Related papers: Taylor Series Kinematics
In this paper, we study two variations of the time discrete Taylor schemes for rough differential equations and for stochastic differential equations driven by fractional Brownian motions. One is the incomplete Taylor scheme which excludes…
Experimental measurements of physical systems often have a limited number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from…
These lecture notes were written for a mini-course that was designed to introduce students and researchers to {\it $q$-series,} which are also called {\it basic hypergeometric series} because of the parameter $q$ that is used as a base in…
Two combined numerical methods for solving semilinear differential-algebraic equations (DAEs) are obtained and their convergence is proved. The comparative analysis of these methods is carried out and conclusions about the effectiveness of…
The Euler-Lagrange equations (EL) are very important in the theoretical description of several physical systems. In this work we have used a simplified form of EL to study one-dimensional motions under the action of a constant force. From…
We study the Jordan frame formulation of generalizations of scalar-tensor theories conceived by replacing the scalar with other fields such as vectors. The generic theory in this family contains higher order time derivative terms in the…
We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…
We present a latent-space formulation of adaptive temporal lifting for continuous-time dynamical systems. The method introduces a smooth monotone mapping $t \mapsto \tau(t)$ that regularizes near-singular behavior of the underlying flow…
Taking inspiration from physical motion, we present a new self-supervised dynamics learning strategy for videos: Video Time-Differentiation for Instance Discrimination (ViDiDi). ViDiDi is a simple and data-efficient strategy, readily…
Thimble regularisation is a possible solution to the sign problem, which is evaded by formulating quantum field theories on manifolds where the imaginary part of the action stays constant (Lefschetz thimbles). A major obstacle is due to the…
The aim of this work is to expose some asymptotic series associated to some expressions involving the volume of the n-dimensional unit ball. All proofs and the methods used for improving the classical inequalities announced in the final…
In this work we present a power series method for solving ordinary and partial differential equations. To demonstrate our method we solve a system of ordinary differential equations describing the movement of a random walker on a…
Cyclic animation is widely used in computer graphics and interactive content.It supports seamless playback in games, VR, and interactive simulation,where short clips must repeat smoothly over long durations. Achievingphysically plausible…
Holderian functions have strong non-linearities, which result in singularities in the derivatives. This manuscript presents several fractional-order Taylor expansions of H\"olderian functions around points of non- differentiability. These…
The theory of the functional sequences and series is presented; uniformly convergent, convergent in the sense of a mean square and weakly convergent sequences and series are considered. Sequential approach to constructing generalized…
A didactical exposition of the classical problem of the trajectory determination of a body, subject to the gravity in a resistant medium, is proposed. Our revisitation is aimed at showing a derivation of the problem solution which should be…
A new method for derivation of the equation of motion from the field equation is proposed. The problem of embedding the singularities in a field satisfying the field equations is discussed.
Inspired by Stein's lemma, we derive two expressions for the joint moments of elliptical distributions. We use two different methods to derive $E[X_{1}^{2}f(\mathbf{X})]$ for any measurable function $f$ satisfying some regularity…
In this paper we present a new theory of calculus over $k$-dimensional domains in a smooth $n$-manifold, unifying the discrete, exterior, and continuum theories. The calculus begins at a single point and is extended to chains of finitely…
Using the lattice paths in $\mathbb{N}\times\mathbb{N}$, we derive a general formula for sequences $\big(T(n,k)\big)$ satisfying the recurrence relation of the form: \begin{equation*} T((n,k)=a_{n,k}T(n-1,k)+b_{n,k}T(n-1,k-1).…