Related papers: Normal functions and maximal order types
We prove that the resonances of long range perturbations of the (semiclassical) Laplacian are the zeroes of natural perturbation determinants. We more precisely obtain factorizations of these determinants of the form $ \prod_{w = {\rm…
Associated with a given suitable function, or a measure, on $\mathbb{R}$, we introduce a correlation function, so that the Wronskian of the Fourier transform of the function is the Fourier transform of the corresponding correlation…
The Fock transform recently introduced by the authors in a previous paper is applied to investigate convergence of generalized functional sequences of a discrete-time normal martingale $M$. A necessary and sufficient condition in terms of…
It is widely claimed that the natural axiom systems$\unicode{x2013}$including the large cardinal axioms$\unicode{x2013}$form a well-ordered hierarchy. Yet, as is well-known, it is possible to exhibit non-linearity and ill-foundedness by…
In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities like the…
The collective dynamics of neural populations are often characterized in terms of correlations in the spike activity of different neurons. Open questions surround the basic nature of these correlations. In particular, what leads to…
We consider a rather general class of evolutionary PDEs involving dissipation (of possibly fractional order), which competes with quadratic nonlinearities on the regularity of the overall equation. This includes as prototype models,…
In some inferential statistical methods, such as tests and confidence intervals, it is important to describe the stochastic behavior of statistical functionals, aside from their large sample properties. We study such behavior in terms of…
According to empirical observations, some pattern formation phenomena in driven many-particle systems are more pronounced in the presence of a certain noise level. We investigate this phenomenon of fluctuation-driven ordering with a…
We establish strong well-posedness for a class of degenerate SDEs of kinetic type with autonomous diffusion driven by a symmetric $\alpha$-stable process under H\"older regularity conditions for the drift term. We partially recover the…
In this article, we first improve the scalar maximal theorem for the Dunkl maximal operator by giving some precisions on the behavior of the constants of this theorem for a general reflection group. Next we complete the vector-valued…
Integro-differential methods, currently exploited in calculus, provide an inexhaustible source of tools to be applied to a wide class of problems, involving the theory of special functions and other subjects. The use of integral transforms…
The superconducting transition in presence of strong columnar disorder parallel to the magnetic field is considered. A solvable model appropriate for description of the broad crossover regime towards the true "glassy" critical behavior is…
In this paper, complex-order derivative and integral filters are proposed, which are consistent with the filters with fractional derivative and integral orders. Compared with the filters designed only with real orders, complex order filters…
This article aims at finding sufficient conditions for a family of meromorphic functions to be normal by involving partial sharing of sets with differential polynomials. Moreover, corresponding results for normal meromorphic functions are…
It is well known that all numbers that are normal of order $k$ in base $b$ are also normal of all orders less than $k$. Another basic fact is that every real number is normal in base $b$ if and only if it is simply normal in base $b^k$ for…
Dilation theory is a paradigm for studying operators by way of exhibiting an operator as a compression of another operator which is in some sense well behaved. For example, every contraction can be dilated to (i.e., is a compression of) a…
Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming $\omega$-string transducers as well as deterministic two-way transducers with look-ahead. In their one-way restriction, the…
A fluctuation theorem relating the work to its optimal average work is presented. The function mediating the relation is increasing and convex, and depends on the switching time $\tau$, driving strength $\delta\lambda/\lambda_0$, and…
Higher order derivatives of functions are structured high dimensional objects which lend themselves to many alternative representations, with the most popular being multi-index, matrix and tensor representations. The choice between them…