相关论文: BMO from dyadic BMO for nonhomogeneous measures

A new notion of cohomology is introduced for MT-spaces, which are measurable and topological spaces whose measurable structure may not agree with the Borel $\sigma$-algebra of their topology. The main examples of MTspaces are measurable…

1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation. The idea is to try to quantify the frequence of discrete Morse matchings with a certain number of critical cells. Our…

The present paper studies a kind of robust optimization problems with constraint. The problem is formulated through Backward Stochastic Differential Equations (BSDEs) with quadratic generators. A necessary condition is established for the…

New constraints on inhomogeneous Lema\^itre-Tolman-Bondi (LTB) models alternative to Dark Energy are presented, focusing on adiabatic profiles with space-independent Big Bang and baryon fraction. The Baryon Acoustic Oscillation (BAO) scale…

We give an entirely new approach to the problem of mutually unbiased bases (MUBs), based on a Fourier analytic technique in additive combinatorics. The method provides a short and elegant generalization of the fact that there are at most…

Mutually unbiased bases (MUBs) are highly symmetric bases on complex Hilbert spaces, and the corresponding rank-1 projective measurements are ubiquitous in quantum information theory. In this work, we study a recently introduced…

We construct a moduli space for Riemann surfaces that is universal in the sense that it represents compact Riemann surfaces of any finite genus. This moduli space is stratifed according to genus, and it carries a metric and a measure that…

We revisit the problem of characterizing band topology in dynamically-stable quadratic bosonic Hamiltonians that do not conserve particle number. We show this problem can be rigorously addressed by a smooth and local adiabatic mapping…

The study of Mutually Unbiased Bases continues to be developed vigorously, and presents several challenges in the Quantum Information Theory. Two orthonormal bases in $\mathbb C^d, B {and} B'$ are said mutually unbiased if $\forall b\in B,…

This article is devoted to nonlinear approximation and estimation via piecewise polynomials built on partitions into dyadic rectangles. The approximation rate is studied over possibly inhomogeneous and anisotropic smoothness classes that…

In this note we show, roughly speaking, that if $\mathcal{B}$ is a Boolean algebra included in the natural way in the collection $\mathcal{D}/_\sim$ of all equivalence classes of natural density sets of the natural numbers, modulo null…

Coordinate-transformation approaches to invisibility cloaking rely on the design of an anisotropic, spatially inhomogeneous "transformation medium" capable of suitably re-routing the energy flux around the region to conceal without causing…

We obtain sharp bounds for the monotonic rearrangement operator from "dyadic-type" classes to "continuous". In particular, for the $\mathrm{BMO}$ space and Muckenhoupt classes. The idea is to connect the problem with a simple geometric…

Conformal prediction has emerged as a popular technique for facilitating valid predictive inference across a spectrum of machine learning models, under minimal assumption of exchangeability. Recently, Hoff (2023) showed that full conformal…

The cosmic microwave background radiation allows us to measure both the geometry and topology of the universe. It has been argued that the COBE-DMR data already rule out models that are multiply connected on scales smaller than the particle…

We consider a very general definition of BMO on a domain in $\mathbb{R}^n$, where the mean oscillation is taken with respect to a basis of shapes, i.e. a collection of open sets covering the domain. We examine the basic properties and…

A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction.…

We present a new, elementary proof of Boyd's interpolation theorem. Our approach naturally yields a noncommutative version of this result and even allows for the interpolation of certain operators on l^1-valued noncommutative symmetric…

We define the non-commutative multiple bi-orthogonal polynomial systems, which simultaneously generalize the concepts of multiple orthogonality, matrix orthogonal polynomials and of the bi-orthogonality. We present quasideterminantal…

Various numerical methods exist for obtaining the radiances inside a canopy of leaves above a partly reflecting ground. In view of testing the accuracy of these diverse methods, it is desirable to have at one's disposal non-trivial models…