Related papers: Multiple correlation sequences not approximable by…
We examine a system of N=2 coupled non-linear delay-differential equations representing financial market dynamics. In such time delay systems, coupled oscillations have been derived. We linearize the system for small time delays and study…
An integer sequence is called realizable if it is the count of periodic points of some map. The Fibonacci sequence $(F_n)$ does not have this property, and the Fibonacci sequence sampled along the squares $(F_{n^2})$ also does not have this…
We are interested in approximation of a multivariate function $f(x_1,\dots,x_d)$ by linear combinations of products $u^1(x_1)\cdots u^d(x_d)$ of univariate functions $u^i(x_i)$, $i=1,\dots,d$. In the case $d=2$ it is a classical problem of…
The deep inelastic scattering data on the nucleon F_2 structure function, accumulated by BCDMS, SLAC and NMC collaborations in fixed-target experiments, are analyzed in the non-singlet approximation within the frameworks of both…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
We show that when screening corrections are included $ \frac{\partial F_{2}(x,Q^{2})}{\partial \ln Q^{2}}$ is consistent with the behaviour that one expects in pQCD. Screening corrections explain the enigma of the Caldwell plot.
In this paper we prove disintegration results for self-conformal measures and affinely irreducible self-similar measures. The measures appearing in the disintegration resemble self-conformal/self-similar measures for iterated function…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
We consider a binary sequence generated by thresholding a hidden continuous sequence. The hidden variables are assumed to have a compound symmetry covariance structure with a single parameter characterizing the common correlation. We study…
A shift-invariant system is a collection of functions $\{g_{m,n}\}$ of the form $g_{m,n}(k) = g_m(k-an)$. Such systems play an important role in time-frequency analysis and digital signal processing. A principal problem is to find a dual…
Although quantum metrology allows us to make precision measurement beyond the standard quantum limit, it mostly works on the measurement of only one observable due to Heisenberg uncertainty relation on the measurement precision of…
Let $(X,\mu)$ be a probability space, $G$ a countable amenable group and $(F_n)_n$ a left F\o lner sequence in $G$. This paper analyzes the non-conventional ergodic averages \[\frac{1}{|F_n|}\sum_{g \in F_n}\prod_{i=1}^d (f_i\circ…
We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…
The measurement of dynamic correlation functions of quantum systems is complicated by measurement backaction. To facilitate such measurements we introduce a protocol, based on weak ancilla--system couplings, that is applicable to arbitrary…
We consider a class of interacting particle systems in continuous space of non-gradient type, which are reversible with respect to Poisson point processes with constant density. For these models, a rate of convergence was recently obtained…
Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that…
We consider intermittent maps T of the interval, with an absolutely continuous invariant probability measure \mu. Kim showed that there exists a sequence of intervals A_n such that \sum \mu(A_n)=\infty, but \{A_n\} does not satisfy the…
In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…
After a brief review of the Fermi-Pasta-Ulam (FPU) conservative system of N nonlinearly coupled oscillators, this paper addresses two problems: first, comparing two indicators for the equipartition, showing that the results are essentially…
A theory of correlations between N photons of given frequencies and detected at given time delays is presented. These correlation functions are usually too cumbersome to be computed explicitly. We show that they are obtained exactly through…