On the optimization of the initial boundary value problem for a conservation law

In the present note, the theory of shift differentiability for the Cauchy problem is extended to the case of an initial boundary value problem for a conservation law. This result allows to exhibit an Euler-Lagrange equation to be satisfied by the extrema of integral functionals defined on the solutions of initial boundary value problems of this kind.     

On the dehydration enthalpies of some beta-aluminas

The energetics of the dehydration reaction of single crystal (Na, Na 50%-Li, Li) and ceramic Na beta-aluminas have been studied.From the dependence of the dehydration enthalpy values on the water content it has been deduced that lattice water can be bound in two different ways i.e. by ion-dipole interactions with conducting cations and by hydrogen bonds with spinel block oxygens. As expected, the first one gives binding energies depending on the nature of the monovalent cation (H=84.5 and 59.4 kJ/mol H₂O for Li and Na beta-alumina respectively). In contrast, the enthalpy change associated with the second one is identical for the three beta-aluminas (H=15.1 kJ/mol H₂O). The ceramic Na beta-alumina undergoes a surface reaction too (with CO₂) leading to the formation of carbonates and bicarbonates.

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Zusammenfassung Die Energetik der Dehydratisierungsreaktion von Einkristallen von Na-, Na (50%)/Li- und Li- sowie von Na--Aluminiumoxid wurde untersucht. Aus der Abhängigkeit der Dehydratisierungsenthalpie vom Wassergehalt ergibt sich, daß Wasser auf zwei verschiedene Weisen gebunden ist, nämlich durch Ion-Dipol-Wechselwirkung mit leitenden Kationen und durch Wasserstoffbrückenbindungen mit Sauerstoffatomen. Wie zu erwarten war werden für die ersteren von der Natur der einwertigen Kationen abhängige Bindungsenergien (H=84.1 kJ/Mol H₂O bzw. 59.4 kJ/Mol H₂O für Li- bzw. Na--Alumina) erhalten. Die auf die zweite Wechselwirkung zurückzuführenden Enthalpieänderung ist dagegen für die drei-Aluminiumoxide identisch (H=15.1 kJ/Mol H₂O). Das keramische Na--Aluminiumoxid zeigt auch eine Oberflächenreaktion mit CO₂, die zur Bildung von Carbonaten und Bicarbonaten führt.

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(Na, Na 50%-Li, Li)- -- . , - . , Li — Na-- , , 84.5 59.4 / ₂. , - 15.1 / ₂. Na- , .

     

The inelastic hard dimer gas: a nonspherical model for granular matter

We study a two-dimensional gas of inelastic smooth hard dimers. Since the collisions between dimers are dissipative, being characterized by a coefficient of restitution alpha<1, and no external driving force is present, the energy of the system decreases in time and no stationary state is achieved. However, the resulting nonequilibrium state of the system displays several interesting properties in close analogy with systems of inelastic hard spheres, whose relaxational dynamics has been thoroughly explored. We generalize to inelastic systems a recently method introduced [G. Ciccotti and G. Kalibaeva, J. Stat. Phys. 115, 701 (2004)] to study the dynamics of rigid elastic bodies made up of different spheres held together by rigid bonds. Each dimer consists of two hard disks of diameter d, whose centers are separated by a fixed distance a. By describing the rigid bonds by means of holonomic constraints and deriving the appropriate collision rules between dimers, we reduce the dynamics to a set of equations which can be solved by means of event-driven simulation. After deriving the algorithm we study the decay of the total kinetic energy, and of the ratio between the rotational and the translational kinetic energy of inelastic dimers. We show numerically that the celebrated Haff's homogeneous cooling law t(-2), describing how the kinetic energy of an inelastic hard-sphere system with a constant coefficient of restitution decreases in time, holds even in the case of these nonspherical particles. We fully characterize this homogeneous decay process in terms of appropriate decay constants and confirm numerically the scaling behavior of the velocity distributions.     

NdFeO3 as a new electrocatalytic material for the electrochemical monitoring of dopamine

A new electrochemical sensor, based on NdFeO₃ nanoparticles as electrocatalytic material, was proposed here for the detection of dopamine (DA). NdFeO₃ nanoparticles were first synthesized by a simple thermal treatment method and subsequent annealing at high temperature (700 °C). The prepared electrocatalytic material has been characterized in detail by SEM-EDX, XRD, and Raman techniques. Characterization results display its sheet-like morphology, constituted by a porous network of very small orthorhombic NdFeO₃ nanoparticles. NdFeO₃ electrocatalytic material was then used to modify the working electrode of screen-printed carbon electrodes (SPCEs). Electrochemical tests demonstrated that NdFeO₃– modified screen-printed carbon electrode (NdFeO₃/SPCE) exhibited a remarkable enhancement of the dopamine electrooxidation, compared to the bare SPCE one. The analytical performance of the developed sensor has been evaluated for the detection of this analyte by means of the square-wave voltammetry (SWV) technique. The modified electrode showed two linear concentration ranges, from 0.5 to 100 μM and 150 to 400 μM, respectively, a limit of detection (LOD) of 0.27 μM (at S/N = 3), and good reproducibility, stability, and selectivity. Additionally, we also report an attempt made to propose the modified sensor for the simultaneous detection of dopamine and uric acid (UA). The procedure was also applied for the determination of dopamine in spiked real samples. So, this paper reports for the first time the use of a modified NdFeO₃ screen-printed electrode for developing an electrochemical sensor for the quantification of important biomolecules.

