Local Approximation by Generalized Baskakov–Durrmeyer Operators

The paper deals with general Baskakov–Durrmeyer operators containing several previous definitions as special cases. The main results include the local rate of convergence, which is proved based on a representation of the kernel functions in terms of Jacobi polynomials and the complete asymptotic expansion for the sequence of these operators. In obtaining the expansion for simultaneous approximation, a key step is the use of a combinatorical identity for derivatives with weights.     

Low temperature synthesis of Co<Subscript>2</Subscript>SiO<Subscript>4</Subscript>/SiO<Subscript>2</Subscript> nanocomposite using a modified sol–gel method

The paper presents a study on the preparation of Co₂SiO₄/SiO₂ nanocomposites by a new modified sol–gel method. We have prepared gels starting from tetraethylorthosilicate (Si(OC₂H₅)₄), cobalt nitrate Co(NO₃)₂·6H₂O and some diols: ethylene glycol (C₂H₆O₂), 1,2propanediol (C₃H₈O₂) and 1,3propanediol (C₃H₈O₂), for a final composition: 30% CoO/70% SiO₂. During the heating of the gels at 140 °C, a redox reaction takes place between NO₃ ⁻ ions and diol with formation of some carboxylate anions. These carboxylate anions react with the Co(II) ions to form coordination compounds embedded in silica matrix, as evidenced by FT-IR spectrometry and thermal analysis. These Co(II) coordinative compounds thermally decompose in the range 250–300 °C to the corresponding oxides: CoO and/or Co₃O₄ inside the matrices pores. When CoO results, it reacts with SiO₂ at low temperature leading to Co₂SiO₄, which crystallizes at 700 °C. XRD patterns of the samples annealed at temperatures lower than 700 °C were characteristic to amorphous phases. The samples annealed at temperatures ≥700 °C, contain Co₂SiO₄ (olivine) as unique crystalline phase inside the amorphous silica matrix, according to XRD patterns. As evidenced by TEM images, Co₂SiO₄ nanoparticles are homogenously dispersed inside the silica matrix.     

ESR study of gamma irradiated 2-methyl nylon3

Gamma radiation-induced radicals of 2-methyl nylon3 (2mN3) have been investigated by electron spin resonance spectrometry. The type of radicals generated, conversion into other radicalic species and their room temperature stability were evaluated. Two types of radicals have been detected. Two different formation mechanisms have been proposed for each radical. As suggested in literature for commercial polyamides, in our system we also observed two different radicals (R1 and R2). Among these radicals, R1 is expected to convert to R2, which is a chemically favorable process.     

Zymographic assay of plant diamine oxidase on entrapped peroxidase polyacrylamide gel electrophoresis. A study of stability to proteolysis

A zymographic assay of diamine oxidase (DAO, histaminase, EC 1.4.3.6), based on a coupled peroxidase reaction, and its behavior at proteolysis in simulated gastric and intestinal conditions, are described. The DAO activity from a vegetal extract of Lathyrus sativus seedlings was directly determined on sodium dodecyl sulfate polyacrylamide electrophoretic gels containing entrapped horseradish peroxidase, with putrescine as substrate of histaminase and ortho-phenylenediamine as co-substrate of peroxidase. The accumulation of azo-aniline, as peroxidase-catalyzed oxidation product, led to well-defined yellow-brown bands on gels, with intensities corresponding to the enzymatic activity of DAO. After image analysis of gels, a linear dependency of DAO content (Coomassie-stained protein bands) and of its enzymatic activity (zymographic bands) with the concentration of the vegetal extract was obtained. In simulated gastric conditions (pH 1.2, 37 °C), the DAO from the vegetal extract lost its enzymatic activity before 15 min of incubation, either in the presence or absence of pepsin. The protein pattern (Coomassie-stained) revealed that the DAO content from the vegetal extract was kept almost constant in the simulated intestinal fluid (containing pancreatin or not), with a slight diminution in the presence of pancreatic proteases. After 10 h of incubation at 37 °C, the DAO enzymatic activity from the vegetal extract was 44.7% in media without pancreatin and 13.6% in the presence of pancreatin, whereas the purified DAO retained only 4.65% of its initial enzymatic activity in the presence of pancreatin.      

