Boundedness and Stability of Impulsively Perturbed Systems in a Banach Space

Consider a linear impulsive equation in a Banach space $$\dot{x}(t)+A(t)x(t) = f(t), ~t \geq 0,$$ $$x(\tau_i +0)= B_i x(\tau_i -0) + \alpha_i,$$ with $\lim_{i \rightarrow \infty} \tau_i = \infty$. Suppose each solution of the corresponding semi-homogeneous equation $$\dot{x}(t)+A(t)x(t) = 0,$$ (2) is bounded for any bounded sequence $\{ \alpha_i \}$. The conditions are determined ensuring (a) the solution of the corresponding homogeneous equation has an exponential estimate; (b) each solution of (1),(2) is bounded on the half-line for any bounded $f$ and bounded sequence $\{ \alpha_i \}$ ; (c) $\lim_{t \rightarrow \infty}x(t)=0$ for any $f, \alpha_i$ tending to zero; (d) exponential estimate of $f$ implies a similar estimate for $x$.Comment: 19 pages, LaTex-fil

Mechanical Properties of Robocast Glass Scaffolds Assessed through Micro-CT-Based Finite Element Models

In this study, the mechanical properties of two classes of robocast glass scaffolds are obtained through Computed micro-Tomography (micro-CT) based Finite Element Modeling (FEM) with the specific purpose to explicitly account for the geometrical defects introduced during manufacturing. Both classes demonstrate a fiber distribution along two perpendicular directions on parallel layers with a (Formula presented.) tilting between two adjacent layers. The crack pattern identified upon compression loading is consistent with that found in experimental studies available in literature. The finite element models have demonstrated that the effect of imperfections on elastic and strength properties may be substantial, depending on the specific type of defect identified in the scaffolds. In particular, micro-porosity, fiber length interruption and fiber detaching were found as key factors. The micro-pores act as stress concentrators promoting fracture initiation and propagation, while fiber detachment reduces the scaffold properties substantially along the direction perpendicular to the fiber plane

Surface Properties and Antioxidant Activity of Silicate and Borosilicate Bioactive Glasses

Herein, silicate and borosilicate bioactive glasses are synthetized and characterized. The antioxidant activity, in the presence and absence of human osteoblasts' progenitor cells, of the different glass compositions, is correlated to the surface properties: wettability, zeta potential, hydroxylation degree, reactivity in simulated body fluid (SBF), and Tris buffer. An enhancing effect of boron in glass reactivity and a stabilizing role of Sr and Mg are evidenced. The scavenging potential of the analyzed bioactive glasses toward reactive oxygen species (ROS) is clearly proved. Moreover, cellular tests confirm the protective effect of the bioactive glasses toward viable cells acting as ROS/RNS species scavenger. The obtained results represent an original improvement of the knowledge concerning the intrinsic antioxidant ability of bioactive glasses with different compositions and the mechanisms involved

Surface Modification of Bioresorbable Phosphate Glasses for Controlled Protein Adsorption

The traditional silicate bioactive glasses exhibit poor thermal processability, which inhibits fiber drawing or sintering into scaffolds. The composition of the silicate glasses has been modified to enable hot processing. However, the hot forming ability is generally at the expense of bioactivity. Metaphosphate glasses, on the other hand, possess excellent thermal processability, congruent dissolution, and a tailorable degradation rate. However, due to the layer-by-layer dissolution mechanism, cells do not attach to the material surface. Furthermore, the congruent dissolution leads to a low density of OH groups forming on the glass surface, limiting the adsorption of proteins. It is well regarded that the initial step of protein adsorption is critical as the cells interact with this protein layer, rather than the biomaterial itself. In this paper, we explore the possibility of improving protein adsorption on the surface of phosphate glasses through a variety of surface treatments, such as washing the glass surface in acidic (pH 5), neutral, and basic (pH 9) buffer solutions followed or not by a treatment with (3-aminopropyl)triethoxysilane (APTS). The impact of these surface treatments on the surface chemistry (contact angle, ζ-potential) and glass structure (FTIR) was assessed. In this manuscript, we demonstrate that understanding of the material surface chemistry enables to selectively improve the adsorption of albumin and fibronectin (used as model proteins). Furthermore, in this study, well-known silicate bioactive glasses (i.e., S53P4 and 13-93) were used as controls. While surface treatments clearly improved proteins adsorption on the surface of both silicate and phosphate glasses, it is of interest to note that protein adsorption on phosphate glasses was drastically improved to reach similar protein grafting ability to the silicate bioactive glasses. Overall, this study demonstrates that the limited cell/phosphate glass biological response can easily be overcome through deep understanding and control of the glass surface chemistry

