Related papers: Computing periods of rational integrals
We give a new practical method for computing subvarieties of projective hypersurfaces. By computing the periods of a given hypersurface X, we find algebraic cohomology cycles on X. On well picked algebraic cycles, we can then recover the…
In this paper, we generalize the Picard-Fuchs equation method to study the bifurcation of limit cycles of perturbed differential systems with two switching lines. We obtain the detailed expression of the corresponding first order Melnikov…
By folding an autonomous system of rational equations in the plane to a scalar difference equation, we show that the rational system has coexisting periodic orbits of all possible periods as well as stable aperiodic orbits for certain…
Periodic classical trajectories are of fundamental importance both in classical and quantum physics. Here we develop path integral techniques to investigate such trajectories in an arbitrary, not necessarily energy conserving hamiltonian…
This paper is devoted to the study of quasi-periodic properties of fractional order integrals and derivatives of periodic functions. Considering Riemann-Liouville and Caputo definitions, we discuss when the fractional derivative and when…
We present an algorithm that determines the Galois group of linear difference equations with rational function coefficients.
We study the growth behaviour of rational linear recurrence sequences. We show that for low-order sequences, divergence is decidable in polynomial time. We also exhibit a polynomial-time algorithm which takes as input a divergent rational…
A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.
We show that dimensional recurrence relation and analytical properties of the loop integrals as functions of complex variable $\mathcal{D}$ (space-time dimensionality) provide a regular way to derive analytical representations of loop…
We consider the problem of numerically integrating functions with hyperplane discontinuities over the entire Euclidean space in many dimensions. We describe a simple process through which the Euclidean space is partitioned into simplices on…
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…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
We compare the performance of several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. We choose for the comparison numerical schemes which preserve the…
In this note, basing on a certain functional equation of the dilogarithm function, we establish nontrivial lower bounds for the $p$-adic valuation (where $p$ is a given prime number) of some type of rational numbers involving harmonic…
Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…
We present an algorithm for the decomposition of periodic financial return data into orthogonal factors of expected return and "systemic", "productive", and "nonproductive" risk. Generally, when the number of funds does not exceed the…
We try to generalize a result of M. Willem on forced periodic oscillations which required the assumption that the forced potential is periodic on spatial variables. In this paper, we only assume its integral on the time variable is…
It is well known that using high-order numerical algorithms to solve fractional differential equations leads to almost the same computational cost with low-order ones but the accuracy (or convergence order) is greatly improved, due to the…
In symbolic integration, the Risch--Norman algorithm aims to find closed forms of elementary integrals over differential fields by an ansatz for the integral, which usually is based on heuristic degree bounds. Norman presented an approach…
Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…