Electron Transfer Processes at Aryl‐Modified Glassy Carbon Electrode

The effect of a layer of electrochemically grafted 4‐diazo‐N,N‐diethylaniline (DEA) groups on the electron transfer kinetics of redox systems, displaying fast and slow heterogeneous electron transfer rate constants at edge and basal planes of carbon, was investigated. The properties of the modified electrode were characterized by cyclic voltammetry using four different inorganic redox systems (Fe(CN) , Co(phen) , Ru(NH₃) , and IrCl in acidic, neutral, and basic media. Two distinct blocking behaviors and electrostatic effects were observed. More precisely, a strong blocking effect of the grafted layer on Fe(CN) and Co(phen) was found, whereas Ru(NH₃) and IrCl showed to be rather unaffected by the presence of the DEA grafted layer.     

Preparation of FexOy/SiO2 nanocomposites by thermal decomposition of some carboxylate precursors formed inside the silica matrix

In this paper we present a study regarding the obtaining of iron oxides embedded in silica matrix, using a modified sol-gel method. This method consists in the formation, inside the silica matrix, of some Fe(III)-carboxylate compounds, resulted in the redox reaction between Fe(NO₃)₃ and diol. We have synthesized four gels, starting from tetra-ethyl orthosilicate, Fe(NO₃)₃·9H₂O and different diols: ethylene glycol, 1,2-propanediol, 1,3-propanediol and 1,4-butanediol, for a final composition 50% Fe₂O₃/50% SiO₂. The obtained gels have been thermally treated at 130°C, when the redox reaction Fe(NO₃)₃-diol took place with formation of the precursors in the xerogels pores. The thermal decomposition of all four precursors took place up to 300°C.     

Last multipliers on Lie algebroids

In this paper we extend the theory of last multipliers as solutions of the Liouville’s transport equation to Lie algebroids with their top exterior power as trivial line bundle (previously developed for vector fields and multivectors). We define the notion of exact section and the Liouville equation on Lie algebroids. The aim of the present work is to develop the theory of this extension from the tangent bundle algebroid to a general Lie algebroid (e.g. the set of sections with a prescribed last multiplier is still a Gerstenhaber subalgebra). We present some characterizations of this extension in terms of Witten and Marsden differentials.     

Variational analysis of fully coupled electro‐elastic frictional contact problems

We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a foundation. The material behavior is described with a nonlinear electro‐elastic constitutive law. The novelty of the model consists in the fact that the foundation is assumed to be electrically conductive and both the frictional contact and the conductivity on the contact surface are described with subdifferential boundary conditions which involve a fully coupling between the mechanical and electrical variables. We derive a variational formulation of the problem which is in the form of a system coupling two hemivariational inequalities for the displacement and the electric potential fields, respectively. Then we prove the existence of a weak solution to the model and, under additional assumptions, its uniqueness. The proofs are based on recent results for inclusions of subdifferential type in Sobolev spaces (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bisected theta series,least r-gaps in partitions,and polygonal numbers

The Ramanujan Journal - The least r-gap, $$g_r(\lambda )$$, of a partition $$\lambda $$ is the smallest positive integer that does not appear at least r times as a part of $$\lambda $$. In this...     

Optimal control of a two-dimensional contact problem

We consider a frictionless contact problem with unilateral constraints for a 2D bar. We describe the problem, then we derive its weak formulation, which is in the form of an elliptic variational inequality of the first kind. Next, we establish the existence of a unique weak solution to the problem and prove its continuous dependence with respect to the applied tractions and constraints. We proceed with the study of an associated control problem for which we prove the existence of an optimal pair. Finally, we consider a perturbed optimal control problem for which we prove a convergence result.