On a characterization of the essential spectra of the sum and the product of two operators

In this paper, we consider the sum and the product of two operators acting on a Banach space and we present some new and quite general conditions to investigate their Wolf, Schechter and Browder essential spectra.     

Classical limit of the tensor product of holomorphic discrete series representations

For three coadjoint orbits \(\mathcal {O}_1, \mathcal {O}_2\) and \(\mathcal {O}_3\) in \(\mathfrak {g}^*\) , the Corwin–Greenleaf function \(n(\mathcal {O}_1 \times \mathcal {O}_2, \mathcal {O}_3)\) is given by the number of \(G\) -orbits in \(\{(\lambda , \mu ) \in \mathcal {O}_1 \times \mathcal {O}_2 \, : \, \lambda + \mu \in \mathcal {O}_3 \}\) under the diagonal action. In the case where \(G\) is a simple Lie group of Hermitian type, we give an explicit formula of \(n(\mathcal {O}_1 \times \mathcal {O}_2, \mathcal {O}_3)\) for coadjoint orbits \(\mathcal {O}_1\) and \(\mathcal {O}_2\) that meet \(\left( [\mathfrak {k}, \mathfrak {k}] + \mathfrak {p}\right) ^{\perp }\) , and show that the formula is regarded as the ‘classical limit’ of a special case of Kobayashi’s multiplicity-free theorem (Progr. Math. 2007) in the branching law to symmetric pairs.     

Transformation of Acetaminophen by Dichromate Oxidation Produces the Toxicants 1,4-Benzoquinone and Ammonium Ions

The reaction of the common pain reliever acetaminophen (paracetamol, 4-acetamidophenol) with dichromate was investigated over time under conditions that simulate wastewater disinfection. The occurrence of the acetaminophen in the water bodies, especially in drinking water resources, has received considerable attentions. In situ chemical oxidation is a promising cost-effective treatment method to remove acetaminophen from water body as it degrades the drug to large extent. Experimental results indicate that the reaction is second order overall and first order with respect to both dichromate and acetaminophen, and has activation energy of 14.1 kJ/mol. The second-order rate constant ranges from 1.56 × 10^?3 to 13.4 × 10^?3 min^?1 at temperature from 35 to 65°C. The acetaminophen degradation rates can be accelerated through increasing reaction temperature and oxidant concentration. The reaction under acid conditions was slightly faster than under alkaline or neutral conditions. Two of the products were unequivocally identified as the toxic compounds 1,4-benzoquinone and ammonium ions. These results demonstrate that acetaminophen is likely to be transformed significantly into toxic product if dichromate is used as an oxidizing agent during wastewater treatment.     

Investigations on Hydrolytic Activities from Stachybotrys microspora and Their Use as an Alternative in Yeast DNA Extraction

Stachybotrys microspora is a filamentous fungus characterized by the secretion of multiple hydrolytic activities (cellulolytic and non-cellulolytic enzymes). The production of these biocatalysts was studied under submerged culture using glucose, cellulose, and wheat bran as carbon sources. Endoglucanases, pectinases, xylanases, β-glucanases, chitinases, and proteases were induced on cellulose-based medium and repressed on glucose in both strains with higher amounts produced by the mutant. β-glucosidases were roughly equally produced by both strains under glucose and cellulose conditions. The yield of chitinases, β-glucanases, and proteases produced by Stachybotrys strains was as much higher than the commercialized lysing enzyme called “zymolyase,” currently used in yeast DNA extraction. In this context, we showed that S. microspora hydrolases can be successfully applied in the extraction of yeast DNA.     

Vendor Management Inventory with consignment contracts and the benefits of cooperative advertising

Most of the cooperative advertising literature has focused on studying the effects of such programs considering marketing variables. This paper integrates production and inventory management with pricing and advertising considerations to assess the effects of cooperative advertising programs in bilateral monopolies. We consider a supply chain where a Vendor Managed Inventory (VMI) along with a consignment contract is implemented to coordinate the chain. We develop and solve a differential model for two games. The first one is a benchmark scenario where no cooperative advertising is offered, while the manufacturer offers the cooperative program in the second game. The main results show that cooperative advertising programs, usually considered as successful marketing initiatives, can be very difficult to implement in a supply chain undertaking a VMI policy with a consignment contract, in which operations and marketing interface is taken into account. A cooperative program mainly hurts the manufacturer’s profits, and can be profit-Pareto-improving only in a few cases. Although the retailer is generally willing to receive a support from the manufacturer, she can opt for a non-cooperative program when the largest part of the supply chain profits goes to the manufacturer. We developed several special cases to strengthen our findings.     

