Related papers: Another universal differential equation
In this work there is established an optimal existence and regularity theory for second order linear parabolic differential equations on a large class of noncompact Riemannian manifolds. Then it is shown that it provides a general unifying…
We study variational problems for curves approximated by B-spline curves. We show that, one can obtain discrete Euler-Lagrange equations, for the data describing the approximated curves. Our main application is to the curve completion…
In the paper, we considered the existence and uniqueness of the global solution in the space of continuously differentiable functions for a nonlinear differential equation with the Caputo fractional derivative of general form. Our main…
In this work, we present some new integration formulas for any order of accuracy as an application of the B-spline relations obtained in [1]. The resulting rules are defined as a perturbation of the trapezoidal integration method. We prove…
A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…
We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are proved. Linear conformable differential equations with…
In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…
We consider discrete optimization problems with interval uncertatinty of objective function coefficients. The interval uncertainty models measurements errors. A pos\-sible optimal solution is a solution that is optimal for some possible…
We establish global universal approximation theorems on spaces of piecewise linear paths, stating that linear functionals of the corresponding signatures are dense with respect to $L^p$- and weighted norms, under an integrability condition…
In this paper we introduce the concept of universal stabilizability: the condition that every solution of a nonlinear system can be globally stabilized. We give sufficient conditions in terms of the existence of a control contraction…
The present note contains the text of lectures discussing the problem of universality in fully developed turbulence. After a brief description of Kolmogorov's 1941 scaling theory of turbulence and a comparison between the statistical…
A binary renewal process is a stochastic process $\{X_n\}$ taking values in $\{0,1\}$ where the lengths of the runs of 1's between successive zeros are independent. After observing ${X_0,X_1,...,X_n}$ one would like to predict the future…
Below, the explicit solution to a certain finite-difference equation is given and the required steps for derivation of these results are outlined. Everything is included as Mathematica formulae, so the notebook itself can be used for…
In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations, numerous tricks have been proposed. The goal of this short review is to recall classical, 19th-century results, completed in 2006 by…
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit…
In this note, we find an equivalent boundary integral equation to the classical $\bar{\partial}$-Neumann problem. The new equation contains an equivalent regularity to the global regularity of the $\bar{\partial}$-Neumann problem. We also…
Recently, we introduced Relative Resolution as a hybrid formalism for fluid mixtures [1]. The essence of this approach is that it switches molecular resolution in terms or relative separation: While nearest neighbors are characterized by a…
Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of…
The real numbers, it is taught at universities, correspond to our idea of a continuum, although the hyperreal numbers are located ``in between'' the real numbers. The number $x + dx$, where $dx$ should be an infinitesimal number and $x$…