Ordered distribution of I and Cl in the low-temperature crystal structure of mutnovskite, Pb4As2S6ICl: An X-ray single-crystal study

To study the temperature-dependent structural changes and to analyze the crystal chemical behavior of the halogens as a function of temperature, a crystal of the recently discovered mineral mutnovskite, ideally Pb₂AsS₃(I,Cl,Br), has been investigated by X-ray single-crystal diffraction methods at 300 and 110 K. At room temperature (RT) mutnovskite was confirmed to possess a centrosymmetric structure-type, space group Pnma, while at low temperature (110 K) it adopts a non-centrosymmetric orthorhombic structure-type, space group Pnm2₁, with a=11.5394(9) Å, b=6.6732(5) Å, c=9.3454(7) Å, V=719.64(9) Å³ and Z=2. Mutnovskite reconverts to the centrosymmetric-type upon returning to RT thus indicating that the phase transition is completely reversible in character. The refinement of the LT-structure leads to a residual factor R=0.0336 for 1827 independent observed reflections [F_o>4σ(F_o)] and 80 variables. The crystal structure of cooled mutnovskite is topologically identical to that observed at RT and the slight structural changes occurring during the phase transition Pnma→Pnm2₁ are mainly restricted to the coordination polyhedra around Pb. The structure solution revealed that I and Cl are ordered into two specific sites. Indeed, the unique mixed (I,Cl) position in the RT-structure (Wyckoff position 4c) transforms into two 2a Wyckoff positions in the LT-structure hosting I and Cl, respectively.     

Cohomology of affine Artin groups and applications

The result of this paper is the determination of the cohomology of Artin groups of type and with non-trivial local coefficients. The main result

is an explicit computation of the cohomology of the Artin group of type with coefficients over the module Here the first standard generators of the group act by -multiplication, while the last one acts by -multiplication. The proof uses some technical results from previous papers plus computations over a suitable spectral sequence. The remaining cases follow from an application of Shapiro's lemma, by considering some well-known inclusions: we obtain the rational cohomology of the Artin group of affine type as well as the cohomology of the classical braid group with coefficients in the -dimensional representation presented in Tong, Yang, and Ma (1996). The topological counterpart is the explicit construction of finite CW-complexes endowed with a free action of the Artin groups, which are known to be spaces in some cases (including finite type groups). Particularly simple formulas for the Euler-characteristic of these orbit spaces are derived.

     

A Tutorial on Computational Cluster Analysis with Applications to Pattern Discovery in Microarray Data

Microarrays offer unprecedented possibilities for the so-called omic, e.g., genomic and proteomic, research. However, they are also quite challenging data to analyze. The aim of this paper is to provide a short tutorial on the most common approaches used for pattern discovery and cluster analysis as they are currently used for microarrays, in the hope to bring the attention of the Algorithmic Community on novel aspects of classification and data analysis that deserve attention and have potential for high reward. R. Giancarlo is partially supported by Italian MIUR grants PRIN “Metodi Combinatori ed Algoritmici per la Scoperta di Patterns in Biosequenze” and FIRB “Bioinformatica per la Genomica e la Proteomica” and Italy-Israel FIRB Project “Pattern Discovery Algorithms in Discrete Structures, with Applications to Bioinformatics”. D. Scaturro is supported by a MIUR Fellowship in the Italy-Israel FIRB Project “Pattern Discovery Algorithms in Discrete Structures, with Applications to Bioinformatics”.     

XPS and AFM characterization of the enzyme glucose oxidase immobilized on SiO(2) surfaces

A process to immobilize the enzyme glucose oxidase on SiO2 surfaces for the realization of integrated microbiosensors was developed. The sample characterization was performed by monitoring, step by step, oxide activation, silanization, linker molecule (glutaraldehyde) deposition, and enzyme immobilization by means of XPS, AFM, and contact angle measurements. The control of the environment during the procedure, to prevent silane polymerization, and the use of oxide activation to obtain a uniform enzyme layer are issues of crucial importance. The correct protocol application gives a uniform layer of the linker molecule and the maximum sample surface coverage. This result is fundamental for maximizing the enzyme bonding sites on the sample surface and achieving the maximum surface coverage. Thin SiO2 layers thermally grown on a Si substrate were used. The XPS Si 2p signal of the substrate was monitored during immobilization. Such a signal is not completely shielded by the thin oxide layer and it is fully suppressed after the completion of the whole protocol. A power spectral density analysis on the AFM measurements showed the crucial role of both the oxide activation and the intermediate steps (silanization and linker molecule deposition) to obtain uniform immobilized enzyme coverage. Finally, enzymatic activity measurements confirmed the suitability of the optimized protocol.     

