Some constructions of biharmonic maps and Chen’s conjecture on biharmonic hypersurfaces

We give several construction methods and use them to produce many examples of proper biharmonic maps including biharmonic tori of any dimension in Euclidean spheres (Theorem 2.2, Corollary 2.3, Corollary 2.4 and Corollary 2.6), biharmonic maps between spheres (Theorem 2.9) and into spheres (Theorem 2.10) via orthogonal multiplications and eigenmaps. We also study biharmonic graphs of maps, derive the equation for a function whose graph is a biharmonic hypersurface in a Euclidean space, and give an equivalent formulation of Chen’s conjecture on biharmonic hypersurfaces by using the biharmonic graph equation (Theorem 4.1) which paves a way for the analytic study of the conjecture.     

Improved biological performance of low modulus Ti-24Nb-4Zr-7.9Sn implants due to surface modification by anodic oxidation

Dental implants are usually made from commercially pure titanium or titanium alloys. The purpose of this study was to evaluate the influence of surface treatment to low modulus Ti-24Nb-4Zr-7.9Sn (TNZS) on cell and bone responses. The TNZS alloy samples were modified using anodic oxidation (AD). Surface oxide properties were characterized by using various surface analytic techniques, involving scanning electron microscopy (SEM) equipped with energy dispersive spectrometer (EDS), X-ray diffractometry (XRD) and surface profilometer. During the AD treatment, porous titanium oxide layer was formed and Ca ions were incorporated into the oxide layer. The viability and morphology of osteoblasts on Ca-incorporated TNZS were studied. The bone responses of Ca-incorporated TNZS were evaluated by pull-out tests and morphological analysis after implantation in rabbit tibiae. The non-treated Ti and TNZS samples were used as the control. Significant increases in cell viability and pull-out forces (p < 0.05) were observed for Ca-incorporated TNZS implants compared with those for the control groups. Porous structures supplied positive guidance cues for osteoblasts to attach. The enhanced cell and bone responses to Ca-incorporated TNZS implants could be explained by the surface chemistry and microtopography.     

Limitations and guidelines for measuring the spectral width of ultrashort light pulses with a scanning Fabry–Pérot interferometer

The measurement of the spectral width of ultrashort light pulses using a Fabry–Pérot interferometer (FPI) is investigated. It is shown, numerically and experimentally, that the measured width critically depends on the pulse properties (such as pulse shape, pulse duration, frequency chirp and wavelength) and on the properties of the FPI (such as the mirror spacing and the mirror reflectivities). The obtained results are of particular importance if the spatial length of the short light pulses is comparable or even shorter than the distance between the FPI mirrors. The derived guideline indicate that the actual spectral width of the ultrashort light pulses is measured with good accuracy only if the finesse F≥40 and the round trip time of the light pulses inside the Fabry–Pérot interferometer is approximately one to three times the pulse duration. Received: 17 December 1999 / Revised version: 14 April 2000 / Published online: 5 July 2000     

C*-dynamical systems that are asymptotically highly anticommutative

It is shown that with probability 1 on , resp. ongx the irrational rotation algebra with respect to the CAT map and the generalized Price-Powers shiftA _X are asymptotically highly anticommutative.     

On the topological theory of self-dual connections over noncompact Riemann surfaces

A topological action for self-dual connections over noncompact Riemann surfaces is proposed. TheJ formulation and the associated linear system are obtained. A new connection is constructed, depending on a Kac-Moody parameter such that its flatness condition is theJ-equation associated to the self-dual problem. The algebra of infinitesimal Bäcklund transformations depending on this Kac-Moody parameter is constructed.     

Equivariant quantization of orbifolds

Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the reasons for the recent interest in quantization of singular spaces, orbifolds, stratified spaces, etc. In this work, we prove the existence of an equivariant quantization for orbifolds. Our construction combines an appropriate desingularization of any Riemannian orbifold by a foliated smooth manifold, with the foliated equivariant quantization that we built in Poncin et al. (2009) [19]. Further, we suggest definitions of the common geometric objects on orbifolds, which capture the nature of these spaces and guarantee, together with the properties of the mentioned foliated resolution, the needed correspondences between singular objects of the orbifold and the respective foliated objects of its desingularization.     

Dijkgraaf–Witten invariants of surfaces and projective representations of groups

We compute the Dijkgraaf–Witten invariants of surfaces in terms of projective representations of groups. As an application we prove that the complex Dijkgraaf–Witten invariants of surfaces of positive genus are positive integers.     

Gd-doping of HfO2

An increase in the density of states between the oxygen 2p bands and the Fermi level is seen with increasing Gd concentrations. In addition, for the Gd-doped HfO₂ films, the Gd 4f photoexcitation peak at 5.5 eV below the valence band maximum was identified using resonant photoemission. Electrical measurements show pronounced rectification properties for lightly-doped Gd:HfO₂ films on p-Si and for heavily-doped Gd:HfO₂ films on n-Si, suggesting a crossover from n-type to p-type behavior with increasing doping level. In addition, there is an increase in the reverse bias current with neutron irradiation.     

Dirichlet norms,capacities and generalized isoperimetric inequalities for Markov operators

We define the notion of p-capacity for a reversible Markov operator on a general measure space and prove that uniform estimates for the ratio of capacity and measure are equivalent to certain imbedding theorems for the Orlicz and Dirichlet norms. As a corollary we get results on connections between embedding theorems and isoperimetric properties for general Markov operators and, particularly, a generalization of the Kesten theorem on the spectral radius of random walks on amenable groups for the case of arbitrary graphs with non-finitely supported transition probabilities.     

A non-linear version of Hunt-Lion's theorem from the point of view of T-accretivity

In the classical topological context, Dellacherie [10] has given a non-linear version of Hunt's theorem characterizing the proper kernels verifying the complete maximum principle as those closing a submarkovian resolvent. In this paper we study the relation between this non-linear version of Hunt's theorem and T-accretivity.