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Advances in Mathematics, ISSN 0001-8708, 01/2020, Volume 360, p. 106889
We prove decoupling inequalities for a class of moment manifolds. These inequalities imply optimal mean value estimates for multidimensional Weyl sums of the... 
Fourier decoupling | Vinogradov mean value
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 03/2017, Volume 2017, Issue 5, pp. 1342 - 1389
We show that whenever s > k( k + 1), then for any complex sequence ( an) n. Z, one has integral([0,1)k) vertical bar Sigma(vertical bar n vertical bar <= X)... 
MATHEMATICS | MEAN-VALUE THEOREM
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2016, Volume 2016, Issue 23, pp. 7137 - 7178
Let F-q[t] be the ring of polynomials over Fq, the finite field of q elements, and let p be its characteristic. Let (G) over tilde (q)(k) be the least integer... 
MATHEMATICS | MEAN-VALUE THEOREM
Journal Article
JOURNAL D ANALYSE MATHEMATIQUE, ISSN 0021-7670, 10/2019, Volume 139, Issue 1, pp. 239 - 263
We combine a classical idea of Postnikov (1956) with the method of Korobov (1974) for estimating double Weyl sums, deriving new bounds on short character sums... 
MATHEMATICS | PRIMES | MEAN-VALUE THEOREM
Journal Article
ACM Transactions on Graphics (TOG), ISSN 0730-0301, 07/2007, Volume 26, Issue 3, pp. 71 - es
In this paper we consider the problem of creating and controlling volume deformations used to articulate characters for use in high-end applications such as... 
rigging | barycentric coordinates | free form deformations | mean value coordinates | Barycentric coordinates | Rigging | Free form deformations | Mean value coordinates
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 11/2019, p. 112728
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2018, Volume 465, Issue 1, pp. 423 - 458
We present several formulae for the large- asymptotics of the modified Hurwitz zeta function , which are valid to all orders. In the case of , these formulae... 
Hurwitz zeta function | Asymptotic series | MATHEMATICS | MATHEMATICS, APPLIED | MEAN-VALUE
Journal Article
ACM TRANSACTIONS ON GRAPHICS, ISSN 0730-0301, 07/2007, Volume 26, Issue 3
In this paper we consider the problem of creating and controlling volume deformations used to articulate characters for use in high-end applications such as... 
COMPUTER SCIENCE, SOFTWARE ENGINEERING | rigging | barycentric coordinates | mean value coordinates | free form deformations
Journal Article
The American Statistician, ISSN 0003-1305, 10/2019, Volume 73, Issue 4, pp. 408 - 410
Feng et al. revealed that the usual mean value theorem (MVT) should not be applied directly to a vector-valued function (e.g., the score function or a general... 
Mean value theorem | Taylor's expansion | Asymptotics | Score function
Journal Article
1968, Addison-Wesley series in chemical engineering., ix, 509
Book
Automatica, ISSN 0005-1098, 02/2020, Volume 112, p. 108708
This paper is devoted to reduced order of unknown inputs observer design. A new structure is proposed, and it includes the dynamics of the estimation error and... 
Pattern search algorithm | Mean value theorem | Nonlinear reduced observer | State estimation | Nonlinear system
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 05/2018, Volume 75, Issue 9, pp. 3139 - 3146
In this paper, we discuss an overdetermined problem for a weighted Poisson’s equation. We prove that if there exists a solution of the weighted Poisson’s... 
Ball | Overdetermined problem | Weighted Laplacian | Mean value properties
Journal Article
ACM Transactions on Graphics (TOG), ISSN 0730-0301, 07/2009, Volume 28, Issue 3, pp. 1 - 9
Seamless cloning of a source image patch into a target image is an important and useful image editing operation, which has received considerable research... 
image editing | gradient domain | matting | Poisson equation | mean-value coordinates | stitching | seamless cloning | Matting | Seamless cloning | Image editing | Mean-value coordinates | Stitching | Gradient domain | COMPUTER SCIENCE, SOFTWARE ENGINEERING
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 02/2020, Volume 43, Issue 3, pp. 1359 - 1379
We address the homogenization of the Vlasov equations using the sigma‐convergence method. Assuming that the electromagnetic field is strong and is highly... 
deterministic homogenization | algebras with mean value | Vlasov equations | sigma‐convergence
Journal Article
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 2019, Volume 149, Issue 6, pp. 1 - 7
AbstractThe classical notions of monotonicity and convexity can be characterized via the nonnegativity of the first and the second derivative, respectively.... 
Chebyshev system | differential inequality | generalized monotonicity | mean value theorem
Journal Article
Acta Arithmetica, ISSN 0065-1036, 2018, Volume 184, Issue 3, pp. 267 - 285
Journal Article
Journal of Convex Analysis, ISSN 0944-6532, 2018, Volume 25, Issue 4, pp. 1279 - 1290
We establish a new inequality of Clarke-Ledyaev type by direct construction. 
Subdifferential | Multidirectional Mean Value Theorem | MATHEMATICS | subdifferential | CLARKE | Multidirectional mean value theorem
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2016, Volume 2016, Issue 9, pp. 2632 - 2646
Write f(k)(alpha; X) = Sigma(x <= X) e(alpha(1)x+ ... + alpha(k)x(k)) (k >= 3). We show that there is a set B subset of [0, 1)(k-2) of full measure with the... 
MATHEMATICS | MEAN-VALUE THEOREM
Journal Article
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