Fractal regularity results on optimal irrigation patterns

In this paper the problem of the regularity, i.e. fractal behaviour, of the minima of the branched transport problem is addressed. We show that, under suitable conditions on the irrigated measure, the minima present a fractal regularity, that is on a given branch of length l the number of branches bifurcating from it whose length is comparable with ε   can be estimated both from above and below by l/ε$l/\epsilon$.     

Negatively buoyant plume dispersion: a comparison of simple mathematical models, hydraulic simulations and field data

Summary The ground-level concentration distribution for negatively buoyant gases of various densities, emitted from stacks with heights, diameters and exit velocities varying in the typical range of geothermal drilling activities, was studied by means of hydraulic simulations performed in neutral conditions at different flow speeds. These measurements, and a few others taken in the field in nearly neutral and unstable atmosphere during tests of CO₂ release from a geothermal well, were compared with the values expected from a Gaussian formula corrected for denser-than-air, tilted plumes. For calculating theoretical concentrations, three couples of horizontal and vertical plume standard deviations as functions of downwind distance from source were employed: those given by Singer-Smith and Briggs and a third one obtained by our group during a previous water channel experiment. Also the maximum ground-level concentration and its distance from the source were measured in each simulation and compared with the prediction of our Gaussian formula, as well as with a best-fit expression given by Meroney. The concentration pattern χ(x, y, 0) given by the corrected Gaussian formula proved to be in good agreement with experimental data, especially in association with Singer-Smith's or our sigmas. When only maximum g.l. concentrations are needed, also the simple formula suggested by Meroney can give a good approximation.

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Riassunto Una serie di simulazioni in vasca senza stratificazione, condotte a varie velocità della vena idraulica, ha permesso di studiare la distribuzione di concentrazione al suolo dovuta a gas con varie densità maggiori di quella dell'aria, emessi da ciminiere con altezze, diametri e velocità di efflusso variabili entro intervalli tipici delle attività di perforazione geotermica. Queste misure, ed alcune altre ottenute in campo in condizioni di atmosfera circa neutra e instabile durante prove di rilascio di CO₂ da un pozzo geotermico, sono state confrontate con i valori attesi in base ad una formula gaussiana corretta per pennacchi inclinati. Nel calcolo delle concentrazioni teoriche si sono impiegate tre diverse coppie di espressioni per le deviazioni standard orizzontale e verticale del pennacchio: quelle date da Singer-Smith e Briggs ed una terza ottenuta dal nostro gruppo durante una precedente esperienza in canale idraulico. In ciascuna prova si è misurata anche la concentrazione massima al suolo e la sua distanza dalla sorgente; queste quantità sono state raffrontate con le previsioni della formula gaussiana e con una espressione empirica proposta da Meroney. Il campo di concentrazione χ(x, y, 0) dato dalla formula gaussiana corretta è risultato in buon accordo con le misure, specialmente se associato alle sigma di Singer-Smith o alle nostre. Quando sia sufficiente una valutazione della concentrazione massima, anche la semplice formula di Meroney può dare una buona approssimazione.

     

Competitive Gold‐Promoted Meyer–Schuster and oxy‐Cope Rearrangements of 3‐Acyloxy‐1,5‐enynes: Selective Catalysis for the Synthesis of (+)‐(S)‐γ‐Ionone and (−)‐(2S,6 R)‐cis‐γ‐Irone

We report a simple, highly stereoselective synthesis of (+)‐(S)‐γ‐ionone and (‐)‐(2S,6R)‐cis‐γ‐irone, two characteristic and precious odorants; the latter compound is a constituent of the essential oil obtained from iris rhizomes. Of general interest in this approach are the photoisomerization of an endo trisubstituted cyclohexene double bond to an exo vinyl group and the installation of the enone side chain through a [(NHC)Au^I]‐catalyzed Meyer–Schuster‐like rearrangement. This required a careful investigation of the mechanism of the gold‐catalyzed reaction and a judicious selection of reaction conditions. In fact, it was found that the Meyer–Schuster reaction may compete with the oxy‐Cope rearrangement. Gold‐based catalytic systems can promote either reaction selectively. In the present system, the mononuclear gold complex [Au(IPr)Cl], in combination with the silver salt AgSbF₆ in 100:1 butan‐2‐one/H₂O, proved to efficiently promote the Meyer–Schuster rearrangement of propargylic benzoates, whereas the digold catalyst [{Au(IPr)}₂(μ‐OH)][BF₄] in anhydrous dichloromethane selectively promoted the oxy‐Cope rearrangement of propargylic alcohols.     

