Numerical Solution of Internet Pricing Scheme Based on Perfect Substitute Utility Function

In this paper we will analyze the internet pricing schemes based on Perfect Substitute utility function for homogeneous and heterogeneous consumers. The pricing schemes is useful to help internet service providers (ISP) in maximizing profits and provide better service quality for the users. The models on every type of consumer is applied to the data traffic in Palembang server in order to obtain the maximum profit to obtain optimal. The models are in the form of nonlinear optimization models and can be solved numerically using LINGO 11.0 to get the optimal solution. The results show that the case when we apply flat fee, USAge-based and two part tariff scheme for homogenous we reach the same profit and heterogeneous on willingness to pay we got higher profit if we apply USAge based and two part tariff schemes. Meanwhile, for the case when we apply USAge based and two part tariff schemes for heterogeneous on demand, we reach better solution than other scheme

SU(3) sphaleron: Numerical solution

We complete the construction of the sphaleron $\widehat{S}$ in $SU(3)$ Yang-Mills-Higgs theory with a single Higgs triplet by solving the reduced field equations numerically. The energy of the $SU(3)$ sphaleron $\widehat{S}$ is found to be of the same order as the energy of a previously known solution, the embedded $SU(2)\times U(1)$ sphaleron $S$. In addition, we discuss $\widehat{S}$ in an extended $SU(3)$ Yang-Mills-Higgs theory with three Higgs triplets, where all eight gauge bosons get an equal mass in the vacuum. This extended $SU(3)$ Yang-Mills-Higgs theory may be considered as a toy model of quantum chromodynamics without quark fields and we conjecture that the $\widehat{S}$ gauge fields play a significant role in the nonperturbative dynamics of quantum chromodynamics (which does not have fundamental scalar fields but gets a mass scale from quantum effects).Comment: 36 pages, 6 figures, v5: published versio

Modified energy for split-step methods applied to the linear Schr\"odinger equation

We consider the linear Schr\"odinger equation and its discretization by split-step methods where the part corresponding to the Laplace operator is approximated by the midpoint rule. We show that the numerical solution coincides with the exact solution of a modified partial differential equation at each time step. This shows the existence of a modified energy preserved by the numerical scheme. This energy is close to the exact energy if the numerical solution is smooth. As a consequence, we give uniform regularity estimates for the numerical solution over arbitrary long tim

Approximate Matching of Analytic and Numerical Solutions for Rapidly Rotating Neutron Stars

We investigate the properties of a closed-form analytic solution recently found by Manko et al. (2000) for the exterior spacetime of rapidly rotating neutron stars. For selected equations of state we numerically solve the full Einstein equations to determine the neutron star spacetime along constant rest mass sequences. The analytic solution is then matched to the numerical solutions by imposing the condition that the quadrupole moment of the numerical and analytic spacetimes be the same. For the analytic solution we consider, such a matching condition can be satisfied only for very rapidly rotating stars. When solutions to the matching condition exist, they belong to one of two branches. For one branch the current octupole moment of the analytic solution is very close to the current octupole moment of the numerical spacetime; the other branch is more similar to the Kerr solution. We present an extensive comparison of the radii of innermost stable circular orbits (ISCOs) obtained with a) the analytic solution, b) the Kerr metric, c) an analytic series expansion derived by Shibata and Sasaki (1998) and d) a highly accurate numerical code. In most cases where a corotating ISCO exists, the analytic solution has an accuracy consistently better than the Shibata-Sasaki expansion. The numerical code is used for tabulating the mass-quadrupole and current-octupole moments for several sequences of constant rest mass.Comment: 18 pages, 9 figures, MNRAS accepted. A Mathematica script for computing analytic solutions and comparing with numerical models can be downloaded at http://www.astro.auth.gr/~niksterg/projects/BertiStergioulas