The condition for pressure isotropy, for spherically symmetric gravitational fields with charged and uncharged matter, is reduced to a recurrence equation with variable, rational coefficients. This difference equation is solved in general using mathematical induction leading to an exact solution to the Einstein field equations which extends the isotropic model of John and Maharaj. The metric fu...

We study the equation (?) ẋ(t) = −h(x(t− 1)) + f(x(t)) for t ≥ 0, x|[−1,0] = x0, where h is an odd function defined by h(y) is equal to a if 0 < y < c, equal to b if y ≥ c, a > b > 0 and c > 0 and f is an odd C function such that sup |f(x)| < b. We first consider the equation ẋ(t) = −h(x(t− 1)), corresponding to f ≡ 0. We find the admissible shapes of rapidlyoscillating symmetric periodic solut...

Based on the well known solution of the timeindependent radiative transfer equation along a ray and on suitable point transformations, general quadrature solutions of the monochromatic transfer equation for plane-parallel, spherically-symmetric and arbitrarily shaped 3D configurations with differential motion are derived for the observer’s and the comoving frame. The source function is assumed ...

many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. for the efficient solution of the above mentioned problems, linear multistep methods or runge-kutta technique are used. for the simulation of chemical procedures the ra...

‎In this paper‎, ‎we propose a feasible interior-point method for‎ ‎convex quadratic programming over symmetric cones‎. ‎The proposed algorithm relaxes the‎ ‎accuracy requirements in the solution of the Newton equation system‎, ‎by using an inexact Newton direction‎. ‎Furthermore‎, ‎we obtain an‎ ‎acceptable level of error in the inexact algorithm on convex‎ ‎quadratic symmetric cone programmin...

We know from Littlewood (1968) that the moments of order 4 of the classical Rudin–Shapiro polynomials Pn(z) satisfy a linear recurrence of degree 2. In a previous article, we developed a new approach, which enables us to compute exactly all the moments Mq(Pn) of even order q for q 32. We were also able to check a conjecture on the asymptotic behavior of Mq(Pn), namely Mq(Pn) ∼ Cq2, where Cq = 2...

This paper presents two methods for accurately computing the periodic regions’ centers. One method fits for the general M-sets with integer index number, the other fits for the general Msets with negative integer index number. Both methods improve the precision of computation by transforming the polynomial equations which determine the periodic regions’ centers. We primarily discuss the general...

We consider the Maxwell-Lorentz equations, i.e., the equation of motion of a charged dust coupled to Maxwell’s equations, on an arbitrary general-relativistic spacetime. We decompose this system of equations into evolution equations and constraints, and we demonstrate that the evolution equations are strongly hyperbolic. This result guarantees that the initial-value problem of the Maxwell-Loren...

We consider the spherically symmetric, asymptotically flat Einstein equations coupled to a suitable matter model and find explicit conditions on the initial data which guarantee the formation of a black hole in the evolution. We establish such results for general matter models characterized by general conditions on the matter quantities, and we prove that the collisionless gas as described by t...

Given the positive integers m,n, solving the well known symmetric Diophantine equation xm+kyn=zm+kwn, where k is a rational number, is a challenge. By computer calculations, we show that for all integers k from 1 to 500, the Diophantine equation x6+ky3=z6+kw3 has infinitely many nontrivial (y≠w) rational solutions. Clearly, the same result holds for positive integers k whose cube-free part is n...