Allyl-Aluminium Compounds

The preparation of aluminium derivatives containing allyl or methallyl groups is reported. Their reactivity and physical properties are discussed.     

Determination of amphetamines in human urine by liquid chromatography with fluorimetric detection using a solid-phase extraction procedure

A precise and feasible HPLC method has been developed for the analysis of amphetamine (AMPH), methamphetamine (MAMPH) and methylenedioxymethamphetamine (MDMA, ecstasy) in human urine. A chromatographic run on a C8 Genesis (150 mm x 4.6 mm, 5 microm) column maintained at 30 degrees C lasts about 17 min, using a mobile phase composed of ACN (12%) and a pH 2.5 phosphate buffer (88%) containing 0.3% triethylamine. Mirtazapine was used as the internal standard. Good linearity was found in the 100-2000 ng/mL concentration range for AMPH and MAMPH and in the 12-2000 ng/mL concentration range for MDMA. The pretreatment of urine samples was carried out by means of a careful SPE procedure on C2 cartridges. The extraction yields were very satisfactory for all analytes, with average values greater than 97%. The leading conditions allowed the determination of AMPH, MAMPH and MDMA with satisfactory precision and accuracy. The method has been successfully applied to the determination of the analytes in urine of AMPH users.     

Bose–Einstein condensation in satisfiability problems

This paper is concerned with the complex behavior arising in satisfiability problems. We present a new statistical physics-based characterization of the satisfiability problem. Specifically, we design an algorithm that is able to produce graphs starting from a k-SAT instance, in order to analyze them and show whether a Bose–Einstein condensation occurs. We observe that, analogously to complex networks, the networks of k-SAT instances follow Bose statistics and can undergo Bose–Einstein condensation. In particular, k-SAT instances move from a fit-get-rich network to a winner-takes-all network as the ratio of clauses to variables decreases, and the phase transition of k-SAT approximates the critical temperature for the Bose–Einstein condensation. Finally, we employ the fitness-based classification to enhance SAT solvers (e.g., ChainSAT) and obtain the consistently highest performing SAT solver for CNF formulas, and therefore a new class of efficient hardware and software verification tools.     

On the Numerical Solution to a Nonlinear Wave Equation Associated with the First Painlev′e Equation: an Operator-Splitting Approach

The main goal of this article is to discuss the numerical solution to a nonlinear wave equation associated with the first of the celebrated Painlevé transcendent ordinary differential equations. In order to solve numerically the above equation, whose solutions blow up in finite time, the authors advocate a numerical methodology based on the Strang’s symmetrized operator-splitting scheme. With this approach, one can decouple nonlinearity and differential operators, leading to the alternate solution at every time step of the equation as follows: (i) The first Painlevé ordinary differential equation, (ii) a linear wave equation with a constant coefficient. Assuming that the space dimension is two, the authors consider a fully discrete variant of the above scheme, where the space-time discretization of the linear wave equation sub-steps is achieved via a Galerkin/finite element space approximation combined with a second order accurate centered time discretization scheme. To handle the nonlinear sub-steps, a second order accurate centered explicit time discretization scheme with adaptively variable time step is used, in order to follow accurately the fast dynamic of the solution before it blows up. The results of numerical experiments are presented for different coefficients and boundary conditions. They show that the above methodology is robust and describes fairly accurately the evolution of a rather “violent” phenomenon.     

Artinian Level Algebras of Low Socle Degree

In this article we study Hilbert functions and isomorphism classes of Artinian level local algebras via Macaulay's inverse system. Upper and lower bounds concerning numerical functions admissible for level algebras of fixed type and socle degree are known. For each value in this range we exhibit a level local algebra with that Hilbert function, provided that the socle degree is at most three. Furthermore, we prove that level local algebras of socle degree three and maximal Hilbert function are graded. In the graded case, the extremal strata have been parametrized by Cho and Iarrobino.     

Coexisting stochastic and coherence resonance in a mean-field dynamo model for Earth’s magnetic field reversals

Using a spherically symmetric mean-field α²-dynamomodel for Earth’s magnetic field reversals, we show thecoexistence of the noise-induced phenomena coherence resonance and stochastic resonance. Stochastic resonance was recentlyinvoked to explain the 100 kyr periodicity in the distribution ofresidence times between reversals.The comparison of the resulting residence time distribution withthe paleomagnetic one allows for some estimate ofthe effective diffusion time of the Earth’s core which may be100 kyr or slightly below rather than200 kyr as it would result from the molecular resistivity.     

Unravelling the Phytochemical Composition and the Pharmacological Properties of an Optimized Extract from the Fruit from Prunus mahaleb L.: From Traditional Liqueur Market to the Pharmacy Shelf

Prunus mahaleb L. fruit has long been used in the production of traditional liqueurs. The fruit also displayed scavenging and reducing activity, in vitro. The present study focused on unravelling peripheral and central protective effects, antimicrobial but also anti-COVID-19 properties exerted by the water extract of P. mahaleb. Anti-inflammatory effects were studied in isolated mouse colons exposed to lipopolysaccharide. Neuroprotection, measured as a blunting effect on hydrogen-peroxide-induced dopamine turnover, was investigated in hypothalamic HypoE22 cells. Antimicrobial effects were tested against different Gram+ and Gram- bacterial strains. Whereas anti-COVID-19 activity was studied in lung adenocarcinoma H1299 cells, where the gene expression of ACE2 and TMPRSS2 was measured after extract treatment. The bacteriostatic effects induced on Gram+ and Gram- strains, together with the inhibition of COX-2, TNFα, HIF1α, and VEGFA in the colon, suggest the potential of P. mahaleb water extract in contrasting the clinical symptoms related to ulcerative colitis. The inhibition of the hydrogen peroxide-induced DOPAC/DA ratio indicates promising neuroprotective effects. Finally, the downregulation of the gene expression of ACE2 and TMPRSS2 in H1299 cells, suggests the potential to inhibit SARS-CoV-2 virus entry in the human host. Overall, the results support the valorization of the local cultivation of P. mahaleb.