Unconditional families in Banach spaces

It is shown that for every separable Banach space X with non-separable dual, the space contains an unconditional family of size . The proof is based on Ramsey Theory for trees and finite products of perfect sets of reals. Among its consequences, it is proved that every dual Banach space has a separable quotient.     

Salicylaldoxime in manganese(III) carboxylate chemistry: Synthesis, structural characterization and physical studies of hexanuclear and polymeric complexes

The use of salicylaldehyde oxime (H₂salox) in manganese(III) carboxylate chemistry has yielded new members of the family of hexanuclear compounds presenting the [Mn₆(μ₃-O)₂(μ₂-OR)₂]¹²⁺ core, complexes [Mn^III₆(μ₃-O)₂(O₂CPh)₂(salox)₆(L₁)₂(L₂)₂] (L₁ = py, L₂ = H₂O (1); L₁ = Me₂CO, L₂ = H₂O (2); L₁ = L₂ = MeOH (3)). Addition of NaOMe to the acetonitrile reaction mixture, afforded the 1D complex [Mn^III₃Na(μ₃-O)(O₂CPh)₂(salox)₃(MeCN)]_n (4), whereas addition of NaClO₄ to the acetone reaction mixture afforded an analogous 1D complex [Mn^III₃Na(μ₃-O)(O₂CPh)₂(salox)₃(Me₂CO)]_n (5). The structures of 1–3 present the [Mn₆(μ₃-O)₂(μ₂-OR)₂]¹²⁺ core and can be described as two [Mn₃(μ₃-O)]⁷⁺ triangular subunits linked by two μ₂-oximato oxygen atoms of the salox²⁻ ligands, which show the less common μ₃-κ²O:κO′:κN coordination mode. The benzoato ligands are coordinated through the usual syn,syn-μ₂-κO:κO′ mode. The 1D polymeric structures of 4 and 5 consist of alternating [Mn₃(μ₃-O)]⁷⁺ subunits and Na⁺ atoms linked through two μ₃-κ²O:κO′:κN and one μ₄-κ²O:κ²O′:κN salox²⁻ ligands as well as one syn,anti-μ₂-κO:κO′ benzoato ligand. DC and AC magnetic susceptibility studies on 1 revealed the stabilization of an S = 4 ground state, and indications of single-molecule magnetism behavior, whereas the DC experimental data from polycrystalline sample of 5 are indicative of antiferromagnetic interactions within the [Mn₃] subunit. Solid state ¹H NMR data of 1 were used to probe the spin-lattice relaxation of the system.     

Acetate/di-2-pyridyl ketone oximate "blend" as a source of high-nuclearity nickel(II) clusters: dependence of the nuclearity on the nature of the inorganic anion present

The use of di-2-pyridyl ketone oxime [(py)2CNOH] in reactions with Ni(O2CMe)2.4H2O, in the presence or absence of extra inorganic anions (N3- and SCN-) has led to Ni4, Ni5, and Ni7 clusters; the magnetic study of the heptanuclear nickel(II) complex reveals an S = 3 ground state.     

Copper inverse-9-metallacrown-3 compounds showing antisymmetric magnetic behaviour

The use of phenyl 2-pyridyl ketoxime (PhPyCNO)/X(-)"blends" (X(-) = OH(-), Cl(-), ClO(4)(-)) in copper chemistry has yielded trinuclear clusters that have been characterized as inverse-9-metallacrown-3 accommodating one or two anions. The magnetic behaviour has shown a large antiferromagnetic interaction. The discrepancy between the Brillouin curve and the experiment has been assigned to the influence of the antisymmetric interaction. By introducing in the magnetization formula the antisymmetric terms derived from the fitting of the susceptibility data the simulated curve become almost superimposable to the experimental one. From the EPR findings it has been shown that the compound [Cu(3)(PhPyCNO)(3)(OCH(3))(Cl)(ClO(4))] () having isosceles magnetic symmetry or lower (delta not equal 0), the antisymmetric exchange is important (G not equal 0) and DeltaE > hv. The structures of the two complexes have been determined by single-crystal X-ray crystallography.     

Temporal graphs

We introduce the idea of temporal graphs, a representation that encodes temporal data into graphs while fully retaining the temporal information of the original data. This representation lets us explore the dynamic temporal properties of data by using existing graph algorithms (such as shortest-path), with no need for data-driven simulations. We also present a number of metrics that can be used to study and explore temporal graphs. Finally, we use temporal graphs to analyse real-world data and present the results of our analysis.     