Around a problem of Nicole Brillouët–Belluot

We determine nontrivial intervals I ⊂ (0,+∞), numbers α ∈ R and continuous bijections f : I → I such that f(x)f−1(x) = xα for every x ∈ I

Bioactive phosphate glass-based fiber with green persistent luminescence

The first biophotonic composite fiber with green persistent luminescence is reported. The composites were drawn from preforms prepared by remelting a bioactive glass with commercial persistent luminescent microparticles (SrAl2O4:Eu2+,Dy3+). The duration of the remelt step should be as short as possible to limit the decomposition of the micro-phosphors during glass preparation, as evidenced using electron microscopy coupled with elemental analysis. The presence of the phosphors in the glass inhibits the drawing of fibers with diameter below about 400 µm. Although the drawing process induces some changes in the Eu2+ ions’ local structure in the phosphors, the fibers still exhibit green afterglow. Despite the presence of the phosphors, the fiber still maintains its bioactive response, as characterized by the release of ions from the glass to the environment and the successive precipitation of a reactive layer within a dicalcium phosphate dehydrate composition.</p

A Grassmann integral equation

The present study introduces and investigates a new type of equation which is called Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann integrations and which is to be obeyed by an unknown function over a (finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann integral equations is explicitly studied for certain low-dimensional Grassmann algebras. The choice of the equation under investigation is motivated by the effective action formalism of (lattice) quantum field theory. In a very general setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional analogues of the generating functionals of the Green functions are worked out explicitly by solving a coupled system of nonlinear matrix equations. Finally, by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi}, {\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the generators of the Grassmann algebra G_2n), between the finite-dimensional analogues G_0 and G of the (``classical'') action and effective action functionals, respectively, a special Grassmann integral equation is being established and solved which also is equivalent to a coupled system of nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann integral equation exist for n=2 (and consequently, also for any even value of n, specifically, for n=4) but not for n=3. If \lambda=1, the considered Grassmann integral equation has always a solution which corresponds to a Gaussian integral, but remarkably in the case n=4 a further solution is found which corresponds to a non-Gaussian integral. The investigation sheds light on the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54], [61], [64], [139] added

Specific trends in phosphate glass crystallization

This paper focusses on investigating and comparing the congruent crystallization of phosphate glasses with different degrees of polymerization. The study was performed both on powders, with different size fractions, and coarse particles which can be assimilated to bulk. From DSC experiments, corroborated by SEM analysis, it was demonstrated that LiPO3 crystallizes from surface whereas LiGe2(PO4)3 crystallizes in the whole volume. Sn2P2O7 presented both phenomena, the nucleation time lag being short enough to observe internal crystallization at the laboratory time scale. Using the non-isothermal Ozawa method, the kinetic parameters of the overall devitrification process were determined in terms of the Avrami exponent and of the activation energy for crystallization. The temperature of the maximum nucleation rate was calculated by using the nucleation adiabatic theory. For the achievement of this calculation, the heat capacity temperature dependence up to melting was determined from DSC experiments. The results were found in a good agreement with the SEM observation and the results of the non-isothermal crystallization study.acceptedVersionPeer reviewe

Structure–properties relationships in fibre drawing of bioactive phosphate glasses

New bioactive phosphate glasses suitable for continuous fibre production are investigated in this work. The structure of both bulk and fibres from Na2O–CaO–MgO–P2O5 glasses has been studied by means of Raman and 31P and 23Na nuclear magnetic resonance spectroscopies, and the structural results have been correlated with the mechanical properties of the fibres and the dissolution rate of the bulk glasses. It has been observed that the mechanical properties of the phosphate glass fibres are influenced by the glass network connectivity, while the dissolution rates are governed by the Qi speciation of the PO4 units. As seen in previous studies, molar volume seems to play an important role in the fragility behaviour of phosphate glasses. Here, a lower molar volume resulting from the increase in the oxygen packing density hinders the cooperative flow of the PO4 units throughout the glass network and, therefore, causes a reduction in the kinetic fragility

Grid refinement in the construction of Lyapunov functions using radial basis functions

Lyapunov functions are a main tool to determine the domain of attraction of equilibria in dynamical systems. Recently, several methods have been presented to construct a Lyapunov function for a given system. In this paper, we improve the construction method for Lyapunov functions using Radial Basis Functions. We combine this method with a new grid refinement algorithm based on Voronoi diagrams. Starting with a coarse grid and applying the refinement algorithm, we thus manage to reduce the number of data points needed to construct Lyapunov functions. Finally, we give numerical examples to illustrate our algorithms