Results 21 to 30 of about 45 (44)

Approximation of Algebraic Curves in Function Spaces of Topological Sequences Connected to Specific Simple Graph Families

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
Algebraic curves and topological sequences play a crucial role in mathematics and graph theory, serving as a bridge between geometry, algebra, and number theory. They facilitate structural analysis in various applications, including chemistry, network analysis, and computer science.
Mohammad Mazyad Hazzazi, Muhammad Imran, Muhammad Nadeem, Muhammad Kamran, Samuel Asefa Fufa, Abdul Rauf Khan   +5 more
wiley   +1 more source

Cover and hitting times of hyperbolic random graphs

Random Structures &Algorithms, Volume 65, Issue 4, Page 915-978, December 2024.
Abstract We study random walks on the giant component of Hyperbolic Random Graphs (HRGs), in the regime when the degree distribution obeys a power law with exponent in the range (2,3)$$ \left(2,3\right) $$. In particular, we first focus on the expected time for a random walk to hit a given vertex or visit, that is, cover, all vertices.
Marcos Kiwi, Markus Schepers, John Sylvester   +2 more
wiley   +1 more source

Realizability of tropical pluri‐canonical divisors

Journal of the London Mathematical Society, Volume 110, Issue 6, December 2024.
Abstract Consider a pair consisting of an abstract tropical curve and an effective divisor from the linear system associated to k$k$ times the canonical divisor for k∈Z⩾1$k \in \mathbb {Z}_{\geqslant 1}$. In this article, we give a purely combinatorial criterion to determine if such a pair arises as the tropicalization of a pair consisting of a smooth ...
Felix Röhrle, Johannes Schwab
wiley   +1 more source

Colouring versus density in integers and Hales–Jewett cubes

Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.
Abstract We construct for every integer k⩾3$k\geqslant 3$ and every real μ∈(0,k−1k)$\mu \in (0, \frac{k-1}{k})$ a set of integers X=X(k,μ)$X=X(k, \mu)$ which, when coloured with finitely many colours, contains a monochromatic k$k$‐term arithmetic progression, whilst every finite Y⊆X$Y\subseteq X$ has a subset Z⊆Y$Z\subseteq Y$ of size |Z|⩾μ|Y|$|Z ...
Christian Reiher, Vojtěch Rödl, Marcelo Sales   +2 more
wiley   +1 more source

A discrete mean value of the Riemann zeta function

Mathematika, Volume 70, Issue 4, October 2024.
Abstract In this work, we estimate the sum ∑0<ℑ(ρ)⩽Tζ(ρ+α)X(ρ)Y(1−ρ)$$\begin{align*} \sum _{0 < \Im (\rho) \leqslant T} \zeta (\rho +\alpha)X(\rho) Y(1\!-\! \rho) \end{align*}$$over the nontrivial zeros ρ$\rho$ of the Riemann zeta function where α$\alpha$ is a complex number with α≪1/logT$\alpha \ll 1/\log T$ and X(·)$X(\cdot)$ and Y(·)$Y(\cdot)$ are ...
Kübra Benli, Ertan Elma, Nathan Ng
wiley   +1 more source

Special cubic zeros and the dual variety

Journal of the London Mathematical Society, Volume 110, Issue 3, September 2024.
Abstract Let F$F$ be a diagonal cubic form over Z$\mathbb {Z}$ in six variables. From the dual variety in the delta method of Duke–Friedlander–Iwaniec and Heath‐Brown, we unconditionally extract a weighted count of certain special integral zeros of F$F$ in regions of diameter X→∞$X \rightarrow \infty$.
Victor Y. Wang
wiley   +1 more source

On a conjecture of Graham on the p$p$‐divisibility of central binomial coefficients

Mathematika, Volume 70, Issue 3, July 2024.
Abstract Let p1,…,pr$p_1,\ldots,p_r$ be pairwise distinct primes. From a theorem of Kummer, each prime pj$p_j$ can divide 2nn${2n \atopwithdelims ()n}$ at most 1+logn/logpj$1 + \log n / \log p_j$ times. We show that, for all ε>0$\varepsilon > 0$, if p1,…,pr$p_1,\ldots,p_r$ are sufficiently large in terms of r$r$ and ε$\varepsilon$, then there exist ...
Ernie Croot, Hamed Mousavi, Maxie Schmidt   +2 more
wiley   +1 more source

Badly approximable grids and k$k$‐divergent lattices

Mathematika, Volume 70, Issue 3, July 2024.
Abstract Let A∈Matm×n(R)$A\in \operatorname{Mat}_{m\times n}(\mathbb {R})$ be a matrix. In this paper, we investigate the set BadA⊂Tm$\operatorname{Bad}_A\subset \mathbb {T}^m$ of badly approximable targets for A$A$, where Tm$\mathbb {T}^m$ is the m$m$‐torus. It is well known that BadA$\operatorname{Bad}_A$ is a winning set for Schmidt's game and hence
Nikolay Moshchevitin, Anurag Rao, Uri Shapira   +2 more
wiley   +1 more source

Reconstructing a rotor from initial and final frames using characteristic multivectors: With applications in orthogonal transformations

Mathematical Methods in the Applied Sciences, Volume 47, Issue 3, Page 1218-1235, February 2024.
If an initial frame of vectors {ei}$$ \left\{{e}_i\right\} $$ is related to a final frame of vectors {fi}$$ \left\{{f}_i\right\} $$ by, in geometric algebra (GA) terms, a rotor, or in linear algebra terms, an orthogonal transformation, we often want to find this rotor given the initial and final sets of vectors.
Anthony Lasenby, Joan Lasenby, Charalampos Matsantonis   +2 more
wiley   +1 more source

Looking into Pascal's Triangle: Combinatorics, Arithmetic, and Geometry

Mathematics Magazine, 1987
Peter Hilton
exaly   +2 more sources