Vibrational spectral studies of ion-ion and ion-solvent interactions. II. Zinc nitrate in water/dioxane mixtures

Raman and infrared spectral data have been collected forp-dioxane and solvated and bound nitrate ions for Zn(NO₃)₂/p-dioxane/water systems. It is concluded that Zn²⁺ is preferentially solvated by water and that this aquation is also responsible for a lower concentration of ion pairs than is found for methanol/Zn(NO₃)₂ solutions for which the dielectric constant of the bulk solvent is similar. Values of K₁ (M^–1), the association constant for Zn(NO₃)⁺, are 0.22±0.02 (2/1 solvent,D=12.6) and 0.071±0.01 (4/1 solvent,D=33.0). The log K₁ against 1/D plot is not linear.     

Vibrational spectral studies of ion-ion and ion-solvent interactions. I. Zinc nitrate in water

Raman and infrared line parameters of Zn(NO₃)₂-H₂O systems ranging from dilute solutions (25°C) to ionic liquids of low water content (75°C) are reported. At 25°C the solutions contain a very low concentration of inner sphere [Zn(ONO₂)(H₂O)₅]⁺, outer sphere [Zn(H₂O)₆]²⁺[NO₃]^–, Zn(H₂O) ₆ ²⁺ , and NO ₃ ^– (aq.). In the ionic liquids the ion triplet also exists. Manifestations of a change from the octahedral coordination of zinc to tetrahedral coordination when the water content is very low include the appearance of a 285 cm^–1 band from the zinc nitrate bond and a shift to higher frequencies of the band from zinc-water.     

Efficient radiation production in long implosions of structured gas-puff Z pinch loads from large initial radius

We have proposed and demonstrated successfully a new approach for generating high-yield K-shell radiation with large-diameter gas-puff Z pinches. The novel load design consists of an outer region plasma that carries the current and couples energy from the driver, an inner region plasma that stabilizes the implosion, and a high-density center jet plasma that radiates. It increased the Ar K-shell yield at 3.46 MA in 200 ns implosions from 12 cm initial diameter by a factor of 2, to 21 kJ, matching the yields obtained earlier on the same accelerator with 100 ns implosions. A new "pusher-stabilizer-radiator" physical model is advanced to explain this result.     

Redox Reorganization: Aluminium Promoted 1,5-Hydride Shifts Allow the Controlled Synthesis of Multisubstituted Cyclohexenes

An efficient synthesis of cyclohexenes has been achieved from easily accessible tetrahydropyrans via a tandem 1,5-hydride shift–aldol condensation. We discovered that readily available aluminium reagents, e.g. Al₂O₃ or Al(O^tBu)₃ are essential for this process, promoting the 1,5-hydride shift with complete regio- and enantiospecificity (in stark contrast to results obtained under basic conditions). The mild conditions, coupled with multiple methods available to access the tetrahydropyran starting materials makes this a versatile method with exceptional functional group tolerance. A wide range of cyclohexenes (>40 examples) have been prepared, many in enantiopure form, showing our ability to selectively install a substituent at each position around the newly forged cyclohexene ring. Experimental and computational studies revealed that aluminium serves a dual role in facilitating the hydride shift, activating both the alkoxide nucleophile and the electrophilic carbonyl group.     

A graph-theoretic approach to interval scheduling on dedicated unrelated parallel machines

We study the problem of scheduling n non-preemptive jobs on m unrelated parallel machines. Each machine can process a specified subset of the jobs. If a job is assigned to a machine, then it occupies a specified time interval on the machine. Each assignment of a job to a machine yields a value. The objective is to find a subset of the jobs and their feasible assignments to the machines such that the total value is maximized. The problem is NP-hard in the strong sense. We reduce the problem to finding a maximum weight clique in a graph and survey available solution methods. Furthermore, based on the peculiar properties of graphs, we propose an exact solution algorithm and five heuristics. We conduct computer experiments to assess the performance of our and other existing heuristics. The computational results show that our heuristics outperform the existing heuristics.     

