A priori bounds in weighted spaces

In unbounded domains we state some a priori bounds for solutions of the Dirichlet problem for linear second order elliptic differential equations in nondivergence form with discontinuous coefficients in weighted spaces. The weight function is related to the distance function from a fixed subset S of ∂Ω.     

Canonical connections with an algebraic curvature tensor field on naturally reductive spaces

We study Ambrose-Singer connections with an algebraic curvature tensor on simply connected manifolds carrying a homogeneous Riemannian structure of class ₃ in the classification given by F. Tricerri and L. Vanhecke.This work was partially supported by MURST.     

Besov-Morrey spaces: Function space theory and applications to non-linear PDE

This paper is devoted to the analysis of function spaces modeled on Besov spaces and their applications to non-linear partial differential equations, with emphasis on the incompressible, isotropic Navier-Stokes system and semi-linear heat equations. Specifically, we consider the class, introduced by Hideo Kozono and Masao Yamazaki, of Besov spaces based on Morrey spaces, which we call Besov-Morrey or BM spaces. We obtain equivalent representations in terms of the Weierstrass semigroup and wavelets, and various embeddings in classical spaces. We then establish pseudo-differential and para-differential estimates. Our results cover non-regular and exotic symbols. Although the heat semigroup is not strongly continuous on Morrey spaces, we show that its action defines an equivalent norm. In particular, homogeneous BM spaces belong to a larger class constructed by Grzegorz Karch to analyze scaling in parabolic equations. We compare Karch's results with those of Kozono and Yamazaki and generalize them by obtaining short-time existence and uniqueness of solutions for arbitrary data with subcritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact, smooth, boundaryless, Riemannian manifolds. BM spaces are defined by means of partitions of unity and coordinate patches, and intrinsically in terms of functions of the Laplace operator.

     

Colloidal Analysis of Particles Extracted from Microalloyed Steels

Different colloidal particle characterization methods are examined for their suitability to determine the particle size distribution of particles extracted from steels. Microalloyed steels are dissolved to extract niobium and titanium carbonitride particles that are important for the mechanical properties of these steels. Such particles have sizes ranging from several nanometers to hundreds of nanometers depending on the precipitation stage during the thermomechanically controlled rolling process. The size distribution of the particles is analyzed by dynamic light scattering (DLS), analytical ultracentrifugation (AUC), and hollow fiber flow field-flow fractionation (HF5) and compared to data obtained for reference particles as well as data from electron microscopy, the standard sizing technique used in metallurgy today. AUC and HF5 provide high-quality size distributions, average over large particle numbers that enables statistical analysis, and yield useful insights for alloy design; however, DLS fails due to a lack of resolution. Important aspects in the conversion and comparison of size distributions obtained for broadly distributed particle systems with different measurement principles and the role of surfactants used in sample preparation are discussed.     

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.     

Are Gait and Balance Problems in Neurological Patients Interdependent? Enhanced Analysis Using Gait Indices,Cyclograms, Balance Parameters and Entropy

Background: Balance and locomotion are two main complex functions, which require intact and efficient neuromuscular and sensory systems, and their proper integration. In many studies the assumption of their dependence is present, and some rehabilitation approaches are based on it. Other papers undermine this assumption. Therefore the aim of this study was to examine the possible dependence between gait and balance in patients with neurological or sensory integration problems, which affected their balance. Methods: 75 patients (52 with neurological diseases, 23 with sensory integration problems) participated in the study. They underwent balance assessment on Kistler force plate in two conditions, six tests on a Balance Biodex System and instrumented gait analysis with VICON. The gait and balances parameters and indices, together with entropy and cyclograms were used for the analysis. Spearman correlation, multiple regression, cluster analysis, and discriminant analysis were used as analytical tools. Results: The analysis divided patients into 2 groups with 100% correctly classified cases. Some balance and gait measures are better in the first group, but some others in the second. Conclusions: This finding confirms the hypothesis that there is no direct link between gait and balance deficits.     

Self-organisation of di(perfluorohexyl)hexane in Langmuir and LB films

Symmetrical triblock semifluorinated n-alkane, di(perfluorohexyl)hexane of the formula F(CF₂)₆(CH₂)₆(CF₂)₆F (abbreviated F₆H₆F₆), has been synthesised and investigated at the air/water interface. Our results show for the first time that this unusual film-forming material, completely hydrophobic in nature and possessing no polar group, is capable of stable film formation at the free water surface. The surface pressure–area isotherm of the studied compound exhibited two regions: corresponding to monotonous pressure rise, followed by a pseudo-plateau region. Visualisation of film structure with Brewster angle microscope (BAM) proved the formation of domains within the pseudo-plateau region. A closer insight into the structure of these domains with atomic force microscope (AFM) proved their ordered, circular shape. The average area of F₆H₆F₆ domain was found to depend on surface pressure value, as it is 4.98 ± 1.75 μm² at π = 1.2 mN/m to 16.54 ± 0.31 μm² at π = 1.7 mN/m. Following performed quantum-chemical calculations, it can be concluded that the observed surface aggregates from F₆H₆F₆ are formed by linear conformers with shifted CF and CH parts. The calculated domain thickness is between 20 and 21 Å, which perfectly agrees with the experimental value estimated from AFM measurements (20.3 ± 1.4 Å).     

Collision Avoidance in Bi-Directional AGV Systems

The use of a bi-directional, as opposed to a one-way, transportation system, can increase the operational efficiency of automated guided vehicles in both manufacturing and warehousing environments. However, the full potential will only be realized if the routeing algorithms pay particular attention to the problem of collision avoidance. This paper is concerned with the development of such an algorithm. The method is based on the use of delays and deviations to avoid collisions that could arise when using the shortest routes for each vehicle, and is applicable to any transportation system which can be represented as a network with known travel times.     

Dynamically Induced Excitonic Instability in Pumped Dirac Materials

Driven and non-equilibrium quantum states of matter have attracted growing interest in both theoretical and experimental studies in condensed matter physics. Recent progress in realizing transient collective states in driven or pumped Dirac materials (DMs) is reviewed herein. In particular, the focus is on optically pumped DMs which are a promising platform for transient excitonic instabilities. Optical pumping combined with the linear (Dirac) dispersion of the electronic spectrum offers a knob for tuning the effective interaction between the photoexcited electrons and holes, and thus provides a way of reducing the critical coupling for excitonic instability. As a result, a transient excitonic condensate could be achieved in a pumped DM while it is not feasible in equilibrium. A unifying theoretical framework is provided for describing transient collective states in 2D and 3D DMs. The experimental signatures are described and numerical estimates of the size of the dynamically induced excitonic gaps and the values of the critical temperatures for several specific systems, are summarized. In addition, general guidelines for identifying promising material candidates are discussed. Finally, comments are provided regarding recent experimental efforts in realizing transient excitonic condensate in pumped DMs, and outstanding issues and possible future directions are outlined.