Some applications of the adjoint to lattice regular measures

Summary In this paper, the principal role is played by the adjoint of a certain bounded linear mapping, whose domain and range are Banach spaces of lattice regular measures. First, the general properties of the adjoint are investigated and it is shown, in particular, how this mapping yields generalizations of many results in Stone-ech Theory, especially matters related to embeddibility. Then, the investigation continues with the mapping properties of the adjoint, and a variety of applications is given to Topological Measure Theory, strong measure repleteness, tightness, and relative compactness.     

Visible light photocatalysis with platinized rutile TiO2 for aqueous organic oxidation

Platinized rutile TiO2 samples containing varying concentrations of Pt were synthesized using Kemira (KE, BET surface area 50 m2/g, from Finland), and Toto HT0270 (HT, BET surface area 2.9 m2/g, from Japan) as the starting materials by solution mixing followed by sintering the precursors. Photocatalytic activities were established for phenol oxidation under visible light (wavelength >400 nm). Our results show optimal performance for 8 wt % platinized KE (8 wt % Pt/KE) and (1/2) wt % platinized HT rutile samples. The specific roles of O2 and visible light were examined using the 8 wt % Pt/KE sample in either N2 gas ambient or no illumination. Separately, 8 wt % platinized SiO2 was tested to compare its performance with that of platinized rutile TiO2. Several other chemicals containing different functional groups (formic acid, salicylic acid, 4-chlorophenol, 2,4,6-trichlorophenol, diethyl phosphoramidate) were selected for photooxidation tests with (1/2) wt % platinized HT rutile. X-ray diffraction reveals Pt metal clusters segregating on the surface of rutile TiO2 particles with increasing Pt weight percent. The Pt cluster surface area broadly increases, while the effective optical band gap steadily decreases with platinization of the rutile samples. These results suggest that Pt clusters on the surface of rutile TiO2 particles serve to mediate electron transfer from rutile to O2, thus facilitating photooxidation of organic chemicals.     

157-nm Laser ablation of polymeric layers for fabrication of biomolecule microarrays

A new methodology for protein microarray fabrication is proposed based on the ablation of polymer film using laser at 157 nm (F₂). The polymer has been selected among others with the criterion of negligible protein adsorption. Improved results have been obtained by pretreatment of the polymer surface with an inert protein. The use of 157-nm laser radiation allowed very good depth control during the polymeric layer ablation process. In addition the importance of laser ablation at 157 nm is based on the fact that irradiated surfaces indicate limited chemical change due to the fact that laser ablation at 157 nm is only photochemical, thus avoiding excessive surface heating and damage. Results of protein microarray fabrication are presented to illustrate the viability of the proposed method.     

Stability,monotonicity and invariant quantities in general polling systems

Consider a polling system withK1 queues and a single server that visits the queues in a cyclic order. The polling discipline in each queue is of general gated-type or exhaustive-type. We assume that in each queue the arrival times form a Poisson process, and that the service times, the walking times, as well as the set-up times form sequences of independent and identically distributed random variables. For such a system, we provide a sufficient condition under which the vector of queue lengths is stable. We treat several criteria for stability: the ergodicity of the process, the geometric ergodicity, and the geometric rate of convergence of the first moment. The ergodicity implies the weak convergence of station times, intervisit times and cycle times. Next, we show that the queue lengths, station times, intervisit times and cycle times are stochastically increasing in arrival rates, in service times, in walking times and in setup times. The stability conditions and the stochastic monotonicity results are extended to the polling systems with additional customer routing between the queues, as well as bulk and correlated arrivals. Finally, we prove that the mean cycle time, the mean intervisit time and the mean station times are invariant under general service disciplines and general stationary arrival and service processes.     

Multinuclear Fe(III) complexes with polydentate ligands of the family of dicarboxyimidazoles: nuclearity- and topology-controlled syntheses and Magneto-structural correlations

Two polydentate ligands of the family of dicarboxyimidazoles, H(2)MeDCBI (= 4,5-dicarboxy-1-methyl-1H-imidazole) and H(3)DCBI (= 4,5-dicarboxyimidazole), have been used in reactions with the [Fe(3,5-(t)()Bu(2)salpn)](+) species {3,5-(t)Bu(2)salpn = the dianion of 1,3-bis-[(3,5-di-tert-butylsalicylidene)amino]propane} to synthesize selectively complexes of different nuclearities. Four complexes have been synthesized: the mononuclear complex [Fe(3,5-(t)Bu(2)salpn)(HMeDCBI)] (1), the two binuclear but topologically different complexes [Fe(3,5-(t)Bu(2)salpn)(MeDCBI)Fe(3,5-(t)Bu(2)salpn)] (2) and {[Fe(3,5-(t)Bu(2)salpn)](2)(HDCBI)} (3), and the trinuclear complex {[Fe(3,5-(t)Bu(2)salpn)](2)(DCBI)Fe(3,5-(t)Bu(2)salpn)} (4). The structures of these complexes have been determined by X-ray crystallography. Variable-temperature direct-current magnetic susceptibility measurements were conducted for all compounds to obtain information about their electronic structure and to investigate the extent of magnetic communication among the Fe(III) centers. The results of these measurements allowed us to correlate the different structural motifs with the possible magnetic interactions that arise in multinuclear complexes of dicarboxyimidazoles. For 1, the room-temperature chi(M)T value reveals an S = (5)/(2) ground state. The data for the binuclear but topologically different complexes 2 and 3, and the trinuclear complex 4 suggest that weak intramolecular antiferromagnetic interactions are present, with interaction parameters ranging from -3.6 to -5.1 cm(-1). Differences in the extent of the magnetic communication between the metal centers through the two different interaction pathways of the ligands MeDCBI and DCBI (either through the imidazole ring or through the carboxylate groups) have been observed in complexes 2-4 that can be explained by the structural differences observed in the crystal structures of these compounds (the separation of the metal centers and the coplanarity of the metal ion orbitals with the pi system of the ligands). Cyclic voltammetry measurements for the mononuclear compound 1 show an irreversible reduction wave that is attributed to Fe(3+) + e(-) --> Fe(2+). The electrochemical behavior of the multinuclear complexes 2-4 is more complicated; however, it indicates that there is a degree of electronic communication between the Fe(III) centers.     

