Correction to: Impact of leg bending in the patient-specific computational fluid dynamics of popliteal stenting

Acta Mechanica Sinica - A Correction to this paper has been published: https://doi.org/10.1007/s10409-021-01066-2     

Covariant Sectors with Infinite Dimension¶and Positivity of the Energy

Let ? be a local conformal net of von Neumann algebras on S ¹ and ρ a M?bius covariant representation of ?, possibly with infinite dimension. If ρ has finite index, ρ has automatically positive energy. If ρ has infinite index, we show the spectrum of the energy always to contain the positive real line, but, as seen by an example, it may contain negative values. We then consider nets with Haag duality on ℝ, or equivalently sectors with non-solitonic extension to the dual net; we give a criterion for irreducible sectors to have positive energy, namely this is the case iff there exists an unbounded M?bius covariant left inverse. As a consequence the class of sectors with positive energy is stable under composition, conjugation and direct integral decomposition. Received: 21 April 1997 / Accepted: 23 September 1997     

FT-IR study on solvent effects in building blocks of bioactive compounds. V

3-Hydroxy-4-hydroxymethyl pyrrolidin-2-ones, easily prepared from the Baylis–Hillman adduct 1-ethyl-4-methyl-2-hydroxy-3-methylenebutanedioate, are useful intermediates in the synthesis of bioactive compounds. In order to understand the mechanism involved in this reaction, vibrational and Montecarlo molecular mechanics conformational analysis on 1-ethyl-4-methyl-2-hydroxy-3-methylenebutanedioate were carried out, confirming the existence of a low energy intramolecular H-bonded five-member ring.     

Long‐range dependence and performance in telecom networks

Telecommunications systems have recently undergone significant innovations. These call for suitable statistical models that can properly describe the behaviour of the input traffic in a network. Here we use fractional Brownian motion (FBM) to model cumulative traffic network, thus taking into account the possible presence of long‐range dependence in the data. A Bayesian approach is devised in such a way that we are able to: (a) estimate the Hurst parameter H of the FBM; (b) estimate the overflow probability which is a parameter measuring the quality of service of a network: (c) develop a test for comparing the null hypothesis of long‐range dependence in the data versus the alternative of short‐range dependence. In order to achieve these inferential results, we elaborate an MCMC sampling scheme whose output enables us to obtain an approximation of the quantities of interest. An application to three real datasets, corresponding to three different levels of traffic, is finally considered. Copyright © 2004 John Wiley & Sons, Ltd.     

Thermodynamic properties of organic compounds in aqueous solution. II. Apparent molal heat capacities of piperidines,morpholines, and piperazines

Apparent molal heat capacities of some piperidine, morpholine, and piperazine derivatives in aqueous solution have been determined by adiabatic calorimetry in the temperature range 20–55°C and in the molality range 0.2–1m. Comparison of experimental values with those calculated through group contributions, found for monofunctional compounds, indicates strong interactions between the hydrophilic centers. An interpretation is given of the possible mechanism of this interaction. Also, values of ΔC _p for the addition reaction of proton to nitrogen centers of mono- and bifunctional organic compounds are examined.     

Substituent-controlled photoisomerization in retinal chromophore models: Fluorinated and methoxy-substituted protonated Schiff bases

The effect of substitution on the intrinsic (i.e. in vacuo) photoisomerization ability of retinal chromophore models has been explored using CASPT2//CASSCF minimum energy path computations to map the S₁ photoisomerization paths of two substituted minimal models of the retinal chromophore: the 2-cis-penta-2,4-dieniminium and the all-trans-epta-2,4,6-trieniminium cations, which have been modified using fluorine or methoxyl substituents as representative examples of electron-withdrawing and electron-releasing groups, respectively. A systematic analysis has been performed involving substitutions in all the possible positions along the chain. It is shown that the photochemical reactivity and photoisomerization efficiency of these systems may be tuned or indeed changed, although this effect strongly depends on the position of the substituent. In particular, we have shown that (i) most of the systems preserves qualitatively the reactivity of the parent (i.e. unsubstituted) compound; (ii) substitution at positions C4 or C6 leads to a different relaxed excited state structure of the chromophore and in general to a very flat photoisomerization path (or to a tiny S₁ energy barrier in some cases); (iii) the nature of the TICT state (i.e. the S₁ → S₀ decay funnel) may be turned from a conical intersection into an excited state minimum; (iv) for the C4 methoxy-substituted system the isomerization path as well as the S₁/S₀ decay funnel involve an unusual torsional angle. Thus, substitution turns out to be a good tool not only to tune the optical properties (i.e. the absorption and emission features) of the chromophore (as we have already shown in a previous work: I. Conti, F. Bernardi, G. Orlandi, M. Garavelli, Mol. Phys. 104 (2006) 915–924), but it may also play a crucial role in tuning and controlling photoisomerization selectivity and efficiency, affecting excited state lifetime and reaction rate. A rationale for these effects is presented, which provides a basis for understanding reactivity properties and the intrinsic photochemical behavior of substituted retinal chromophores.     

On the intrinsic definition of local observables

In a theory of local field algebras satisfying the split property, we introduce an algebra generated by the local energy-momentum operators obtained from the canonical local implementation of translations, and possibly by the local charges operators. We discuss the relations of this algebra to the given algebra of local observables and take some steps toward the characterization of theories where they coincide. In the presence of spontaneously broken symmetries, we present a no-go theorem.