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A commuting tuple of n operators (S 1 , ... , S n − 1 , P) defined on a Hilbert space H , for which the closed symmetrized polydisc Γ n = { (∑ i = 1 n z i , ∑ 1 ≤ i < j ≤ n z i z j , ... , ∏ i = 1 n z i) : | z i | ≤ 1 , i = 1 , ... , n } is a spectral set is called a Γ n -contraction. Also a triple of commuting operators (A , B , P) for which the closed tetrablock E ‾ is a spectral set is called an E -contraction, where E = { (x 1 , x 2 , x 3) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 ∀ z , w ∈ D ‾ }. There are several decomposition theorems for contraction operators in the literature due to Sz. Nagy, Foias, Levan, Kubrusly, Foguel and few others which reveal structural information of a contraction. In this article, we obtain analogues of six such major theorems for both Γ n -contractions and E -contractions. In each of these decomposition theorems, the underlying Hilbert space admits a unique orthogonal decomposition which is provided by the last component P. The central role in determining the structure of a Γ n -contraction or an E -contraction is played by positivity of some certain operator pencils and the existence of a unique operator tuple associated with a Γ n -contraction or an E -contraction. [ABSTRACT FROM AUTHOR]

Abstract: We present the first principles calculations of the thermodynamical properties of magnesium hydride (MgH2) over a temperature range of 0–1000K. The phonon dispersions are determined within the density functional framework and are used to calculate the free energy of MgH2 within the quasiharmonic approximation (QHA) at each cell volume and temperature T. Using the free energies the thermal equation of state (EOS) is derived at several temperatures. From the thermal EOS structural parameters such as the equilibrium cell volume (V 0) and elastic properties, namely, bulk modulus (K 0) and its pressure derivative are computed. The free energies are also used to calculate various thermodynamical properties within QHA. These include internal energy E, entropy S, specific heat capacity at constant pressure C P, thermal pressure P thermal(V, T) and volume thermal expansion ΔV/V (%). The good agreement of calculated values of S and C P with experimental data exhibits that QHA can be used as a tool for calculating the thermodynamical properties of MgH2 over a wide temperature range. P thermal(V,T) increases strongly with T at all the volumes but it is a slowly varying function of volume for T =298–500K. According to Karki [B.B. Karki, Am. Miner. 85 (2000) 1447] such volume based variations can be neglected and so it is possible to estimate the thermal EOS only with the knowledge of the measured P thermal(V, T) versus temperature at ambient pressure and isothermal compression data at ambient temperature. Temperature dependence of ΔV/V(%) shows that V 0 increased with increase in temperature. However, the percentage decrease in K 0 superseded this percentage increase in V 0 even at temperatures moderately higher than 298K. Therefore, we suggest application of temperature (T >298K) as an approach to enhance the hydrogen storage capacity of MgH2 because of its better compressibility at these temperatures. [Copyright &y& Elsevier]

Abstract Remnant obtained from chemical retting of coconut fibre was found to have an exorbitant COD, BOD, TDS, sulphide content having blackish brown colour. Traditional (physico-chemical) treatment could not reduce its COD, TDS, colour substantially. Further, the traditional method was lengthy, consumed huge chemicals and time. Present paper reports a quicker, simpler, economic i.e., an industrially viable method to separate the chemicals and biomass by employing electrocoagulation (EC). The performance of EC was analyzed by keeping temperature, and pH of remnant constant, while varying current flow (100–2000 mA), time (15–90 min) and number of iron electrodes (2,4,6). Efficacy of EC was evaluated in terms of reduction in conductivity, pH, TDS, COD, TOC, colour and quantity of sludge generated from the wastewater. Six electrodes with 2000 mA current flow for 90 min were found to give noticeable reduction on COD (92.8%), TOC (56%), TDS (99%), and colour. To reduce pH, and TDS to an acceptable level, filtration with activated charcoal was attempted on recovered water from EC. Resultant water was also found to have acceptable LC 50 value for safe disposal. Carbon content (53%) in the sludge was high, contained lignin and cellulose whiskers also, as revealed from the EDX and FTIR, SEM respectively. Cost of EC ($ 0.087 USD/L) was found to be much less as compared to traditional method ($ 0.384 USD/L). Graphical abstract Image 1 Highlights • Remnant of chemical retting of coconut fibre was treated by electrocoagulation. • Optimum treatment condition is 6 electrodes, pH 7, 90 min and 2000 mA. • COD (80%), TOC (56%), TDS, darkness of colour were remarkably reduced. • Lethal concentration of 135 mg/L indicates its safer disposability. • Cost (USD/L) of electrolysis 0.087 as compared to chemical process 0.38. [ABSTRACT FROM AUTHOR]

Vinblastine (VLB), a cytotoxic alkaloid is used extensively against various cancer types and the crystal structure of its tubulin complex is already known. Multitarget affinity of vinblastine has been investigated and the nature of binding with biological receptors namely, duplex DNA and Human serum albumin (HSA) has been compared to the binding characteristics of its known complex with natural high affinity receptor tubulin using molecular docking and QM–MM calculations. VLB is found to interact with DNA as well as HSA protein, though, with weaker affinity as compared to tubulin. Analysis of various docked complexes revealed that the H-bonds and cation–pi bonds do not have significant contribution to the binding interactions and despite its large size, VLB remains in relaxed conformation and fits in the hydrophobic regions on the receptors. [ABSTRACT FROM AUTHOR]