Related papers: Logistic Map Potentials
For the delayed logistic equation $x_{n+1} = a x_n (a-x_{n-1})$ it is well known that the nontrivial fixed point is locally stable for $1<a\leq 2$, and unstable for $a>2$. We prove that for $1<a\leq 2$ the fixed point is globally stable, in…
We study discrete Schroedinger operators with compactly supported potentials on the square lattice. Constructing spectral representations and representing S-matrices by the generalized eigenfunctions, we show that the potential is uniquely…
Lower and upper probabilities, also known as Choquet capacities, are widely used as a convenient representation for sets of probability distributions. This paper presents a graphical decomposition and exact propagation algorithm for…
We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra 1(2), 1973, pp. 163-171]. Our algorithms are based on…
A way to derive an explicit formulae in terms of the potentials, if they are finite-gap, for the solutions of spectral problems and corresponding algebraic curves is presented.
Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary…
In this work, we consider the approximate reconstruction of high-dimensional periodic functions based on sampling values. As sampling schemes, we utilize so-called reconstructing multiple rank-1 lattices, which combine several preferable…
An effective method for generating linear equations of maximal symmetry in their much general normal form is obtained. In the said normal form, the coefficients of the equation are differential functions of the coefficient of the term of…
In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…
We construct a simple symplectic map to study the dynamics of eccentric orbits in non-spherical potentials. The map offers a dramatic improvement in speed over traditional integration methods, while accurately representing the qualitative…
We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger…
We study a general transition operator, generated by a random walk on a graph $X$; in particular we give necessary and sufficient condition on the matrix coefficient (1-step transition probablilities) to be a bounded operator from…
We study the computation of equilibrium points of electrostatic potentials: locations in space where the electrostatic force arising from a collection of charged particles vanishes. This is a novel scenario of optimization in which…
We present an algorithm for steering the output of a linear system from a feasible initial condition to a desired target position, while satisfying input constraints and non-convex output constraints. The system input is generated by a…
How many key-value associations can a $d\times d$ linear memory store? We show that the answer depends not only on the $d^2$ degrees of freedom in the memory matrix, but also on the retrieval criterion. In an isotropic Gaussian model for…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…
Using unitarity methods, we compute, for several massive two-dimensional models, the cut-constructible part of the one-loop 2->2 scattering S-matrices from the tree-level amplitudes. We apply our method to various integrable theories,…
The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a…
One-parameter generalizations of the logarithmic and exponential functions have been obtained as well as algebraic operators to retrieve extensivity. Analytical expressions for the successive applications of the sum or product operators on…