Wodzicki residue for operators on manifolds with cylindrical ends

We define the Wodzicki Residue TR(A) for A belonging to a space of operators with double order, denoted \({L^{m_1,m_2}_{\rm cl}}\). Such operators are globally defined initially on \({\mathbb{R}^n}\) and then, more generally, on a class of non-compact manifolds, namely, the manifolds with cylindrical ends. The definition is based on the analysis of the associate zeta function ζ(A, z). Using this approach, under suitable ellipticity assumptions, we also compute a two terms leading part of the Weyl formula for a positive selfadjoint operator \({A\in L^{m_1,m_2}_{\rm cl}}\) in the case m ₁ = m ₂.     

Integrated NMR and computational study of push-pull NLO probes: interplay of solvent and structural effects

In this study we combined QM calculations and NMR measurements to understand at a detailed level the complex interplay of structural/electronic properties with the effects of the solvent in the NLO activity of push-pull systems, quantified in terms of variations of the static hyperpolarizability. Different parameters (bond lengths and bond length alternation, vibrational frequencies, electronic charge distribution) are introduced and tested to rationalize both the solvent sensitivity of three molecular systems (namely, p-nitroaniline, ethyl 4-ammino benzoate, and 5-nitro-1H-indole) and the differences among them. This analysis has finally allowed us to establish a clear correlation between the charge transfer behavior of the systems, their NLO properties, and NMR parameters also validating simplified but effective chemical analyses based on resonance limit forms.     

Nitridosilicates and oxonitridosilicates: from ceramic materials to structural and functional diversity

Silicates are one of the most important classes of compounds on this planet, and more than 1000 silicates have been identified in the mineral kingdom. Additionally, several hundreds of artificial silicates have been synthesized. The substitution of oxygen by nitrogen leads to the structurally diverse and manifold class of nitridosilicates. Silicon nitride, one of the most important non-oxidic ceramic materials, is the binary parent compound of nitridosilicates, and it symbolizes the inherent material properties of these refractory compounds. However, prior to the last decades, a broad systematic investigation of nitridosilicates had not been accomplished. In the meantime, these and related compounds have reached a remarkable level of industrial application. This review illustrates recent progress in synthesis and structure-property relationships and also applications of nitridosilicates, oxonitridosilicates, and related SiAlONs.     

A molecular dynamics study of structure, stability and fragmentation patterns of sodium bis(2-ethylhexyl)sulfosuccinate positively charged aggregates in vacuo

Positively charged supramolecular aggregates formed in vacuo by n AOTNa (sodium bis(2-ethylhexyl)sulfosuccinate) molecules and n(c) additional sodium ions, i.e. [AOT(n)Na(n+n(c))](n(c)), have been investigated by molecular dynamics (MD) simulations for n = 1-20 and n(c) = 0-5. Statistical analysis of physical quantities like gyration radii, atomic B-factors and moment of inertia tensors provides detailed information on their structural and dynamical properties. Even for n(c) = 5, all stable aggregates show a reverse micelle-like structure with an internal solid-like core including sodium counterions and surfactant polar heads surrounded by an external layer consisting of the surfactant alkyl chains. Moreover, the aggregate shapes may be approximated by rather flat and elongated ellipsoids whose longer axis increases with n and n(c). The fragmentation patterns of a number of these aggregates have also been examined and have been found to markedly depend on the aggregate charge state. In one particular case, for which experimental findings are available in the literature, a good agreement is found with the present fragmentation data.     

Graph problems arising from parameter identification of discrete dynamical systems

This paper focuses on combinatorial feasibility and optimization problems that arise in the context of parameter identification of discrete dynamical systems. Given a candidate parametric model for a physical system and a set of experimental observations, the objective of parameter identification is to provide estimates of the parameter values for which the model can reproduce the experiments. To this end, we define a finite graph corresponding to the model, to each arc of which a set of parameters is associated. Paths in this graph are regarded as feasible only if the sets of parameters corresponding to the arcs of the path have nonempty intersection. We study feasibility and optimization problems on such feasible paths, focusing on computational complexity. We show that, under certain restrictions on the sets of parameters, some of the problems become tractable, whereas others are NP-hard. In a similar vein, we define and study some graph problems for experimental design, whose goal is to support the scientist in optimally designing new experiments.     

Log‐symmetric regression models: information criteria and application to movie business and industry data with economic implications

This work deals with log‐symmetric regression models, which are particularly useful when the response variable is continuous, strictly positive, and following an asymmetric distribution, with the possibility of modeling atypical observations by means of robust estimation. In these regression models, the distribution of the random errors is a member of the log‐symmetric family, which is composed by the log‐contaminated‐normal, log‐hyperbolic, log‐normal, log‐power‐exponential, log‐slash and log‐Student‐t distributions, among others. One way to select the best family member in log‐symmetric regression models is using information criteria. In this paper, we formulate log‐symmetric regression models and conduct a Monte Carlo simulation study to investigate the accuracy of popular information criteria, as Akaike, Bayesian, and Hannan‐Quinn, and their respective corrected versions to choose adequate log‐symmetric regressions models. As a business application, a movie data set assembled by authors is analyzed to compare and obtain the best possible log‐symmetric regression model for box offices. The results provide relevant information for model selection criteria in log‐symmetric regressions and for the movie industry. Economic implications of our study are discussed after the numerical illustrations.     

Reaction of CO2 with a Vanadium(II) Aryl Oxide: Synergistic Activation of CO2/Oxo Groups towards H‐Atom Radical Abstraction

Treatment of divalent (ONNO)V(TMEDA) ( 1 ; ONNO=[2,4‐Me₂‐2‐(OH)C₆H₂CH₂]₂N(CH₂)₂NMe₂) with CO₂ afforded [(ONNO)V]₂(μ‐OH)(μ‐formate) ( 2 ). Whereas the bridging hydroxo and formate groups both originated from CO₂, the H atoms present on the two residues were obtained through H‐atom radical abstraction from the solvent. DFT calculations revealed an initially linear CO₂ bonding mode, followed by deoxygenation, and highlighted a synergistic effect between the so‐formed oxo group and an additional bridging CO₂ residue in promoting radical behavior.