Related papers: A Zerocrossing Analysis
An overview of quantum-mechanical methods to generate cross-section data for electron collisions with atoms and molecules is presented. Particular emphasis is placed on the time-independent close-coupling approach, since it is particularly…
An overdamped system with a linear restoring force and two multiplicative colored noises is considered. Noise amplitudes depend on the system state $x$ as $x$ and $|x|^{\alpha}$. An exactly soluble model of a system is constructed due to…
We investigate the zeros of two one-parameter families of harmonic functions and describe how the number of zeros depends on the parameter. Our functions have the property that all zeros lie on certain rays in the complex plane and thus we…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
In this reply, we resolve the apparent discrepancy raised in the "Comment on Inferring broken detailed balance in the absence of observable currents" [arXiv:2112.08978v1]. We stress that the non-instantaneous transition paths originate from…
The suitable basis functions for approximating periodic function are periodic, trigonometric functions. When the function is not periodic, a viable alternative is to consider polynomials as basis functions. In this paper we will point out…
We used analytical methods to study the interaction of electrons with shunted models consisting of a rectangular, triangular, or delta function. potential barrier in series with a pre-barrier region at zero potential. In each model the…
Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to…
The paper overviews and investigates several nonparametric methods of estimating covariograms. It provides a unified approach and notation to compare the main approaches used in applied research. The primary focus is on methods that utilise…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
We examine the Casimir effect for a perfectly conducting cylinder of elliptical section, taking as reference the known case of circular section. The zero-point energy of this system is evaluated by the mode summation method, using the…
A QM/MM implementation for periodic systems is reported. This is done for the case of molecules and for systems with two and three-dimensional periodicity, which is suitable to model electrolytes in contact with electrodes. Tests on…
In this paper will be introduced large, probably complete family of complex base systems, which are 'proper' - for each point of the space there is a representation which is unique for all but some zero measure set. The condition defining…
We demonstrate that extremely rapid and weak periodic and non-periodic signals can easily be detected by using the autocorrelation of intensity as a function of time. We use standard radio-astronomical observations that have artificial…
Based on the partition of parameter space, two algorithms for computing the rational univariate representation of zero-dimensional ideals with parameters are presented in the paper. Unlike the rational univariate representation of…
We study "vacuum crossing", which occurs when the vacua of a theory are exchanged as we vary some periodic parameter $\theta$ in a closed loop. We show that vacuum crossing is a useful non-perturbative tool to study strongly-coupled quantum…
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. We show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
Aiming for a systematic feature-extraction from time series, we introduce the iterated-sums signature over arbitrary commutative semirings. The case of the tropical semiring is a central, and our motivating example. It leads to features of…