Reactions of metal iodides as a simple route to heterometallics: synthesis, structural transformations, thermal and luminescent properties of novel hybrid iodoargentate derivatives templated by [YL8]3+ or [YL7]3+ cations (L = DMF or DMSO)

A 1 : 3 molar reaction of YI3 and AgI in dimethylformamide (DMF) in the presence of NH4I afforded [Y(DMF)8][Ag3(mu3-I)(mu-I)3I2] (1) with good yield, whereas the similar reaction in dimethylsulfoxide (DMSO) gave complexes [Y(DMSO)8][Ag2(mu-I)3I2] (2) and/or [Y(DMSO)8]2[Ag4(mu3-I)2(mu-I)4I2][I]2 (3), depending on the reaction and crystallization conditions. These discrete heterometallic hybrid compounds 1-3 undergo solid- and solution-state transformations via condensation of iodoargentate anions. So in the confined and solvent-free environment of paratone, crystals of 1 transformed into a 1D zig-zag structure [Y(DMF)8]3+[Ag6(mu4-I)2(mu3-I)2(mu-I)5]1infinity(3-) (4), whereas those of 2 were first converted into 3 and finally into [Y(DMSO)7]4[Ag4(mu3-I)4I4]3 (5). In solution phase, re-crystalization of 1 or 2 from DMSO-toluene gave 3 as an exclusive species, whereas reaction of 1 with 3 equiv of AgI in DMF afforded 4 with good yield. Alternatively, 4 could also be synthesized with excellent yield from a 1 : 6 molar reaction of YI3 and AgI. The above transformations suggest that, for a given metal-organic cation, an iodometallate cluster with higher nuclearity is thermodynamically more stable. Single crystal X-ray structures are reported for all the compounds and a mechanism for the structural transformation of 2 to 3 is proposed. In addition, spectroscopic, thermo-gravimetric and luminescent properties of the complexes 1, 3 and 4, which were obtained exclusively and in pure form, are also described.     

Bounded enumeration reducibility and its degree structure

We study a strong enumeration reducibility, called bounded enumeration reducibility and denoted by ≤_be, which is a natural extension of s-reducibility ≤_s. We show that ≤_s, ≤_be, and enumeration reducibility do not coincide on the ${\Pi^0_1}$ –sets, and the structure ${\boldsymbol{\mathcal{D}_{\rm be}}}$ of the be-degrees is not elementarily equivalent to the structure of the s-degrees. We show also that the first order theory of ${\boldsymbol{\mathcal{D}_{\rm be}}}$ is computably isomorphic to true second order arithmetic: this answers an open question raised by Cooper (Z Math Logik Grundlag Math 33:537–560, 1987).     

Optimizing X‐ray mirror thermal performance using matched profile cooling

To cover a large photon energy range, the length of an X‐ray mirror is often longer than the beam footprint length for much of the applicable energy range. To limit thermal deformation of such a water‐cooled X‐ray mirror, a technique using side cooling with a cooled length shorter than the beam footprint length is proposed. This cooling length can be optimized by using finite‐element analysis. For the Kirkpatrick–Baez (KB) mirrors at LCLS‐II, the thermal deformation can be reduced by a factor of up to 30, compared with full‐length cooling. Furthermore, a second, alternative technique, based on a similar principle is presented: using a long, single‐length cooling block on each side of the mirror and adding electric heaters between the cooling blocks and the mirror substrate. The electric heaters consist of a number of cells, located along the mirror length. The total effective length of the electric heater can then be adjusted by choosing which cells to energize, using electric power supplies. The residual height error can be minimized to 0.02 nm RMS by using optimal heater parameters (length and power density). Compared with a case without heaters, this residual height error is reduced by a factor of up to 45. The residual height error in the LCLS‐II KB mirrors, due to free‐electron laser beam heat load, can be reduced by a factor of ～11 below the requirement. The proposed techniques are also effective in reducing thermal slope errors and are, therefore, applicable to white beam mirrors in synchrotron radiation beamlines.     

