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We construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered from an entirely new perspective.…
We consider an isothermal compressible fluid evolving on a cosmological background which may be either expanding or contracting toward the future. The Euler equations governing such a flow consist of two nonlinear hyperbolic balance laws…
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.
In this Article, several aspects of the asymptotic dynamics of finite-dimensional open quantum systems are explored. First, after recalling a structure theorem for the peripheral map, we discuss sufficient conditions and a characterization…
We propose a new asymptotic expansion for the fractional $p$-Laplacian with precise computations of the errors. Our approximation is shown to hold in the whole range $p\in(1,\infty)$ and $s\in(0,1)$, with errors that do not degenerate as…
This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of ordinary differential equations. In particular, we use results from ergodic theory and the asymptotic theory of $C_0$-semigroups to obtain a…
We determine the effect on the computational complexity of a conformal anomaly using the Complexity=Action prescription of the gauge/gravity correspondence. To allow the involvement of said anomaly, we extend previous studies to include…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
The problem of integer partitions is addressed using the microcanonical approach which is based on the analogy between this problem in the number theory and the calculation of microstates of a many-boson system. For ordinary…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
Rapid growth of constraints is often observed in free evolutions of highly gravitating systems. To alleviate this problem we investigate the effect of adding spatial derivatives of the constraints to the right hand side of the evolution…
We introduce a class of group endomorphisms -- those of finite combinatorial rank -- exhibiting slow orbit growth. An associated Dirichlet series is used to obtain an exact orbit counting formula, and in the connected case this series is…
This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of…
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…
The paper studies asymptotic behavior of the loss probability for the $GI/M/m/n$ queueing system as $n$ increases to infinity. The approach of the paper is based on applications of classic results of Tak\'acs (1967) and the Tauberian…
Two long-standing problems with the post-Newtonian approximation for isolated slowly-moving systems in general relativity are: (i) the appearance at high post-Newtonian orders of divergent Poisson integrals, casting a doubt on the soundness…
We study the number of representations of an integer n=F(x_1,...,x_s) by a homogeneous form in sufficiently many variables. This is a classical problem in number theory to which the circle method has been succesfully applied to give an…
Under the Riemann Hypothesis, we improve the error term in the asymptotic formula related to the counting lattice problem studied in a first part of this work. The improvement comes from the use of Weyl's bound for exponential sums of…
This paper studies the feedback stabilization of abstract Cauchy problems with unbounded output operators by finite-dimensional controllers. Both necessary conditions and sufficient conditions for feedback stabilizability are presented. The…