Stability in kinetic theory of vehicular traffic

Summary We prove existence and uniqueness of the solution of a linearized version of the kinetic equation of vehicular traffic on a highway by using the theory of semigroups of linear bounded operators.We assume that a perturbation is introduced at the entrance of the highway, i. e., at x=0 and that it continues for a given time interval [0, ].We then study the behaviour of such a perturvation at values of x close to zero by using perturbation theory for linear operators.Finally, we prove that the perturbation attenuates and approaches zero as x+, i. e. at a large distance from the entrance of the highway.

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Sommario Si prova l'esistenza e l'unicità della soluzione dell'equazione linearizzata del traffico automobilistico su un'autostrada con un'entrata in corrispondenza di x=0.Si studia poi il comportamento di una perturbazione, dovuta per esempio all'uscita da una partita di calcio, e si mostra come tale perturbazione si attenui al crescere della distanza dall'ingresso dell'autostrada.

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Work performed under the auspices of the National Research Council (C.N.R., Gruppo Nazionale per la Fisica Matematica).     

On the dynamics of the perturbations in an ionized gas dominated by charge exchange

Summary An ionized gas whose dynamics is dominated by charge exchange is considered. The following two problems are studied: the time behaviour of sinusoidal waves in a uniform equilibrium; the propagation in a bounded equilibrium of sinusoidal oscillations forced to the wall. It is shown, in particular, that the equilibria considered, not necessarily thermal equilibria, are stable for any form of the distribution function.

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Sommario Si considera un gas ionizzato, non necessariamente in equilibrio termico, la cui dinamica sia dominata dal processo di scambio di carica, e si studiano i seguenti due problemi: evoluzione temporale di onde sinusoidali su un equilibrio uniforme; propagazione di oscillazioni sinusoidali forzate alla parete in un equilibrio spazialmente limitato. Si mostra in particolare la stabilitá degli equilibri per qualunque forma della funzione di distribuzione.

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Research supported in part by C.N.R., G.N.F.M.     

Comparison of the molecular structures of five benzene derivatives as determined independently by gas-phase electron diffraction in two different laboratories: a perspective

The merits and limitations of gas-phase electron diffraction as a technique for determining accurately the structures of small organic molecules are demonstrated by comparing the molecular structures of five benzene derivatives studied in two different laboratories. The existence of many possible representations of the structure of a molecule (r _a, r _g, r _α, r _α⁰, r _e, …), implying differences in the physical meaning of geometrical parameters, is discussed in some detail as it may cause difficulties in a comparison. Also illustrated are different ways of estimating and expressing uncertainties in the geometrical parameters from a gas-phase electron diffraction study.     

KRS and Powers of determinantal ideas

The goal of this paper is to determine Göbner bases of powers of determinantal ideals and to show that the Rees algebras of (products of) determinantal ideals are normal and Cohen–Macaulay if the characteristic of the base field is non-exceptional. Our main combinatorial result is a generalization of Schensted's Theorem on the Knuth–Robinson–Schensted correspondence.     

ATLAS discovery potential for a heavy charged Higgs boson

The sensitivity of the ATLAS detector to the discovery of a heavy charged Higgs boson is presented. Assuming a heavy SUSY spectrum, the most promising channels above the top quark mass are H^± → tb and H^± → τ^±ν_τ which provide coverage in the low and high tanβ regions up to ∼ 600 GeV. The achievable precisions on the charged Higgs mass and tanβ determination are also discussed. The H^± → W^± h⁰ channel, though restricted to a small MSSM parameter space, shows a viable signal in NMSSM where the parameter space is less constrained. The observation of the channel H⁻ → τ⁻_L ν_τ + c.c. may constitute a distinctive evidence for models with singlet neutrinos in large extra dimensions.     

Real perturbations of complex polynomials

In this article the dynamics of generic C^r (r ≥ 3) perturbations of complex polynomials are considered. The attention is focused on the determination of the existence of large or invariant components of the complement of the basin of ∞, where the interesting dynamics occur.     

