相关论文: On the solution of Waring Problem with a multiplic…
A nonnegative number d_infinity, called asymptotic dimension, is associated with any metric space. Such number detects the asymptotic properties of the space (being zero on bounded metric spaces), fulfills the properties of a dimension, and…
We prove that the $\ell^2 \to \ell^2$ norm of the $r$-variation seminorm of spherical means on the hypercube admits no dimension-free bounds for any $r \in [1, \infty)$ when the variation is taken over all possible radii. Furthermore, we…
An asymptotic formula for the variance of squarefree numbers in arithmetic progressions of given modulus was obtained by Nunes (see reference [3]). We improve one of the error terms.
In this paper, we derive an asymptotic closed--form expression for the error bound on extrapolation of doubly selective mobile MIMO wireless channels. The bound shows the relationship between the prediction error and system design…
We investigate the asymptotic formula for the number of representations of a large positive integer as a sum of $k$-th powers of integers represented as the sums of three positive cubes, counted with multiplicities. We also obtain a lower…
Asymptotic formulae are established for the number of natural numbers $m$ with largest square-free divisor not exceeding $m^{\vartheta}$, for any fixed positive parameter $\vartheta$. Related counting functions are also considered.
In this paper we improve the estimate for the remainder term in the asymptotic formula concerning the circle problem in an arithmetic progression.
We introduce the notion of asymptotic cohomology based on the bounded cohomology and define cohomological asymptotic dimension $\as_{\Z} X$ of metric spaces. We show that it agrees with the asymptotic dimension $\as X$ when the later is…
This paper studies the minimal conditions under which we can establish asymptotic formulae for Waring's problem and other additive problems that may be tackled by the circle method. We confirm in quantitative terms the well-known heuristic…
We study the isoperimetric problem in product spaces equipped with the uniform distance. Our main result is a characterization of isoperimetric inequalities which, when satisfied on a space, are still valid for the product spaces, up a to a…
The positivity of the Bondi mass has been proven in 4 dimensions, but in higher dimensions the issue remains open. The formalism of the present paper has been developed to investigate this and is well suited to the higher dimensional case.…
We present a variational framework for studying the existence and regularity of solutions to elliptic free boundary problems that do not necessarily minimize energy. As applications, we obtain mountain pass solutions of critical and…
A subset of the finite dimensional hypercube is said to be equilateral if the distance of any two distinct points equals a fixed value. The equilateral dimension of the hypercube is defined as the maximal size of its equilateral subsets. We…
We prove an asymptotic formula for the Fourier transform of the arithmetic surface measure associated to the Waring--Goldbach problem and provide several applications, including bounds for discrete spherical maximal functions along the…
We investigate the relation between the subleading soft graviton theorem and asymptotic symmetries in gravity in even dimensions $d=2+2m$ higher than four. After rewriting the subleading soft graviton theorem as a Ward identity, we argue…
This paper establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and…
We discuss the numerous advantages of using dimensionless equations in non-relativistic quantum mechanics. Dimensionless equations are considerably simpler and reveal the number of relevant parameters in the models. They are less prone to…
For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior…
Using a result of Dranishnikov and Smith we prove that, under some conditions, the asymptotic power dimension of a proper metric space coincides with the dimension of its subpower corona.
We give asymptotics for correlation sums linked with the distribution of squarefree numbers in arithmetic progressions over a fixed modulus. As a particular case we improve a result of Blomer concerning the variance.