Multiplicative maps preserving the higher rank numerical ranges and radii

Let M_n be the semigroup of n×n complex matrices under the usual multiplication, and let S be different subgroups or semigroups in M_n including the (special) unitary group, (special) general linear group, the semigroups of matrices with bounded ranks. Suppose Λ_k(A) is the rank-k numerical range and r_k(A) is the rank-k numerical radius of A∈M_n. Multiplicative maps ?:S→M_n satisfying r_k(?(A))=r_k(A) are characterized. From these results, one can deduce the structure of multiplicative preservers of Λ_k(A).     

Rhenium(I) polypyridine biotin isothiocyanate complexes as the first luminescent biotinylation reagents: synthesis, photophysical properties, biological labeling, cytotoxicity, and imaging studies

We report here the design of the first class of luminescent biotinylation reagents derived from rhenium(I) polypyridine complexes. These complexes [Re(N-N)(CO)(3)(py-biotin-NCS)](PF(6)) (py-biotin-NCS = 3-isothiocyanato-5-(N-((2-biotinamido)ethyl)aminocarbonyl)pyridine; N-N = 1,10-phenanthroline (phen) (1a), 3,4,7,8-tetramethyl-1,10-phenanthroline (Me(4)-phen) (2a), 4,7-diphenyl-1,10-phenanthroline (Ph(2)-phen) (3a)), containing a biotin unit and an isothiocyanate moiety, have been synthesized from the precursor amine complexes [Re(N-N)(CO)(3)(py-biotin-NH(2))](PF(6)) (py-biotin-NH(2) = 3-amino-5-(N-((2-biotinamido)ethyl)aminocarbonyl)pyridine; N-N = phen (1c), Me(4)-phen (2c), Ph(2)-phen (3c)). To investigate the amine-specific reactivity of the isothiocyanate complexes 1a-3a, they have been reacted with a model substrate ethylamine, resulting in the formation of the thiourea complexes [Re(N-N)(CO)(3)(py-biotin-TU-Et)](PF(6)) (py-biotin-TU-Et = 3-ethylthioureidyl-5-(N-((2-biotinamido)ethyl)aminocarbonyl)pyridine; N-N = phen (1b), Me(4)-phen (2b), Ph(2)-phen (3b)). All the rhenium(I) complexes have been characterized, and their photophysical properties have been studied. The avidin-binding properties of the thiourea complexes 1b-3b have been examined by the 4'-hydroxyazobenzene-2-carboxylic acid (HABA) assay. Titration results indicated that the complexes exhibited emission enhancement by ca. 1.4-1.5-fold upon binding to avidin, and the lifetimes were elongated to ca. 0.8-2.0 micros. Additionally, we have biotinylated bovine serum albumin (BSA) with the isothiocyanate complexes. All the resultant rhenium-BSA bioconjugates displayed intense and long-lived orange-yellow to greenish-yellow emission upon irradiation in aqueous buffer under ambient conditions. The avidin-binding properties of the bioconjugates have been investigated using the HABA assay. Furthermore, the cytotoxicity of the thiourea complexes 1b-3b toward the HeLa cells has been examined by the 3-(4,5-dimethyl-2-thiazolyl)-2,5-diphenyltetrazolium bromide (MTT) assay. The IC50 values were determined to be ca. 17.5-28.5 microM, which are comparable to that of cisplatin (26.7 microM) under the same conditions. The cellular uptake of complex 3b has been investigated by fluorescence microscopy, and the results showed that the complex was localized in the perinuclear region after interiorization.     

Maps preserving the nilpotency of products of operators

Let B(X) be the algebra of all bounded linear operators on the Banach space X, and let N(X) be the set of nilpotent operators in B(X). Suppose ?:B(X)→B(X) is a surjective map such that A,B∈B(X) satisfy AB∈N(X) if and only if ?(A)?(B)∈N(X). If X is infinite dimensional, then there exists a map f:B(X)→C?{0} such that one of the following holds:

(a)

There is a bijective bounded linear or conjugate-linear operator S:X→X such that ? has the form A?S[f(A)A]S^-1.

(b)

The space X is reflexive, and there exists a bijective bounded linear or conjugate-linear operator S : X′ → X such that ? has the form A ? S[f(A)A′]S⁻¹.

If X has dimension n with 3 ? n < ∞, and B(X) is identified with the algebra M_n of n × n complex matrices, then there exist a map f:M_n→C?{0}, a field automorphism ξ:C→C, and an invertible S ∈ M_n such that ? has one of the following forms: