Article
Mathematics, Applied
Mate Matolcsi, Imre Z. Ruzsa
Summary: By constructing nonnegative exponential sums, we provide upper bounds on the cardinality of any set B-q in cyclic groups Z(q) in which the difference set B-q - B-q avoids cubic residues modulo q.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS
(2021)
Article
Automation & Control Systems
Phan Thanh Nam, Le Quang Thuan, Tran Ngoc Nguyen, Hieu Trinh
Summary: This paper proposes an extended comparison principle and computational method for continuous-time linear positive time-delay systems, which effectively derives tighter exponential estimates for the state vector. The effectiveness of the developed method is illustrated through numerical examples.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Article
Automation & Control Systems
Xingao Zhu, Shutang Liu, Yuangong Sun
Summary: This paper studies the problem of finite-time state bounding for homogeneous nonlinear positive systems with time-varying delay and bounded disturbance for the first time. By using a different approach from the Lyapunov-Krasovskii functional technique, the authors formulate an explicit criterion for the existence of a special ball that all the state trajectories of the systems converge within it in finite time. The main result is further extended to general nonlinear time-variant systems.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Mathematics
Xiaoxue Li, Li Chen
Summary: This article focuses on studying the calculating problem of the hybrid power mean of two-term exponential sums and quartic Gauss sums using analytic methods. The study leads to the derivation of two interesting linear recurrence formulas and the discovery of some asymptotic formulas as applications.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics
Shaofan Cao, Tingting Wang
Summary: This paper introduces an interesting third-order linear recurrence formula for calculating hybrid power means, which involves two-term exponential sums and cubic Gauss sums. By applying this formula, exact computational formulas for hybrid power means of trigonometric sums are obtained.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics
David Conlon, Jeck Lim
Summary: We prove that there exists an absolute constant c>0, such that |A+lambda center dot A|> eclog|A||A| for any finite subset A and transcendental number lambda in R. This result is best possible up to the constant c, as shown by the construction of Konyagin and Laba.
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Francesco Paolo Gallinaro
Summary: Zilber's Exponential-Algebraic Closedness Conjecture states that algebraic varieties in C-n x (C-x)(n) intersect the graph of complex exponentiation, unless that contradicts the algebraic and transcendence properties of exp. We establish a case of the conjecture, showing that it holds for varieties which split as the product of a linear subspace of the additive group and an algebraic subvariety of the multiplicative group. This amounts to solving certain systems of exponential sums equations, and it generalizes old results of Zilber, which required the linear subspace to either be defined over a generic subfield of the real numbers, or it to be any subspace defined over the reals assuming unproved conjectures from Diophantine geometry and transcendence theory. The proofs use the theory of amoebas and tropical geometry.
SELECTA MATHEMATICA-NEW SERIES
(2023)
Article
Mathematics, Applied
Rui Zhang, Yang Li, Xiaofei Yan
Summary: This paragraph mentions a function phi(x) with bounded derivatives, and provides the number of ways to write a number as a product of three factors, as well as an asymptotic formula for a nonlinear exponential sum.
Article
Mathematics
Lan Qi, Xingxing Lv
Summary: The paper aims to study the computational problem of a hybrid power mean using analytic method and properties of classical Gauss sums. A four-order linear recurrence formula is provided for this problem. Mathematica software can be used to obtain all values of this kind of hybrid power mean.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Andras Kroo
Summary: This paper investigates L-p Marcinkiewicz-Zygmund type inequalities for general exponential sums, providing specific conditions under which certain inequalities hold for particular point sets. The results show that the cardinality of these point sets depends on parameters epsilon and Lambda logarithmically, making the bound almost independent of degree and separation. Furthermore, the study extends to multivariate exponential sums and demonstrates stronger results for sums with nonnegative coefficients.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics
Roman Holowinsky, Ritabrata Munshi, Zhi Qi
Summary: In this paper, we use the Bessel delta-method, along with new variants of the van der Corput method in two dimensions, to prove non-trivial bounds for GL(2) exponential sums beyond the Weyl barrier.
ADVANCES IN MATHEMATICS
(2023)
Article
Mathematics
Jiamin Li, Jing Ma
Summary: By generalizing Bombieri and Iwaniec's double large sieve inequality, an estimation on three-dimensional exponential sums with constant perturbation is obtained. This estimation is then applied to a specific mathematical problem, resulting in an improved result.
INDAGATIONES MATHEMATICAE-NEW SERIES
(2023)
Article
Mathematics
Niranjan Balachandran, Eshita Mazumdar
Summary: This paper investigates the properties of sequences in Z(n) under different conditions, including restricted sequences and weighted sequences. The main focus is on determining the minimum length of sequences that satisfy specific criteria.
DISCRETE MATHEMATICS
(2021)
Article
Mathematics
Ciprian Demeter
Summary: We prove essentially sharp bounds for the L-p restriction of weighted Gauss sums to monomial curves. Getting the L-2 upper bound combines the TT* method for matrices with the first and second derivative test for exponential sums. The matching lower bound follows via constructive interference on short blocks of integers, near the critical point of the phase function.
MATHEMATISCHE ANNALEN
(2023)
Article
Mathematics, Applied
Laszlo Merai
Summary: This article investigates the properties of polynomials in two sets A and B, and proves that when A and B are large enough, their sum A + B will have an irreducible divisor of large degree.
FINITE FIELDS AND THEIR APPLICATIONS
(2022)
