On the p-length of some finite p-soluble groups

The main aim of this paper is to give structural information of a finite group of minimal order belonging to a subgroup-closed class of finite groups and whose p-length is greater than 1, p a prime number. Alternative proofs and improvements of recent results about the influence of minimal p-subgroups on the p-nilpotence and p-length of a finite group arise as consequences of our study.     

Eigenvalues of a statistical mechanics matrix

We consider the problem of finding the spectrum of an n × n matrix which arises in the study of a certain model of long-range interactions in a one-dimensional statistical mechanics system. Our analysis exhibits a curious resemblance of the suitably normalized distribution of eigenvalues to the Marčenko–Pastur law in the limit n → ∞.     

Wisp-like structures in vertical gas–liquid pipe flow revealed by wire mesh sensor studies

A conductance wire mesh sensor system has been employed on a vertical 67 mm diameter pipe with the up flow of air and water mixtures. The measuring system provides time and cross-sectionally resolved information about the spatial distribution of the phases. Statistical information can be extracted and used to identify flow patterns. The fully resolved data has revealed a hitherto unreported structure has been seen in churn flow which could be linked to the wisps in wispy-annular flow.     

Evaluation of Transparent Optical Network Performance in Presence of Incoherent Homodyne Crosstalk

A simple method to evaluate the performance of transparent optical networks (TON) that takes into account the incoherent homodyne crosstalk, signal distortion, inter-symbol interference (ISI), amplified spontaneous emission (ASE) noise, and arbitrary optical and electrical filters is proposed. This method combines the effect of the incoherent homodyne crosstalk with an exhaustive Gaussian approximation for the influence of ASE noise, signal distortion, and ISI. It is shown that the incoherent homodyne crosstalk penalty depends on the ASE noise accumulated in the TON, ISI, and extinction ratio. The proposed method estimates are compared with experimental results published by other authors. Good agreement is observed for one, two, and four incoherent homodyne crosstalk signals, revealing that the proposed method provides accurate estimates even when the methods based on a Gaussian approximation for the incoherent homodyne crosstalk fail. The proposed method is used to assess the performance of a TON composed by optical add-drop multiplexers based on arrayed waveguide gratings. Results reveal that incoherent homodyne crosstalk, ASE noise, and ISI impair the TON performance and, therefore, none can be neglected in the TON design.     

A version of Stöber synthesis enabling the facile prediction of silica nanospheres size for the fabrication of opal photonic crystals

A sol-gel synthesis procedure based on the method proposed by Stöber et al. (J Colloid Interface Sci 26:302–315, 1968) has been adopted for the one-step preparation of mono-dispersed silica nanospheres. An excellent control of the particle diameter over a wide range is obtained by varying the amount of silicon alkoxide only, while the concentration of all other components is kept fixed: this allows the fabrication of artificial opals with a finely tuned and precisely predictable lattice parameter.     

A domain decomposition method for linear exterior boundary value problems

In this paper, we present a domain decomposition method, based on the general theory of Steklov-Poincaré operators, for a class of linear exterior boundary value problems arising in potential theory and heat conductivity. We first use a Dirichlet-to-Neumann mapping, derived from boundary integral equation methods, to transform the exterior problem into an equivalent mixed boundary value problem on a bounded domain. This domain is decomposed into a finite number of annular subregions, and the Dirichlet data on the interfaces is introduced as the unknown of the associated Steklov-Poincaré problem. This problem is solved with the Richardson method by introducing a Dirichlet-Robin-type preconditioner, which yields an iteration-by-subdomains algorithm well suited for parallel computations. The corresponding analysis for the finite element approximations and some numerical experiments are also provided.     

Finite element techniques in plane limit problems

Summary Limit analysis of plane structures is formulated by applying a finite element linear programming technique that was previously proposed by the same author.Three different element models are considered: the constant stress compatible model, the linear stress equilibrium model, the quadratic stress equilibrium model. Some notes are devoted to the construction of the stress fields with reference to the adopted method.Some suitably chosen numerical applications are then proposed in order to compare the different approaches as far as numerical efficiency and result accuracy are concerned. The possibility of improving the linear programming procedure is also discussed, and in particular a method is proposed to find out an initial feasible vector on the basis of mechanical considerations, in order to overcome the necessity of the so-called M-phase of the simplex method.Numerical results are given together with the comments.

---

Sommario Si formula il problema dell'analisi limite di strutture piane secondo un metodo degli elementi finiti già proposto dall'autore.Nel presente lavoro vengono considerati tre diversi modelli di elementi e precisamente: il modello congruente a sforzo costante e quelli equilibrati a campi di sforzo lineare e quadratico. La costruzione dei tre modelli viene presentata in dettaglio nell'ambito del metodo adottato.Vengono quindi presentati alcuni esempi di applicazione opportunamente scelti, con lo scopo di confrontare l'efficienza numerica e l'accuratezza di risultati ottenuti con l'impiego dei tre modelli. Si discute inoltre la possibilità di migliorare l'efficacia dell'algoritmo matematico ed in particolare si suggerisce un metodo che, individuando una soluzione ammissibile di partenza sulla scorta di considerazioni meccaniche, permette di evitare la cosiddetta fase M della programmazione lineare.I commenti sono accompagnati dai risultati numerici.

---

---

Research supported by the C.N.R. (Italian National Research Council).     

Two different products from the reaction of 1‐aryl‐5‐chloro‐3‐methyl‐1H‐pyrazole‐4‐carbaldehyde with cyclohexylamine when the aryl substituent is phenyl or pyridin‐2‐yl: hydrogen‐bonded sheets versus dimers

Cyclohexylamine reacts with 5‐chloro‐3‐methyl‐1‐(pyridin‐2‐yl)‐1H‐pyrazole‐4‐carbaldehyde to give 5‐cyclohexylamino‐3‐methyl‐1‐(pyridin‐2‐yl)‐1H‐pyrazole‐4‐carbaldehyde, C₁₆H₂₀N₄O, (I), formed by nucleophilic substitution, but with 5‐chloro‐3‐methyl‐1‐phenyl‐1H‐pyrazole‐4‐carbaldehyde the product is (Z)‐4‐[(cyclohexylamino)methylidene]‐3‐methyl‐1‐phenyl‐1H‐pyrazol‐5(4H)‐one, C₁₇H₂₁N₃O, (II), formed by condensation followed by hydrolysis. Compound (II) crystallizes with Z′ = 2, and in one of the two independent molecular types the cyclohexylamine unit is disordered over two sets of atomic sites having occupancies of 0.65 (3) and 0.35 (3). The vinylogous amide portion in each compound shows evidence of electronic polarization, such that in each the O atom carries a partial negative charge and the N atom of the cyclohexylamine portion carries a partial positive charge. The molecules of (I) contain an intramolecular N—H...N hydrogen bond, and they are linked by C—H...O hydrogen bonds to form sheets. Each of the two independent molecules of (II) contains an intramolecular N—H...O hydrogen bond and each molecular type forms a centrosymmetric dimer containing one R₂²(4) ring and two inversion‐related S(6) rings.