Interaction of a finite quantum system with an infinite quantum system that contains a single one-parameter eigenvalue band

Interaction of a finite quantum system that contains ρ eigenvalues and eigenstates with an infinite quantum system that contains a single one-parameter eigenvalue band is considered. A new approach for the treatment of the combined system is developed. This system contains embedded eigenstates with continuous eigenvalues , and, in addition, it may contain isolated eigenstates with discrete eigenvalues . Two ρ × ρ eigenvalue equations, a generic eigenvalue equation and a fractional shift eigenvalue equation are derived. It is shown that all properties of the system that interacts with the system can be expressed in terms of the solutions to those two equations. The suggested method produces correct results, however strong the interaction between quantum systems and . In the case of the weak interaction this method reproduces results that are usually obtained within the formalism of the perturbation expansion approach. However, if the interaction is strong one may encounter new phenomena with much more complex behavior. This is also the region where standard perturbation expansion fails. The method is illustrated with an example of a two-dimensional system that interacts with the infinite system that contains a single one-parameter eigenvalue band. It is shown that all relevant completeness relations are satisfied, however strong the interaction between those two systems. This provides a strong verification of the suggested method.     

Catalytic asymmetric intermolecular Stetter reaction of glyoxamides with alkylidenemalonates

An asymmetric intermolecular Stetter reaction of glyoxamide and alkylidenemalonates has been developed. Catalyzed by a novel N-heterocyclic carbene, the Stetter adducts are formed in good yield and excellent enantioselectivity. The presence of a sensitive epimerizable stereocenter is tolerated under these mildly basic reaction conditions if a bulky amine base is used. The products may be further elaborated to provide synthetically useful intermediates.     

Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models

We consider the at-the-money (ATM) strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behaviour of the slope for infinite activity exponential Lévy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity ATM digital call options, using Mellin transform asymptotics. Finally, we discuss when the ATM slope is consistent with the steepness of the smile wings, as given by Lee’s moment formula.     

A diastereoselective intermolecular heck reaction of 1,3-dioxepins

A highly diastereoselective intermolecular Heck reaction of 1,3-dioxepins is reported. Substitution at both the 2- and 4-positions of the dioxepin directs the Pd coordination and subsequent olefin insertion to provide the trans-disubstituted adduct in good yield and high diastereoselectivity. Chemoselective Heck reaction occurs at the dioxepin alkene in the presence of other olefinic functional groups. A labeling study has been conducted which suggests that the reaction is under kinetic control.     

Evaluation of the Potential Release Tendency of Metals and Metalloids from the Estuarine Sediments: Case Study of Raša Bay

Assessing the environmental quality of coastal systems is important not only for the management and protection of such areas, but also for improving the quality of water resources. Since sediment itself can often be a source of certain toxic elements, in addition to information on the distribution of metals in the water column and in the sediment itself, it is useful to determine the bioavailable forms of individual elements, particularly toxic ones. In this study, water and sediment geochemical data were supplemented with oxyanion mobility in sediments estimated by diffusion gradients in thin film (DGTs). The data obtained indicate that the chemical composition of the water in the Raša River estuary primarily reflects the high input of suspended sediment from the catchment, the mixing of freshwater and seawater, and to a lesser extent the effects of anthropogenic activities. Although sediment composition is primarily determined by geological and hydrodynamic conditions in the catchment, it also indicates moderate enrichment in Co, Cr, Mo and Ni. In contrast, the distribution of oxyanions in sediment pore water indicates the influence of sediment as a source of some elements in the bottom water; e.g., sediment contributes to 40% of the arsenic bottom water budget. The obtained depth profiles of the oxyanion distribution in the sediment pore water indicate an early onset of suboxic to anoxic conditions in Raša Bay, which is prone to rapid sedimentation. All this demonstrates the need to consider the bioavailable forms of elements when assessing environmental quality, as the lack of such information can lead to an incomplete assessment, especially in dynamic coastal systems such as estuaries.     

One‐Pot Mechanosynthesis with Three Levels of Molecular Self‐Assembly: Coordination Bonds,Hydrogen Bonds and Host–Guest Inclusion

Liquid‐assisted grinding (LAG) was used to combine three levels of molecular self‐assembly into a one‐pot mechanochemical approach for the construction of metal–organic materials. The approach was applied for the construction of three adducts of cobalt(II) dibenzoylmethanate with isonicotinamide, nicotinamide and imidazole, to screen for their inclusion compounds. The one‐pot process consists of: i) The coordination‐driven binding of addends to the equatorially‐protected metal ion, resulting in “wheel‐and‐axle”‐shaped complexes; ii) self‐assembly of resulting complexes by way of hydrogen‐bonded synthons to form metal–organic inclusion hosts; iii) in situ inclusion of the grinding liquid in the resulting host. This approach provided quantitatively and within 20 min the known inclusion compounds of the bis(isonicotinamide) adduct in a single synthetic step. Changing the liquid phase in LAG was used to explore the inclusion behaviour of new wheel‐and‐axle adducts with nicotinamide and imidazole, revealing several inclusion compounds, as well as two polymorphs, of the bis(nicotinamide) host. Preliminary results suggest that one‐pot LAG is superior to solution synthesis in screening for metal–organic inclusion compounds. The difference between the methods is rationalised in terms of reactant solubility and solvent competition. In contrast to the nicotinamide adduct, the bis(imidazole) adduct did not form inclusion compounds. The difference in the inclusion properties of the two adducts is rationalised by structural information gathered by single crystal and powder X‐ray diffraction.