Blue shifts of the C-H stretching vibrations in hydrogen-bonded and protonated trimethylamine. Effect of hyperconjugation on bond properties

The optimized geometry of isolated trimethylamine (TMA), its hydrogen bond complexes with phenol derivatives and protonated TMA is calculated at the B3LYP/6-31++G(d,p) level. A natural bond orbital (NBO) analysis on these systems is carried out at the same level of theory. In isolated TMA, one of the C-H bond in each of the three CH(3) groups is more elongated than the two other ones. As revealed by the NBO data, this results from a hyperconjugative interaction from the N lone pair to the sigma*(C-H) orbitals of the C-H bonds being in a transoid position with respect to the N lone pair. The formation of an intermolecular OH...N hydrogen bond with phenols results in a decrease of the lone pair effect. A linear correlation is found between the decrease in occupation of the sigma*(C-H) orbitals and the decrease in the hyperconjugative interaction energy in the complexes and isolated TMA. Complex formation with phenols results in a blue shift of 55-74 cm(-1) of the C-H stretching vibrations involved in the lone pair effect. Smaller blue shifts between 14 and 23 cm(-1) are predicted for the other C-H bonds. In these complexes, a linear correlation is found between the frequency shifts and the elongation of the C-H bonds. Protonation of TMA results in a nearly equalization of all the C-H distances and a blue shift of 180 cm(-1) of the C-H bonds involved in hyperconjugation with the N lone pair.     

Local atomic structures of single-component metallic glasses

In this study we examine the structural properties of single-component metallic glasses of aluminum. We use a molecular dynamics simulation based on semi-empirical many-body potential, derived from the embedded atom method (EAM). The radial distribution function (RDF), common neighbors analysis method (CNA), coordination number analysis (CN) and Voronoi tessellation are used to characterize the metal’s local structure during the heating and cooling (quenching). The simulation results reveal that the melting temperature depends on the heating rate. In addition, atomic visualization shows that the structure of aluminum after fast quenching is in a glassy state, confirmed quantitatively by the splitting of the second peak of the radial distribution function, and by the appearance of icosahedral clusters observed via CNA technique. On the other hand, the Wendt-Abraham parameters are calculated to determine the glass transition temperature (T_g), which depends strongly on the cooling rate; it increases while the cooling rate increases. On the basis of CN analysis and Voronoi tessellation, we demonstrate that the transition from the Al liquid to glassy state is mainly due to the formation of distorted and perfect icosahedral clusters.     

Performance characteristics of an ion chromatographic method for the quantitation of citrate and phosphate in pharmaceutical solutions

The performance of an ion chromatographic method for measuring citrate and phosphate in pharmaceutical solutions is evaluated. Performance characteristics examined include accuracy, precision, specificity, response linearity, robustness, and the ability to meet system suitability criteria. In general, the method is found to be robust within reasonable deviations from its specified operating conditions. Analytical accuracy is typically 100 +/- 3%, and short-term precision is not more than 1.5% relative standard deviation. The instrument response is linear over a range of 50% to 150% of the standard preparation target concentrations (12 mg/L for phosphate and 20 mg/L for citrate), and the results obtained using a single-point standard versus a calibration curve are essentially equivalent. A small analytical bias is observed and ascribed to the relative purity of the differing salts, used as raw materials in tested finished products and as reference standards in the analytical method. The assay is specific in that no phosphate or citrate peaks are observed in a variety of method-related solutions and matrix blanks (with and without autoclaving). The assay with manual preparation of the eluents is sensitive to the composition of the eluent in the sense that the eluent must be effectively degassed and protected from CO(2) ingress during use. In order for the assay to perform effectively, extensive system equilibration and conditioning is required. However, a properly conditioned and equilibrated system can be used to test a number of samples via chromatographic runs that include many (> 50) injections.     

Formation and Structural Characterization of Metal Complexes derived from Thiosalicylic Acid

The formation and structural aspects of some metal complexes of thiosalicylic acid (TSA) were studied. The μ‐bridging tetra‐coordinated Ru complex, [Ru(C₆H₄(CO₂)(μ‐S)(H₂O)]₂ ( 1 ) was formed by hydrothermal reaction of TSA with RuCl₃. The complexes [M(dtdb)(phen)(H₂O)]_n ( 2 – 4 ) (M = Zn^II, Co^II, Ni^II, dtdb = 2,2′‐dithiodibenzoate anion, phen = 1,10‐phenanthroline) were obtained by the slow diffusion technique and the in situ S–S bond formation was confirmed by elemental, spectral and X‐ray analysis. Reaction of TSA with CuCl₂ and 2,2′‐bipyridine (bipy) under the slow diffusion technique yielded the dimer [Cu(tdb)(bipy)] ( 5 ) (tdb = thiodibenzoic acid), where the in situ generation of 2,2′‐thiodibenzoic acid was observed.     

Comparison of the thermal performances of two nanofluids at low temperature in a plate heat exchanger

The objective of this study is to compare experimentally the thermal performances of two types of commercial nanofluids. The first is composed of oxides of alumina (γAl₂O₃) dispersed in water and the second one is aqueous suspensions of nanotubes of carbons (CNTs). The viscosity of the nanofluids is measured as a function of the temperature between 2 and 10 °C. An experimental device, containing three thermal buckles controlled in temperature and greatly instrumented permits to study the thermal convective transfers. The evolution of the convective coefficient permits to study the convective thermal transfers. The evolution of the convective coefficient is presented according to the Reynolds number, at low temperature from 0 to 10 °C and for the two aforementioned nanofluids. An assessment of the pressure drops in the circuit as well as of the powers of the circulator and outputs is dealt with.