Iterative Methods for Pseudomonotone Variational Inequalities and Fixed-Point Problems

In this paper, we introduce an iterative scheme for finding a common element of the set of solution of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known schemes: extragradient and approximate proximal methods. We derive some necessary and sufficient conditions for strong convergence of the sequences generated by the proposed scheme.     

Minimization of vectors of curvilinear functionals on the second order jet bundle: sufficient efficiency conditions

Strongly motivated by its possible applications in Mechanics, in our previous work (Pitea and Postolache (Optim. Lett. doi:10.1007/s11590-010-0272-0, 2011)), we initiated an optimization theory for the second order jet bundle. We considered the problem of minimization of vectors of curvilinear functionals (well known as mechanical work), thought as multi-time multi-objective variational problems, subject to PDE and/or PDI constraints. Within this framework, we introduced necessary conditions. As natural continuation of our results in Pitea and Postolache (Optim. Lett. doi:10.1007/s11590-010-0272-0, 2011), the present work introduces a study of sufficient efficiency conditions. While the background in Sect. 2 is introductory, the theory in Sect. 3 is new as a whole, containing our results.     

Self-organizable vesicular columns assembled from polymers dendronized with semifluorinated Janus dendrimers act as reverse thermal actuators

The synthesis and structural analysis of polymers dendronized with self-assembling Janus dendrimers containing one fluorinated and one hydrogenated dendrons are reported. Janus dendrimers were attached to the polymer backbone both from the hydrogenated and from the fluorinated parts of the Janus dendrimer. Structural analysis of these dendronized polymers and of their precursors by a combination of differential scanning calorimetry, X-ray diffraction experiments on powder and oriented fibers, and electron density maps have demonstrated that in both cases the dendronized polymer consists of a vesicular columnar structure containing fluorinated alkyl groups on its periphery. This vesicular columnar structure is generated by a mechanism that involves the intramolecular assembly of the Janus dendrimers into tapered dendrons followed by the intramolecular self-assembly of the resulting dendronized polymer in a vesicular column. By contrast with conventional polymers dendronized with self-assembling tapered dendrons this new class of dendronized polymers acts as thermal actuators that decrease the length of the supramolecular column when the temperature is increased and therefore, are called reverse thermal actuators. A mechanism for this reversed process was proposed.     

Coherent acoustic wave propagation in media with pair-correlated spheres

Propagation of plane compressional waves in a non-viscous fluid with a dense distribution of identical spherical scatterers is investigated. The analysis is based on the multiple scattering approach proposed by Fikioris and Waterman, and is generalized to include arbitrary choice of the pair-correlation functions used to represent the distribution of the scatterers. A closed form solution for the effective wavenumber as a function of the concentration of pair-correlated finite-size spheres is derived up to the second order. In the limit of uncorrelated point-scatterers, this solution is identical to that obtained by Lloyd and Berry. Different pair-correlation functions are exemplified and compared, and the resulting differences discussed.     

View factors in a finite length axysymmetric cylindrical annulus enclosure

View factor – defined as fraction of total outgoing radiation from surface 1 intercepted by surface 2 – is a key concept in solving the radiative heat transfer in systems of surfaces. Analytical forms of the view factor have been developed by means of integration for many conventional systems of 2D and 3D surfaces in various spatial positions. However, little investigation has been carried out for situations in which there is no complete visibility between the surfaces involved in radiative exchange due to configuration of 3D surfaces or due to presence of interposing object that obstruct partially the mutual visibility.Radiative heat exchange was modeled in a finite length cylindrical annulus consisting of non-isothermal diffusely-emitting surfaces. The canonical definition of the view factor was extended by means of an analytical approach to both 3D and 2D surfaces with shading effects (incomplete mutual visibility) and numerical algorithms were developed in order to calculate view factors values and test view factor algebra rules. The system considered in this paper was an axysymmetric cylindrical annulus – frequently used in many heat transfer applications. View factor values for various surface elements were calculated by means of numerical integration. View factor algebra rules – summation and reciprocity – were verified.     

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.     

On a non-homogeneous eigenvalue problem involving a potential: An Orlicz–Sobolev space setting

In this paper we study a non-homogeneous eigenvalue problem involving variable growth conditions and a potential V. The problem is analyzed in the context of Orlicz–Sobolev spaces. Connected with this problem we also study the optimization problem for the particular eigenvalue given by the infimum of the Rayleigh quotient associated to the problem with respect to the potential V when V lies in a bounded, closed and convex subset of a certain variable exponent Lebesgue space.     

Pseudosymmetric braidings, twines and twisted algebras

A laycle is the categorical analogue of a lazy cocycle. Twines (introduced by Bruguières) and strong twines (as introduced by the authors) are laycles satisfying some extra conditions. If c is a braiding, the double braiding c² is always a twine; we prove that it is a strong twine if and only if c satisfies a sort of modified braid relation (we call such cpseudosymmetric, as any symmetric braiding satisfies this relation). It is known that the category of Yetter-Drinfeld modules over a Hopf algebra H is symmetric if and only if H is trivial; we prove that the Yetter-Drinfeld category _HYD^H over a Hopf algebra H is pseudosymmetric if and only if H is commutative and cocommutative. We introduce as well the Hopf algebraic counterpart of pseudosymmetric braidings under the name pseudotriangular structures and prove that all quasitriangular structures on the 2ⁿ⁺¹-dimensional pointed Hopf algebras E(n) are pseudotriangular. We observe that a laycle on a monoidal category induces a so-called pseudotwistor on every algebra in the category, and we obtain some general results (and give some examples) concerning pseudotwistors, inspired by the properties of laycles and twines.     

Real map germs and higher open book structures

The paper focusses on the existence of higher open book structures defined by real map germs \({\psi : (\mathbb{R}^m ,0) \to (\mathbb{R}^p ,0)}\) such that Sing \({\psi \cap \psi^{-1}(0) \subset \{0\}}\). A general existence criterion is proved, with view to weighted-homogeneous maps.     

Some remarks on time-dependent variational problems and their asymptotic behaviour

The subject matter of this paper is the asymptotic behaviour of quasi-static variational inequalities, as regards physical parameters like the friction coefficient, compliance coefficient, etc. By convex duality, the quasi-static problems can be recast into the forms of standard evolution problems, whose study relies on well-known methods. In this framework the stability with respect to small friction coefficients reduces to long time behaviour for evolution problems.