Interaction of oxovanadium(IV) with carboxylic ligands in aqueous solution: A thermodynamic and visible spectrophotometric study

The hydrolysis of VO²⁺ and the complex with sulfate were studied potentiometrically, spectrophotometrically and calorimetrically, in NaCl aqueous solution (0 < I ≤ 1 mol L^− 1) and at t = 25 °C. The formation of two hydrolytic species VO(OH)⁺ and VO₂(OH)₂²⁺ and one complex with sulfate was found, with log β = − 5.65 for the reaction VO²⁺ + H₂O = VO(OH)⁺ + H⁺, log β = − 7.02 for the reaction 2VO²⁺ + 2H₂O = (VO)₂(OH)₂²⁺ + 2H⁺ and log K = 1.73 for VOSO₄⁰ species (at I = 0.1 mol L^− 1 and t = 25 °C). For these species, using calorimetric data, ΔH and TΔS values were also obtained. By using the above values, interactions of VO²⁺ with acetate (ac), malonate (mal), succinate (suc), 1,2,3-propanetricarboxylate (tca) and 1,2,3,4-butanetetracarboxylate (btc) ligands were studied potentiometrically and spectrophotometrically. The formation of ML⁺, ML₂⁰ and MLOH⁰ for ac; ML⁰, MLH⁺, ML₂²⁻ and ML₂H⁻ for mal; ML⁰, MLH⁺ and MLOH⁻ for suc; ML⁻ and MLH⁰ for tca and ML²⁻, MLH⁻ and MLH₂⁰ for btc were found. Formation constants are reported at I = 0.1 mol L^− 1, together with SIT parameters for the dependence on ionic strength. By visible spectrophotometric measurements, λ_max and ε_max values for the relevant species in solution were determined.     

Finite difference solution of Euler equations arising in variational image segmentation

This paper deals with finite-difference approximations of Euler equations arising in the variational formulation of image segmentation problems. We illustrate how they can be defined by the following steps: (a) definition of the minimization problem for the Mumford–Shah functional (MSf), (b) definition of a sequence of functionals Γ-convergent to the MSf, and (c) definition and numerical solution of the Euler equations associated to the kth functional of the sequence. We define finite difference approximations of the Euler equations, the related solution algorithms, and we present applications to segmentation problems by using synthetic images. We discuss application results, and we mainly analyze computed discontinuity contours and convergence histories of method executions. This revised version was published online in June 2006 with corrections to the Cover Date.     

An algebraic spin and statistics theorem

A spin-statistics theorem and a PCT theorem are obtained in the context of the superselection sectors in Quantum Field Theory on a 4-dimensional spacetime. Our main assumption is the requirement that the modular groups of the von Neumann algebras of local observables associated with wedge regions act geometrically as pure Lorentz transformations. Such a property, satisfied by the local algebras generated by Wightman fields because of the Bisognano-Wichmann theorem, is regarded as a natural primitive assumption.Dedicated to Hans Borchers on the occasion of his seventieth birthdaySupported in part by MURST and CNR-GNAFA.     

Epifluorescence and light microscopy evidencing structural and functional polymorphism of ribosomal DNA in fish (Teleostei: Astyanax fasciatus)

New karyotypic data are presented for the Astyanax fasciatus species complex from four different locations on the Upper Tibagi River in the state of Paraná, Brazil. Chromosome markers were analyzed using conventional (Ag-NOR) and molecular (FISH with 18S biotinylated probes) methods. Two cytotypes were found in cell counts with diploid number 2n = 48 chromosomes and 2n = 50 chromosomes, previously denominated Cytotype A and B, respectively. Two specific patterns of Ag-NORs markers (ribosomal gene activity) were found, with intra-population and inter-population variations. Cytotype A exhibited two to three chromosomes with NOR sites in the metaphases analyzed. In Cytotype B specimens, up to three markers were found, demonstrating greater intra-population and inter-population variation. All individuals with only one chromosome pair with NORs were located in the telomeric region of the short arm of Chromosome 5. This characteristic was interpreted as ancestral for the species. Another identified pattern revealed a site in the telomeric region probably in the long arm of Chromosome 4 and another submetacentric chromosome with bitelomeric marks exclusively in specimens with 2n = 50 chromosomes. In the FISH analysis (ribosomal gene structure), five to seven markers were identified in Cytotype A and three to seven markers were identified in Cytotype B. Structural chromosome events and/or transposable elements are required to explain the ribosomal gene location diversity in these organisms. The results of the present study corroborate the hypothesis that the A. fasciatus of the Upper Tibagi River region constitute a species complex.