Perturbations of Christoffel–Darboux Kernels: Detection of Outliers

Foundations of Computational Mathematics - Two central objects in constructive approximation, the Christoffel–Darboux kernel and the Christoffel function, encode ample information about the...     

Necessary and Sufficient Conditions for Viability for Nonlinear Evolution Inclusions

We consider the viability problem for nonlinear evolutions inclusions of the form u′(t)?∈?Au(t)?+?F(u(t)), where A is an m-dissipative (possible nonlinear and multi-valued) operator acting in a Banach space X, K?X is a nonempty, locally closed set and $F:K{\user1{ \rightsquigarrow }}X$ is with nonempty, convex, closed and bounded values. We define the concept of A-quasi-tangent set to K at a given point ξ?∈?K and we prove a necessary condition for C ⁰-viability expressed in terms of this new tangency concept. We next show that, under various natural extra-assumptions, the necessary condition is also sufficient. We extend the results to the quasi-autonomous case, we deal with the existence of noncontinuable or even global C ⁰-solutions and, as applications, we deduce a comparison result and a sufficient condition for null controllability.     

Experimental and theoretical evidence of the first Au(i)...Bi(iii) interaction

Complex [Au(C6F5)2][Bi(C6H4CH2NMe(2)-2)2] displays the first example of an interaction between Au(I) and Bi(III), the nature of which is shown to be consistent with the presence of a high ionic contribution (79%) and a dispersion type (van der Waals) interaction (21%).     

Thermal Degradation of Trioxane-Dioxqlane Copolymers Obtained with Boron Trifluoride-Acrylonitrile Complex as Initiator

The thermal degradation of certain trioxane-dioxolane copolymers obtained with boron trifluoride-acrylonitrile complex as initiator has been investigated. The thermal stability of samples, discussed in terms of topoenergetic values, was related both to copolymer composition and conversion. The most thermostable copolymers (～5% weight loss at 300°C in air), having 5–8% dioxolane units, had the highest intrinsic viscosity in the series and were isolated at 35–50% conversion. The results obtained were compared with similar data for a commercial tri-oxane-ethylene oxide copolymer containing 95% formal units.     

The Interaction of Collinear Gaps of Arbitrary Charge in a Two Dimensional Dimer System

The correlation of gaps in dimer systems was introduced by Fisher and Stephenson (Phys Rev 132:1411–1431, 1963), who looked at the interaction of two monomers generated by the rigid exclusion of dimers on the closely packed square lattice. In previous work we considered the analogous problem on the hexagonal lattice, and we extended the set-up to include the correlation of any finite number of monomer clusters. For fairly general classes of monomer clusters we proved that the asymptotics of their correlation is given, for large separations between the clusters, by a multiplicative version of Coulomb’s law for 2D electrostatics. However, our previous results required that the monomer clusters consist (with possibly one exception) of an even number of monomers. In this paper we determine the asymptotics of general defect clusters along a lattice diagonal in the square lattice (involving an arbitrary, even or odd number of monomers), and find that it is given by the same Coulomb law. We also obtain a conceptual interpretation for the multiplicative constant as the product of the correlations of the individual clusters.     

Strongly anisotropic diffusion problems; asymptotic analysis

The subject matter of this paper concerns anisotropic diffusion equations: we consider heat equations whose diffusion matrices have disparate eigenvalues. We determine first and second order approximations, we study the well-posedness of them and establish convergence results. The analysis relies on averaging techniques, which have been used previously for studying transport equations whose advection fields have disparate components.     

Chemical Investigation on Various Aromatic Compounds Polymerization in Low Pressure Helium Plasma

Remarkable properties of plasma polymer films are greatly dependent not only on the chemical structure of precursor but also on the reactor design and the deposition conditions. In many industrial applications it is a challenge to control the plasma polymer structure. In this paper we investigate the chemical transformation of various aromatic compounds, such as activation and fragmentation of substituent-part, aromatic ring opening, during plasma polymerization process. Polymerized films are deposited in a low-frequency capacitively coupled plasma-enhanced chemical vapour deposition reactor, working at low pressure. The chemical composition of plasma-polymerized films is elucidated by Fourier-transform infrared spectroscopy, solid-state carbon-13 nuclear magnetic resonance spectroscopy, and X-ray photoelectron spectroscopy. Based on spectroscopic measurements, the intermediary reactions during film growth may be presumed.     

Birkhoff Completeness in Institutions

We develop an abstract proof calculus for logics whose sentences are ‘Horn sentences’ of the form: and prove an institutional generalization of Birkhoff completeness theorem. This result is then applied to the particular cases of Horn clauses logic, the ‘Horn fragment’ of preorder algebras, order-sorted algebras and partial algebras and their infinitary variants. the restriction of a logic to Horn sentences     

Viability for Differential Inclusions on Graphs

Let X be a Banach space, I a nonempty, bounded interval and let $K:I\leadsto X$ be a given multi-valued function. We rephrase the concept of tangent set introduced by Cârj? et al. (Trans Amer Math Soc, 2008; Viability, Invariance and Applications. North-Holland Mathematics Studies, vol. 207. Elsevier, 2007) by saying that a bounded set $E\subseteq X$ is right tangent to at if $\liminf_{h\downarrow0}{1}/{h}\,\text{\rm dist}(\xi+hE;K(\tau+h))=0$ . Next, by using a tangency condition expressed in the terms of this concept, we establish several necessary and sufficient conditions for viability referring to differential inclusions on graphs.     

Towards a Bioactive Food Packaging: Poly(Lactic Acid) Surface Functionalized by Chitosan Coating Embedding Clove and Argan Oils

Here we introduce a new method aiming the immobilization of bioactive principles onto polymeric substrates, combining a surface activation and emulsion entrapment approach. Natural products with antimicrobial/antioxidant properties (essential oil from Syzygium aromaticum—clove and vegetal oil from Argania spinosa L—argan) were stabilized in emulsions with chitosan, a natural biodegradable polymer that has antimicrobial activity. The emulsions were laid on poly(lactic acid) (PLA), a synthetic biodegradable plastic from renewable resources, which was previously activated by plasma treatment. Bioactive materials were obtained, with low permeability for oxygen, high radical scavenging activity and strong inhibition of growth for Listeria monocytogenes, Salmonella Typhimurium and Escherichia coli bacteria. Clove oil was better dispersed in a more stable emulsion (no separation after six months) compared with argan oil. This leads to a compact and finely structured coating, with better overall properties. While both clove and argan oils are highly hydrophobic, the coatings showed increased hydrophilicity, especially for argan, due to preferential interactions with different functional groups in chitosan. The PLA films coated with oil-loaded chitosan showed promising results in retarding the food spoilage of meat, and especially cheese. Argan, and in particular, clove oil offered good UV protection, suitable for sterilization purposes. Therefore, using the emulsion stabilization of bioactive principles and immobilization onto plasma activated polymeric surfaces we obtained a bioactive material that combines the physical properties and the biodegradability of PLA with the antibacterial activity of chitosan and the antioxidant function of vegetal oils. This prevents microbial growth and food oxidation and could open new perspectives in the field of food packaging materials.