his classical work on partitions and divisor functions, MacMahon introduced the two \(q\)-series \(A_k(q)\) and \(C_k(q)\), which have since been shown to be quasimodular forms and are closely linked to partition functions, modular forms, and infinite product identities.
Xia, Ernest X. W. +2 more
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