Enantioselective Synthesis of Acyclic Orthogonally Functionalized Compounds Bearing a Quaternary Stereocenter Using Chiral Ammonium Salt Catalysis

We herein report an asymmetric protocol to access a series of orthogonally functionalized acyclic chiral target molecules containing a quaternary stereogenic center by carrying out the enantioselective α-alkylation of novel orthogonally functionalized dioxolane-containing cyanoacetates under chiral ammonium salt catalysis. By using just 1 mol % of Maruoka's spirocyclic ammonium salt catalysts enantioselectivities up to e.r.=97.5 : 2.5 could be achieved and further functional group manipulations of the products were carried out as well.     

An efficient method for solving free-boundary diffusion problems

Summary A new method is introduced for solving free-boundary problems for the heat equation. The method is shown to be uniformly convergent both for first type and nonlinear second type boundary conditions. Approximate solutions are obtained by discretization of the time variable and recursive solution at each time step of classical heat conduction linear problems in slabs of known thickness. An error estimate is given. Numerical tests are presented in a few cases in which exact solutions are known.

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Sommario Si introduce un nuovo metodo per la soluzione di problemi a contorno libero per l'equazione del calore. Si dimostra la convergenza uniforme del metodo sia per condizioni al contorno del primo tipo che per condizioni al contorno del secondo tipo non lineari. Le soluzioni approssimate sono ottenute discretizzando la variabile temporale e risolvendo ricorsivamente ad ogni passo un classico problema lineare di conduzione in uno strato di spessore noto. E' data una stima dell'errore. Per alcuni casi nei quali è nota la soluzione esatta sono presentate prove numeriche.

     

On the turbulent couette flow of an incompressible fluid with temperature-dependent viscosity

Summary Starting from energy and Navier-Stokes equations with temperature-dependent viscosity, we have obtained the Reynolds equations for the mean values of velocity, temperature and pressure. We have then applied these equations to the Couette flow; on the well-known hypothesis of mixing-length and Prandtl turbulent number, the above mentioned relations have been written in a more amenable form.Some general considerations concerning the reciprocal dependence between temperature and velocity gradients at wall have been deduced.Finally some solutions numerically obtained for several values of Reynolds number are given and discussed in some detail to point out the influence of the temperature-dependent viscosity.

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Sommario Introducendo nelle equazioni dell'energia e di Navier-Stokes le parti medie e fluttuanti della velocità, temperatura, pressione e viscosità, vengono ricavate le cosiddette equazioni di Reynolds, ossia le equazioni che descrivono i campi di velocità e temperatura medi. Dal confronto di quest'ultime, in cui la viscosità è considerata dipendente dalla temperatura, con quelle originarie di Reynolds si deduce la forma che nel caso in esame assumono gli sforzi apparenti.Successivamente le equazioni ottenute vengono applicate al moto a Couette e discusse, dopo aver introdotto in esse le ipotesi della lunghezza di miscelamento e del numero di Prandtl turbolento; da questa analisi vengono tratte alcune conclusioni di carattere generale riguardanti i legami tra il campo dinamico e quello termico. Infine vengono date alcune soluzioni ottenute per via numerica, le quali illustrano l'influenza che sulle distribuzioni di temperatura e velocità viene esercitata dalla dipendenza della viscosità dalla temperatura.

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Stefan — like problems with space — dependent latent heat

Summary A wide class of one-dimensional heat conduction problems with phase change is considered on the assumption that the latent heat is a given function of the position of the separation plane between the two phases: L=[s(t)].Some sufficient conditions for the existence and uniqueness of the solution in a given time-interval are given. This work permits the generalization of some previous results and the investigation of some cases of particular interest.

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Sommario Si studia una vasta classe di problemi di conduzione unidimensionale del calore in presenza di cambiamento di fase, nel caso in cui il calore latente sia funzione della posizione del fronte di separazione tra le due fasi: L=[s(t)].Si trovano delle condizioni sufficienti per l'esistenza e la unicità della soluzione del problema in un certo intervallo di tempo; si mostra infine che la trattazione permette di generalizzare risultati già noti e di estendere lo studio a casi di particolare interesse.

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Work performed within the Research Group (Grant. no. 115.2210) of the C.N.R.     

