Repulsive Gravitation in the Kerr-Newman Field

It is shown that uncharged test particles, released from rest at infinity in the Kerr-Newman field, stop and rebound when the radial coordinate r takes the value r₀ = Q²/(2M). This expression corresponds to the position of a stationary source of the Kerr-Newman field found by the author. It represents the surface of a massive oblate ellipsoid of revolution undergoing rigid rotation. Besides, the magnitude of r₀ guarantees that no violation of causality occurs throughout spacetime. Although the test particles' angular momenta are always zero, they acquire a rotational motion as a consequence of the dragging of inertial frames.     

Supersymmetry and bosonization in three dimensions

We discuss on the possible existence of a supersymmetric invariance in purely fermionic planar systems and its relation to the fermion-boson mapping in three-dimensional quantum field theory. We consider, as a very simple example, the bosonization of free massive fermions and show that, under certain conditions on the masses, this model displays a supersymmetric-like invariance in the low energy regime. We construct the purely fermionic expression for the supercurrent and the non-linear supersymmetry transformation laws. We argue that the supersymmetry is absent in the limit of massless fermions where the bosonized theory is non-local.     

Generative Art with Swarm Landscapes

We present a generative swarm art project that creates 3D animations by running a Particle Swarm Optimization algorithm over synthetic landscapes produced by an objective function. Different kinds of functions are explored, including mathematical expressions, Perlin noise-based terrain, and several image-based procedures. A method for displaying the particle swarm exploring the search space in aesthetically pleasing ways is described. Several experiments are detailed and analyzed and a number of interesting visual artifacts are highlighted.     

Selecting an Effective Entropy Estimator for Short Sequences of Bits and Bytes with Maximum Entropy

Entropy makes it possible to measure the uncertainty about an information source from the distribution of its output symbols. It is known that the maximum Shannon’s entropy of a discrete source of information is reached when its symbols follow a Uniform distribution. In cryptography, these sources have great applications since they allow for the highest security standards to be reached. In this work, the most effective estimator is selected to estimate entropy in short samples of bytes and bits with maximum entropy. For this, 18 estimators were compared. Results concerning the comparisons published in the literature between these estimators are discussed. The most suitable estimator is determined experimentally, based on its bias, the mean square error short samples of bytes and bits.     

Numerical solution of an optimal investment problem with proportional transaction costs

This paper mainly concerns the numerical solution of a nonlinear parabolic double obstacle problem arising in a finite-horizon optimal investment problem with proportional transaction costs. The problem is initially posed in terms of an evolutive HJB equation with gradient constraints and the properties of the utility function allow to obtain the optimal investment solution from a nonlinear problem posed in one spatial variable. The proposed numerical methods mainly consist of a localization procedure to pose the problem on a bounded domain, a characteristics method for time discretization to deal with the large gradients of the solution, a Newton algorithm to solve the nonlinear term in the governing equation and a projected relaxation scheme to cope with the double obstacle (free boundary) feature. Moreover, piecewise linear Lagrange finite elements for spatial discretization are considered. Numerical results illustrate the performance of the set of numerical techniques by recovering all qualitative properties proved in Dai and Yi (2009) [6].     

Quantum Information of the Aharanov–Bohm Ring with Yukawa Interaction in the Presence of Disclination

We investigate quantum information by a theoretical measurement approach of an Aharanov–Bohm (AB) ring with Yukawa interaction in curved space with disclination. We obtained the so-called Shannon entropy through the eigenfunctions of the system. The quantum states considered come from Schrödinger theory with the AB field in the background of curved space. With this entropy, we can explore the quantum information at the position space and reciprocal space. Furthermore, we discussed how the magnetic field, the AB flux, and the topological defect influence the quantum states and the information entropy.     

Hermitian quadratic eigenvalue problems of restricted rank

We consider a quadratic eigenvalue problem such that the second order term is a Hermitian matrix of rank r, the linear term is the identity matrix, and the constant term is an arbitrary Hermitian matrix . Of the n+r solutions that this problem admits, we show at least n-r to be real and located in specific intervals defined by the eigenvalues of A, whence at most 2r are nonreal occuring in possibly repeated conjugate pairs.     

On the representation of a class of contractive matrix-valued functions

By a decomposition of L₊²(Cⁿ) in two orthogonal subspaces we obtain a representation of a matrix-valued function of the class $\text{J}$Π, defined by Arov (Darlington realization of matrix-valued functions, Izv. Akad. Nauk. SSSR, Ser. Mat. Tom.37 (1973), No. 6); (Math. USSR Izvestija7 (1973), No. 6, 1295–1326). Real matrix-valued functions of this class play an important role in methods of synthesis of scattering matrices of linear passive n-ports.     

Local Power Properties of Kernel Based Goodness of Fit Tests

If (X_i, i ) is a strictly stationary process with marginal density function f, we are interested in testing the hypothesis H₀: {f=f₀}, where f₀ is given. We consider different test statistics based on integrated quadratic forms measuring the proximity between f_n, a kernel estimator of f, and f₀, or between f_n and its expected value computed under H₀. We study the asymptotic local power properties of the testing procedures under local alternatives. This study generalizes to the multidimensional case in a context of dependence the corresponding one made by P. J. Bickel and M. Rosenblatt in 1973 (Ann. Statist.1, 1071–1095).