Some trends in the theory of groups with finitely many normalizers

Ricerche di Matematica - This paper provides an account of results and methods from the theory of infinite groups admitting only finitely many normalizers of subgroups with a given property. Some...     

Primal separation for 0/1 polytopes

 The 0/1 primal separation problem is: Given an extreme point xˉ of a 0/1 polytope P and some point x ^*, find an inequality which is tight at xˉ, violated by x ^* and valid for P or assert that no such inequality exists. It is known that this separation variant can be reduced to the standard separation problem for P. We show that 0/1 optimization and 0/1 primal separation are polynomial time equivalent. This implies that the problems 0/1 optimization, 0/1 standard separation, 0/1 augmentation, and 0/1 primal separation are polynomial time equivalent. Then we provide polynomial time primal separation procedures for matching, stable set, maximum cut, and maximum bipartite graph problems, giving evidence that these algorithms are conceptually simpler and easier to implement than their corresponding counterparts for standard separation. In particular, for perfect matching we present an algorithm for primal separation that rests only on simple max-flow computations. In contrast, the known standard separation method relies on an explicit minimum odd cut algorithm. Consequently, we obtain a very simple proof that a maximum weight perfect matching of a graph can be computed in polynomial time. Received: August 20, 2001 / Accepted: April 2002 Published online: December 9, 2002 RID="⋆" ID="⋆" This research was developed while the author was on leave at the Istituto di Analisi dei Sistemi ed Informatica, Viale Manzoni 30, 00185 Roma, supported by the project TMR-DONET nr. ERB FMRX-CT98-0202 of the European Union. Mathematics Subject Classification (2000): 90C10, 90C60, 90C57     

Equivalence of Non-equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model

We construct different equivalent non-equilibrium statistical ensembles in a simple yet instructive \(N\) -degrees of freedom model of atmospheric turbulence, introduced by Lorenz in 1996. The vector field can be decomposed into an energy-conserving, time-reversible part, plus a non-time reversible part, including forcing and dissipation. We construct a modified version of the model where viscosity varies with time, in such a way that energy is conserved, and the resulting dynamics is fully time-reversible. For each value of the forcing, the statistical properties of the irreversible and reversible model are in excellent agreement, if in the latter the energy is kept constant at a value equal to the time-average realized with the irreversible model. In particular, the average contraction rate of the phase space of the time-reversible model agrees with that of the irreversible model, where instead it is constant by construction. We also show that the phase space contraction rate obeys the fluctuation relation, and we relate its finite time corrections to the characteristic time scales of the system. A local version of the fluctuation relation is explored and successfully checked. The equivalence between the two non-equilibrium ensembles extends to dynamical properties such as the Lyapunov exponents, which are shown to obey to a good degree of approximation a pairing rule. These results have relevance in motivating the importance of the chaotic hypothesis. in explaining that we have the freedom to model non-equilibrium systems using different but equivalent approaches, and, in particular, that using a model of a fluid where viscosity is kept constant is just one option, and not necessarily the only option, for describing accurately its statistical and dynamical properties.     

Groups with Polycyclic Non-Normal Subgroups

The structure of groups in which many subgroups have a certain property X has been investigated for several choices of the property X. Groups whose non-normal subgroups satisfy certain finite rank conditions are studied in this article. In particular, a classification of groups in which every subgroup is either normal or polycyclic is given.(Dedicated to Mario Curzio on the occasion of his 70th birthday)1991 Mathematics Subject Classification: 20F16     

On optimal regularity of free boundary problems and a conjecture of De Giorgi

We present a general theory to study optimal regularity for a large class of nonlinear elliptic systems satisfying general boundary conditions and in the presence of a geometric transmission condition on the free boundary. As an application we give a full positive answer to a conjecture of De Giorgi on the analyticity of local minimizers of the Mumford‐Shah functional. © 2004 Wiley Periodicals, Inc.     

Semicircular limits on the free Poisson chaos: Counterexamples to a transfer principle

We establish a class of sufficient conditions ensuring that a sequence of multiple integrals with respect to a free Poisson measure converges to a semicircular limit. We use this result to construct a set of explicit counterexamples showing that the transfer principle between classical and free Brownian motions (recently proved by Kemp, Nourdin, Peccati and Speicher (2012)) does not extend to the framework of Poisson measures. Our counterexamples implicitly use kernels appearing in the classical theory of random geometric graphs. Several new results of independent interest are obtained as necessary steps in our analysis, in particular: (i) a multiplication formula for free Poisson multiple integrals, (ii) diagram formulae and spectral bounds for these objects, and (iii) a counterexample to the general universality of the Gaussian Wiener chaos in a classical setting.     

