In this talk we extend the Polyakov-quark-meson model to N f = 2 + 1 quark flavors and study its bulk thermodynamics at finite temperatures in mean-field approximation. Three different Polyakov-loop potentials are considered. Our findings are confronted to recent QCD lattice simulations of the RBC-Bielefeld and HotQCD collaborations. Furthermore, the finite chemical potential expansion of the q...

Since the early work of Moore, and perfected for the linear autonomous case by Lohner, it is known that preconditioning based on enclosing the accumulated errors in suitably chosen coordinate systems allows for effective suppression of the wrapping effect. The amount of error that needs to be accounted for itself can be significantly reduced by representing flows in terms of polynomials in the ...

I survey developments over the last decade in harmonic analysis on Lie groups relative to a heat kernel measure. These include analogs of the Hermite expansion, the Segal-Bargmann transform, and the Taylor expansion. Some of the results can be understood from the standpoint of geometric quantization. Others are intimately related to stochastic analysis.

In this article, we have investigate a Taylor collocation method, which is based on collocation method for solving fractional pantograph equation. This method is based on first taking the truncated fractional Taylor expansions of the solution function in the mathematical model and then substituting their matrix forms into the equation. Using the collocation points, we have the system of nonline...

We examine the isentropic QCD equation of state within a quasiparticle model being adjusted to first principle QCD calculations of two quark flavours. In particular, we compare with Taylor expansion coefficients of energy and entropy densities and with the isentropic trajectories describing the hydrodynamical expansion of a heavy-ion collision fireball.

In this paper, we present random matrix methods for determining the capacity of uncorrelated MIMO channels having partial channel state information, i.e., statistical knowledge of the channel parameters. We show that it is possible to approximate the MIMO channel capacities by Taylor series expansions in order to apply large-scale analysis using random matrix methods. For an adequate approximat...

In this paper a computational algorithm for nonlinear balanced realization and model reduction based on Taylor series expansion is proposed. This algorithm requires recursive computations with respect to the order of the Taylor series in which we need to solve linear equations with unknown parameters in each step. Furthermore, the proposed method is applied to a double pendulum system. Some num...

Achieving improved order of accuracy for a hydrodynamic numerical method is a continuing quest. The discrete approximate solution error, in general, can be expressed as a truncation of a Taylor series expansion. This paper presents a weak statement perturbation methodology retaining block-tridiagonal forms that can reduce, or annihilate in special cases, the Taylor series truncation error to hi...

In this paper, we consider the problem of best approximation in e,(n), 1 5 p 5 co. If h,, 1 5 p < co, denotes the best &-approximation of the element h E W " from a proper affine subspace K of W " , h @ K, then limp,1 h p-h* where h; is a best er-approximation of h from K, the i, so-called natural best er-approximation. We prove that, for every T E A, the best &approximations have a Taylor expa...

We apply an improved Taylor expansion method, which is a variational scheme to the Ising model in two dimensions. This method enables us to evaluate the free energy and magnetization in strong coupling regions from the weak coupling expansion, even in the case of a phase transition. We determine the approximate value of the transition point using this scheme. In the presence of an external magn...