Crossed products and entropy of automorphisms

Let be an exact C∗-algebra, let G be a locally compact group, and let be a C∗-dynamical system. Each automorphism α_g induces a spatial automorphism Ad_λg on the reduced crossed product . In this paper we examine the question, first raised by E. Størmer, of when the topological entropies of α_g and Ad_λg coincide. This had been answered by N. Brown for the particular case of discrete abelian groups. Using different methods, we extend his result to preservation of entropy for α_g when the subgroup of Aut(G) generated by the corresponding inner automorphism Ad_g has compact closure. This property is satisfied by all elements of a wide class of groups called locally [FIA]⁻. This class includes all abelian groups, both discrete and continuous, as well as all compact groups.     

On Solution to an Optimal Shape Design Problem in 3-Dimensional Linear Magnetostatics

In this paper we present theoretical, computational, and practical aspects concerning 3-dimensional shape optimization governed by linear magnetostatics. The state solution is approximated by the finite element method using Nédélec elements on tetrahedra. Concerning optimization, the shape controls the interface between the air and the ferromagnetic parts while the whole domain is fixed. We prove the existence of an optimal shape. Then we state a finite element approximation to the optimization problem and prove the convergence of the approximated solutions. In the end, we solve the problem for the optimal shape of an electromagnet that arises in the research on magnetooptic effects and that was manufactured afterwards.     

Smooth Scalar-on-Image Regression via Spatial Bayesian Variable Selection

We develop scalar-on-image regression models when images are registered multidimensional manifolds. We propose a fast and scalable Bayes’ inferential procedure to estimate the image coefficient. The central idea is the combination of an Ising prior distribution, which controls a latent binary indicator map, and an intrinsic Gaussian Markov random field, which controls the smoothness of the nonzero coefficients. The model is fit using a single-site Gibbs sampler, which allows fitting within minutes for hundreds of subjects with predictor images containing thousands of locations. The code is simple and is provided in the online Appendix (see the “Supplementary Materials” section). We apply this method to a neuroimaging study where cognitive outcomes are regressed on measures of white-matter microstructure at every voxel of the corpus callosum for hundreds of subjects.     

An Exact Class of Bulk Field Potentials onto the 5D-Warp of de Sitter Spacetime

In the five-dimensionally warped FRW Universe, we integrate the corresponding Einstein equations for a scalar source depending only on the extra-dimension. It yields a de Sitter brane and a specific warp factor for which we derive the effective bulk field potentials. These are generalizing some of the previously proposed forms in the literature.     

On the wrinkling of a pre-stressed annular thin film in tension

Asymptotic properties of the neutral stability curves for a linear boundary eigenvalue problem which models the wrinkling instability of an annular thin film in tension are considered. The film is subjected to imposed radial displacement fields on its inner and outer boundaries and, when these loads are sufficiently large, the film is susceptible to wrinkling. The critical values at which this onset occurs are dictated by the solution of a fourth-order ordinary differential eigensystem whose eigenvalue λ is a function of μ(?1), a quantity inversely proportional to the non-dimensional bending stiffness of the film, and n, the number of half-waves of the wrinkling pattern that sets in around the annular domain. Previously, Coman and Haughton [2006. Localised wrinkling instabilities in radially stretched annular thin films. Acta Mech. 185, 179-200] employed the compound matrix method together with a WKB technique to characterise the form of λ(μ,n) which essentially is related to a turning point in a reduced eigenproblem. The asymptotic analysis conducted therein pertained to the case when this turning point was not too close to the inner edge of the annulus. However, in the thin film limit μ→∞, the wrinkling load and the preferred instability mode are given by a modified eigenvalue problem that involves a turning point asymptotically close to the inner rim. Here WKB and boundary-layer asymptotic methods are used to examine these issues and comparisons with direct numerical simulations made.     

An invariance principle for stationary random fields under Hannan’s condition

We establish an invariance principle for a general class of stationary random fields indexed by Z^d${\mathbb{Z}}^d$, under Hannan’s condition generalized to Z^d${\mathbb{Z}}^d$. To do so we first establish a uniform integrability result for stationary orthomartingales, and second we establish a coboundary decomposition for certain stationary random fields. At last, we obtain an invariance principle by developing an orthomartingale approximation. Our invariance principle improves known results in the literature, and particularly we require only finite second moment.     

Dynamics of Phloridzin and Related Compounds in Four Cultivars of Apple Trees during the Vegetation Period

Apple trees (Malus domestica Borgh) are a rich source of dihydrochalcones, phenolic acids and flavonoids. Considering the increasing demand for these phytochemicals with health-benefitting properties, the objective of this study was to evaluate the profile of the main bioactive compounds—phloridzin, phloretin, chlorogenic acid and rutin—in apple tree bark, leaves, flower buds and twigs. The variety in the phenolic profiles of four apple tree cultivars was monitored during the vegetation period from March to September using chromatography analysis. Phloridzin, the major glycoside of interest, reached the highest values in the bark of all the tested cultivars in May (up to 91.7 ± 4.4 mg g⁻¹ of the dried weight (DW), cv. ‘Opal’). In the leaves, the highest levels of phloridzin were found in cv. ‘Opal’ in May (82.5 ± 22.0 mg g⁻¹ of DW); in twigs, the highest levels were found in cv. ‘Rozela’ in September (52.4 ± 12.1 mg g⁻¹ of DW). In the flower buds, the content of phloridzin was similar to that in the twigs. Aglycone phloretin was found only in the leaves in relatively low concentrations (max. value 2.8 ± 1.4 mg g⁻¹ of DW). The highest values of rutin were found in the leaves of all the tested cultivars (10.5 ± 2.9 mg g⁻¹ of DW, cv. ‘Opal’ in September); the concentrations in the bark and twigs were much lower. The highest content of chlorogenic acid was found in flower buds (3.3 ± 1.0 mg g⁻¹ of DW, cv. ‘Rozela’). Whole apple fruits harvested in September were rich in chlorogenic acid and phloridzin. The statistical evaluation by Scheffe’s test confirmed the significant difference of cv. ‘Rozela’ from the other tested cultivars. In conclusion, apple tree bark, twigs, and leaves were found to be important renewable resources of bioactive phenolics, especially phloridzin and rutin. The simple availability of waste plant material can therefore be used as a rich source of phenolic compounds for cosmetics, nutraceuticals, and food supplement preparation.     

Interference of white light in tandem configuration of birefringent crystal and sensing birefringent fiber

Spectral interference of white-light beams propagating through a tandem configuration of birefringent crystal and sensing birefringent fiber is analyzed theoretically and experimentally. The spectral interference law is expressed analytically under the condition of a Gaussian response function of a spectrometer taking into account the dispersion of birefringence in the crystal and in the fiber. Two types of spectral interferograms are modeled knowing dispersion characteristics of the sensing fiber and using a quartz crystal of the positive or a calcite crystal of the negative birefringence. The theoretical analysis is accompanied by two experiments employing a highly birefringent fiber and a birefringent quartz crystal of two suitable thicknesses. Within both experiments the spectral interference fringes are resolved in accordance with the theory with phases dependent on the fiber length.     

Secondary bifurcations and localisation in a three-dimensional buckling model

This paper revisits the effect of secondary bifurcations on the post-buckling response of a simple 3D system of elastically restrained beams, first discussed by Luongo in [19]. Our main objective is to show how to construct a uniform asymptotic expression for the localised buckling patterns experienced by this model. The governing equation is formulated as a fourth-order eigenvalue problem with non-constant coefficients and then a complex WKB technique is employed to yield the localised instability patterns. Numerical simulations supporting the analytical findings are included as well.