Graphical abstract

     

Synthesis,coordination to Rh(I), and hydroformylation catalysis of new beta-aminophosphines bearing a dangling nitrogen group: an unusual inversion of a Rh-coordinated P center

Variants of the beta-aminophosphine L(1) [Ph(2)PCH(2)CH(Ph)NHPh] containing additional nitrogen donor functions have been prepared. These functions are branched off the C atom adjacent to the P atom, or the P atom itself. Ligand [Ph(2)PCH(o-C(6)H(4)NMe(2))CH(Ph)NHPh] has been obtained as a mixture of two diastereomers L(3A) and L(3B) by lithiation of L(2) [Ph(2)PCH(2)(o-C(6)H(4)NMe(2))] with n-BuLi followed by PhCH=NPh addition and hydrolysis. The diastereomers have been separated by fractional crystallization from ethanol. Ligand Et(2)NCH(2)P(Ph)CH(2)CH(Ph)NHPh has been obtained as a mixture of two diastereomers L(5A) and L(5B)(starting with P-Ph reductive cleavage of L(1) by lithium and subsequent hydrolysis to give PhP(H)CH(2)CH(Ph)NHPh (mixture of two diastereomers L(4A) and L(4B)). The latter reacts with diethylamine and formaldehyde to afford the L(5) diastereomeric mixture. Complexes RhCl(CO)(L) (L = L(3A), 1(A); L(3B), 1(B); L(5A/B), 2(A/B)) were obtained by reaction of [RhCl(CO)(2)](2) and the appropriate ligand or ligand mixture. Complexes 1(A), 1(B), and 2(A) have been isolated in pure form and characterized by classical techniques and by single-crystal X-ray diffraction. All structures exhibit a bidentate kappa-P,kappa-N(NHPh) mode similar to the complex containing L(1). While complexes 1(A) or 1(B) are stable in CDCl(3) solution, complex 2(A) slowly converts to its diastereomer 2(B). This unexpected epimerization appears to take place by inversion at the Rh-coordinated P center, an apparently unprecedented phenomenon. A mechanism based on a reversible P-C bond oxidative addition is proposed. The influence of the pendant nitrogen function of the diaminophosphines L(3A) and L(5A/B) on the rhodium catalytic activity in styrene hydroformylation has been examined and compared to that of the aminophosphines L(1) or L(2). The observed trends are related to the basicity of the dangling amine function and to its proximity to the metal center.     

Spin forbidden chemical reactions of transition metal compounds. New ideas and new computational challenges

Many reactions of transition metal compounds involve a change in spin. These reactions may proceed faster, slower--or at the same rate as--otherwise equivalent processes in which spin is conserved. For example, ligand substitution in [CpMo(Cl)2(PR3)2] is faster than expected, whereas addition of dinitrogen to [Cp*Mo(Cl)(PMe3)2] is slow. Spin-forbidden oxidative addition of ethylene to [Cp*Ir(PMe3)] occurs competitively with ligand association. To explain these observations, we discuss the shape of the different potential energy surfaces (PESs) involved, and the energy of the minimum energy crossing points (MECPs) between them. This computational approach is of great help in understanding the mechanisms of spin-forbidden reactions, provided that accurate calculations can be used to predict the relevant PESs. Density functional theory, especially using gradient-corrected and hybrid functionals, performs reasonably well for the difficult problem of predicting the energy splitting between different spin states of transition metal complexes, although careful calibration is needed.     

Quantitative analysis of relative protein contents by Western blotting: comparison of three members of the dystrophin-glycoprotein complex in slow and fast rat skeletal muscle

We have developed a method for accurate quantitative analysis and statistical comparison of the relative contents of the dystrophin-glycoprotein complex (DGC) in skeletal muscle. This method was applied to compare DGC contents in slow (soleus) and in fast (extensor digitorum longus, EDL) rat skeletal muscles. The quantitative analysis combines a modified bicinchoninic acid (BCA) assay with Western blotting and enhanced chemiluminescence (ECL). This combination allows the use of high levels of detergents and reducing reagents essential for extracting DGC. In addition, the evaluation of the total amount of proteins in each sample makes it possible to have a reference and to accurately compare relative protein levels without using a specific standard. With a large gradient gel, we could concomitantly compare two groups (n = 9) and quantify all protein contents differing highly in their molecular masses (from 35 kDa to 427 kDa). Each experiment was triplicated and normalized; the two muscles were compared using the Mann-Whitney test (P<0.001) to establish their protein content. The DGC relative levels for the slow muscle soleus and the fast muscle EDL differed significantly: dystrophin, beta-dystroglycan, and gamma-sarcoglycan levels were 130%, 110% and 120% higher in the soleus, respectively. The differences observed in the expression level of cytoskeletal associated protein (dystrophin) and transmembranous anchorage components may correspond to a physiological response of the muscle fibers to duration, magnitude, and frequency of the imposed mechanical loading.     

Synthesis of fused purinoquinazolines. Three new heterocyclic ring systems

The Ullmann reaction of 8-aminotheophylline or 8-aminocaffeine with 2-chlorobenzoic acid and of 8-bromotheophylline with ethyl-2-aminobenzoate afforded derivatives of three new heterocyclic systems: purino[7,8-α]quinazoline-5,9,11(6H,8H,10H)-trione, purino[8,9-b]quinazoline-2,4,11(1H,3H,5H)-trione and purino[8,7-b]quinazoline-2,4,6(1H,3H,11H)-trione, respectively.     

Two families of mixed finite elements for second order elliptic problems

Summary Two families of mixed finite elements, one based on triangles and the other on rectangles, are introduced as alternatives to the usual Raviart-Thomas-Nedelec spaces. Error estimates inL ² () andH ^–5 () are derived for these elements. A hybrid version of the mixed method is also considered, and some superconvergence phenomena are discussed.