Experimental and Theoretical Study of Helium Broadening and Shift of HCO+ Rotational Lines

An experimental and theoretical study of pressure broadening and pressure shift of HCO⁺ rotational lines perturbed by collisions with He is presented. Results are reported from measurements at 88 K for the lines j=4←3, 5←4 and 6←5 with frequencies ranging from 0.35 to 0.54 THz. Using a new CCSD(T)/aug‐cc‐pVQZ potential energy surface for the He–HCO⁺ interaction, the collisional line shape parameters are studied from fully quantum and semiclassical calculations. Results from the quantum treatment are in satisfactory agreement with experiments whereas the semiclassical approach can lead to appreciable differences. A study of the dependence of line width Γ and shift s as a function of the translational energy shows the presence of quantum oscillations. Calculations on a previous Hartree–Fock‐based potential energy surface lead to quite similar results for the collisional line shape parameters. Using a simplified version of the potential morphing method it is found that the line width Γ is particularly sensitive to the long‐range part of the potential energy surface. This also explains the success of the first line‐broadening calculations which date back to the 1950s.     

Iridoids Isolation from a Phytochemical Study of the Medicinal Plant Teucrium parviflorum Collected in Iraqi Kurdistan

Herbal medicines are still widely practiced in Kurdistan Region-Iraq, especially by people living in villages on mountainous regions. Among plants belonging to the genus Teucrium (family Lamiaceae), which are commonly employed in the Kurdish traditional medicine, we have analyzed, for the first time, the methanol and aqueous methanol extracts of T. parviflorum aerial parts. The plant is mainly used by Kurds to treat jaundice, liver disorders and stomachache. We aimed to determine the phytochemical profile of the extracts and the structures of the main components, so to provide a scientific rationale for the ancient use of the plant in the ethno-pharmacological field. TLC analysis of the two extracts on silica gel and reversed phase TLC plates, using different visualization systems, indicated similar contents and the presence of phenolics, flavonoids, terpenoids and sugars. The chlorophyll-free extracts exhibited weak/no antimicrobial activities against a panel of bacteria (MICs = 800–1600 µg/mL) and fungal strains (MICs ≥ 5 mg/mL). At the concentration of 600 µg/mL, the methanol extract showed moderate antiproliferative effects against A549 and MCF-7 cancer cell lines in the MTS assay. Moreover, both extracts exhibited a significant dose-dependent free radical scavenging action against the 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical (EC₅₀ = 62.11 and 44.25 μg/mL, respectively). In a phytochemical study, a high phenolic content (77.08 and 81.47 mg GAE/g dry extract, respectively) was found in both extracts by the Folin–Ciocalteu assay. Medium pressure liquid chromatographic (MPLC) separation of the methanol extract on a reversed phase cartridge eluted with a gradient of MeOH in H₂O, afforded two bioactive iridoid glucosides, harpagide (1) and 8-O-acetylharpagide (2). The structures of 1 and 2 were established by spectral data, chemical reactions, and comparison with the literature. Interestingly, significant amounts of hepatotoxic furano neo-clerodane diterpenoids, commonly occurring in Teucrium species, were not detected in the extract. The wide range of biological activities reported in the literature for compounds 1 and 2 and the significant antiradical effects of the extracts give scientific support to the traditional use in Iraqi Kurdistan of T. parviflorum aerial parts for the preparation of herbal remedies.     

Wetting behavior of porous silicon surfaces functionalized with a fulleropyrrolidine

We report the immobilization of a fulleropyrrolidine, bearing a dec-9-ynyl functionality, on silicon surfaces through a thermal hydrosilylation protocol. Contact angle measurements on porous silicon (PS) surfaces reveal an unusual dependence of the angle with the PS roughness that apparently contradicts Wenzel's formula. This result has been explained by an extension of Wenzel's model in which the critical angle, which discriminates between the hydrophilic/hydrophobic character of a solid material, is substantially reduced below 90 degrees by surface roughness.     

Physical and electrochemical properties of N-alkyl-N-methylpyrrolidinium bis(fluorosulfonyl)imide ionic liquids: PY13FSI and PY14FSI

Two ionic liquids based upon N-alkyl-N-methylpyrrolidinium cations (PY(1R)(+)) (R=3 for propyl or 4 for butyl) and the bis(fluorosulfonyl)imide (FSI(-)), N(SO2F)2(-), anion have been extensively characterized. The ionic conductivity and viscosity of these materials are found to be among the highest and lowest, respectively, reported for aprotic ionic liquids. Both ionic liquids crystallize readily on cooling and undergo several solid-solid phase transitions on heating prior to melting. PY13FSI and PY14FSI are found to melt at -9 and -18 degrees C, respectively. The thermal stability of PY13FSI and PY14FSI is notably lower than for the analogous salts with the bis(trifluoromethanesulfonyl)imide (TFSI(-)), N(SO2CF3)2(-), anion. Both ionic liquids have a relatively wide electrochemical stability window of approximately 5 V.