On a class of nonlinear integral equations

In this paper we consider abstract equations of the typeK _ν ν +ν =w ₀, in a closed convex subset of a separable Hilbert spaceH. For eachv in the closed convex subset,K _v :H →H is a bounded linear map. As an application of our abstract result we obtain an existence result for nonlinear integral equations of the typeν(s)+ν(s)∫ ₀ ¹ k(s,t)ν(t)dt =W ₀(s) in the spaceL ² [0,1].     

Non-isothermal thermoanalytical studies on the salt roasting of chalcopyrite using KCl

In an earlier study [1], the isothermal kinetics of salt roasting of chalcopyrite under an oxidizing atmosphere using KCl was studied in the temperature range 523–773 K. The salt roasting reaction was found to be chemically controlled at temperatures below 600 K both under static air and oxygen atmosphere. At higher temperatures, the process was not thermally activated because of a change in the chemistry of the process. In the present study, the salt roasting of chalcopyrite using KCl under oxygen and static air atmosphere was studied by non-isothermal thermoanalytical studies up to 723 K. The effect of salt content, heating rate and particle size on the salt roasting behavior was studied using TG/DTA techniques at a programmed linear heating rate. The TG and DTA studies reveal two distinct chemical processes, one operative up to 620 K and the other from 620 to 723 K. The integral method of Coats and Redfern was used for the treatment of non-isothermal kinetic data. The non-isothermal analysis confirmed the chemical control mechanism at temperatures below 620 K. However, the activation energy for the process derived from non-isothermal thermogravimetric analysis is almost twice as that deduced from isothermal measurements. In the temperature range 620–723 K, the kinetic data still obeys the interfacial reaction control model although the activation energy in this temperature range is very low.     

Stereodivergent Transformation of Azepino[3,4,5-cd]indoles En Route to Nature-Inspired Scaffolds

Azepino[3,4,5-cd]indole derivatives represent the core scaffold of important natural products and biologically relevant compounds. Therefore, the establishment of step- and atom-economic strategies to access this class of compounds is of paramount importance. To this end, complexity-to-diversity (CtD) strategy has become one of the most important tools that transforms complex molecules into diverse skeleta. However, many of the reactions that could be employed in CtD are restricted by the functional handles exist in these molecules. This limits the achievement of the desired skeletal diversity. Herein, an efficient and step-economic strategy to access a diverse collection of azepino-[3,4,5-cd]indole architectures through a cascade that combines Pictet-Spengler with Michael addition, is described. This was achieved by reacting cyclohexadienone acetaldehydes 2 a – 2 d with indolyl-4-ethyl amine 1 . Employing a CtD strategy on the developed azepino-[3,4,5-cd]indoles, a rapid rearrangement reaction that provided a modular, chemo- and diastereoselective access to diverse collection of spiro azepinocarbazole nature-inspired frameworks, was encountered.     

Methanol diffusion rates through the anode diffusion layer in direct methanol fuel cells from limiting current measurements

Metal foams may be used in direct methanol fuel cells to feed reactants to the catalyst layer and to collect current from the resulting electrochemical reaction. Although the mass transfer from the metal foam to the underlying gas diffusion layer (GDL) is diffusion-dominated, it is found that at a fixed methanol concentration, the limiting current density increases with increasing methanol flow rates. This unexpected result is attributed to the more efficient removal of product CO₂ from the GDL. A methodology is developed to estimate the effective diffusion coefficient of methanol in the anode diffusion layer from limiting current density measurements, and to extract the fraction of GDL volume occupied by CO₂.     

Functional GPCR microarrays

This paper describes G-protein-coupled receptor (GPCR) microarrays on porous glass substrates and functional assays based on the binding of a europium-labeled GTP analogue. The porous glass slides were made by casting a glass frit on impermeable glass slides and then coating with gamma-aminopropyl silane (GAPS). The emitted fluorescence was captured on an imager with a time-gated intensified CCD detector. Microarrays of the neurotensin receptor 1, the cholinergic receptor muscarinic 2, the opioid receptor mu, and the cannabinoid receptor 1 were fabricated by pin printing. The selective agonism of each of the receptors was observed. The screening of potential antagonists was demonstrated using a cocktail of agonists. The amount of activation observed was sufficient to permit determinations of EC50 and IC50. Such microarrays could potentially streamline drug discovery by helping integrate primary screening with selectivity and safety screening without compromising the essential functional information obtainable from cellular assays.     

