Results 11 to 20 of about 9,377,044 (73)
Sumsets and monomial projections of veronese varieties [PDF]
, 2022 Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Rosa M. Miró-Roig[en] The main purpose of this paper is to study the so-called sumsets problem.
Llenas i Segura, Sixte Oriol
core +6 more sources
On the dimension of iterated sumsets [PDF]
, 2009 Let A be a subset of the real line. We study the fractal dimensions of the k-fold iterated sumsets kA, defined as kA = A+...+A (k times). We show that for any non-decreasing sequence {a_k} taking values in [0,1], there exists a compact set A such that kA
Schmeling, Jörg, Shmerkin, Pablo
core +3 more sources
Restricted sumsets in multiplicative subgroups [PDF]
, 2023 We establish the restricted sumset analog of the celebrated conjecture of S\'{a}rk\"{o}zy on additive decompositions of the set of nonzero squares over a finite field.
Yip, Chi Hoi
core +1 more source
A strengthening of Freiman's 3k−4$3k-4$ theorem
Bulletin of the London Mathematical Society, Volume 55, Issue 5, Page 2363-2381, October 2023., 2023 Abstract In its usual form, Freiman's 3k−4$3k-4$ theorem states that if A$A$ and B$B$ are subsets of Z${\mathbb {Z}}$ of size k$k$ with small sumset (of size close to 2k$2k$), then they are very close to arithmetic progressions. Our aim in this paper is to strengthen this by allowing only a bounded number of possible summands from one of the sets.
Béla Bollobás +2 more
wiley +1 more source
Augmented Design with Additive Manufacturing Methodology: Tangible Object-Based Method to Enhance Creativity in Design for Additive Manufacturing [PDF]
, 2021 Additive manufacturing (AM) brings new design potential compared with traditional manufacturing. Nevertheless, traditional manufacturing knowledge remains embedded in the minds of designers and is a real cognitive barrier to design in AM.
BUISINE, Stéphanie +6 more
core +1 more source
Diameter‐free estimates for the quadratic Vinogradov mean value theorem
Proceedings of the London Mathematical Society, Volume 126, Issue 1, Page 76-128, January 2023., 2023 Abstract Let s⩾3$s \geqslant 3$ be a natural number, let ψ(x)$\psi (x)$ be a polynomial with real coefficients and degree d⩾2$d \geqslant 2$, and let A$A$ be some large, non‐empty, finite subset of real numbers. We use Es,2(A)$E_{s,2}(A)$ to denote the number of solutions to the system of equations ∑i=1s(ψ(xi)−ψ(xi+s))=∑i=1s(xi−xi+s)=0,$$\begin ...
Akshat Mudgal
wiley +1 more source
A superadditivity and submultiplicativity property for cardinalities of sumsets [PDF]
, 2010 For finite sets of integers A1, . . . ,An we study the cardinality of the n-fold sumset A1 + · · · + An compared to those of (n − 1)-fold sumsets A1 + · · · + Ai−1 + Ai+1 + · · · + An.
Matolcsi, Máté +5 more
core +1 more source
Journal of the London Mathematical Society, Volume 106, Issue 4, Page 2927-2958, December 2022., 2022 Abstract In this paper, we study additive properties of finite sets of lattice points on spheres in three and four dimensions. Thus, given d,m∈N$d,m \in \mathbb {N}$, let A$A$ be a set of lattice points (x1,⋯,xd)∈Zd$(x_1, \dots , x_d) \in \mathbb {Z}^d$ satisfying x12+⋯+xd2=m$x_1^2 + \dots + x_{d}^2 = m$.
Akshat Mudgal
wiley +1 more source
Generalized Additive Models with Unknown Link Function Including Variable Selection [PDF]
, 2013 The generalized additive model is a well established and strong tool that allows to model smooth effects of predictors on the response. However, if the link function, which is typically chosen as the canonical link, is misspecified, substantial bias is ...
Gerhard Tutz +3 more
core +1 more source
A Guide to Additive Manufacturing [PDF]
, 2022 This open access book gives both a theoretical and practical overview of several important aspects of additive manufacturing (AM). It is written in an educative style to enable the reader to understand and apply the material.
core +1 more source