Complexes derived from the general copper(II)/maleamic acid/N,N′,N′′-chelate reaction systems: Synthetic,reactivity, structural and spectroscopic studies

The synthetic investigation of the Cu^II/maleamate(−1) ion (HL⁻)/N,N′,N′′-chelate general reaction system has allowed access to compounds [Cu₂(HL)₂(bppy)₂](ClO₄)₂·H₂O (1·H₂O), [Cu(HL)(bppy)(ClO₄)] (2) and [Cu(HL)(terpy)(H₂O)](ClO₄) (4) (bppy = 2,6-bis(pyrazol-1-yl)pyridine, terpy = 2,2′;6′,2′′-terpyridine). In the absence of externally added hydroxides, compound [Cu₂(L′)₂(bppy)₂](ClO₄)₂ (3) was obtained from MeOH solutions; L′⁻ is the monomethyl maleate(−1) ligand which is formed in situ via the Cu^II-assisted HL⁻ → L′⁻ transformation. In the case of tptz-containing (tptz = 2,4,6-tris(2-pyridyl)-1,3,5-triazine) reaction systems, the Cu^II-assisted hydrolysis of tptz to pyridine-2-carboxamide (L1) afforded complex [Cu(L1)₂(NO₃)₂] (5). The crystal structures of 1–5 are stabilized by intermolecular hydrogen bonding and π–π stacking interactions. Characteristic IR bands of the complexes are discussed in terms of the known structures and the coordination modes of the ligands.     

Investigation of the zinc(II) acetylacetonate/benzotriazole reaction system in the presence of bridging N,N′-ligands: Pentanuclear, enneanuclear and polymeric complexes

The reaction of Zn(acac)₂ with btaH (1,2,3-benzotriazole) in dmf yielded the pentanuclear complex [Zn₅(bta)₆(acac)₄(dmf)]·dmf (1·dmf). In the presence of pyrazine, the pentanuclear [Zn₅(bta)₆(acac)₄(dmf)]·3.7dmf (2·3.7dmf) and enneanuclear [Zn₉(bta)₁₂(acac)₆]·6dmf (3·6dmf) complexes were formed, whereas in the presence of 4,4′-bpy the 1D coordination polymer [Zn(acac)₂(4,4′-bpy)]_n (4) was isolated. The molecular structures of 1·dmf and 2·3.7dmf reveal that the [Zn₅] clusters consist of four Zn^II ions which span the corners of a tetrahedron and the fifth resides at its centre. The molecular structure of 3·6dmf reveals that the [Zn₉] clusters consist of two corner sharing tetrahedra and the structure can be described as the addition of two [Zn₅] clusters of 1·dmf and/or 2·3.7dmf followed by the simultaneous abstraction of [Zn(acac)₂] and dmf molecules; this alternative was accomplished by recrystallization of 1·dmf from dmf which yielded 3·6dmf. Each of the μ₃-κN:κN′:κN′′ benzotriazolate ligands in 1·dmf, 2·3.7dmf and 3·6dmf spans an edge of the tetrahedron. The molecular structure of 4 reveals mononuclear [Zn(acac)₂] units bridged via 4,4′-bpy molecules to 1D coordination polymer. Characteristic IR bands of the four complexes are discussed in terms of the coordination modes of the ligands and known structures.     

Synthesis, crystal structure, and magnetic studies of one-dimensional cyano-bridged Ln3+-Cr3+ complexes with bpy as a blocking ligand

The reaction of Ln(NO3)3.aq with K3[Cr(CN)6] and 2,2'-bipyridine (bpy) in a water/ethanol solution led to two families of complexes: 4 one-dimensional (1D) complexes of the formula trans-[Cr(CN)4(mu-CN)2Ln(H2O)3(bpy)2]n.4nH2O.3.5nbpy (Ln3+ = La, Ce, Pr, and Nd) and 10 1D complexes of the formula trans-[Cr(CN)4(mu-CN)2Ln(H2O)4(bpy)]n.3.5nH2O.1.5nbpy (Ln3+ = Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, and Lu). The structures for the fourteen complexes [LaCr]n (1), [CeCr]n (2), [PrCr]n (3), [NdCr]n (4), [NdCr]n (4'), [SmCr]n (5), [EuCr]n (6), [TbCr]n (7), [DyCr]n (8), [HoCr]n (9), [ErCr]n (10), [TmCr]n (11), [YbCr]n (12), and [LuCr]n (13) have been solved. Complexes 1-4 crystallize in the orthorhombic space group Pbam and are isomorphous; complexes 4'-13 crystallize in the triclinic space group PI and are isomorphous. The X-ray structural characterization of complexes 1-4 shows the presence of a discrete decameric water cluster built around a cyclic hexameric core stabilized by the solid-state structure, which represents another new mode of association of water molecules. The Ln3+-Cr3+ magnetic interaction is negligible in 6 and 12, antiferromagnetic in 2, 4', 7, 8, 9, 10, and 11, and unresolved for 3. The complex 5 is a ferrimagnet because its magnetic studies suggest the onset of a very weak ferromagnetic three-dimensional ordering.