Related papers: Elementary discrete and continuous interplay
This note presents an approach to studying the iterates of a mapping whose restriction to the complement of a finite set is continuous and open. The main examples to which the approach can be applied are piecewise monotone mappings defined…
We investigate bifurcation phenomena between slow and fast convergences of synchronization errors arising in the proposed synchronization system consisting of two identical nonlinear dynamical systems linked by a common noisy input only.…
The concept of statistical convergence based on asymptotic density is introduced in this article through nets. Some possible extensions of classical results for statistical convergence of sequences are obtained in this article, with…
This article discusses entanglement between two subsystems, one with discrete degrees of freedom and the other with continuous degrees of freedom. The overlap integral between continuous variable wave functions emerges as an important…
Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…
It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In…
Asymptotic formula is derived for the behavior of the fundamental solution of the second-order elliptic self-adjoint operator with a piecewise-smooth coefficient in front of the senior derivatives near the discontinuity surface of the…
We study the statistical fluctuations (such as the variance) of causal set quantities, with particular focus on the causal set action. To facilitate calculating such fluctuations, we develop tools to account for correlations between causal…
These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
We consider the model selection problem for a large class of time series models, including, multivariate count processes, causal processes with exogenous covariates. A procedure based on a general penalized contrast is proposed. Some…
Purely numerical methods do not always provide an accurate way to find all the global solutions to nonlinear ODE on infinite intervals. For example, finite-difference methods fail to capture the asymptotic behavior of solutions, which might…
A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…
In this paper, multiplexing of discrete chaotic signals in the presence of noise is investigated. Existing methods are based on chaotic synchronization which is susceptible to noise and parameter mismatch. Furthermore, these methods fail…
Deep--elastic scattering and its role in discrimination of the possible absorptive and reflective asymptotic scattering mechanisms are discussed with emphasis on the difference in the experimental signatures related to production processes.
Turbulence is known to show intermittency. That is, statistical properties vary with the length scale in a way not accounted for by statistical similarity where dimensionless ratios of moments are constant. Intermittency occurs even in the…
Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical techniques based on maximum likelihood and related methods. Recently Ghosh et al. (2013) proposed a general class…
We consider minimization problems in the calculus of variations set in a sequence of domains the size of which tends to infinity in certain directions and such that the data only depend on the coordinates in the directions that remain…
We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…
We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of…