A basis for the linear theory of elastic stability of structures

Summary In this paper a consistent linear theory of stability of elastic structures is given and the problem of the neutral equilibrium of a continuum composed by an elastic material with high stiffness to the strains is studied. All the particular cases, as the buckling of beams, plates, shells etc., ensue and their classification in regard of their significance is given. There are comparisons with other theories.

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Sommario In questa Nota viene formulata una consistente teoria lineare della stabilità dell'equilibrio delle strutture elastiche e si tratta il problema dell'equilibrio indifferente di un continuo costituito da un materiale elastico con elevata rigidità alla deformazione. Tutti i casi particolari di instabilità euleriana delle travi, piastre, gusci ecc., discendono come casi particolari e di questi viene fornita una classifica nei riguardi della loro importanza. Si fanno infine confronti con altre trattazioni.

     

Novel Copolymers of Styrene. 16. Halogen Ring-Disubstituted Methyl 2-Cyano-3-Phenyl-2-Propenoates

Electrophilic trisubstituted ethylenes, ring-disubstituted methyl 2-cyano-3-phenyl-2-propenoates, RPhCH?C(CN)CO₂CH₃, where R is 2,5-dichloro, 3,5-dichloro, 2,3-difluoro, 3-chloro-2-fluoro, 3-chloro-4-fluoro, 4-chloro-3-fluoro, 2-chloro-5-nitro, and 2-chloro-6-nitro were prepared and copolymerized with styrene. The monomers were synthesized by the piperidine catalyzed Knoevenagel condensation of ring-disubstituted benzaldehydes and methyl cyanoacetate, and characterized by CHN analysis, IR, ¹H and ¹³C-NMR. All the ethylenes were copolymerized with styrene (M₁) in solution with radical initiation (ABCN) at 70°C. The compositions of the copolymers were calculated from nitrogen analysis and the structures were analyzed by IR, ¹H and ¹³C-NMR. The order of relative reactivity (1/r₁) for the monomers is 4-Cl-3-F (4.87) > 2,3-F₂ (4.49) > 3-Cl-4-F (3.50) > 3-Cl-2-F (2.96) > 2-Cl-5-NO₂ (2.02) > 2,5-Cl₂ (1.54) > 2-Cl-6-NO₂ (1.00) > 3,5-Cl₂ (0.41). Relatively high T_g of the copolymers in comparison with that of polystyrene indicates a decrease in chain mobility of the copolymer due to the high dipolar character of the trisubstituted ethylene monomer unit. Decomposition of the copolymers in nitrogen occurred in two steps, first in the 200–500ºC range with residue (1.5–34.5% wt), which then decomposed in the 500-800ºC range.     

EEG Fractal Analysis Reflects Brain Impairment after Stroke

Stroke is the commonest cause of disability. Novel treatments require an improved understanding of the underlying mechanisms of recovery. Fractal approaches have demonstrated that a single metric can describe the complexity of seemingly random fluctuations of physiological signals. We hypothesize that fractal algorithms applied to electroencephalographic (EEG) signals may track brain impairment after stroke. Sixteen stroke survivors were studied in the hyperacute (<48 h) and in the acute phase (∼1 week after stroke), and 35 stroke survivors during the early subacute phase (from 8 days to 32 days and after ∼2 months after stroke): We compared resting-state EEG fractal changes using fractal measures (i.e., Higuchi Index, Tortuosity) with 11 healthy controls. Both Higuchi index and Tortuosity values were significantly lower after a stroke throughout the acute and early subacute stage compared to healthy subjects, reflecting a brain activity which is significantly less complex. These indices may be promising metrics to track behavioral changes in the very early stage after stroke. Our findings might contribute to the neurorehabilitation quest in identifying reliable biomarkers for a better tailoring of rehabilitation pathways.     

Enantioselective Catalytic [4+1]-Cyclization of ortho-Hydroxy-para-Quinone Methides with Allenoates

The first highly asymmetric catalytic synthesis of densely functionalized dihydrobenzofurans is reported, which starts from ortho-hydroxy-containing para-quinone methides. The reaction relies on an unprecedented formal [4+1]-annulation of these quinone methides with allenoates in the presence of a commercially available chiral phosphine catalyst. The chiral dihydrobenzofurans were obtained as single diastereomers in yields up to 90 % and with enantiomeric ratios up to 95:5.