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We introduce the syncopated Bessel beam, a new class of exact solutions to the paraxial equation obtained by means of a sinusoidal modulation of the azimuthal phase at the source. This modulation imposes a phase rhythm that deliberately…
In statistical physics and information theory, although the exponent of the partition function is often of our primary interest, there are cases where one needs more detailed information. In this paper, we present a general framework to…
We calculate synchrotron radiation in three-dimensional pseudo-Newtonian magnetohydrodynamic simulations of radiatively inefficient accretion flows. We show that the emission is highly variable at optically thin frequencies, with order of…
This manuscript goes through the fundamental connections between statistical mechanics and estimation theory by focusing on the particular problem of compressive sensing. We first show that the asymptotic analysis of a sparse recovery…
Asymptotic expansions of Green functions and spectral densities associated with partial differential operators are widely applied in quantum field theory and elsewhere. The mathematical properties of these expansions can be clarified and…
In this paper, we investigate the asymptotic error distributions of symplectic methods for stochastic Hamiltonian systems and further provide Hamiltonian-specific analysis that clarifies the superiority of symplectic methods. Our…
We provide abstract, general and highly uniform rates of asymptotic regularity for a generalized stochastic Halpern-style iteration, which incorporates a second mapping in the style of a Krasnoselskii-Mann iteration. This iteration is…
Analytic combinatorics studies the asymptotic behaviour of sequences through the analytic properties of their generating functions. This article provides effective algorithms required for the study of analytic combinatorics in several…
Solutions to network optimization problems have greatly benefited from developments in nonlinear analysis, and, in particular, from developments in convex optimization. A key concept that has made convex and nonconvex analysis an important…
We present a method for synthesizing recursive functions that satisfy both a functional specification and an asymptotic resource bound. Prior methods for synthesis with a resource metric require the user to specify a concrete expression…
The paper presents a new and simple range characterization for the spherical mean transform of functions supported in the unit ball in even dimensions. It complements the previous work of the same authors, where they solved an analogous…
The paper considers a universal approach that allows one to quite simply obtain nonlinear asymptotic estimates of various summation functions. It is shown the application of this approach to the asymptotic estimation of divergent Dirichlet…
In this paper, we develop a systematical approach in applying an asymptotic method of moving planes to investigate qualitative properties of positive solutions for fractional parabolic equations. We first obtain a series of needed key…
We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…
In the article, new asymptotic approximation of the $n$th order is obtained and proposed to be used in calculations of radiation propagation without scattering in optically thick media; the asymptotic approximation is much simpler and more…
We study certain resonance-counting functions for potential scattering on infinite cylinders or half-cylinders. Under certain conditions on the potential, we obtain asymptotics of the counting functions, with an explicit formula for the…
In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.
In this paper, we analyze the asymptotic behavior of a system of interacting reinforced stochastic processes $({\bf Z}_n, {\bf N}_n)_n$ on a directed network of $N$ agents. The system is defined by the coupled dynamics ${\bf…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
Summation arithmetic functions with asymptotically independent terms are studied in the paper, the limit of which is the law of normal distribution. Assertions about the asymptotic behavior of the indicated functions are proved.