Synthesis and structural characterization of syndiotactic trans‐1,2 and cis‐1,2 polyhexadienes

The (E) isomer in mixtures of (E) and (Z) 1,3‐hexadiene was polymerized with the system CoCl₂(PⁱPrPh₂)₂‐MAO, a highly active and stereospecific catalyst for the preparation of 1,2 syndiotactic polybutadiene. A new crystalline polymer with a melting point of 109 °C was obtained. The polymer was characterized by IR, NMR (¹³C, ¹H in solution and ¹³C in the solid‐state), X‐ray diffraction, DSC, GPC and it was found to have a trans‐1,2 syndiotactic structure with a 5.18 ± 0.04 Å fiber periodicity. Since only the (E) isomer was polymerized, at the end of the reaction we were able to separate the (Z) isomer, which was ultimately polymerized with CpTiCl₃‐MAO at low temperature, obtaining a low molecular weight, stereoregular polymer that, characterized by IR and NMR methods, was found to exhibit a cis‐1,2 syndiotactic structure, never reported before. Molecular mechanics calculations were carried out on the trans‐1,2 syndiotactic polymer and structural models consistent with the X‐ray diffraction data are proposed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5339–5353, 2007     

On the problem of the elastic plate on one-sided foundation

Summary Solution existence, uniqueness and regularity are analyzed for the elastic plate on unilateral elastic foundation problem. Some results are also given for the one-sided rigid foundation case.

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Sommario Si studiano l'esistenza, l'unicità e la regolarità delle soluzioni del problema della piastra elastica su fondazione elastica unilaterale. Sono anche dati alcuni risultati per il caso di fondazione rigida unilaterale.

     

On the evolutions of the discontinuities of orders ⩾ m in solutions for quasi-linear systems of PDEs of order m,or for the linearizations of these systems

Summary One considers a system L[u]=0 of PDEs, quasi-linear (according to [1]) and of order m, which possesses a bicharacteristic line , as it happens in the hyperbolic case. For v=0, , –m (>0) let u(^v) be a discontinuity wave of order m+v that solves the system above and whose discontinuity hypersurface includes . The corresponding transport equations along are considered. Furthermore some interesting cases are pointed out, in which these equations turn out to be mutually equivalent in a suitable sense. Some theorems are stated to compare the transport equations for the discontinuities of the above kinds, that are connected with the systems d^hL[u]/dt^h=0 (h=0, , –m) and/or the linearization of the system L[u]=0 around any regular solution of it.

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Sommario Si considera un sistema L[u]=0 di equazioni alle derivate parziali, quasi lineare (secondo [1]) e di ordine m, il quale sia dotato di qualche bicaratteristica , come accade nel caso iperbolico. Per v=0, , –m(>0) sia u(^v) un'onda di discontinuità di ordine m+v risolvente il detto sistema e avente ipersuperficie di discontinuità contenente Si considerano le relative equazioni di trasporto lungo e si determinano casi interessanti in cui queste equazioni sono mutuamente equivalenti in senso opportuno. Si stabiliscono teoremi di confronto per il trasporto delle discontinuità del tipo suddetto, relative ai sistemi d^hL[u]/dt^h=0 (h=0, , –m) e/o alla linearizazione del sistema L[u]=0 attorno a qualche sua soluzione regolare.

     

Natural estrogens in dairy products: Determination of free and conjugated forms by ultra high performance liquid chromatography with tandem mass spectrometry

Natural estrogens are synthesized by mammals in different amounts depending on the developmental stage and pregnancy/lactation period, and they may pass into milk, where they are mostly present as glucuronated and sulfated forms. In modern dairy practices, about 75% of milk is produced from pregnant cows; therefore, the amount of hormones that may pass into milk could be of concern. While estrogen determination in milk has been investigated in depth, the individual determination of estrogens and their conjugated forms in dairy products has not been fully addressed. The aim of this work was to develop and assess a sensitive method, using the peculiar retention properties of graphitized carbon black, to extract natural free estrogens and their major conjugated metabolites, without any enzymatic cleavage, from yogurt, cheese, and butter. The free and conjugated estrogens were eluted in two distinct fractions from the solid‐phase extraction cartridge and analyzed separately by ultra high performance liquid chromatography coupled to tandem mass spectrometry. Recoveries were higher than 80% for all the three sample typologies. The highest matrix effects were observed for butter, which was richest in lipid content, but was below 30%. A survey on some commercial dairy products suggests that production processes decreased estrogen content.