Liouville and geodesic Ricci solitons

On a tangent bundle endowed with a pseudo-Riemannian metric of complete lift type two classes of Ricci solitons are obtained: a 1-parameter family of shrinking Liouville Ricci solitons if the base manifold is Ricci flat and a steady geodesic Ricci soliton if the base manifold is flat. A nonexistence result of geodesic Ricci solitons for the tangent bundle of a non-flat space form is also provided. To cite this article: M. Crasmareanu, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Polyaniline/Maleic Acid Copolymers Composites: Synthesis and Characterization

Summary: Polyaniline/maleic acid copolymers composites were synthesized by chemical in situ polymerization of aniline using ammonium peroxidisulfate as oxidant, in the presence of water soluble copolymers containing carboxylic groups. Fine dispersions of composite materials, soluble in N,N-dimethylformamide or dimethyl sulfoxide were obtained which can be processed as thin films and membranes for application as proton-conductive materials for electrolyte membranes of fuel cells. The composites were characterized by FTIR spectroscopy and thermal methods.     

Existence Theorems in the Geometrically Non-linear 6-Parameter Theory of Elastic Plates

In this paper we show the existence of global minimizers for the geometrically non-linear equations of elastic plates, in the framework of the general 6-parameter shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates.     

Novel nanocomposite membranes from cellulose acetate and clay‐silica nanowires

In this study, a new class of heterogeneous membranes based on cellulose acetate (CA) polymer and a complex filler clay‐silica nanowires (SiO₂NWs) was investigated for potential biomedical applications. SiO₂NWs were synthesized using natural clay through a facile sol–gel method and were dispersed in the polymer solution by sonication in the 1.25, 2.5, and 5% weight ratio to the CA acetate polymer. Membranes were subsequently prepared via phase inversion by precipitation of the CA polymer in water. The pristine CA membrane and SiO₂NWs based nanocomposites membranes were characterized using different characterization techniques. The presence of the SiO₂NWs in the CA membrane was found to significantly enhance the protein retention, water wettability and thermal as well as mechanical properties in comparison to the pristine CA membrane. Water flows studies at different temperatures and the retention of bovine serum albumin have been studied and the nanocomposite membranes were found to exhibit superior performances compared with the pristine CA membranes. SiO₂NWs‐CA membranes showed a much higher stability to the water temperature change during separation than CA membranes. Morphological changes clearly revealed that the composite membrane were much more compact than the pristine CA membranes. The rabbit dermal fibroblasts cell viability in cultures after 72 hr of incubation was found to be greater than 80%. These newly synthesized composite membranes exhibit a high potential to be used for various medical applications because of their non‐cytotoxic characteristics. Copyright © 2016 John Wiley & Sons, Ltd.     

Conditional Monte Carlo method for dynamic systems with random properties

A method is developed for calculating moments and other properties of states X(t) of dynamic systems with random coefficients depending on semi-Markov processes ξ(t) and subjected to Gaussian white noise. Random vibration theory is used to find probability laws of conditional processes X(t)∣ξ(·). Unconditional properties of X(t) are estimated by averaging conditional statistics of this process corresponding to samples of ξ(t). The method is particularly efficient for linear systems since X(t)∣ξ(·) is Gaussian during periods of constant values of ξ(t), so that and its probability law is completely defined by the process mean and covariance functions that can be obtained simply from equations of linear random vibration. The method is applied to find statistics of an Ornstein-Uhlenbeck process X(t) whose decay parameter is a semi-Markov process ξ(t). Numerical results show that X(t) is not Gaussian and that the law of this process depends essentially on features of ξ(t). A version of the method is used to calculate the failure probability for an oscillator with degrading stiffness subjected to Gaussian white noise.     

