Related papers: Complex Dynamics of a Second Order Rational Differ…
For a discrete function $f\left( x\right) $ on a discrete set, the finite difference can be either forward and backward. However, we observe that if $ f\left( x\right) $ is a sum of two functions $f\left( x\right) =f_{1}\left( x\right)…
The Schrodinger equation for stationary states in a central potential is studied in an arbitrary number of spatial dimensions, say q. After transformation into an equivalent equation, where the coefficient of the first derivative vanishes,…
We derive a change of variable formula for $C^1$ functions $U:\R_+\times\R^m\to\R$ whose second order spatial derivatives may explode and not be integrable in the neighbourhood of a surface $b:\R_+\times\R^{m-1}\to \R$ that splits the state…
Recently, there has been substantial interest in studying the dynamics of quantum theory beyond that of states, in particular, the dynamics of channels, measurements, and higher-order transformations. Ref. [Phys. Rev. X 8(1), 011047 (2018)]…
For a discrete function $f\left( x\right) $ on a discrete set, the finite difference can be either forward and backward. If $f\left( x\right) $ is a sum of two such functions $f\left( x\right) =f_{1}\left( x\right) +f_{2}\left( x\right) $,…
In this paper it is dealt with the following system of difference equations x_{n+1}=((a_{n})/(x_{n}))+((b_{n})/(y_{n})), y_{n+1}=((c_{n})/(x_{n}))+((d_{n})/(y_{n})), n in N_0, where the initial values x_0,y_0 are positive real numbers and…
The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the…
This paper deals with the following elliptic equation \begin{equation*} -2\sigma^{2}\Delta z+\left\| \nabla z\right\| ^{2}+4\alpha z=4\left\| x\right\| ^{2}\text{ for }x\in \mathbb{R}^{N}\text{, (}% N\geq 1\text{),} \end{equation*}% where…
In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…
Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of large scales, discussed in [Phys. Rev. D…
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…
For parameter identification problems the Fr\'echet-derivative of the parameter-to-state map is of particular interest. In many applications, e.g. in seismic tomography, the unknown quantity is modeled as a coefficient in a linear…
The second-order equation in the (1/2,0)+(0,1/2) representation of the Lorentz group has been proposed by A. Barut in the beginning of the 70s. It permits to explain the mass splitting of leptons e,mu,tau. Recently, the interest has grown…
Bifurcations of dynamical systems, described by a second order differential equations and by an impact condition are studied. It is shown that the variation of parameters when the number of impacts of a periodic solution increases, leads to…
We give a framework for dealing with 0-1 laws (for first order logic) such that expanding by further random structure tend to give us another case of the framework. From another perspective we deal with 0-1 laws when the number of solutions…
In contextual dynamic pricing, a seller sequentially prices goods based on contextual information. Buyers will purchase products only if the prices are below their valuations. The goal of the seller is to design a pricing strategy that…
We identify many new solvable subcases of the general dynamical system characterized by two autonomous first-order ordinary differential equations with purely quadratic right-hand sides; the solvable character of these dynamical systems…
The critical behavior of many physical systems involves two competing $n^{}_1-$ and $n^{}_2-$component order-parameters, ${\bf S}^{}_1$ and ${\bf S}^{}_2$, respectively, with $n=n^{}_1+n^{}_2$. Varying an external control parameter $g$,…
In this paper we consider maps on the plane which are similar to quadratic maps in that they are degree 2 branched covers of the plane. In fact, consider for $\alpha$ fixed, maps $f_c$ which have the following form (in polar coordinates):…
A complete solution to the multiplier version of the inverse problem of the calculus of variations is given for a class of hyperbolic systems of second-order partial differential equations in two independent variables. The necessary and…