Aromaticity of corazulenic fullerenes

A novel class of non-classical fullerenes, having pentagon–heptagon pairs, as in azulene, is modeled. The various coverings, sometimes alternating azulenic and benzenic units, are designed by some new sequences of map operations or generalized operations. The hypothetical azulenic fullerenes are characterized by PM3 semiempirical data and POAV1 strain energy SE. Their aromaticity is discussed in the light of several criteria. The HOMA index of aromaticity enabled evaluation of global and local aromaticity of the designed fullerenes.     

Numerical approximation of a viscoelastic frictional contact problemApproximation numérique d'un problème viscoélastique de contact avec frottement

We consider a fully discrete scheme for a quasistatic frictional contact problem between a viscoelastic body and an obstacle. The contact is bilateral, the friction is modeled with Tresca's law and the behavior of the material is described with a viscoelastic constitutive law with long memory. We state an existence and uniqueness result for the discrete solution, followed by error estimate results. Then, we present numerical simulations in the study of a two-dimensional test example. To cite this article: Á. Rodríguez-Arós et al., C. R. Mecanique 334 (2006).     

Analysis of viscoelastic contact with normal compliance,friction and wear diffusionAnalyse d'un problème viscoélastique avec compliance normale,frottement et diffusion d'usure

We consider a quasistatic problem of frictional contact between a viscoelastic body and a moving foundation. The contact is with wear and is modeled by normal compliance and a law of dry friction. The novelty in the model is that it allows for the diffusion of the wear debris over the potential contact surface. Such kind of phenomena arise in orthopaedic biomechanics and influence the properties of joint prosthesis. We derive a weak formulation of the problem and state that, under a smallness assumption on the problem data, there exists a unique weak solution for the model. To cite this article: M. Shillor et al., C. R. Mecanique 331 (2003).     

Characterisation of nickel–zinc ferrite/silica nanocomposites with low ferrite concentration obtained by an improved modified sol–gel method

The paper presents a study regarding the structure, morphology and magnetic behaviour of x% (Ni_0.65Zn_0.35Fe₂O₄)/(100 − x)% SiO₂ ferrimagnetic nanocomposites for low Ni–Zn ferrite concentration (x = 5, 10, 15, 20 and 30 mass percent) obtained by an improved modified sol–gel method. The obtained gels and nanocomposites have been characterized by fast Fourier transform-infrared (FT-IR) spectrometry, X-ray diffraction (XRD), transmission electron microscopy (TEM) and magnetic measurements (MM). The addition of a supplementary quantity of diol in the synthesis, corresponding to a molar ratio EG : TEOS = 1:1, and the control of the thermal treatment applied to the precursor xerogels tetraethylortosilicate (TEOS)–metal nitrates (MN)–ethylene glycol (EG) leads to fine (~2–9 nm), almost spherical Ni–Zn ferrite nanoparticles homogenously dispersed inside the amorphous SiO₂ matrix. TEM images reveal the fine nature and the narrow size distribution of the ferrite nanoparticles. Nanoparticles diameter increases with the ferrite concentration and with the annealing temperature. For all concentrations of ferrite in SiO₂ and all annealing temperature, we have obtained Ni_0.65Zn_0.35Fe₂O₄ ferrite as single phase (proven by XRD) in the amorphous silica matrix, only after a pre-treatment of synthesized gels, at 573 K, for 3 h. The magnetic behaviour of ferrite nanoparticles in quasi-static magnetic fields is very particular, depending on the annealing temperature and the ferrite content in silica matrix. We have obtained superparamagnetic behaviour for the nanocomposites, for a concentration of 30% ferrite in SiO₂ at high annealing temperature, of 1,273 K.     

Turn-on fluorescence in tetraphenylethylene-based metal-organic frameworks: an alternative to aggregation-induced emission

Coordinative immobilization of functionalized tetraphenylethylene within rigid porous metal-organic frameworks (MOFs) turns on fluorescence in the typically non-emissive tetraphenylethylene core. The matrix coordination-induced emission effect (MCIE) is complementary to aggregation-induced emission. Despite the large interchromophore distances imposed by coordination to metal ions, a carboxylate analogue of tetraphenylethylene anchored by Zn(2+) and Cd(2+) ions inside MOFs shows fluorescence lifetimes in line with those of close-packed molecular aggregates. Turn-on fluorescence by coordinative ligation in a porous matrix is a powerful approach that may lead to new materials made from chromophores with molecular rotors. The potential utility of MCIE toward building new sensing materials is demonstrated by tuning the fluorescence response of the porous MOFs as a function of adsorbed small analytes.     

Reductive electrosynthesis of crystalline metal-organic frameworks

Electroreduction of oxoanions affords hydroxide equivalents that induce selective deposition of crystalline metal-organic frameworks (MOFs) on conductive surfaces. The method is illustrated by cathodic electrodeposition of Zn(4)O(BDC)(3) (MOF-5; BDC = 1,4-benzenedicarboxylate), which is deposited at room temperature in only 15 min under cathodic potential. Although many crystalline phases are known in the Zn(2+)/BDC(2-) system, MOF-5 is the only observed crystalline MOF phase under these conditions. This fast and mild method of synthesizing MOFs is amenable to direct surface functionalization and could impact applications requiring conformal coatings of microporous MOFs, such as gas separation membranes and electrochemical sensors.     

History-dependent subdifferential inclusions and hemivariational inequalities in contact mechanics

We consider a class of subdifferential inclusions involving a history-dependent term for which we provide an existence and uniqueness result. The proof is based on arguments on pseudomonotone operators and fixed point. Then we specialize this result in the study of a class of history-dependent hemivariational inequalities. Such kind of problems arises in a large number of mathematical models which describe quasistatic processes of contact between a deformable body and an obstacle, the so-called foundation. To provide an example we consider a viscoelastic problem in which the frictional contact is modeled with subdifferential boundary conditions. We prove that this problem leads to a history-dependent hemivariational inequality in which the unknown is the velocity field. Then we apply our abstract result in order to prove the unique weak solvability of the corresponding contact problem.     

Corrigendum to “on the restricted partition function”

The Ramanujan Journal - This article is a corrigendum to our paper (Cimpoea? and Nicolae in Ramanujan J 473:565–588, 2018).     

Combinatorial proofs of two theorems related to the number of even parts in all partitions of n into distinct parts

The Ramanujan Journal - Recently, Andrews and Merca considered the number of even parts in all partitions of n into distinct parts and obtained new combinatorial interpretations for this number....     

Development of boundary element method to dynamic problems for porous media

Biot's consolidation theory is extended to a general class of viscoelastic bodies defined by Riemann-Stieltjes integral convolutions. From a new reciprocity theorem, proved for the governing equations including the inertia terms, the basic integral representations of the displacement fields and pore pressure are obtained. It is shown that, in the absence of internal inputs, a formulation of the dynamic problem in terms of the boundary unknown fields only is possible.