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.     

Field-induced π-polarization in barrelene derivatives: a computational study based on structural variation

Barrelene, H–C(CH=CH)₃C–H, is an unsaturated polycyclic hydrocarbon containing three isolated double bonds in a non-planar arrangement. We have studied the transmission of field effects through the barrelene framework by analyzing the small structural changes occurring in the phenyl group of many Ph–C(CH=CH)₃C–X molecules, where X is a variable substituent. Molecular geometries have been determined by quantum chemical calculations at the HF/6-31G* and B3LYP/6-311++G** levels of theory. Comparison with the results obtained for the corresponding saturated molecules, the bicyclo[2.2.2]octane derivatives Ph–C(CH₂–CH₂)₃C–X, reveals a small, but significant, field-induced π-polarization of the barrelene cage, especially when the remote substituent is a charged group. Additional evidence of π-polarization is obtained by comparing the electric dipole moments of the two sets of uncharged molecules. The structural variation of the barrelene cage caused by the variable substituent in Ph–C(CH=CH)₃C–X molecules has also been investigated. It is much larger than that of the phenyl group and depends primarily on the electronegativity of the substituent. Particularly pronounced is the concerted variation of the non-bonded distance between the bridgehead carbons of the cage, r(C···C) ₁ ^BARR , and the average of the three C–C–C angles at the cage carbon bonded to the variable substituent, α ₁ ^BARR . A scattergram of r(C···C) ₁ ^BARR versus the corresponding parameter for bicyclo[2.2.2]octane derivatives, r(C···C) ₁ ^BCO , shows that the variation of r(C···C) ₁ ^BARR becomes gradually less pronounced than that of r(C···C) ₁ ^BCO as the electronegativity of the substituent increases.     

Bias in modal parameters using the direct and iterative RFP identification procedures

In the rational fraction polynomial method [1] the identification of modal parameters is obtained through a direct linear least-square optimization technique but a particular form of fitting error is minimized. An iterative algorithm has been recently developed which uses the true fitting error [2]. In this paper a statistical analysis is developed to estimate the bias effects on the identified parameters when the data are polluted with noise. Both the direct and iterative procedures are considered. Numerical simulations are used to validate the results predicted by the theoretical analysis, which shows that the iterative approach is by far more efficient than the direct method.A first version of this paper was presented at 17th Int. Seminar on Modal Analysis, Leuven (Belgium), 23–25 September 1992, and preprinted in the Proceedings.