Character degree graphs that are complete graphs

Let be a finite group, and write for the set of degrees of irreducible characters of . We define to be the graph whose vertex set is , and there is an edge between and if . We prove that if is a complete graph, then is a solvable group.

     

Mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with non-smooth coefficients

We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with low regularity of the coefficients. We then use them to prove the parabolic strong maximum principle and the parabolic Harnack inequality. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C¹-boundary, the other stated for sets with finite perimeter.     

Similarity analysis and exact solutions for a general discrete two-velocity model of Boltzmann equation

Summary This paper concerns with the similarity analysis for a general discrete two-velocity model of the Boltzmann equation introduced by Illner [12]. We find the general groups of invariance and we get some exact solutions, recovering general results which contain either solutions extensively described in the literature or undiscovered ones.

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Sommario In questa nota si applica l'analisi dei gruppi infinitesimi di trasformazione ad un modello generale discreto a due velocità dell'equazione di Boltzmann introdotto da Illner [12]. Si trovano i più generali gruppi di invarianza e si ottengono alcune soluzioni esatte, ritrovando risultati generali che contengono sia soluzioni ampiamente descritte in letteratura che nuove soluzioni.

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Work supported by the C.N.R. through the G.N.F.M.     

Similar Structural Dynamics for the Degradation of CH3NH3PbI3 in Air and in Vacuum

We investigate the degradation path of MAPbI₃ (MA=methylammonium) films over flat TiO₂ substrates at room temperature by means of X‐ray diffraction, spectroscopic ellipsometry, X‐ray photoelectron spectroscopy, and high‐resolution transmission electron microscopy. The degradation dynamics is found to be similar in air and under vacuum conditions, which leads to the conclusion that the occurrence of intrinsic thermodynamic mechanisms is not necessarily linked to humidity. The process has an early stage, which drives the starting tetragonal lattice in the direction of a cubic atomic arrangement. This early stage is followed by a phase change towards PbI₂. We describe how this degradation product is structurally coupled with the original MAPbI₃ lattice through the orientation of its constituent PbI₆ octahedra. Our results suggest a slight octahedral rearrangement after volatilization of HI+CH₃NH₂ or MAI, with a relatively low energy cost. Our experiments also clarify why reducing the interfaces and internal defects in the perovskite lattice enhances the stability of the material.     

Potential of prodendronic polyamines with modulated segmental charge density as novel coating for fast and efficient analysis of peptides and basic proteins by CE and CE‐MS

In this work, the suitability of a new polymer family has been investigated as capillary coatings for the analysis of peptides and basic proteins by CE. This polymer family has been designed to minimize or completely prevent protein–capillary wall interactions and to modify the EOF. These coating materials are linear polymeric chains bearing as side cationizable moiety a dentronic triamine derived from N,N,N’,N’‐tetraethyldiethylenetriamine (TEDETA), which is linked to the backbone through a spacer (unit labeled as TEDETAMA). Four different polymers have been prepared and evaluated: a homopolymer which comprised only of those cationizable repetitive units of TEDETAMA, and three copolymers that randomly incorporate TEDETAMA together with neutral hydrosoluble units of N‐(2‐hydroxypropyl) methacrylamide (HPMA) at different molar percentages (25:75, 50:50 and 75:25). It has been demonstrated that the composition of the copolymers influences the EOF and therefore the separation of the investigated biopolymers. Among the novel polymers studied, poly‐(TEDETAMA‐co‐HPMA) 50:50 copolymer was successfully applied as coating material of the inner capillary surface in CE‐UV and CE‐MS, providing EOF reversing together with fast and efficient baseline separation of peptides and basic proteins. Finally, the feasibility of the polymer‐coated capillary was shown through the analysis of lysozyme in a cheese sample.     

Ni‐Catalyzed Asymmetric Cycloisomerization of Dienes by Using TADDOL Phosphoramidites

A library of α,α,α,α‐tetraaryl‐1,3‐dioxolane‐4,5‐dimethanol (TADDOL)‐based phosphoramidites has been synthesized and applied in the Ni‐catalyzed cycloisomerization of different dienes. Through the systematic variation of the three structural motifs of the lead structure, that is, the amine moiety, the protecting group, and the aryl substituents, the ligand features could be optimized for the asymmetric cycloisomerization of the model substrate diethyl diallylmalonate. The substrate scope of the new catalytic system was extended to other diallylic substrates, including unsymmetrical dienes. Overall remarkably high activities of up to approximately 13 500 h^?1, very high selectivities toward five‐membered exo‐methylenecyclopentanes, and enantioselectivities of up to 92 % ee have been achieved.     

Wave features of a hyperbolic model for the within-season dynamics of insect pathogens

Hyperbolic models are suitable for describing invasive phenomena with a well-defined boundary. In fact, for a class of hyperbolic reaction–diffusion models derived in the context of extended thermodynamics (ET), the non-existence of smooth travelling waves has been proved under suitable assumptions on the wave speed. In this paper a hyperbolic model for the within-season dynamics of insect pathogens is derived and smooth and discontinuous travelling wave solutions are investigated. Validation of the model in point is also accomplished by searching for numerical solutions of the system of PDEs.     

Determination of the elongational viscosity of polymer melts by melt spinning experiments. A comparison with different experimental techniques

In this work, melt spinning experiments were tentatively used for the determination of the elongational viscosity of polymer melts at different levels of tensile strain and strain rate. The materials examined were two high-density polyethylene grades for blow moulding with similar number-average molecular mass but different polydispersity index. The data from melt spinning tests were compared with transient extensional viscosity data obtained by uniform isothermal tensile tests, performed by means of an extensional rheometer, as well as with those produced by converging flow tests (Cogswell model). The results showed that for high strain and strain rate levels, the melt spinning experiments provide elongational viscosity data quite close to the transient extensional viscosity values obtained from the tensile tests.     

Mechanism insights into an unexpected isomerisation reaction observed during conversion of N-benzyl piperazinones to corresponding N-benzyl thio-piperazinones

An interesting and surprising rearrangement was observed during the reaction of 4-N-benzyl piperazinone derivatives with Lawesson’s reagent as a thionating agent. Investigation into the possible mechanism responsible for these results is reported herein.     

Fast analysis of amino acids in wine by capillary electrophoresis with laser-induced fluorescence detection

A fast analytical method has been developed for the determination of nine amino acids, together with serotonin, in wine samples of different origin and vintage. The method is based on capillary electrophoresis coupled to laser-induced fluorescence detection. Separation was obtained by using a fused-silica capillary (75?μm id, 74.0?cm total length, 60.0?cm length to detector) and a background electrolyte composed of carbonate buffer (20?mM, pH 9.2), applying a 20?kV voltage. Direct hydrodynamic injection of wine samples was made after an original microwave-assisted derivatisation step with 5-(4,6-dichlorotriazinyl)aminofluorescein. Fluorescence was induced by an Ar-Ion laser, exciting at 488?nm. Good linearity (r(2) >0.9990) was obtained for all considered analytes and sensitivity was also good, with limits of detection in the 7-50?ng/mL range. The method was successfully applied for the analysis of commercial Italian wines and thus seems to be suitable for the determination of the relevant amino acids and serotonin, providing good results in terms of accuracy and precision, together with the advantage of a very fast, microwave-assisted derivatisation procedure. Future applications of the method are planned to check for wine adulterations and commercial frauds.