Studies regarding the formation from metal nitrates and diol of NiM 2 III O4 spinels, inside a silica matrix

The present study deals with preparation and characterization of spinel mixed oxide systems NiM ₂ ^III O₄, where M^III?=?Fe^III, Cr^III. In order to obtain 50% NiFe₂O₄/50% SiO₂ and 50% NiCr₂O₄/50% SiO₂ nanocomposite, we have used a versatile route based on the thermal decomposition inside the SiO₂ matrix, of some particular precursors, coordination compounds of the involved M^II and M^III cations with dicarboxylate ligands. The ligands form in the redox reaction between metal nitrates mixture and 1,3-propanediol at the heating around 140?°C of the gels (tetraethylorthosilicate?Cmetal nitrates?C1,3-propanediol?Cwater). The as-obtained precursors, embedded in silica gels, have been characterized by FT-IR spectrometry and thermal analysis. Both precursors thermally decompose up to 350?°C leading to the formation of the corresponding metal oxides inside the silica matrix. X-ray diffraction of the annealed powders have evidenced the formation of NiFe₂O₄ starting with 600?°C, and NiCr₂O₄ starting with 400?°C. This behavior can be explained by the fact that, by thermal decomposition of the Fe(III) carboxylate at 300?°C, the spinelic phase ??-Fe₂O₃ is formed, which interacts with the NiO, forming the ferrite nuclei. By thermal decomposition of chromium carboxylate, a nonstoichiometric chromium oxide (Cr₂O_3+x ) is formed. In the range 380?C400?°C, Cr₂O_3+x turns into Cr₂O₃ which immediately interacts with NiO leading to the formation of nickel chromites nuclei inside the pores of silica matrix. Both spinels have been obtained as nanocrystalites homogenously dispersed as resulted from XRD and TEM data.     

G-凸空间的择一原理和极大极小不等式

Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems concerning maximal elements, analytic alternatives and minimax inequalities.     

Measurements of structure-induced polarization features in forward scattering from collections of cylindrical fibers

Many applications in remote sensing, material sciences and biomedical field are characterized by a transition domain between single scattering and multiple-scattering regimes. This regime is described by typical polarization features which can be used to retrieve structural information. An electronically agile technique was used for measuring in real time the Stokes vectors of light incident on and emerging from an inhomogeneous medium. Subsequently, the Mueller matrix associated with the scattering medium is determined. We focus our attention on forward scattering from systems consisting of random as well as partially oriented long cylindrical fibers. We discuss the effects of: (1) shape of individual scattering centers, (2) structure parameter, and (3) optical density of the scattering medium. The anisotropic behavior of the structure function at different packing fractions determines nontrivial characteristics of the polarization transfer. The complex effective index of refraction can be polarization dependent as a result of the optical anisotropy due to both the shape of the individual scatterers and the structure characteristics of the scattering system. Some of the Mueller matrix elements are shown to be related to the optical anisotropy of the system for the case of long cylindrical fibers. The polarization efficiency, the structure parameter, and the packing fraction are used to quantify this relationship. We also found that some of the matrix elements are more sensitive to the degree of structural anisotropy and the packing fraction, while other elements are sensitive to structural non-uniformities across the investigated area.     

Thermal stresses in cylindrical Cosserat elastic shells

We consider the problem of thermal stresses in cylindrical elastic shells, modelled as Cosserat surfaces. In the theory of Cosserat shells, the thermal effects are described generally by means of two temperature fields. The problem consists in finding the equilibrium of the shell under the action of a given temperature distribution. The temperature fields are assumed to be general polynomial functions in the axial coordinate, whose coefficients depend on the circumferential coordinate.     

PEO‐b‐PCL Block Copolymers: Synthesis,Detailed Characterization,and Selected Micellar Drug Encapsulation Behavior

Summary: A series of poly(ethylene glycol)‐block‐poly(ε‐caprolactone) diblock copolymers was synthesized and fully characterized. In particular, MALDI‐TOF MS results revealed interesting new insights into their molecular architecture. Small and defined micelles could be prepared from these block copolymers. Utilizing a high‐throughput screening approach, it was observed that these micelles are able to encapsulate/solubilize different guest molecules (e.g. drugs) depending on the solubility of the guest in water. Furthermore, it could be proven that a guest is located within a micelle and that these micelles can be utilized as transport vehicles for the encapsulated guest molecules.

PEO‐b‐PCL diblock copolymers can encapsulate small guest molecules in the core of the polymeric micelles.