Density computations for real quadratic units

In order to study the density of the set of positive integers for which the negative Pell equation is solvable in integers, we compute the norm of the fundamental unit in certain well-chosen families of real quadratic orders. A fast algorithm that computes 2-class groups rather than units is used. It is random polynomial-time in as the factorization of is a natural part of the input for the values of we encounter. The data obtained provide convincing numerical evidence for the density heuristics for the negative Pell equation proposed by the second author. In particular, an irrational proportion of the real quadratic fields without discriminantal prime divisors congruent to 3 mod 4 should have a fundamental unit of norm .

     

An energy-transport model for semiconductors derived from the Boltzmann equation

An energy-transport model is rigorously derived from the Boltzmann transport equation of semiconductors under the hypothesis that the energy gain or loss of the electrons by the phonon collisions is weak. Retaining at leading order electron-electron collisions and elastic collisions (i.e., impurity scattering and the elastic part of phonon collisions), a rigorous diffusion limit of the Boltzmann equation can be carried over, which leads to a set of diffusion equations for the electron density and temperature. The derivation is given in both the degenerate and nondegenerate cases.     

Critical behavior of self-avoiding walks on fractals

Using a new graph counting technique suitable for self-similar fractals, exact 18th-order series expansions for SAWs on some Sierpinski carpets are generated. From them, the critical fugacityx _c and critical exponents _SAW and _SAW are obtained. The results show a linear dependence of the critical fugacity with the average number of bonds per site of the lattices studied. We find for some carpets with low lacunarity that _SAW<0.75, thus violating the relation _SAW(fractal) > _SAW (d) for SAWs on the fractals which are embedded in ad-dimensional Euclidean space.     

O(N) vector model with twisted boundary conditions

Prompted by a recent article of Chakravarty, we reexamine theO(N) vector model with twisted boundary conditions ind dimensions in the various frameworks of the =d–2 expansion, the =4–d expansion, and the large-N expansion. These continuum models describe the physics below the critical temperatureT _c and nearT _c of a latticeO(N) spin model. We determine the effect of the twisting on finite-size scaling functions, for various geometries.On leave from G. Nadjakov Institute of Solid State Physics, 1784 Sofia, Bulgaria.     

Classical fluids of negative heat capacity

It is shown that new parametersX can be defined such that the heat capacity C_xT(S/T)_x is negative, even when the canonical ensemble [i.e., at fixed T=(U/S)_Y and YX] is stable. This implies an extension of the classical theory of polytropes from ideal gases to general fluids. As examples of negative heat capacity systems we treat blackbody radiation and general gas systems with nonsingular _T. For the case of a simple ideal gas we even exhibit an apparatus which enforces a constraint X(p, V)=const that makes C_x<0. We then show that it is possible to infer the statistical mechanics of canonicallyunstable systems-for which even the traditional heat capacities are negative-by imposing constraints that stabilize the associated noncanonical ensembles. Two explicit models are discussed.     

The Kissinger law and isokinetic effect: Part II. Experimental analysis

On the basis of copper sulphate pentahydrate thermal dissociation, for analyzed reactions I to IV, 6 thermokinetic equations was discussed. Arrhenius law parameters were determined and the isokinetic effect (IE) and Kissinger law appearing was analyzed. It was found that only dependence resulting from isokinetic effect, in the form k _m=q/T _m, relates to the suitable thermokinetic Eq. (2) and Kissinger law in modified form (14). The confirmation was made that the possibility of determining the averaged activation energy from thermokinetic equations using suitable correction coefficients exists.This revised version was published online in November 2005 with corrections to the Cover Date.     

A review of the role of DSC analysis in the design of fluorozirconate glasses for fibre optic applications

The relatively poor thermal stability of fluorozirconate glasses is a major factor preventing the realisation of their true potential for fibre optic applications. A range of methods based on both isothermal and non-isothermal DSC techniques, which can be employed to evaluate the thermal stability of fluorozirconate glasses, are described. The relevance of these thermal stability criteria to the design of fluorozirconate compositions capable of yielding high quality optical fibres is discussed.     

A new class of aromatic polyetheraroylhydrazides. I. Synthesis and chemical–physical characterization

A series of new aromatic polyetheraroylhydrazides incorporating 4-oxybenzoyl units has been synthesized, whose general formula was [CONHNHCO? O? O–(CH₂)_x? O? phenyl O-CONHNHCOO]_n with x values in the range of 2 to 12. The increasing number of methylene units in the backbone gave rise to polymers which melted before the hydrazidic linkage underwent thermal cyclation to oxadiazole. Moreover, many polymers showed multiple endotherms on melting. X-ray diffraction studies confirmed a crystalline organization of polyhydrazides for methylene units above 4. © 1993 John Wiley & Sons, Inc.     

Closer asymptotic approximations for the distributions of the power divergence goodness-of-fit statistics

Summary The members of the power divergence family of statistics all have an asymptotically equivalent χ² distribution (Cressie and Read [1]). An asymptotic expansion for the distribution function is derived which shows that the speed of convergence to this asymptotic limit is dependent on λ. Known results for Pearson'sX ² statistic and the log-likelihood ratio statistic then appear as special cases in a continuum rather than as separate (unrelated) expansions.     

Rheological properties of the aqueous mixtures of cationic-anionic surfactants

The rheological properties of the aqueous mixtures of cationic-anionic surfactants, both in single-phase systems and in aqueous two-phase systems, have been studied. Bizarre rheological properties —negative thixotropy, viscoelasticity and hihg viscosity of shear rate dependent at relatively low concentration — have been observed. An unusual viscosity change, that is, viscosity lowering with increasing concentration, was obtained. The negative thixotropy might be due to the existence of lamellar or sheet-like micelles, viscoelasticity might be induced by rodlike and lamellar or sheet-like micelles, the high viscosity might be a consequence of the formation of network by long rodlike micelles and the concentration-induced viscosity lowering could be interpreted in terms of the decrease of micellar dimensions with concentration.