A modular approach to the synthesis of 2,3,4-trisubstituted tetrahydrofurans

A highly diastereoselective Lewis acid-mediated [1,3] rearrangement of 1,3-dioxepins is the key step along a modular route to 2,3,4-trisubstituted tetrahydrofurans.     

The newtonian limit of hermitian gravity

We construct the gauge invariant potentials of Hermitian Gravity [1] and derive the linearized equations of motion they obey. A comparison reveals a striking similarity to the Bardeen potentials of general relativity. We then consider the response to a point particle source, and discuss in what sense the solutions of Hermitian Gravity reduce to the Newtonian potentials. In a rather intriguing way, the Hermitian Gravity solutions exhibit a generalized reciprocity symmetry originally proposed by Born in the 1930s. Finally, we consider the trajectories of massive and massless particles under the influence of a potential. The theory correctly reproduces the Newtonian limit in three dimensions and the nonrelativistic acceleration equation. However, it differs from the light deflection calculated in linearized general relativity by 25 %. While the specific complexification of general relativity by extension to Hermitian spaces performed here does not agree with experiment, it does possess useful properties for quantization and is well-behaved around singularities as described in [1]. Another form of complex general relativity may very well agree with experimental data.     

Energy Properties and Biomass Yield of Miscanthus x Giganteus Fertilized by Municipal Sewage Sludge

The application of municipal sewage sludge as fertilizer in the production of non-food energy crops is an environmentally and economically sustainable approach to sewage sludge management. In addition, the application of municipal sewage sludge to energy crops such as Miscanthus x giganteus is an alternative form of recycling nutrients and organic material from waste. Municipal sewage sludge is a potential source of heavy metals in the soil, some of which can be removed by growing energy crops that are also remediation agents. Therefore, the objective of the research was to investigate the effect of municipal sewage sludge applied at three different rates of 1.66, 3.22 and 6.44 t/ha on the production of Miscanthus. Based on the analyses conducted on the biomass of Miscanthus fertilized with sludge from the wastewater treatment plant in three fertilization treatments, it can be concluded that the biomass of Miscanthus is a good feedstock for the process of direct combustion. Moreover, the application of the largest amount of municipal sewage sludge during cultivation had no negative effect on the properties of Miscanthus biomass. Moreover, the cellulose and hemicellulose content of Miscanthus is ideal for the production of second-generation liquid biofuels. Fertilizer treatments had no effect on the content of cellulose and lignin, while a significant statistical difference was found for hemicellulose.     

Visible and NIR luminescence of nanocrystalline β-Ga2O3:Er prepared by solution combustion synthesis

In this paper we report on facile solution combustion synthesis of erbium doped β-Ga₂O₃ with urea as fuel. The product was characterized using powder X-ray diffraction and transmission electron microscopy (TEM). X-ray diffraction and TEM showed that the material is nanostructured. Luminescence properties of β-Ga₂O₃:Er are studied with excitation in near infrared (Nd:YAG laser at 1064 nm) and visible (argon laser at 514.5 nm). A strong NIR emission of Er³⁺ in the window of minimal optical loss in silica based optical fibers, due to the ⁴I_13/2→⁴I_15/2 transition at 1.55 μm has been observed. Codoping with Yb³⁺ significantly increases the intensity of that important emission.     

Dynamics and stability of evolutionary optimal strategies in duopoly

Central European Journal of Operations Research - In this paper, we analyse the company behaviour in duopoly taking into account the most common strategies, including dominant, reactive,...     

Leading terms of relations for standard modules of the affine Lie algebras $$C_{n}^{(1)}$$ C n ( 1 )

The Ramanujan Journal - In this paper, we give a combinatorial parametrization of leading terms of defining relations for the vacuum level k standard modules for the affine Lie algebra of type...     

Exploring the relationship between cocrystal stability and symmetry: is Wallach's rule applicable to multi-component solids?

Comparison of structure and hydration stability of pairs of chiral and racemic binary cocrystals indicates that the racemic solid is more stable than the chiral one; we illustrate that this difference might arise from intermolecular (crystal packing) factors in one case, while intramolecular (molecular conformation) factors are more significant in the other.     

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.     

Isostructural materials achieved by using structurally equivalent donors and acceptors in halogen-bonded cocrystals

We demonstrate the supramolecular and structural equivalence of two halogen-bond donors (I and Br) and three acceptors (O, NH and S) through the synthesis of seven isostructural halogen-bonded cocrystals, involving six different molecules: 1,4-dibromo- and 1,4-diiodotetrafluorobenzene (donors) and thiomorpholine, thioxane, morpholine, and piperazine (acceptors). The formation of isostructural cocrystals indicates how cocrystallization may be used to overcome shape and functional group dissimilarities that control molecular arrangement in the solid state. The differences in composition between the seven isostructural cocrystals directly affect the strength and nature of halogen bonds between their constituents, allowing the systematic variation of cocrystal physical properties, in particular the melting point, without affecting their crystal structure. Replacement of each O or S halogen-bond acceptor with an NH group provided an approximate 70 degrees C increase in melting point, whereas the replacement of I with Br as the halogen-bond donor lowered the melting point of the resulting solid by a similar amount.