Einstein's general theory of relativity poses many problems to the quantum theory of point particle fields. Among them is the fate of a massive point particle. Since its rest mass exists entirely within its Schwarzschild radius, in the classical solutions of Einstein's theory, the respective system should be a black hole. We address this issue using exact results in a new approach to quantum gr...

Up to a global scaling, the geometry of foams squeezed between two solid plates (2D GG foams) essentially depends on two independent parameters: the liquid volume fraction and the degree of squeezing (bubble thickness to diameter ratio). We describe it in two main asymptotic regimes: fully dry floor tiles, where the Plateau border radius is smaller than the distance between the solid plates, an...

Let P be a probability distribution on R (equipped with an Euclidean norm). Let r, s > 0 and assume (αn)n≥1 is an (asymptotically) L(P )-optimal sequence of n-quantizers. In this paper we investigate the asymptotic behavior of the maximal radius sequence induced by the sequence (αn)n≥1 and defined to be for every n ≥ 1, ρ(αn) = max{|a|, a ∈ αn}. We show that if card(supp(P )) is infinite, the m...

In this paper, we shall study the convergence of Taylor approximations for backward Loewner differential equation (driven by Brownian motion) near origin. More concretely, whenever initial condition (which lies in upper half plane) is small and has form $Z_{0} = \varepsilon i$, show these exhibit an $O(\varepsilon)$ error provided time horizon $\varepsilon^{2+\delta}$ $\delta > 0$. Statements t...

Magnitude is an invariant of metric spaces with origins in enriched category theory. Using potential theoretic methods, Barceló and Carbery gave an algorithm for calculating the magnitude of any odd dimensional ball in Euclidean space, and they proved that it was a rational function of the radius of the ball. In this paper an explicit formula is given for the magnitude of each odd dimensional b...

Particle simulations in fields ranging from biochemistry to astrophysics require evaluation of the interactions between all pairs of particles separated by less than some fixed interaction radius. The extent to which such simulations can be parallelized has historically been limited by the time required for inter-processor communication. Recently, Snir [1] and Shaw [2] independently introduced ...

The goal of this research is to optimize multigrid methods for higher order accurate space-time discontinuous Galerkin discretizations. The main analysis tool is discrete Fourier analysis of twoand three-level multigrid algorithms. This gives the spectral radius of the error transformation operator which predicts the asymptotic rate of convergence of the multigrid algorithm. In the optimization...

I report on recent progress in our understanding of the structure of CDM halos, and in particular of the inner mass profile of galaxysized systems. Numerical simulations have consistently shown that the density profiles of CDM halos steepen monotonically from the center outwards, with slopes shallower than isothermal near the center and steeper than isothermal near the virial radius. Ongoing de...

We investigate the mass profile of ΛCDM halos using a suite of numerical simulations spanning five decades in halo mass, from dwarf galaxies to rich galaxy clusters. These halos typically have a few million particles within the virial radius (r200), allowing robust mass profile estimates down to radii below 1% of r200. Our analysis confirms the proposal of Navarro, Frenk & White (NFW) that the ...

Abstract In this article, we study a generalized Bohr radius $R_{p, q}(X), p, q\in [1, \infty )$ defined for complex Banach space X . particular, determine the exact value of q}(\mathbb {C})$ cases (i) $p, 2]$ , (ii) $p\in (2, ), and (iii) [2, Moreover, consider an n -variable version q}^n(X)$ quantity q}(X)$ q}^n(\mathcal {H})$ infinite-dimensional Hilbert $\mathcal {H}$ precise asymptotic as ...