We present a new variational characterization of breather solutions any equation the focusing Gardner hierarchy. This hierarchy is characterized by nonnegative index n, and 2n + 1 represents order corresponding PDE member. In this paper, we first show existence such breathers, that they are (2n+1)th-order equation. Then prove universality property, in sense all these satisfy same fourth station...

This paper introduces a new method for solving ordinary differential equations (ODEs) that enhances existing methods that are primarily based on finding integrating factors and/or point symmetries. The starting point of the new method is to find a non-invertible mapping that maps a given ODE to a related higher-order ODE that has an easily obtained integrating factor. As a consequence, the rela...

The paper deals with polyhedral estimates for reachable tubes of differential systems with a multiplicative uncertainty, namely linear systems with set-valued uncertainties in initial states, additive inputs and coefficients of the system. We present nonlinear parametrized systems of ordinary differential equations (ODE) which describe the evolution of the parallelotope-valued estimates for rea...

Ordinary differential equation (ODE) systems are commonly used many different fields. The de-facto method to implement an ODE system in Python programming using SciPy requires the entire system to be implemented as a single function, which only allow for inline documentation. Although each equation can be broken up into sub-equations, there is no compart-mentalization of sub-equations to its OD...

BACKGROUND/AIMS 9-[2-(phosphonomethoxy)ethyl]guanine (PMEG) is one of the most active antiproliferative compounds in a series of acyclic nucleoside phosphonates and is active in intraperitoneal P388 tumors in mice. METHODS We synthesized octadecyloxyethyl (ODE) and hexadecyloxypropyl esters of PMEG and compared their antiproliferative activity with unmodified PMEG in primary human fibroblasts...

In this study, accurate analytical solution for the nonlinear free vibration of an oscillator with inertia and static type cubic nonlinearities is derived. This solution is called He’s Variational Iteration Method (VIM). Comparing this method with numerical integration solutions using a built-in ODE-solver in MATLAB and He’s Homotopy Analysis Method (HAM) is shown its drastic approximation. By ...

It is known that non-isomorphic coupled cell networks can have equivalent dynamics. Such networks are said to be ODE-equivalent and are related by a linear algebra condition involving their graph adjacency matrices. A network in an ODE-equivalence class is said to be minimal if it has a minimum number of edges. When studying a given network in an ODE-class it can be of great value to study inst...