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Suppose $\mathcal{A}$ is a separable unital ASH C*-algebra, $\mathcal{R}$ is a sigma-finite II$_{\infty}$ factor von Neumann algebra, and $\pi,\rho :\mathcal{A}\rightarrow\mathcal{R}$ are unital $\ast$-homomorphisms such that, for every…
Let $X$ be a convex co-compact hyperbolic surface and let $\delta$ be the Hausdorff dimension of the limit set of the underlying discrete group. We show that the density of the resonances of the Laplacian in strips ${\sigma\leq \re(s) \leq…
A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented. This construction is based on a near-best uniform rational interpolant of the inverse square root function on the…
We present a comprehensive set of convergence tests which explore the role of various numerical parameters on the equilibrium structure of a simulated dark matter halo. We report results obtained with two independent, state-of-the-art,…
We report the discovery of deuterium absorption in the very metal-poor ([Fe/H] = -2.88) damped Lyman-alpha system at z_abs = 3.06726 toward the QSO SDSS J1358+6522. On the basis of 13 resolved D I absorption lines and the damping wings of…
We derive the density profile of cold dark matter halos using a self-similar accretion model. We show that if the clumpiness of the infalling matter is taken into account, then the inner density slope, d(log{rho})/d(log{r}), is close to -1.…
We develop an analytic approach to evaluating the density $\rho ({\cal E},\Gamma)$ of complex resonance poles with real energies $\mathcal{E}$ and widths $\Gamma$ in the pure reflection problem from a one-dimensional disordered sample with…
Consider the Monge-Kantorovich problem of transporting densities $\rho_0$ to $\rho_1$ on $\mathbb{R}^d$ with a strictly convex cost function. A popular relaxation of the problem is the one-parameter family called the entropic cost problem.…
In this paper, we study the relationship between the type problem and the asymptotic behaviour of the first (Dirichlet) eigenvalues $\lambda_1(B_r)$ of ``balls'' $B_r:=\{\rho<r\}$ on a complete Riemannian manifold $M$ as $r\rightarrow…
Motivated by the dawn of precision cosmology and the wealth of forthcoming high precision and volume galaxy surveys, in this paper we study the effects of inhomogeneities on light propagation in a flat \Lambda CDM background. To this end we…
Suppose $k\nmid n$ and $H$ is an $n$-vertex $k$-uniform hypergraph. A near perfect matching in $H$ is a matching of size $\lfloor n/k\rfloor$. We give a divisibility barrier construction that prevents the existence of near perfect matchings…
In this paper, we introduces and undertake as a systematical investigation of the class $\mathcal{P}_{\mathcal{H}}^{0}(\alpha,M)$ of normalized harmonic mappings $f = h + \overline{g}$ in the unit disk $\mathbb{D}$, defined by the…
Using two sets of large $N$-body simulations, we study the origin of the correlations of halo assembly time ($z_{\rm f}$), concentration ($v_{\rm max}/v_{\rm 200}$) and spin ($\lambda$) with the large-scale evolved density field at given…
High-resolution N--body simulations show a remarkable similarity in the structure of dark matter halos formed through dissipationless hierarchical clustering. Independent of halo mass, power spectrum, and cosmological parameters, the…
Let $K$ be the attractor of a linear iterated function system (IFS) $S_j(x)=\rho_jx+b_j,$ $j=1,\cdots,m$, on the real line satisfying the generalized finite type condition (whose invariant open set $\mathcal{O}$ is an interval) with an…
In this article, we test the conclusion of Donato et al. (2009) concerning the universality of the DM halo surface density $\mu_{0D}=\rho_0r_0$. According to our study, the dispersion of values of $\mu_{0D}$ is twice higher than that found…
Densely-packed bundles of biological filaments (filamentous proteins) are common and critical structural elements in range of biological materials. While most bundles form from intrinsically straight filaments, there are notable examples of…
This is the second in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars.…
We propose a new density estimation algorithm. Given $n$ i.i.d. observations from a distribution belonging to a class of densities on $\mathbb{R}^d$, our estimator outputs any density in the class whose "perceptron discrepancy" with the…
We report that the neutral hydrogen (HI) mass density of the Universe ($\rho_{HI}$) increases with cosmic time since $z \sim 5$, peaks at $z \sim 3$, and then decreases toward $z \sim 0$. This is the first result of Qz5, our spectroscopic…