Backward bifurcations in simple vaccination models

We describe and analyze by elementary means some simple models for disease transmission with vaccination. In particular, we give conditions for the existence of multiple endemic equilibria and backward bifurcations. We extend the results to include models in which the parameters may depend on the level of infection.     

Solving Sequences of Refined Multistage Stochastic Linear Programs

Multistage stochastic programs with continuous underlying distributions involve the obstacle of high-dimensional integrals where the integrands' values again are given by solutions of stochastic programs. A common solution technique consists of discretizing the support of the original distributions leading to scenario trees and corresponding LPs which are – up to a certain size – easy to solve. In order to improve the accuracy of approximation, successive refinements of the support result in rapidly expanding scenario trees and associated LPs. Hence, the solvability of the multistage stochastic program is limited by the numerical solvability of sequences of such expanding LPs. This work describes an algorithmic technique for solving the large-scale LP of refinement ν based on the solutions at the previous ν?1 refinements. Numerical results are presented for practical problem statements within financial applications demonstrating significant speedup (depending on the size of the LP instances).     

Rook theory and cycle-counting permutation statistics

A statistic is found to combinatorially generate the cycle-counting q-hit numbers, defined algebraically by Haglund [Adv. in Appl. Math. 17 (1996) 408–459]. We then define the notion of a cycle-Mahonian pair of statistics (generalizing that of a Mahonian statistic), and show that our newly discovered statistic is part of such a pair. Finally, we note a second example of a cycle-Mahonian pair of statistics which leads us to define the stronger property of being a cycle-Euler–Mahonian pair.     

Simultaneous determination of trace cadmium and mercury in Chinese herbal medicine by non-dispersive atomic fluorescence spectrometry using intermittent flow vapor generator.

A method was proposed for the simultaneous determination of trace cadmium and mercury by vapor generation non-dispersive atomic fluorescence spectrometry using an intermittent flow system. The effects of the parameters on the performance were studied systematically. The parameters such as acid concentration of the reaction medium, flow rate of the carrier gas and shield gas, the observation height and the atomizer temperature, etc. which affected the sensitivity, were optimized. Ascorbic acid, cobalt ion and thiourea were used as enhancement reagents or masking agents to enhance the generation efficiency of the volatile species of Cd and Hg. The mechanisms of their effects on vapor generation were investigated. In the presence of thiourea and ascorbic acid, the influences of some coexisting elements on the determination of cadmium and mercury were investigated. The detection limits (3sigma) were 0.010 microg l(-1) for Cd and 0.019 microg l(-1) for Hg, respectively. The relative standard deviations for Cd and Hg at 1.00 microg l(-1) were 2.6% and 0.97% (n = 11), respectively. The proposed method has been satisfactorily applied to the determination of trace cadmium and mercury in Chinese herbal medicine.     

Thermodynamic Limit and Proof of Condensation for Trapped Bosons

We study condensation of trapped bosons in the limit when the number of particles tends to infinity. For the noninteracting gas we prove that there is no phase transition in any dimension, but in any dimension, at any temperature the system is 100% condensated into the one-particle ground state. In the case of an interacting gas we show that for a family of suitably scaled pair interactions, the Gross–Pitaevskii scaling included, a less-than-100% condensation into a single-particle eigenstate, which may depend on the interaction strength, persists at all temperatures.     

Spin Axioms in Different Geometries of Relativistic Continuum Physics

The 24 components of the relativistic spin tensor consist of 3 + 3 basic spin fields and 9 + 9 constitutive fields. Empirically only three basic spin fields and nine constitutive fields are known. This empirem can be expressed by two spin axioms, one of them denying purely relativistic spin fields, and the other one relating the three additional basic fields and the nine additional constitutive fields to the known (and measurable) ones. This identification by the spin axioms is material-independent and does not mix basic spin fields with constitutive properties. The approaches to the Weyssenhoff fluid and the Dirac-electron fluid found in literature are discussed with regard to these spin axioms. The conjecture is formulated, that another reduction from six to three basic spin fields which does not obey the spin axioms introduces special material properties by not allowed mixing of constitutive and basic fields.     

Large-scale nonlocality in “doubly special relativity” with an energy-dependent speed of light

There are two major alternatives for violating the (usual) Lorentz invariance at large (Planckian) energies or momenta—either not all inertial frames (in the Planck regime) are equivalent (e.g., there is an effectively preferred frame) or the transformations from one frame to another are (nonlinearly) deformed (“doubly special relativity”). We demonstrate that the natural (and reasonable) assumption of an energy-dependent speed of light in the latter method goes along with violations of locality/separability (and even translational invariance) on macroscopic scales.