相关论文: Cross-sections of multibrot sets
Using class field theory, we prove a restriction on the intersection of the maximal abelian extensions associated with different number fields. This restriction is then used to improve a result of Rosen and Silverman about the linear…
The intersection graph of a family of sets $\{S_{1},S_{2},\ldots,S_{n}\}$ is a graph whose vertex set is $\{S_{1},S_{2},\ldots,S_{n}\}$ and two distinct vertices are adjacent if the intersection of the corresponding sets is non-empty.…
Suppose that $k$ is a non-negative integer and a bipartite multigraph $G$ is the union of $$N=\left\lfloor \frac{k+2}{k+1}n\right\rfloor -(k+1)$$ matchings $M_1,\dots,M_N$, each of size $n$. We show that $G$ has a rainbow matching of size…
We show that intersection graphs of compact convex sets in R^n of bounded aspect ratio have asymptotic dimension at most 2n+1. More generally, we show this is the case for intersection graphs of systems of subsets of any metric space of…
We compute cross sections for events where two pairs of partons scatter off each other in the same $\gamma\gamma$ reaction, giving rise to at least 3 high--{\mbox{$p_T^{}$}} jets. Unlike in {\mbox{$p \bar p$}}\ collisions we find the signal…
We completely describe in terms of Hausdorff measures the size of the set of points of the circle that are covered infinitely often by a sequence of random arcs with given lengths. We also show that this set is a set with large…
We investigate the fusion cross sections of light nuclei in the presence of linearly polarized intense laser fields. By combining the Coulomb-Volkov solutions with the complex spherical square-well nuclear potential, we derive an explicit…
The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a drawing of $G$. In this paper, we study the crossing numbers of $K_{m}\times P_n$ and $K_{m}\times C_n$.
A sequence of $d+1$ signs $+$ and $-$ beginning with a $+$ is called a {\em sign pattern (SP)}. We say that the real polynomial $P:=x^d+\sum _{j=0}^{d-1}a_jx^j$, $a_j\neq 0$, defines the SP $\sigma :=(+$,sgn$(a_{d-1})$, $\ldots$,…
Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses. By self-intersection number one means the…
We provide a complete and explicit characterization of the exposed extreme rays of the cone of sums of nonnegative circuit (SONC) polynomials. The criterion we derive is purely combinatorial and depends only on the existence of certain…
Coherent bremsstrahlung of high energy electrons moving in a three-dimensional imperfect periodic lattice consisting of a complicated system of atoms is considered. On the basis of the normalized probability density function of the…
We prove an estimate on intersection pairing of homology classes in hyperbolic 4-manifolds in terms of Thurston norms of these classes.
We consider the following question: Given $n$ lines and $n$ circles in $\mathbb{R}^3$, what is the maximum number of intersection points lying on at least one line and on at least one circle of these families. We prove that if there are no…
Given a set of positive reals, we provide a necessary and sufficient condition for a free Borel flow to admit a cross section with all distances between adjacent points coming from this set.
An amoeba is the image of a subvariety of an algebraic torus under the logarithmic moment map. We consider some qualitative aspects of amoebas, establishing some results and posing problems for further study. These problems include…
A subset $A$ of $[n] = \{1, \dots, n\}$ is $k$-separated if, when the elements of $[n]$ are considered on a circle, between any two elements of $A$ there are at least $k$ elements of $[n]$ that are not in $A$. A family $\mathcal{A}$ of sets…
A family of generalized composite intersecting S-brane solutions with orthogonal intersection rules is described.
For a Generalized Baumslag-Solitar group $G$ with underling graph a tree, we calculate the intersection $\gamma_{\omega}(G)$ of the lower central series and the intersection $(N_{p})_{\omega}(G)$ of the subgroups of finite index some power…
We study a class of intersecting D-brane models in which fermions localized at different intersections interact via exchange of bulk fields. In some cases these interactions lead to dynamical symmetry breaking and generate a mass for the…