Weak approximation by bounded Sobolev maps with values into complete manifolds

We have recently introduced the trimming property for a complete Riemannian manifold $N^n$ as a necessary and sufficient condition for bounded maps to be strongly dense in $W^{1,p}(B^m;N^n)$ when $p\in \{1,\dots ,m\}$. We prove in this note that, even under a weaker notion of approximation, namely the weak sequential convergence, the trimming property remains necessary for the approximation in terms of bounded maps. The argument involves the construction of a Sobolev map having infinitely many analytical singularities going to infinity.     

On the trees associated to plane curve singularities and ideals

Si comparano diverse nozioni d’equisingolarità per le curve tracciate sopra una superficie complessa liscia, e per gli ideali di dimensione finita dell’anello locale d’uno dei suoi punti. Si vede che, in generale, questi nozioni sono diverse, ma (per le curve) queste coincidono se esse fossero membri della stessa famiglia continua.     

Continued fraction calculation of the eigenvalues of tridiagonal matrices arising from the Schroedinger equation

The usual Sturmanian sequence for finding the eigenvalues of a tridiagonal matrix arising from the radial Schroedinger equation is found to be unstable. A self-stabilising continued fraction approach is suggested.     

Spatio-temporal anomalous diffusion imaging: results in controlled phantoms and in excised human meningiomas

Recently, we measured two anomalous diffusion (AD) parameters: the spatial and the temporal AD indices, called γ and α, respectively, by using spectroscopic pulse gradient field methods. We showed that γ quantifies pseudo-superdiffusion processes, while α quantifies subdiffusion processes. Here, we propose γ and α maps obtained in a controlled heterogeneous phantom, comprised of packed micro-beads in water and in excised human meningiomas. In few words, α maps represent the multi-scale spatial distribution of the disorder degree in the system, while γ maps are influenced by local internal gradients, thus highlighting the interface between compartments characterized by different magnetic susceptibility. γ maps were already obtained by means of AD stretched exponential imaging and α-type maps have been recently achieved for fixed rat brain with the aim of highlighting the fractal dimension of specific brain regions. However, to our knowledge, the maps representative of the spatial distribution of α and γ obtained on the same controlled sample and in the same excised tissue have never been compared. Moreover, we show here, for the first time, that α maps are representative of the spatial distribution of the disorder degree of the system.     

Future contributions to Journal of Chemical Crystallography

Future contributions to Journal of Chemical Crystallography     

A versatile route to potential dihydrofolate reductase inhibitors via the hitherto unknown 6-benzyl-2-(O-methyl)uracils: Synthesis of isotrimethoprim

The synthesis of 2, 4-diamino-6-(3, 4, 5-trimethoxybenzyl)pyrimidine (isotrimethoprim) has been accomplished starting from 2-(O-methyl)-6-(3, 4, 5-trimethoxybenzyl)uracil by standard procedures. The benzyluracil derivative has been obtained by reacting O-methylisourea sulphate and ethyl 3, 4, 5-trimethoxyphenacetylace-tate.     

Synthesis of 4-(pyrazol-5-yl)-1,2,4-triazole-3-thiones

Condensation of pyrazolyl isothiocyanates 2 with N-substituted hydrazines provided the 2-methyl/phenyl-4-(pyrazol-5-yl)thiosemicarbazides 3 . Cyclization of 3 with formic acid-acetic anhydride or with triethyl orthoacetate-acetic anhydride provided 4-(pyrazol-5-yl)-l,2,4-triazole-3-thiones 4a-f and 5-methyl-4-(pyrazol-5-yl)-1,2,4-triazole-3-thiones 4g-I respectively.     

[1,2,3,4-Tetrakis(α/β-d-galactopyranos-6-yl)phthalocyaninato]zinc(II): a water-soluble phthalocyanine

A novel water-soluble asymmetrical sugar-phthalocyanine was prepared via a statistical cross-condensation of tetrakis(1,2:3,4-di-O-isopropylidene-α-d-galactopyranos-6-yl)phthalonitrile with phthalonitrile. The new compound, with amphiphilic character, can be useful as a selective photosensitizer in photodynamic therapy, as well as for constructing phthalocyanine-based supramolecular systems.     

Variable coordination modes of NO2(-) in a series of Ag(I) complexes containing triorganophosphines, -arsines,and -stibines. Syntheses,spectroscopic characterization (IR, 1H and 31P NMR,electrospray ionization mass), and structures of [AgNO2(R(3)E)(x)] adducts (E = P,As, Sb,x = 1-3)

Adducts of triorganophosphine, triphenylarsine, and triphenylstibine with silver(I) nitrite have been synthesized and characterized both in solution ((1)H, (31)P NMR) and in the solid state (IR, single-crystal X-ray structure analysis). In addition aggregates of AgNO(2) and ER(3) (E = P, As, Sb) have been identified in solution by electrospray ionization mass spectrometry (ESI-MS). The topology of the structures in the solid state was found to depend on the nature of ER(3) and on the stoichiometric ratio AgNO(2):ER(3). The adducts AgNO(2):EPh(3) (1:1) (E = P or Sb) are one-dimensional polymers, the role of NO(2)(-) being to bridge successive metal atoms by coordination of the two oxygens to one silver atom and the nitrogen lone pair to a successive Ag. The adduct AgNO(2):P(o-tolyl)(3) (1:1) is mononuclear, due to steric hindrance of the phosphine, the nitrite being O,O'-bidentate, a rare example of a quasi-linear P-Ag-X array. AgNO(2):P(p-F-C(6)H(4))(3) (1:1) is a dimer, the nitrite being coordinated through both oxygens, the first unidentate, the second bridging bidentate. P(o-tolyl)(3) and Pcy(3) form 1:2 adducts, also mononuclear, the nitrite still an O,O'-chelate. In contrast, the adduct AgNO(2):AsPh(3) (1:2) is a centrosymmetric dimer, essentially an aggregate of a pair of [Ag(O(2)N)(AsPh(3))(2)] arrays with one nitrite oxygen being the bridging atom. The adducts AgNO(2):EPh(3) (1:3) (E = As, Sb) are mononuclear, the nitrite behaving as a consistently strong O,O'-chelate. The E = As adduct is a triclinic solvated form, whereas the unsolvated E = Sb species is monoclinic. ESI-MS spectra of acetonitrile solutions of these complexes show the existence of [Ag(ER(3))](+), [Ag(CH(3)CN)](+), [Ag(CH(3)CN)(2)](+), [AgCl(2)](-), [Ag(NO(2))(2)](-), [Ag(ER(3))(CH(3)CN)](+), and [Ag(ER(3))(2)](+) as well as higher aggregates [Ag(2)(NO(2))(ER(3))(2)](+), [Ag(2)(NO(2))(3)](-) and [Ag(2)Cl(2)(NO(2))](-), which are less prevalent.