Generalized Jacobi Identities and Ball-Box Theorem for Horizontally Regular Vector Fields

Consider a family $\mathcal{H}:= \{X_{j} =: f_{j}\cdot\nabla: j=1,\ldots , m\}$ of C ¹ vector fields in ? ⁿ and let s∈?. We assume that for all p∈{1,…,s} and j ₁,…,j _p ∈{1,…,m} the horizontal derivatives $X_{j_{1}}X_{j_{2}}\cdots X_{j_{p-1}}f_{j_{p}}$ exist and are Lipschitz continuous with respect to the control distance defined by  $\mathcal{H}$ . Then we show that different notions of commutator agree. This involves an accurate analysis of some algebraic identities involving nested commutators which seem to have an independent interest. Our principal applications are a ball-box theorem, the doubling property, and the Poincaré inequality for Hörmander vector fields under an intrinsic “horizontal regularity” assumption on their coefficients.     

Ideal homoatomic and heteroatomic photonic crystal molecules

A local tuning of the modes of photonic crystal systems both to blue and to red sides of the resonance is implemented by nano-infiltration/evaporation of water and laser micro-oxidation. This technology is used to completely control coupled photonic nanocavities (photonic crystal molecules). Beside the standard condition of zero detuning between identical modes of the two cavities (homoatomic molecule), we are also able to produce coupling between two modes of different polarization and spatial distribution (heteroatomic molecule).     

Analysis of the essential oil of Amsonia illustris

The root and leaf essential oils, present in trace amounts in Amsonia illustris Woods. (Apocynaceae), were isolated by steam distillation and their chemical constituents identified by GC-FID and GC-MS. More than 80% of the thirty volatile compounds in the leaf oil were identified, the major constituents being mainly sesquiterpenes like a-humulene (14.5%), beta-caryophyllene (12.4%) and guaiol (11.6%). The volatile ingredients of the root oil were pinocampheol, methyl salicylate, (2E,4E)- decadienal, eugenol and trans-isoeugenol.     

Glucocorticoids Directly Affect Hyaluronan Production of Orbital Fibroblasts; A Potential Pleiotropic Effect in Graves’ Orbitopathy

Orbital connective tissue expansion is a hallmark of Graves’ orbitopathy (GO). In moderate-to-severe active GO, glucocorticoids (GC) are the first line of treatment. Here we show that hydrocortisone (HC), prednisolone (P), methylprednisolone (MP), and dexamethasone (DEX) inhibit the hyaluronan (HA) production of orbital (OF) and dermal (DF) fibroblasts. HA production of GO OFs (n = 4), NON-GO OFs (n = 4) and DFs (n = 4) was measured by ELISA. mRNA expression of enzymes of HA metabolism and fibroblast proliferation was examined by RT-PCR and BrdU incorporation, respectively. After 24 h of GC treatment (1µM) HA production decreased by an average of 67.9 ± 3.11% (p < 0.0001) in all cell cultures. HAS2, HAS3 and HYAL1 expression in OFs also decreased (p = 0.009, p = 0.0005 and p = 0.015, respectively). Ten ng/mL PDGF-BB increased HA production and fibroblast proliferation in all cell lines (p < 0.0001); GC treatment remained effective and reduced HA production under PDGF-BB-stimulated conditions (p < 0.0001). MP and DEX reduced (p < 0.001, p = 0.002, respectively) PDGF-BB-induced HAS2 expression in OFs. MP and DEX treatment decreased PDGF-BB stimulated HAS3 expression (p = 0.035 and p = 0.029, respectively). None of the GCs tested reduced the PDGF-BB stimulated proliferation rate. Our results confirm that GCs directly reduce the HA production of OFs, which may contribute to the beneficial effect of GCs in GO.     

Water quality of two glacial alpine Italian lakes

The purpose of this study was to characterize, in a period of one year, two glacial lakes, Alice and Meugliano, located in an alpine reservoir on the basis of physical and chemical features. The two lakes show two periods of mixing: one in the spring and one in the autumn, so can be classified as dimictic lakes. They are characterized by pH, alkalinity, low conductivity and and quite dilute ionic concentrations. With regard to nutrients, most nitrogen occurred in the nitric form in the superficial layers. During the period of thermal stratification, in the anoxic layer NO3- decreases and NH4+ increases, confirming the activity of the anaerobic denitrificant bacteria. Total and soluble phosphorus levels show homogeneity during the cold period at different depths, while with stratification concentrations increase in the hypolimnium and metalimnium. In both lakes there is an inverse correlation between transparency and chlorophyll a. To evaluate the trophic state the conventional criteria of Nurnberg 2 and four lake trophic indices (TSIs) are used. Both evaluations suggest that the two lakes are eutrophic, with worse conditions in Alice. Deviations of the trophic states, based on the relation between TSIs, indicate that factors other than phosphorous limit the algal biomass, and that non-algal particles influence light attenuation     

X-ray crystal structure of the copper(II)bis(2,2′-dipyridyl)dithiocarbamate,produced by an unusual reaction of CS2 with Cu−N bonds

The title compound was obtained from a CS₂ solution of bis(2,2-dipyridylamido)copper(II), by insertion of solvent into this complex. In the structure of the dithiocarbamate the metal atom is approximately square-planar coordinated by four S atoms from two chelating ligands. Considering the long interactions between the metal center and the S(2) atom from a centrosymmetrically related complex [Cu(1)...S(2)=3.230 Å], double bridged dimers are formed with the copper atoms in an elongated square-pyramidal coordination. The crystals are monoclinic, space groupP2 ₁/n witha=14.549(3),b=11.662(3)c=15.329(4) Å and =114.79(2)°.     

An enantioselective synthetic route to cis-2,4-disubstituted and 2,4-bridged piperidines

A synthetic route to enantiopure cis-2,4-disubstituted and 2,4-bridged piperidines is reported, the key step being a stereoselective conjugate addition of an organocuprate to a phenylglycinol-derived unsaturated lactam bearing a substituent at the 8a-position.