On the time to reach a critical number of infections in epidemic models with infective and susceptible immigrants.

In this paper we examine the time T to reach a critical number K0 of infections during an outbreak in an epidemic model with infective and susceptible immigrants. The underlying process X, which was first introduced by Ridler-Rowe (1967), is related to recurrent diseases and it appears to be analytically intractable. We present an approximating model inspired from the use of extreme values, and we derive formulae for the Laplace-Stieltjes transform of T and its moments, which are evaluated by using an iterative procedure. Numerical examples are presented to illustrate the effects of the contact and removal rates on the expected values of T and the threshold K0, when the initial time instant corresponds to an invasion time. We also study the exact reproduction number Rexact,0 and the population transmission number Rp, which are random versions of the basic reproduction number R0.

Critical behavior of the specific heat in glass formers

We show numeric evidence that, at low enough temperatures, the potential energy density of a glass-forming liquid fluctuates over length scales much larger than the interaction range. We focus on the behavior of translationally invariant quantities. The growing correlation length is unveiled by studying the finite-size effects. In the thermodynamic limit, the specific heat and the relaxation time diverge as a power law. Both features point towards the existence of a critical point in the metastable supercooled liquid phase.

Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions which includes as particular cases the su(1|1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su(1|1) permutation operator and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low-energy excitations and the low-temperature behavior of the free energy, which coincides with that of a (1+1)-dimensional conformal field theory (CFT) with central charge c=1 when the chemical potential lies in the critical interval (0,E(π)), E(p) being the dispersion relation. We also analyze the von Neumann and Rényi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson (1+1)-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge c=1. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su(1|1) elliptic chain.

The Critical Strips of the Sums 1 + 2z + ... + nz

We give a partition of the critical strip, associated with each partial sum 1 + 2z + ... + nz of the Riemann zeta function for Re z < −1, formed by infinitely many rectangles for which a formula allows us to count the number of its zeros inside each of them with an error, at most, of two zeros. A generalization of this formula is also given to a large class of almost-periodic functions with bounded spectrum.

Privileged Regions in Critical Strips of Non-lattice Dirichlet Polynomials

This paper shows, by means of Kronecker’s theorem, the existence of infinitely many privileged regions called r -rectangles (rectangles with two semicircles of small radius r ) in the critical strip of each function Ln(z):= 1−∑nk=2kz , n≥2 , containing exactly [Tlogn2π]+1 zeros of Ln(z) , where T is the height of the r -rectangle and [⋅] represents the integer part.

High-Resolution N2 Adsorption Isotherms at 77.4 K: Critical Effect of the He Used During Calibration

Accurate characterization of the microporous structure in porous solids is of paramount importance for several applications such as energy and gas storage, nanoconfinement reactions, and so on. Among the different techniques for precise textural characterization, high-precision gas adsorption measurement of probe molecules at cryogenic temperatures (e.g., N2 at 77.4 K and Ar at 87.3 K) is the most widely used, after appropriate calibration of the sample holder with a probe gas, which does not experience physisorption processes. Although traditionally helium has been considered not to be adsorbed in porous solids at cryogenic temperatures, here we show that even at 77.4 K (high above its boiling temperature, 4 K) the use of He in the calibration step can give rise to erroneous interpretations when narrow micropores/constrictions are present.

The hosiery industry: Report on the cost of production of hosiery in the United States

At head of title: Department of Commerce. Bureau of Foreign and Domestic Commerce. E.E. Pratt, Chief ...

The knit-underwear industry: Report on the cost of production of knit underwear in the United States

At head of title: Department of Commerce. Bureau of Foreign and Domestic Commerce. E.E. Pratt, Chief ...

The women's muslin-underwear industry: report on the cost of production of women's muslin underwear in the United States

Department of Commerce, Bureau of Foreign and Domestic Commerce.