The one-dimensional Boltzmann gas: The ergodic hypothesis and the phase portrait of small systems

The concept of ergodicity and its application to microcanonical systems composed of few particles of different mases are clarified. The distribution functions in position and velocity are theoretically derived and numerically verified. Moreover, we deal with a one-dimensional Boltzmann gas where the order relation (connected to the one dimensionality) brings constraints depending on the two classes of boundary conditions enforced (reflecting, periodic). The numerical simulations on a one-dimensional Boltzmann gas act as real experiments and allow us to play on the constraints to which the system is subjected.     

Vanadia-titania catalyst: II. Qualitative kinetic behavior

An improvement of catalytic properties has been observed at low vanadium loading in liquid-phase cumene oxidation, which is due to modification of the chemical nature of the surface as a result of active phase-support interaction.     

Comparison of the effectiveness of recent extraction procedures for antibiotic residues in bovine muscle tissues

Acetonitrile extraction followed by primary-secondary amine dispersive SPE cleanup QuEChERS (quick, easy, cheap, effective, rugged, and safe), was compared to pressurized liquid extraction (PLE) using water at 70 degrees C for 10 min at 1500 psi for the determination of 16 veterinary drugs in bovine muscle tissues by LC/MS/MS. PLE was significantly more effective for the extraction of veterinary drugs (ranging from 69 to 103% with RSD < or = 18%) than QuEChERS (ranging from 19 to 89% with RSD < or = 19%). Linearity of the calibration curves was obtained over the range considered from 10 microg/kg or LOQ to 1000, microg/kg) with r2 > or = 0.99 for all the analytes by both methods. Although an internal standard was used, matrix effects were corrected using matrix- matched standards. LODs were from 5 to 30 microg/kg for PLE and from 10 to 100 microg/kg for QuEChERS. To establish and assess the most efficient conditions for each extraction method, statistical parametric and nonparametric tests were used. PLE with water almost eliminates the use or generation of hazardous wastes. The two methods were applied successfully in a routine analysis during surveys in 2008.     

Manganese(II) complexes of scorpiand-like azamacrocycles as MnSOD mimics

Mn(II) complexes of scorpiand-type azamacrocycles constituted by a tretrazapyridinophane core appended with an ethylamino tail including 2- or 4-quinoline functionalities show very appealing in vitro SOD activity. The observed behaviour is related to structural and electrochemical parameters.     

A new type of antiferrodistortive structure in a double perovskite with Pb

We have found a new structural transition in Pb(2)MnReO(6) at 410 K. Above this temperature, Pb(2)MnReO(6) is cubic with disordered and dynamic atomic displacements manifested in the large thermal parameters of Pb and O atoms. Below 410 K, the antiferrodistortive shift of 2/3 of Pb(2+) cations away from the high-symmetry cubic site produces a new type of monoclinic cell. The unit cell expands at the transition and the heat capacity shows a peak with thermal hysteresis. These features agree with a first order transition. The entropy content of the transition is quite low indicating that the structural disorder has not been completely removed in the low temperature phase. The monoclinic phase of Pb(2)MnReO(6) shows thermally activated conductivity which does not vary when an external magnetic field is applied. A change in the slope of the resistivity curve, observed at the structural phase transition temperature, is related to a slight difference in the activation energy between both phases. It suggests that the condensation of the distortions likely affects the conduction mechanism. The isothermal magnetization measurements reveal the presence of ferromagnetic contributions below 85 K. The ac magnetic susceptibility shows a dynamic peak at 50 K and, in addition, zero-field-cooled and field-cooled magnetization curves diverge strongly below 80 K. These features might be signature of magnetic inhomogeneity. Magnetic loops, obtained at 5 K, do not show saturation in fields up to 9 T. Furthermore, the measured coercivity increases sharply at low temperature indicating an abrupt change in the magnetic anisotropy. We show that all these magnetic properties point out to a ferrimagnetic ordering of Mn and Re atoms in an intermediate valence state.     

Schatten-Herz Operators,Berezin Transform and Mixed Norm Spaces

For p, q > 0 we study operators T on the Bergman space \({A_{2}(\mathbb{D)}}\) in the disk such that \({\left(\sum_{j}\Vert T\Delta_{j}\Vert_{p}^{q}\right)^{1/q}<\infty,}\) where the norms \({\Vert\cdot\Vert_{p}}\) are in the Schatten class S _p (A ₂), the projection \({\Delta_{j}f=\sum_{n\in I_{j}}a_{n}z^{n}}\) for \({f(z)=\sum_{n=0}^{\infty}a_{n}z^{n}}\) and \({I_{j}=[2^{j}-1,2^{j+1} )\cap(\mathbb{N}\cup\{0\})}\) for \({j\in\mathbb{N}\cup\{0\}.}\) We consider the relation of this property with mixed norms of the Berezin transform of T and of the related function \({f_{T}(z)={\Vert}T(k_{z})\Vert}\) where k _z is the normalized Bergman kernel. These classes of operators denoted by S(p, q) are closely related when assumed to be positive with other sets of operators, like the class of positive operators on A ₂ for which \({\left(\sum_{j\geq0}(\sum_{n\in I_{j}}|\left\langle T^pe_{n},e_{n}\right\rangle |)^{q/p}\right)^{1/q}<\infty}\) , where \({\{e_{n}\}_{n\geq0}}\) is the canonical basis of A ₂; also we study the relation of Toeplitz operators in S(p, q) with the Schatten-Herz classes, where the decomposition is through dyadic annuli of the domain \({\mathbb{D}}\) .     

It's in the Fine Print: Erasable Three‐Dimensional Laser‐Printed Micro‐ and Nanostructures

3D printing, on all scales, is currently a vibrant topic in scientific and industrial research as it has enormous potential to radically change manufacturing. Owing to the inherent nature of the manufacturing process, 3D printed structures may require additional material to structurally support complex features. Such support material must be removed after printing—sometimes termed subtractive manufacturing—without adversely affecting the remaining structure. An elegant solution is the use of photoresists containing labile bonds that allow for controlled cleavage with specific triggers. Herein, we explore state‐of‐the‐art cleavable photoresists for 3D direct laser writing, as well as their potential to combine additive and subtractive manufacturing in a hybrid technology. We discuss photoresist design, feature resolution, cleavage properties, and current limitations of selected examples. Furthermore, we share our perspective on possible labile bonds, and their corresponding cleavage trigger, which we believe will have a critical impact on future applications and expand the toolbox of available cleavable photoresists.     

Fourier analysis with respect to bilinear maps

Several results about convolution and about Fourier coefficients for X-valued functions defined on t he torus satisfying the condition sup ｜｜y｜｜=1∫-π^π｜｜ B （f （e^iθ）, y）｜｜dθ/2π〈 ∞ for a bounded bilinear map B ： X × Y → Z are presented and some applications are given.     

Discretization and Transference of Bisublinear Maximal Operators

We develop a general condition for automatically discretizing strong type bisublinear maximal estimates that arise in the context of the real line. In particular, this method applies directly to Michael Lacey’s strong type boundedness results for the bisublinear maximal Hilbert transform and for the bisublinear Hardy-Littlewood maximal operator, furnishing the counterpart of each of these two results (without changes to the range of exponents) for the sequence spaces We then take up some transference applications of discretized maximal bisublinear operators to maximal estimates and almost everywhere convergence in Lebesgue spaces of abstract measures. We also broaden the scope of such applications, which are based on transference from by developing general methods for transplanting bisublinear maximal estimates from arbitrary locally compact abelian groups.