Interaction of mixed-donor macrocycles containing the 1,10-phenanthroline subunit with selected transition and post-transition metal ions: metal ion recognition in competitive liquid-liquid solvent extraction of Cu(II), Zn(II), Pb(II), Cd(II), Ag(I), and Hg(II)

Two new mixed aza-thia crowns 5-aza-2,8-dithia[9]-(2,9)-1,10-phenanthrolinophane (L(4)) and 2,8-diaza-5-thia[9]-(2,9)-1,10-phenanthrolinophane (L(7)) have been synthesized and characterized. The coordination behavior of L(4) and L(7) toward the metal ions Cu(II), Zn(II), Pb(II), Cd(II), Hg(II), and Ag(I) was studied in aqueous solution by potentiometric methods, in CD3CN/D2O 4:1 (v/v) by (1)H NMR titrations and in the solid state. The data obtained were compared with those available for the coordination behavior toward the same metal ions of structurally analogous mixed donor macrocyclic ligands L(1)-L(3), L(5), L(6): all these contain a phenanthroline subunit but have only S/O/N(aromatic) donor groups in the remaining portion of the ring and are, therefore, less water-soluble than L(4) and L(7). The complexes [Cd(NO3)2(L(5))], [Pb(L(7))](ClO4)2 x 1/2MeCN, [Pb(L(4))](ClO4)2 x MeCN, and [Cu(L(7))](ClO4)2 x 3/2MeNO2 were characterized by X-ray crystallography. The efficacy of L(1)-L(7) in competitive liquid-liquid metal ion extraction of Cu(II), Zn(II), Cd(II), Pb(II), Ag(I), and Hg(II) was assessed. In the absence of Hg(II), a clear extraction selectivity for Ag(I) was observed in all systems investigated.     

Synthesis, characterization, and DFT/TD-DFT calculations of highly phosphorescent blue light-emitting anionic iridium complexes

Highly phosphorescent blue-light-emitting anionic iridium complexes (C4H9)4N[Ir(2-phenylpyridine)2(CN)2] (1), (C4H9)4N[Ir(2-phenyl-4-dimethylaminopyridine)2(CN)2] (2), (C4H9)4N[Ir(2-(2,4-difluorophenyl)-pyridine)2(CN)2] (3), (C4H9)4N[Ir(2-(2,4-difluorophenyl)-4-dimethylaminopyridine)2(CN)2] (4), and (C4H9)4N[Ir(2-(3,5-difluorophenyl)-4-dimethylaminopyridine)2(CN)2] (5) were synthesized and characterized using NMR, UV-vis absorption, and emission spectroscopy and electrochemical methods. In these complexes color and quantum yield tuning aspects are demonstrated by modulating the ligands with substituting donor and acceptor groups on both the pyridine and phenyl moieties of 2-phenylpyridine. Complexes 1-5 display intense photoluminescence maxima in the blue region of the visible spectrum and exhibit very high phosphorescence quantum yields, in the range of 50-80%, with excited-state lifetimes of 1-4 micros in acetonitrile solution at 298 K. DFT and time dependent-DFT calculations were performed on the ground and excited states of the investigated complexes to provide insight into the structural, electronic, and optical properties of these systems.     

Different Faces of the Shearlet Group

Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrable representations of the shearlet groups provide not only the basis for the shearlet transforms but also for a very natural definition of scales of smoothness spaces, called shearlet coorbit spaces. The aim of this paper is twofold: first we discover isomorphisms between shearlet groups and other well-known groups, namely extended Heisenberg groups and subgroups of the symplectic group. Interestingly, the connected shearlet group with positive dilations has an isomorphic copy in the symplectic group, while this is not true for the full shearlet group with all nonzero dilations. Indeed we prove the general result that there exist, up to adjoint action of the symplectic group, only one embedding of the extended Heisenberg algebra into the Lie algebra of the symplectic group. Having understood the various group isomorphisms it is natural to ask for the relations between coorbit spaces of isomorphic groups with equivalent representations. These connections are examined in the second part of the paper. We describe how isomorphic groups with equivalent representations lead to isomorphic coorbit spaces. In particular we apply this result to square integrable representations of the connected shearlet groups and metaplectic representations of subgroups of the symplectic group. This implies the definition of metaplectic coorbit spaces. Besides the usual full and connected shearlet groups we also deal with Toeplitz shearlet groups.     

Variation of Loewner Chains,Extreme and Support Points in the Class $$S^0$$ in Higher Dimensions

We introduce a family of natural normalized Loewner chains in the unit ball, which we call “geräumig”—spacious—which allow us to construct, by means of suitable variations, other normalized Loewner chains which coincide with the given ones from a certain time on. We apply our construction to the study of support points, extreme points, and time-\(\log M\)-reachable mappings in the class \(S^0\) of mappings admitting parametric representation.     

Contact points and fractional singularities for semigroups of holomorphic self-maps of the unit disc

We study boundary singularities which can appear for infinitesimal generators of one-parameter semigroups of holomorphic self-maps of the unit disc. We introduce “regular” fractional singularities and characterize them in terms of the behavior of the associated semigroups and K?nigs functions. We also provide necessary and sufficient geometric criteria on the shape of the image of the K?nigs function for having such singularities. In order to do this, we study contact points of semigroups and prove that any contact (not fixed) point of a one-parameter semigroup corresponds to a maximal arc on the boundary to which the associated infinitesimal generator extends holomorphically as a vector field tangent to this arc.