in Gaussian units and in spherical coordinates where a(t) is the radius of the shell, Q is the total surface charge, and H(x, x0) = ∫ x −∞ δ(x ′ − x0) dx′ is the Heaviside step function. However, magnetic charges do not exist, so we cannot have a radial magnetic field of the form (1). That is, the magnetic field is zero, B = 0 everywhere, no matter what is the time dependence a(t) of the radius...

We examine the quark mass dependence of the pion vector form factor, particularly the curvature (mean quartic radius). We focus our study on the consequences of assuming that the coupling constant of the ρ to pions, gρππ, is largely independent of the quark mass while the quark mass dependence of the ρ–mass is given by recent lattice data. By employing the Omnès representation we can provide a ...

The matrix calculus is widely applied in various branches of mathematics and control system engineering. In this paper properties of real matrices with nonnegative elements are studied. The classical Collatz theorem is unique and immediately applicable to estimating the spectral radius of nonnegative irreducible matrices. The coherence property is identified. Then the Perron–Frobenius theorem a...

Using a support vector machine (SVM) requires to set the values of two types of hyperparameters: the soft margin parameter C and the parameters of the kernel. To perform this model selection task, the method of choice is cross-validation. Its leave-one-out variant is known to produce an estimator of the generalization error which is almost unbiased. Its major drawback rests in its time requirem...

This paper investigates the accuracy of using circles to store polygon boundaries. Can a series of xy points be accurately replaced by a smaller array of variably-sized circles used in a non space filling sense to approximate to the edge of the polygon? Two measures were used to ascertain this, areal error and visual error. A vector dataset representing the island of Rarotonga was converted fro...

The equation of state provided by effective models strongly interacting matter should comply with the restrictions imposed current astrophysical observations on compact stars. Using given (axial-)vector meson extended linear sigma model, we determine mass-radius relation and study whether these are satisfied under assumption that most star is filled quark matter. We dependence parameters model.

An efficient Monte Carlo method for multidimensional integration is proposed and studied. The method is based on Sobol’s sequences. Each random point in s-dimensional domain of integration is generated in the following way. A Sobol’s vector of dimension s (ΛΠτ point) is considered as a centrum of a sphere with a radius ρ. Then a random point uniformly distributed on the sphere is taken and a ra...

This work investigates the optimization and validation of Support Vector Machines (SVMs) for land cover classification from multispectral aerial imagery and lidar data. For the optimization step, a new method based on a curve fitting technique was applied to minimize the grid search for the Gaussian Radius Basis Function (RBF) parameters. The validation step was based on two experiments. In the...

A serious drawback of kernel methods, and Support Vector Machines (SVM) in particular, is the difficulty in choosing a suitable kernel function for a given dataset. One of the approaches proposed to address this problem is Multiple Kernel Learning (MKL) in which several kernels are combined adaptively for a given dataset. Many of the existing MKL methods use the SVM objective function and try t...

We test a sample of satellites of isolated primary galaxies, extracted from the 2dF Galaxy Redshift Survey (2dFGRS), for any tendency to be aligned along (or against) the primary-to-satellite radius vector. If tidal effects induce such an alignment, it would contaminate recent measurements of galaxy halo masses which use the coherent alignment induced on background galaxies by gravitational len...