Matrix valued Jacobi polynomials

For every value of the parameters α,β>−1 we find a matrix valued weight whose orthogonal polynomials satisfy an explicit differential equation of Jacobi type.     

Reagent-controlled diastereoselective aminations with a new chiral nosyloxycarbamate

The synthesis of a new chiral nosyloxycarbamate derived from Helmchen's auxiliary is described. Reactions performed with this aminating reagent successfully give the formation of diastereomeric allylic carbamates or diastereomeric aziridines starting from different kinds of olefins.     

BAL resin for the preparation of secondary amines

Although amino acids anchored through the amino function to BAL resins can not easily be released from the resin by treatment with neat trifluoroacetic acid, we have shown that secondary amines can be obtained from BAL resins using trifluoroacetic acid solutions.     

A novel potent non‐nucleoside reverse transcriptase inhibitor acyl­thio­carbamate derivative with extensive intra­molecular π–π inter­actions

In the crystal structure of the novel acyl­thio­carbamate derivative O‐[2‐(1,3‐dioxo‐2,3‐dihydro‐1H‐isoindol‐2‐yl)­ethyl] N‐(4‐methyl­phenyl)‐N‐(3‐nitro­benzoyl)thio­carbamate, C₂₅H₁₉N₃O₆S, intra‐ and inter­molecular π–π inter­actions occur between the phthalimide and N‐benzoyl moieties. The partial atomic charges, calculated by ab initio methods, are consistent with the observed structure.     

Slow two-phase flow through a sinusoidal channel

The two-phase flow through a symmetric sinusoidal channel is studied by means of a regular perturbation analysis, where the small parameter is defined as the ratio between the amplitude of variation of the channel wall and the average thickness of the non-wetting phase. Results are valid for Reynolds numbers of the same order of magnitude as that of the expansion parameter. It is thus found that the fluid-fluid interface presents a wavy shape characterized by an amplitude and a phase-shift with respect to the fixed solid-fluid interface. Instabilities of the two-phase flow can arise for large values of the viscosity, flow rate and phase thickness ratios. Results are expected to be a first step towards the understanding of the hydrodynamics of trickle bed reactors, where several flow regimes are possible.     

Dynamic Forces Produced by Swinging Bells

The swinging of bells on belfries is a classical problem in structural dynamics and has been addressed in the Central European specialized bibliography. To carry out our study, the different modalities of swinging bells have been classified in “systems” according to their most relevant characteristics in three groups: Central European, English and Spanish systems. Each group presents some singular characteristics of frequency and oscillation, unbalance and/or turning rate, which give rise to different forces variable in time on their supporting structures. We have analyzed the three systems and, compared the maximum values of the horizontal and vertical forces that appear on the structure as well as its main harmonics. Besides the parameters analyzed, the complete dynamic study of the structure, and therefore the evaluation of its dynamic amplification factor (D.A.F.), requires the knowledge of its dynamic characteristics: main frequencies and damping ratio.     

Remarks on a Paper of M. Ochiai

This note is related to a nice short paper of M. Ochiai. We prove in a very fast way that the two-parameter family of Heegaard diagrams, constructed by Ochiai, encodes the genuine three-sphere. The result is obtained, up to isotopy, by using a sequence of only three moves in this order: a Whitehead–Zieschang reduction, a band sum and a cancellation of a handle.     

Teoremi di completezza connessi con equazioni ellittiche di ordine superiore in due variabili in un campo con contorno angoloso

Polynomials solutions of the elliptic equation (1.1) are considered in a domain whose boundary has edges but no cusps. It is shown that by using such solutions it is possible to built complete systems of vectors in suitable function spaces.