A geometric formula for Haefliger knots

Haefliger has shown that a smooth embedding of the (4k−1)-sphere in the 6k-sphere can be knotted in the smooth sense. In this paper, we give a formula with which we can detect the isotopy class of such a Haefliger knot. The formula is expressed in terms of the geometric characteristics of an extension, analogous to a Seifert surface, of the given embedding. In particular, the Hopf invariant associated to the extension plays a crucial role. This leads us to a new characterisation of Haefliger knots.     

Likelihood and conditional likelihood inference for generalized additive mixed models for clustered data

Lin and Zhang (J. Roy. Statist. Soc. Ser. B 61 (1999) 381) proposed the generalized additive mixed model (GAMM) as a framework for analysis of correlated data, where normally distributed random effects are used to account for correlation in the data, and proposed to use double penalized quasi-likelihood (DPQL) to estimate the nonparametric functions in the model and marginal likelihood to estimate the smoothing parameters and variance components simultaneously. However, the normal distributional assumption for the random effects may not be realistic in many applications, and it is unclear how violation of this assumption affects ensuing inferences for GAMMs. For a particular class of GAMMs, we propose a conditional estimation procedure built on a conditional likelihood for the response given a sufficient statistic for the random effect, treating the random effect as a nuisance parameter, which thus should be robust to its distribution. In extensive simulation studies, we assess performance of this estimator under a range of conditions and use it as a basis for comparison to DPQL to evaluate the impact of violation of the normality assumption. The procedure is illustrated with application to data from the Multicenter AIDS Cohort Study (MACS).     

Effects of vitrification suppression on structure morphology, conductivity and dielectric properties of vanadium phosphate glasses

Vitrification suppression in the (V₂O₅)_1−x (P₂O₅)_x glasses where x=0.10, 0.15, 0.20, and 0.25 was controlled by changing the rate of quenching glasses. The structure variations occurring in the glasses were detected by differential thermal analysis and optical microscope. The results implied the separation and growth of V₂O₅ orthorhombic microcrystal in the samples with x=0.10 and 0.15 whereas other samples did not illustrate remarkable changes in their microstructure. However, in temperature range between 300 and 473 K a semiconducting behavior for all samples appears during the study of electrical conductivity-temperature dependence. A decrease in conductivity values accompanied with some variations in activation energies by reducing quenching rate was observed. The conductivity results suggested that the conduction occurs by the phonon assisted hopping of a small polaron between V⁴⁺ and V⁵⁺ states at relatively higher temperature range above θ_D/2. Whereas at relatively low temperatures the conduction may occur by electron jumping between filled and empty states at Fermi level in the disordered matrix besides polaronic conduction. Reasonable values for the density of localized states, carrier concentration and carrier mobility were estimated and discussed. Also, dielectric constant and dielectric loss were studied as a function of frequency at different temperatures confirming the structure variations in the glass system.     

Analysis of Suzuki, Shanker, and Kumar formulations under strong compressions

A critical analysis of the Suzuki, Shanker, and Kumar formulations is presented by studying different classes of materials under high pressure. A similar trend for all the materials studied in the present work, demonstrates that Suzuki formulation is not capable to yield compression behaviour of solids. The Shanker formulation improves the results obtained by the Suzuki formulation in small compression range (0.9<V/V₀<1). For further compressions Shanker formulation also fails. On the other hand, the Kumar formulation is found to work well for the entire range of pressure. The reasons for the failure of Suzuki and Shanker formulations are discussed.     

Defect clusters in titanium-substituted spinel-related lithium ferrite

The cation distribution in spinel-related titanium-substituted lithium ferrite, Li_0.5+0.5xFe_2.5−1.5xTi_xO₄ has been explored using interatomic potential and ab initio calculations. The results suggest that the cation distribution with Ti⁴⁺ substituting for Fe³⁺ on octahedral B sites and excess Li⁺ substituting for Fe³⁺ on tetrahedral A sites is stabilised by the formation of clusters of two octahedrally coordinated Ti⁴⁺ ions and one tetrahedrally coordinated Li⁺ ion linked through a common oxygen.     

Charge density study under high pressure

The experimental and analytical method of the high-pressure powder experiment at BL10XU, SPring-8, is described. There is no doubt that BL10XU must be one of the most appropriate beam lines for high pressure X-ray diffraction experiment taking advantage of third generation synchrotron source. As an example of the advanced charge density study under high pressure, the structural change of Cs₂Au₂Br₆ by applying pressure is studied by Rietveld/MEM analysis. It reveals that the structural change of Cs₂Au₂Br₆ by applying pressure occurs basically at electron level, such as valence state change and chemical bonding, which may be called the electronic phase transition.     

Partially Classical States of a Boson Field

Employing positive-definiteness arguments we analyse Boson field states, which combine classical and quantum mechanical features (signal and noise), in a constructive manner. Mathematically, they constitute Bauer simplexes within the convex, weak-*-compact state space of the C*-Weyl algebra, defined by a presymplectic test function space (smooth one-Boson wave functions) and are affinely homeomorphic to a state space of a classical field. The regular elements are expressed in terms of weak distributions (probability premeasures) on the dual test function space. The Bauer simplex arising from the bare vacuum is shown to generalize the quantum optical photon field states with positive P-functions.     

Infrared absorption and reflectivity of double perovskite Sr2FeWO6

In this work we present temperature dependent infrared reflectivity and absorption of Sr₂FeWO₆ between 700 and 17 K measured from 40 to 10000 cm⁻¹. The reflectivity spectra show well defined phonon bands peaking at 143, 227, 377 and 625 cm⁻¹ assigned to overlapping vibrational modes split from those active in cubic perovskite. We have also verified that this compound is structurally stable in the whole temperature range and that its optical gap at ∼750 cm⁻¹ (95 meV) undergoes only a minor high temperature decrease ascribed to new thermally accessible levels.     

Epoxy based coatings on glass: strengthening mechanisms

Glass may be strengthened by epoxy coatings although the strengthening mechanisms remain unclear. Possible strengthening mechanisms are reviewed and are used to analyse strength data for both a solvent based and a water based coating system. The coatings either fill (solvent based coatings), or partially fill (water based coatings) surface cracks and it is shown that closure stresses arising from the thermal expansion mismatch of the coating within these cracks can account for the observed degrees of strengthening. It is also demonstrated that other suggested mechanisms such as flaw healing cannot fully account for the observed degree of strengthening.     

Laplacians and the Cheeger Inequality for Directed Graphs

We consider Laplacians for directed graphs and examine their eigenvalues. We introduce a notion of a circulation in a directed graph and its connection with the Rayleigh quotient. We then define a Cheeger constant and establish the Cheeger inequality for directed graphs. These relations can be used to deal with various problems that often arise in the study of non-reversible Markov chains including bounding the rate of convergence and deriving comparison theorems.Received September 8, 2004