Related papers: A density theorem for weighted Fekete sets
We consider the problem of constructing a weakly-continuous mapping extending continuous mapping defined on a dense set of a topological space to the entire space. Theorem on necessary and sufficient conditions for the existence of such an…
In this oaper, we prove some fixed point theorems in metric vector spaces, in which the continuity is not required for the considered mappings to satisfy. We provide some concrete examples to demonstrate these theorems. We also give some…
For a smooth, projective family of homogeneous varieties defined over a number field, we show that if potential density holds for the rational points of the base, then it also holds for the total space. A conjecture of Campana and…
We investigate dense lineability and spaceability of subsets of $\ell_\infty$ with a prescribed number of accumulation points. We prove that the set of all bounded sequences with exactly countably many accumulation points is densely…
In this project we show the existence of arbitrary length arithmetic progressions in model sets and Meyer sets in the Euclidean $d$-space. We prove a van der Waerden type theorem for Meyer sets. We show that pure point subsets of Meyer sets…
Let $A$ be a subset of positive relative upper density of $\PP^d$, the $d$-tuples of primes. We prove that $A$ contains an affine copy of any finite set $F\subs\Z^d$, which provides a natural multi-dimensional extension of the theorem of…
We study the problem of determining the distribution of vertices of a particular given type in the set of all Feynman tree graphs in quantum field theories. We show that in almost all cases a Gaussian distribution arises asymptotically, and…
We prove a generalization of Kannan's fixed point theorem, based on a recent result of Vittorino Pata.
We prove the existence of infinite dense free sets (in the usual topology) for set mappings on the reals, under reasonable assumptions.
We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual…
We study packing densities for set partitions, which is a generalization of packing words. We use results from the literature about packing densities for permutations and words to provide packing densities for set partitions. These results…
Green and Tao famously proved in 2005 that any subset of the primes of fixed positive density contains arbitrarily long arithmetic progressions. Green had previously shown that in fact any subset of the primes of relative density tending to…
We prove Union-Closed sets conjecture.
We consider the scattering of an arbitary incident plane wave which is a tempered distribution by a two-dimensional wedge.
Scattering of a scalar particle on a crystalline plane with quadratic cell and identical fixed scatterers is solved precisely. Contradiction of the standard scattering theory is pointed out.
We establish a fixed-point theorem for the face maps that consist in deleting the $i$th entry of an ordered set. Furthermore, we show that there exists random finite sets of integers that are almost invariant under such deletions.…
We prove a centre manifold theorem for a map along a manifold-with-boundary of fixed points, and provide an application to the study of gradient descent with large step size on two-layer matrix factorisation problems.
We prove a pointwise version of the multi-dimensional central limit theorem for convex bodies. Namely, let X be an isotropic random vector in R^n with a log-concave density. For a typical subspace E in R^n of dimension n^c, consider the…
We present a quantitative version of Guessing Geodesics, which is a well-known theorem that provides a set of conditions to prove hyperbolicity of a given metric space. This version adds to the existing result by determining an explicit…
We prove an analogue of the fixed-point theorem for the case of definably amenable groups.