相关论文: Extensions of democracy-like properties for sequen…
In [25], T. Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps, with a focus on the $\mathbf n$-$t$-quasi-greedy property that is based on them. Building upon this foundation, our…
In this paper, we establish new advances in the theory started by T. Oikhberg in [15] where the author joins greedy approximation theory with the use of sequences with gaps. Concretely, we address and partially answer three open questions…
I present a new property of prime numbers that leads to a generalization of Cramer's conjecture. The study of the gap between consecutive primes is treated as a special case of the gap between consecutive terms of sequences having a certain…
In this paper we extend some set theoretic concepts of numerical semigroups for arbitrary sub-semigroups of natural numbers. Then we characterized gapsets which leads to a more efficient computational approach towards numerical semigroups…
This paper is devoted to theoretical aspects on optimality of sparse approximation. We undertake a quantitative study of new types of greedy-like bases that have recently arisen in the context of nonlinear $m$-term approximation in Banach…
Simple methods permit to generalize the concepts of iteration and of recursive processes. We shall see briefly on several examples what these methods generate. In additive sequences, we shall encounter not only the golden or the silver…
We shall present a new characterization of greedy bases and 1-greedy bases in terms of certain functionals defined using distances to one dimensional subspaces generated by the basis. We also introduce a new property that unifies the…
We continue our study of the Thresholding Greedy Algorithm when we restrict the vectors involved in our approximations so that they either are supported on intervals of $\mathbb N$ or have constant coefficients. We introduce and…
We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex number. They can be arrived at through various algorithms, as…
Recently, generalizations of the classical Three Gap Theorem to higher dimensions attracted a lot of attention. In particular, upper bounds for the number of nearest neighbor distances have been established for the Euclidean and the maximum…
We prove optimal embeddings for nonlinear approximation spaces in terms of weighted Lorentz sequence spaces, with the weights depending on the democracy functions of the basis. As applications we recover known embeddings for $N$-term…
We show for several computational problems how classical greedy algorithms for special cases can be derived in a simple way from dynamic programs for the general case: interval scheduling (restricted to unit weights), knapsack (restricted…
Cheeger-type inequalities in which the decomposability of a graph and the spectral gap of its Laplacian mutually control each other play an important role in graph theory and network analysis, in particular in the context of expander…
We study recurrence, and multiple recurrence, properties along the $k$-th powers of a given set of integers. We show that the property of recurrence for some given values of $k$ does not give any constraint on the recurrence for the other…
For many standard models of random structure, first-order logic sentences exhibit a convergence phenomenon on random inputs. The most well-known example is for random graphs with constant edge probability, where the probabilities of…
Let $p_n$ denote the $n$th prime and $g_n:=p_{n+1}-p_n$ the $n$th prime gap. We demonstrate the existence of infinitely many values of $n$ for which $g_n>g_{n+1}>\cdots>g_{n+m}$ with $m\gg \log\log\log n$ and similarly for the reversed…
We study the problem of extending a state on an abelian $C^*$- subalgebra to a tracial state on the ambient $C^*$-algebra. We propose an approach that is well-suited to the case of regular inclusions, in which there is a large supply of…
We study and compare different Graph Neural Network extensions that increase the expressive power of GNNs beyond the Weisfeiler-Leman test. We focus on (i) GNNs based on higher order WL methods, (ii) GNNs that preprocess small substructures…
Greedy expansions with prescribed coefficients have been introduced by V. N. Temlyakov in the frame of Banach spaces. The idea is to choose a sequence of fixed (real) coefficients $\{c_n\}_{n=1}^\infty$ and a fixed set of elements…
In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…