Differential equations over polynomially bounded o-minimal structures

We investigate the asymptotic behavior at of non-oscillatory solutions to differential equations a$">, where is definable in a polynomially bounded o-minimal structure. In particular, we show that the Pfaffian closure of a polynomially bounded o-minimal structure on the real field is levelled.

     

Construction of best Bregman approximations in reflexive Banach spaces

An iterative method is proposed to construct the Bregman projection of a point onto a countable intersection of closed convex sets in a reflexive Banach space.

     

Properties of a three-dimensional photonic jet

By focusing light with a sphere several wavelengths in diameter, we can obtain a photonic nanojet [Opt. Express 13, 526 (2005)]: if light is focused on the surface of the sphere, the width of the beam stays smaller than the wavelength along a distance of propagation of approximately two wavelengths and reaches a high intensity. We use the rigorous Mie theory to analyze the basic properties of the photonic jet in the general three-dimensional polarized case. This fast algorithm allows us to determine the influence of the radius and the refractive index of the sphere on the photonic jet. The polarization response is also studied. We observe that high-intensity concentrations and subwavelength focusing are two different effects. Their basic properties are analyzed, and explanations are proposed.     

Acoustic properties of wood in tridimensional representation of slowness surfaces

Mechanical behaviour of wood considered as an orthotropic solid can be determined with ultrasonic technique. The propagation phenomena in wood are complex and theoretically are regulated by Christoffel's equation. Three type of waves can propagate in wood. During the propagation phenomena three slowness sheets are observed, corresponding to a fast longitudinal wave (inner sheet) and two shear waves, one fast and one slow (outer sheet). These waves are submitted continuously to mode conversion phenomena. The polarization angle changes when the propagation direction is out of the principal directions of symmetry of the material. In this article an analysis of the propagation phenomena in tridimensional representation is performed for different wood species. This approach contributes to the understanding of dynamic aspects of particle displacement associated with the wave fronts propagation. Globally, the anisotropy of each species, expressed by their acoustical behaviour is well represented.     

On the geometry of master-slave synchronization

In 1990, Pecora and Carroll reported the observation that one can synchronize the orbits of two identical dynamical systems, which may be chaotic, by feeding state variables of one of them to the other one with no feedback, a phenomenon often called master-slave synchronization. We report here some results on the theory of master-slave synchronization for maps and flows, which are all inspired by a similar geometric and coordinate independent point of view to the one introduced in master-slave synchronization by Tresser, Worfolk, and Bass. Our results are variations on the theme that projection often can compensate for expansion.(c) 2002 American Institute of Physics.     

BMP-6 Loaded Polyelectrolyte Complex Nanoparticles Inducing Osteogenic Differentiation and Apoptosis of Malignant Plasma Cells for Local Treatment of Multiple Myeloma

In the malignant plasma cell disease multiple myeloma (MM), bone lesions and resulting fractures caused by MM cell (MMC) accumulation represent a major cause of morbidity and mortality. Despite recent advantages in systemic treatment, residual MMCs remain, especially in bone lesions. Therefore an interfacial delivery system for local treatment of MM and induced bone disease based on polyelectrolyte complex nanoparticles (PEC NP) loaded with bone morphogenetic protein 6 (BMP-6) inducing de-novo bone formation and MMC apoptosis is presented herein. BMP-6 loaded PEC NP are fabricated by defined mixing bio-related cationic and anionic polysaccharides and BMP-6 according to molar ratio of BMP-6/PEC-NP of 1/3. BMP-6/PEC NP bound to a model substrate releases 10% BMP-6 sustainably within two weeks as accessed by infrared spectroscopy. BMP-6 loaded PEC NP adheres to cell membranes of MMCs and MSCs and activated phosphorylation of Smad 1/5. Osteogenic differentiation (ALP-concentration) is enhanced in MSCs (p < 0.05). All patient samples (10/10) of MMCs show significant induction of apoptosis (median 84%, p < 0.05). Finally, BMP-6/PEC NP are successfully integrated in a commercial hyaluronic acid based hydrogel material revealing MMC death as principal proof for the local treatment of MM induced bone lesions.     

Research Note

Formulas are derived for consistent evaluation of permutationally totally symmetric and determinantally antisymmetric powers of generalized combinations in which irreducible representations may occur with either positive or negative weights.     

Non-local order in Mott insulators,duality and Wilson loops

It is shown that the Mott insulating and superfluid phases of bosons in an optical lattice may be distinguished by a non-local ‘parity order parameter’ which is directly accessible via single site resolution imaging. In one dimension, the lattice Bose model is dual to a classical interface roughening problem. We use known exact results from the latter to prove that the parity order parameter exhibits long range order in the Mott insulating phase, consistent with recent experiments by Endres et al. [M. Endres, M. Cheneau, T. Fukuhara, C. Weitenberg, P. Schauß, C. Gross, L. Mazza, M.C. Bañuls, L. Pollet, I. Bloch, et al., Science 334 (2011) 200]. In two spatial dimensions, the parity order parameter can be expressed in terms of an equal time Wilson loop of a non-trivial U(1)$U\left(1\right)$ gauge theory in 2+1$2+1$ dimensions which exhibits a transition between a Coulomb and a confining phase. The negative logarithm of the parity order parameter obeys a perimeter law in the Mott insulator and is enhanced by a logarithmic factor in the superfluid.