Entanglement dynamics in two-qubit open system interacting with a squeezed thermal bath via quantum nondemolition interaction

We analyze the dynamics of entanglement in a two-qubit systeminteracting with an initially squeezed thermal environment via aquantum nondemolition system-reservoir interaction, with the systemand reservoir assumed to be initially separable. We compare andcontrast the decoherence of the two-qubit system in the case wherethe qubits are mutually close-by (`collective regime’) or distant(`localized regime’) with respect to the spatial variation of theenvironment. Sudden death of entanglement (as quantified byconcurrence) is shown to occur in the localized case rather than inthe collective case, where entanglement tends to `ring down’.A consequence of the QND character of the interaction is that thetime-evolved fidelity of a Bell state never falls below \(1/\sqrt{2}\),a fact that is useful for quantum communication applicationslike a quantum repeater. Usinga novel quantification of mixed state entanglement, we show thatthere are noise regimes where even though entanglementvanishes, the state is still available forapplications like NMR quantum computation, because of the presenceof a pseudo-pure component.     

Symmetries in the representation of grain boundary-plane distributions

Symmetries play a crucial role in the theoretical analysis and visualization of the five macroscopic grain boundary parameters, including the misorientation (three parameters) and the orientation of the boundary-plane (two parameters). The symmetry aspects of the misorientation spaces are very well documented and in this article all possible boundary-plane symmetries are enumerated for the 32 crystallographic point groups. It is observed that the boundary-plane spaces exhibit a wide variety of point group symmetries, which depend both on the crystallographic point group and on the corresponding misorientation (i.e. location in the fundamental zone). The list of symmetries presented here should serve as a guide for graphical representations of not only the distributions of boundary-plane orientations but also for the representation of boundary-plane related properties such as energy, mobility etc.     

RCM/PCC oxidation strategy for synthesis of functionalized cyclic α,β-unsaturated lactones: synthesis of (+)-triacetoxygoniotriol and its diastereomers

A novel methodology leading to the synthesis of (+)-triacetoxygoniotriol 2 from d-glucose is described. Construction of the core six-membered α,β-unsaturated lactone moiety involved ring closing metathesis (RCM) followed by a PCC oxidation. Later exploiting the pseudo-symmetry of d-glucose three other diastereomers of triacetoxygoniotriol were synthesized using the developed methodology.     

Statistical Mechanics and the Climatology of the Arctic Sea Ice Thickness Distribution

We study the seasonal changes in the thickness distribution of Arctic sea ice, g(h), under climate forcing. Our analytical and numerical approach is based on a Fokker–Planck equation for g(h) (Toppaladoddi and Wettlaufer in Phys Rev Lett 115(14):148501, 2015), in which the thermodynamic growth rates are determined using observed climatology. In particular, the Fokker–Planck equation is coupled to the observationally consistent thermodynamic model of Eisenman and Wettlaufer (Proc Natl Acad Sci USA 106:28–32, 2009). We find that due to the combined effects of thermodynamics and mechanics, g(h) spreads during winter and contracts during summer. This behavior is in agreement with recent satellite observations from CryoSat-2 (Kwok and Cunningham in Philos Trans R Soc A 373(2045):20140157, 2015). Because g(h) is a probability density function, we quantify all of the key moments (e.g., mean thickness, fraction of thin/thick ice, mean albedo, relaxation time scales) as greenhouse-gas radiative forcing, \(\Delta F_0\), increases. The mean ice thickness decays exponentially with \(\Delta F_0\), but much slower than do solely thermodynamic models. This exhibits the crucial role that ice mechanics plays in maintaining the ice cover, by redistributing thin ice to thick ice-far more rapidly than can thermal growth alone.     

Spectrophotometric determination of nitrogen dioxide in air

Summary A sensitive spectrophotometric method for the determination of trace amounts of nitrogen dioxide, after fixing it as nitrite in alkaline sodium arsenite solution, is described. The reaction is based on the diazo-coupling of p-nitroaniline with chromotrophic acid in acetate medium (pH 6±0.5). The azo dye formed has its absorption maximum at 515 nm, with a molar absorptivity of 3.7×10⁴ l mol^–1 cm^–1. Beer's law is obeyed over the range 0–20 g of nitrite. The relative standard deviation is 2.5% for ten determinations of 10 g of nitrite. The effect of interfering gases and ions on the determination is discussed. The method has been applied to the determination of residual nitrogen dioxide in a laboratory fume cupboard and the results are compared with those obtained by the widely used sulphanilamide — NEDA method. Down to 0.5 g of nitrite can be determined.