In this paper, we develop discontinuous Galerkin (DG) methods to solve ideal special relativistic hydrodynamics (RHD). In RHD, the density and pressure are positive. Units are normalized so that the speed of light is c = 1. Therefore, the velocity of the fluid has magnitude less than 1. To construct physically relevant numerical approximations, we develop a bound-preserving limiter to the schem...

Geometric branch-and-bound methods are popular solution algorithms in deterministic global optimization to solve problems in small dimensions. The aim of this paper is to formulate a geometric branch-and-bound method for constrained global optimization problems which allows the use of arbitrary bounding operations. In particular, our main goal is to prove the convergence of the suggested method...

Given a univariate polynomial P with a k-fold multiple root or a k-fold root cluster near some e z, we discuss various different methods to compute a disc near e z which either contains exactly or contains at least k roots of P . Many of the presented methods are known, some are new. We are especially interested in rigorous methods, that is taking into account all possible effects of rounding e...

We consider the problem of minimizing a continuously differentiable function of several variables subject to simple bound constraints where some of the variables are restricted to take integer values. We assume that the first order derivatives of the objective function can be neither calculated nor approximated explicitly. This class of mixed integer nonlinear optimization problems arises frequ...

Bound states of heavy ¯ qq quarks are reviewed within the context of QCD. First of all, we consider the calculations which can be performed ab initio, which includes ¯ tt with principal quantum number n up to four, ¯ bb states with n = 1 and (to a lesser extent) ¯ bb with n = 2 and ¯ cc for n = 1. Among the results, we report a very precise O(α 4 s) evaluation of b, c quark masses from quarkoni...

Full-rate (FR) and full-diversity (FD) are attractive features in MIMO systems. We refer to systems which achieve both FR and FD simultaneously as FRFD systems. Nonorthogonal STBCs can achieve FRFD without feedback, but their ML decoding complexities are high. V-BLAST without precoding achieves FR but not FD. FRFD can be achieved in VBLAST through precoding given full channel state information ...

In this talk I review the history of models of strong decays, from the original model through applications to charmonium, light and charmed mesons, glueballs and hybrids. Our current rather limited understanding of the QCD mechanism of strong decays is stressed. Regarding current and future applications of strong decay models, we note that in certain channels the very strong coupling predicted ...

Trust-region methods for solving large bound-constrained nonlinear systems are considered. These allow for spherical or elliptical trust-regions where the search for an approximate solution is restricted to a low dimensional space. A general formulation for these methods is introduced and global and superlinear/quadratic convergence is shown under standard assumptions. Viable approaches for imp...

The formalism for describing hadrons using a light-cone Hamiltonian of SU(N) gauge theory on a coarse transverse lattice is reviewed. Physical gauge degrees of freedom are represented by disordered flux fields on the links of the lattice. A renormalised light-cone Hamiltonian is obtained by making a colour-dielectric expansion for the link-field interactions. Parameters in the Hamiltonian are r...

In the book Boolean Function Complexity by Stasys Jukna [7], two lower bound techniques for Tree-like Cutting Plane proofs (henceforth, “Tree-CP proofs”) using Karchmer-Widgerson type communication games (henceforth, “KW games”) are presented: The first, applicable to Tree-CP proofs with bounded coefficients, translates Ω(t) deterministic lower bounds on KW games to 2 logn) lower bounds on Tree...