Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks

In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coin and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated.     

Self-consistency in non-extensive thermodynamics of highly excited hadronic states

The self-consistency of a thermodynamical theory for hadronic systems based on the non-extensive statistics is investigated. We show that it is possible to obtain a self-consistent theory according to the asymptotic bootstrap principle if the mass spectrum and the energy density increase q-exponentially. A direct consequence is the existence of a limiting effective temperature for the hadronic system. We show that this result is in agreement with experiments.     

Planar Line Processes for Void and Density Statistics in Thin Stochastic Fibre Networks

Using results for the distribution of perimeters of random polygons arising from random lines in a plane, we obtain new analytic approximations to the distributions of areas and local line densities for random polygons and compute various limiting properties of random polygons. Using simulation, we show that the lengths of adjacent sides of polygons generated by random line processes in the plane are correlated with ρ=0.616±0.001.     

Thermal degradation and flame retardance in copolymers of methyl methacrylate with diethyl(methacryloyloxymethyl)phosphonate

Methyl methacrylate (MMA) has been free radically copolymerized, both in bulk and in solution, with diethyl(methacryloyloxymethyl)phosphonate (DEMMP), to give polymers which are significantly flame retarded when compared with PMMA, as indicated by the results of limiting oxygen index (LOI) measurements, UL 94 tests, and the results of cone calorimetric experiments. The physical and mechanical properties of the copolymers are similar to those of PMMA, except that the bulk copolymers are slightly crosslinked, and are better than those of PMMA flame retarded to a similar extent by some phosphate and phosphonate additives. Examination of the some of the gaseous products of pyrolysis and combustion, and of chars produced on burning, show that flame retardation occurs in the copolymers by both a condensed-phase and a vapour-phase mechanism. The condensed-phase mechanism is shown to involve generation of phosphorus acid species followed by reaction of these with MMA units giving rise to methacrylic acid units. The methacrylic acid units subsequently form anhydride links, which probably impede depolymerization of the remaining MMA sequences, resulting in evolution of less MMA (the major fuel when MMA-based polymers burn). By undergoing decarboxylation, leading to interchain cyclisation and, eventually, to aromaticisation, the anhydride units are probably also the principal precursors to char.     

Multiple dependent state sampling plans for lot acceptance based on measurement data

This paper proposes a multiple dependent (or deferred) state sampling plan by variables for the inspection of normally distributed quality characteristics. The decision upon the acceptance of the lot is based on the states of the preceding lots (dependent state plan) or on the states of the forthcoming lots (deferred state plan). The lot acceptance probability is derived and the two-point approach to determining the plan parameters is described. The advantages of this new variables plan over conventional sampling plans are discussed. Tables are constructed for the selection of parameters of this plan under the specific values of the producer’s and consumer’s risks, indexed by acceptable quality level and limiting quality level, when the standard deviation is known or unknown.     

A New Flow Instrument for Conductance Measurements at Elevated Temperatures and Pressures: Measurements on NaCl(aq) to 458 K and 1.4 MPa

A new flow electrical conductance instrument was constructed and tested on dilute NaCl solutions up to 458 K, and on more concentrated solutions (maximum 0.436 mol⋅kg⁻¹) at 373 K. The results of the new instrument agreed with those of previous authors within the estimated experimental errors. The model of Bernard et al. (J. Phys. Chem. 96, 3833–3840 (1992), MSA) was found to represent the high-temperature results without introducing an ion-pairing equilibrium constant. The Fuoss–Hsia conductance equation as given by Fernandez-Prini was found to represent the dilute concentrations with Λ° (NaCl) as the only adjustable parameter. It was found that Λ° (NaCl) could be expressed as a function of solvent viscosity and density by using three parameters found by regression of literature results between 278.15 and 523 K. This equation along with the FHFP theory permits the equivalent conductivity of dilute sodium chloride solutions to be calculated within the accuracy of the existing experimental measurements.     

Effect of Temperature on the Volumetric Properties of [Difurylmethane+(C<Subscript>2</Subscript>–C<Subscript>6</Subscript>) Alkan-1-ol] Binary Systems: Analyses of New and Literature Density Data in the Temperature Range 288.15–308.15 K

Densities, ρ, of the binary systems {difurylmethane + (ethanol or propan-1-ol or butan-1-ol or pentan-1-ol or hexan-1-ol)} have been measured with an Anton Paar DMA 4500 vibrating-tube densimeter over the entire composition range at 288.15 and 308.15 K and atmospheric pressure. The measured and literature densities of [difurylmethane + n-alkanol] binary systems have been used to check the validity of the relationship describing the dependence of density on composition. This relation is useful for obtaining interpolated ρ values corresponding to the experimental data. Excess molar volumes (V _m^E) of each mixture, limiting (V _m,i ^E,∞) and excess partial (V _m,i ^E) molar volumes and the limiting partial molar expansion (E _p,i ^∞) of both components of each binary system have been examined to provide insight into the temperature variations of the intermolecular interactions and molecular packing efficiencies. The results have been discussed in terms of specific intermolecular interactions and structural effects.     

Electrical Conductance Studies in Aqueous Solutions with Ascorbate Ions

Conductivity measurements in dilute aqueous solutions of L-ascorbic acid, sodium-L-ascorbate, magnesium-L-ascorbate, calcium-L-ascorbate and ferrous-L-ascorbate were performed in the (288.15 to 323.15) K temperature range. The limiting molar conductances of the ascorbic anion, λ^∘(HAsc⁻, T), and the dissociation constants of ascorbic acid, K(T), were derived by the use of the Debye-Hückel equation for the activity coefficients and the Onsager and Quint and Viallard conductivity equations.     

倾斜煤柱稳定性的弹塑性分析

考虑煤体的塑性软化性质,通过极限平衡法分析了煤层倾角对煤柱稳定性的影响,并通过产例验证了该法的合理性。