Ultratrace determination of 1,2,4-trichlorobenzene in waste water by purge and trap/gas chromatography coupled to different detectors: Flame ionization (FID), electron capture (ECD), and multiple ion detection-mass spectrometry (MID-MS)

High resolution gas chromatography (HRGC) coupled to a “purge and trap” extraction-injection technique is described as a method of determining 1,2,4-trichlorobenzene in water at levels as low as parts-per-trillion (ppt). In order to investigate the interference from other volatile organic compounds (VOCs) several detection systems were compared: flame ionization, electron capture, and mass spectrometry-multiple ion detection. Concentrations ranging from 15 to 600 ng/L were analyzed in 20 ml standard aqueous solutions. The mean accuracy of the method varied from 89 to 103%, and its mean precision varied from ± 0.85 to ± 7.5 % for all detectors. The detection limits were 20 ng/L for FID, 2 ng/L for ECD and 0.5 ng/L for MID-MS detectors. The procedure was successfully applied to the analysis of industrial waste waters. The necessity of an appropriate internal standard to improve the quantitative determination and to determine possible losses or degradation of 1,2,4-trichlorobenzene during handling or storage is discussed.     

Fabrication and analysis of a directional coupler written in glass by nanojoule femtosecond laser pulses

A directional coupler written in a glass sample by the focused 400-nm output from a 25-fs oscillator is reported. The coupler is single mode; the splitting ratio is 1.9 dB at 633 nm. A refractive-index profile of the waveguide with a magnitude of Dn = 4.5 x 10(-3) was retrieved from a near-field mode pattern.     

Minimal Legendrian submanifolds of S and absolutely area-minimizing cones

We use minimal Legendrian submanifolds in spheres to construct examples of absolutely area-minimizing cones and we prove a result about Legendrian 2-tori in S⁵.     

Principi variazionali nella teoria lineare delle miscele di due solidi elastici

Riassunto In questa nota gli Autori stabiliscono dei principi variazionali che caratterizzano in maniera completa il più generale problema ai limiti sia della statica sia della dinamica di una miscela isotropa di due solidi elastici lineari. Questi principi sono del tutto generali poichè non si richiede agli stati o processi ammissibili di soddisfare ad alcuna delle equazioni di campo e delle condizioni iniziali o al contorno. Tale risultato viene ottenuto esprimendo i problemi considerati in forma operazionale.

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Summary In this paper the Authors establish variational principles which characterize the most general boundary-value problem for statics and dynamics of an isotropic mixture of two linear elastic solids. These principles are completely general because the admissible states or processes are not required to meet any of the field equations, boundary or initial conditions and they are obtained by expressing the problems in operator form.

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Il lavoro è stato eseguito nell’ambito del Gruppo Nazionale per la Fisica Matematica del C.N.R.     

Maslov form and J-volume of totally real immersions

On every totally real submanifold Mⁿ of ⁿ, one can define a Maslov class analogous to the one defined for the Lagrangian submanifolds of ⁿ. We define here a closed 1-form, expressed in terms of the extrinsic local geometric invariants of Mⁿ and the complex structure of ⁿ, whose cohomology class is the Maslov class of Mⁿ. This generalizes to the totally real case, the result of Morvan (1981). This 1-form can still be defined if the ambient space ⁿ is substituted by a Kahler manifold , but it is not closed in general. However, we can build a variational problem on the space of totally real immersions, whose critical points are totally real submanifolds whose form defined above vanishes identically. In the case where , we give a characterization and many examples of such submanifolds. Finally we study the second variation and prove a stability result for the critical submanifolds of a Kahler manifold with non-positive Ricci tensor. This extends the well-known results on Lagrangian submanifolds of      

Su un caso di non esistenza e su uno di esistenza e unicità della soluzione di un problema della magnetoidrodinamica stazionaria

Riassunto In questa nota si affrontano alcune questioni di esistenza e unicità della soluzione classica del problema del moto stazionario di un fluido omogeneo, incomprimibile, perfetto, elettricamente condutore attorno ad un ostacolo dielettrico e scarico in un punto del quale è situato un dipolo magnetico. Precisamente, si dimostra dapprima che, nel caso in cui il fluido abbia conduttività finita, il problema suddetto non ammette soluzione se al campo cinetico e al campo magnetico sono imposte condizioni all'infinito alquanto restrittive. Si dimostra poi che opportune ipotesi all'infinito assicurano l'esistenza e l'unicità della soluzione del medesimo problema nel caso in cui il fluido sia un conduttore perfetto.

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Summary This paper deals with some questions of classical solution existence and uniqueness for the problem of the steady flow of an homogeneous, incompressible, perfect, electrically conducting fluid past a dielectric and discharged obstacle in which a magnetic dipole is situated. More precisely, in the first place the non-existence of solutions of the above mentioned problem is proved for fluids of finite conductivity, if rather restrictive conditions are placed on behavior of the kinetic and magnetic fields at infinity. In the next place an existence and uniqueness theorem is established for perfectly conducting fluids.

     

Sulla influenza della polarizzazione delle radio-onde nei fenomeni di interazione ionosferica

Riassunto Si studia l'influenza della polarizzazione delle radio-onde su alcuni fenomeni non lineari nella ionosfera tramite una nuova e più completa relazione funzionale fra i vettori densità di corrente e campo elettrico. Tale studio riguarda la comparsa di onde di banda laterale e la loro dipendenza dalle direzioni di polarizzazione delle onde interagenti.

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Summary The influence of radio wave polarization on some nonlinear phenomena in the inosphere is studied through a new and more complete functional relation between current density and electric field vectors. This study is concerned with the occurrence of ?sideband? waves and their dependence on the polarization directions of interacting waves.

     

A critical radius for unit Hopf vector fields on spheres

The volume of a unit vector field V of the sphere (n odd) is the volume of its image V() in the unit tangent bundle. Unit Hopf vector fields, that is, unit vector fields that are tangent to the fibre of a Hopf fibration are well known to be critical for the volume functional. Moreover, Gluck and Ziller proved that these fields achieve the minimum of the volume if n = 3 and they opened the question of whether this result would be true for all odd dimensional spheres. It was shown to be inaccurate on spheres of radius one. Indeed, Pedersen exhibited smooth vector fields on the unit sphere with less volume than Hopf vector fields for a dimension greater than five. In this article, we consider the situation for any odd dimensional spheres, but not necessarily of radius one. We show that the stability of the Hopf field actually depends on radius, instability occurs precisely if and only if In particular, the Hopf field cannot be minimum in this range. On the contrary, for r small, a computation shows that the volume of vector fields built by Pedersen is greater than the volume of the Hopf one thus, in this case, the Hopf vector field remains a candidate to be a minimizer. We then study the asymptotic behaviour of the volume; for small r it is ruled by the first term of the Taylor expansion of the volume. We call this term the twisting of the vector field. The lower this term is, the lower the volume of the vector field is for small r. It turns out that unit Hopf vector fields are absolute minima of the twisting. This fact, together with the stability result, gives two positive arguments in favour of the Gluck and Ziller conjecture for small r.