The inorganic perspective of nerve growth factor: interactions of Cu2+ and Zn2+ with the N-terminus fragment of nerve growth factor encompassing the recognition domain of the TrkA receptor

There is a significant overlap between brain areas with Zn(2+) and Cu(2+) pathological dys-homeostasis and those in which the nerve growth factor (NGF) performs its biological role. The protein NGF is necessary for the development and maintenance of the sympathetic and sensory nervous systems. Its flexible N-terminal region has been shown to be a critical domain for TrkA receptor binding and activation. Computational analyses show that Zn(2+) and Cu(2+) form pentacoordinate complexes involving both the His4 and His8 residues of the N-terminal domain of one monomeric unit and the His84 and Asp105 residues of the other monomeric unit of the NGF active dimer. To date, neither experimental data on the coordination features have been reported, nor has one of the hypotheses according to which Zn(2+) and Cu(2+) may have different binding environments or the Ser1 α-amino group could be involved in coordination been supported. The peptide fragment, encompassing the 1-14 sequence of the human NGF amino-terminal domain (NGF(1-14)), blocked at the C terminus, was synthesised and its Cu(2+) and Zn(2+) complexes characterized by means of potentiometric and spectroscopic (UV/Vis, CD, NMR, and EPR) techniques. The N-terminus-acetylated form of NGF(1-14) was also investigated to evaluate the involvement of the Ser1 α-amino group in metal-ion coordination. Our results demonstrate that the amino group is the first anchoring site for Cu(2+) and is involved in Zn(2+) coordination at physiological pH. Finally, a synergic proliferative activity of both NGF(1-14) and the whole protein on SHSY5Y neuroblastoma cell line was found after treatment in the presence of Cu(2+). This effect was not observed after treatment with the N-acetylated peptide fragment, demonstrating a functional involvement of the N-terminal amino group in metal binding and peptide activity.     

Base promoted synthesis of activated cyclopropanes bearing homologated carbonyl groups via tandem Michael addition-intramolecular enolate trapping

A simple base promoted intramolecular Michael initiated ring closure reaction of γ-hydroxyenone derived diphenyl phosphinates with 1,3-indandione, enabled the synthesis of novel activated cyclopropanes with homologated carbonyl moiety in good yield. Promising levels of enantioselectivity are achieved when using cinchona derivatives as promoters.     

Spectral theory for commutative algebras of differential operators on Lie groups

The joint spectral theory of a system of pairwise commuting self-adjoint left-invariant differential operators L₁,…,Ln on a connected Lie group G is studied, under the hypothesis that the algebra generated by them contains a “weighted subcoercive operator” of ter Elst and Robinson (1998) [52]. The joint spectrum of L₁,…,Ln in every unitary representation of G is characterized as the set of the eigenvalues corresponding to a particular class of (generalized) joint eigenfunctions of positive type of L₁,…,Ln. Connections with the theory of Gelfand pairs are established in the case L₁,…,Ln generate the algebra of K-invariant left-invariant differential operators on G for some compact subgroup K of Aut(G).     

Deligne��s representation theory in complex rank and objects of integral type

Working with Pierre Deligne??s category of representations of the ??symmetric group S _t with t a complex number?? we give negative answers to certain questions on ${\otimes}$ -categories raised by Bruno Kahn and Charles A. Weibel.     

Vibrational analysis of x-ray absorption fine structure thermal factors by ab initio molecular dynamics: the Zn(II) ion in aqueous solution as a case study

In this work, we consider a new combination of vibrational analysis and normal-like mode decomposition of Debye-Waller factors of solvated ions entirely based on molecular dynamics data. Such a novel time-dependent analysis procedure provides a direct link between x-ray absorption fine structure parameters and normal mode contributions for an ion-solvent system. The potentialities of such a methodology rely on two fundamental aspects which distinguish it from already available tools. First, a general vibrational analysis that does not require any Gaussian or harmonic model for describing atomic fluctuations in liquids. Second, a very accurate sampling of the short range motions around the structural probe via the recently developed atom centered density matrix propagation/general liquid optimized boundary method. This novel molecular dynamics methodology is based on an integrated ab initio/classical potential using localized basis functions and nonperiodic boundary conditions. As a case study we have chosen the Zn(II) ion in aqueous solution. The consistency of our results and the observed good agreement with experiments show how the key support to advanced structural techniques from molecular dynamics can be further expanded and investigated.     

Development and validation of a liquid chromatography/electrospray ionization tandem mass spectrometry method for the quantification of latanoprost free acid in rabbit aqueous humor and ciliary body

A rapid, selective and sensitive method for quantification of latanoprost free acid in rabbit aqueous humor (AH) and ciliary body (CB) using reverse phase-high performance liquid chromatography coupled with electrospray ionization (ESI)-mass spectrometry/mass spectrometry has been developed and validated. Quantification in AH and CB was achieved by stable isotope dilution employing tetra-deuterated analog of latanoprost free acid, used as internal standard. Sample preparation was based on protein precipitation with methanol in AH, and on liquid extraction with a mixture of ethyl acetate and isopropanol 60:40 (v/v) in CB. Elution was achieved on an octylsilica (C8) column, using an isocratic elution method. Detection was performed on a triple quadrupole mass spectrometer, using ESI in positive ion selected reaction monitoring mode. Calibration curves were linear in the validated concentration ranges of 10-160 ng/mL in AH and 80-1280 ng/g in CB. The accuracy and precision values, obtained from three different sets of quality control samples, each analyzed in triplicate on three different days, were within the generally accepted criteria for analytical methods (< 15%). The limit of detection was 30.66 pg/mL in AH and 237.75 pg/g in CB. The assay proved to be accurate and precise when applied to the in vivo study of latanoprost free acid in rabbit AH and CB after single administration of an eye drops containing latanoprost.