1-Ethyl-1H-3-nitrobenzopyrano[4,3,2-cd]isoindole: a novel heterocyclic ring system bearing an unusually labile deuterium-exchangeable aromatic proton

The ease of deuterium exchange of the aromatic H2 of the novel heterocycle 1-ethyl-1H-3-nitrobenzopyrano[4,3,2-cd]isoindole was studied by NMR and theoretical calculations.     

Synthesis and structural characterization of trinuclear Cu(II)-pyrazolato complexes containing mu(3)-OH, mu(3)-O, and mu(3)-Cl ligands. Magnetic susceptibility study of [PPN](2)[(mu(3)-O)Cu(3)(mu-pz)(3)Cl(3)

The nine-membered [-Cu(II)-N-N-](3) ring of trimeric copper-pyrazolato complexes provides a sturdy framework on which water is twice deprotonated in consecutive steps, forming mu(3)-OH and mu(3)-O species. In the presence of excess chlorides the mu(3)-O(H) ligand is replaced by two mu(3)-Cl ions. The interconversion of mu(3)-OH and mu(3)-O and the exchange of mu(3)-O(H) and mu(3)-Cl are reversible, and the three species involved have been structurally characterized: [PPN][Cu(3)(mu(3)-OH)(mu-pz)(3)Cl(3)(thf)].CH(2)Cl(2) (1a), monoclinic P2(1)/n, a = 10.055(2) A, b = 35.428(5) A, c = 15.153(2) A, beta = 93.802(3) degrees, V = 5386(1) A(3), Z = 4; [Bu(4)N][Cu(3)(mu(3)-OH)(mu-pz)(3)Cl(3)] (1b), triclinic P-1, a = 9.135(2) A, b = 13.631(2) A, c = 14.510(2) A, alpha = 67.393(2) degrees, beta = 87.979(2) degrees, gamma = 80.268(3) degrees, V = 1643.2(4) A(3), Z = 2; [PPN](2)[Cu(3)(mu(3)-O)(mu-pz)(3)Cl(3)] (2), monoclinic P2/c, a = 12.807(2) A, b = 13.093(2) A, c = 23.139(4) A, beta = 105.391(3) degrees, V = 3741(1) A(3), Z = 2; [PPN](2)[Cu(3)(mu(3)-Cl)(2)(mu-pz)(3)Cl(3)].0.75H(2)O.0.5CH(2)Cl(2) (3a), triclinic P-1, a = 14.042(2) A, b = 23.978(4) A, c = 25.195(4) A, alpha = 76.796(3) degrees, beta = 79.506(3) degrees, gamma = 77.629(3) degrees, V = 7988(2) A(3), Z = 4; [Bu(4)N](2)[Cu(3)(mu(3)-Cl)(2)(mu-pz)(3)Cl(3)] (3b), monoclinic C2/c, a = 17.220(2) A, b = 15.606(2) A, c = 20.133(2) A, beta = 103.057(2) degrees, V = 5270(1) A(3), Z = 4; [Et(3)NH][Cu(3)(mu(3)-OH)(mu-pz)(3)Cl(3)(pzH)] (4), triclinic P-1, a = 11.498(2) A, b = 11.499(2) A, c = 12.186(2) A, alpha = 66.475(3) degrees, beta = 64.279(3) degrees, gamma = 80.183(3) degrees, V = 1331.0(5) A(3), Z = 2. Magnetic susceptibility measurements show that the three copper centers of 2 are strongly antiferromagnetically coupled with J(Cu-Cu) = -500 cm(-1).     

Development and validation of a UPLC‐UV method for the determination of daptomycin in rabbit plasma

Daptomycin (DPT) is a lipopeptide antibiotic with potent bactericidal activity in vitro against Gram‐positive bacteria, which has attracted the attention of the scientific community due to its unique mechanism of action and due to the immediate need for new antibiotics in the era of multidrug resistance. In order to assess its pharmacokinetics in rabbits a new analytical method has been developed and validated using ultra performance liquid chromatography in conjugation with ultraviolet detection for the quantitation of the antibiotic in rabbit plasma, using the internal standard methodology. The separation was achieved employing a C₁₈ column with gradient elution using 0.1% aq. trifluoroacetic acid and methanol. The total analysis time was 2.5 min. The sample pretreatment employed protein precipitation with acetonitrile–methanol mixture and centrifugation. The method was validated in terms of linearity, precision, accuracy, sensitivity, robustness, short‐term and freeze–thaw stability and was applied to the quantification of DPT in plasma samples obtained from rabbits treated with 25 mg kg^?1 DPT. Copyright © 2009 John Wiley & Sons, Ltd.