On Descartes’ rule for polynomials with two variations of signs

Lithuanian Mathematical Journal - For sequences of d + 1 signs + and ? beginning with a + and having exactly two variations of sign, we give some sufficient conditions for the (non)existence...     

Nanocrystalline TiO2-HClO4:A novel,efficient and recyclable catalyst for the chemoselective N-Boc protection of amines under solvent-free conditions

Nanocrystalline TiO₂-HClO₄,as newly reported catalyst,has been used as an efficient and reusable catalyst for the chemoselective N-Boc protection of amines.The clean,mild acidity condition, quantitative yields of products,short reaction time and low reaction temperature are attractive features of this reaction.In practice,this method is a combination of a satisfactory synthesis and more significantly easy product isolation and purification.     

Ruthenium‐Catalyzed Reductive Methylation of Imines Using Carbon Dioxide and Molecular Hydrogen

The use of the well‐defined [Ru(triphos)(tmm)] catalyst, CO₂ as C₁ source, and H₂ as reducing agent enabled the reductive methylation of isolated imines, as well as the direct coupling of amines with aldehydes and the subsequent reductive methylation of the in situ formed imines. The method, which afforded the corresponding N‐methyl amines in very good to excellent yields, was also used for the preparation of the antifungal agent butenafine in one step with no apparent waste, thus increasing the atom efficiency of its synthesis.     

Efficient and green syntheses of novel γ-aminophosphonate and phosphine oxide derivatives

Two synthetic protocols leading to novel γ-aminophosphonate and phosphine oxide derivatives, by reductive amination of γ-phosphonylketones, are reported. The first method involved a two-step procedure. Imine intermediates were first isolated from the p-toluenesulfonic acid-catalyzed reaction of primary amines with γ-ketophosphonates and phosphine oxides, then reduced with NaBH₄ in refluxing ethanol. The second method consists of a one-pot procedure which includes the condensation of γ-ketophosphonates and phosphine oxides with primary amines, in the presence of molecular sieves, followed by reduction with NaBH₄. These methods offer significant advantages over prior reports, such as efficiency, generality, and good yields. Furthermore, they are green protocols avoiding hazardous hydrides and solvents.     

Log-Polynomial Period Functions for Hecke Groups

In this article we shall determine the automorphic integrals of positive and negative integral weight associated with the full modular group and some Hecke groups. This will be done by using the Hecke Correspondence. We will also give a characterization of multiplier systems of real weight for Hecke groups.     

Pristine and supported ZnO-based catalysts for phenazopyridine degradation with direct solar light

In search for safe techniques to manage waste pharmaceutical compounds drained in water, solar-driven degradation of phenazopyridine (a model drug) was investigated in aqueous media using different ZnO-based catalyst systems. Naked ZnO, CdS-sensitized ZnO (ZnO/CdS) and activated carbon-supported ZnO (AC/ZnO) have been studied. Both naked ZnO and AC/ZnO were highly efficient in mineralizing phenazopyridine, reaching complete removal in ～50 min, with AC/ZnO having the higher edge. The ZnO/CdS system showed lower efficiency, due to screening of light by CdS. Moreover, the tendency of CdS to leach out Cd²⁺ ions discouraged the use of CdS as sensitizer in this work. In both ZnO and AC/ZnO systems, the photo-degradation reaction was induced by the UV tail of the solar light. The visible region, with wavelength longer than 400 nm, failed to induce photo-degradation. The reaction was faster with higher catalyst loading, until a maximum efficiency was reached at a certain concentration. The rate of reaction increased with higher drug concentrations up to a certain limit. The effect of pH value was studied, and the catalysts showed highest efficiencies at pH close to 7. Stability of ZnO to degradation was studied. Both catalyst systems showed lowered efficiencies on recovery and reuse. The results suggest that complete mineralization of waste drugs, commonly dumped in sewage water, with direct solar light is a potentially feasible strategy using the AC/ZnO catalyst.     

Density functional investigations on structural and electronic properties of anionic and neutral sodium clusters Na(N) (N = 40-147): comparison with the experimental photoelectron spectra

Density functional calculations have been carried out to obtain low energy equilibrium geometries of anionic and neutral sodium clusters over a wide range of sizes 40 ≤ N ≤ 147, where N is the number of atoms. An exhaustive search for the low energy equilibrium geometries has been carried out. The density of states of the lowest energy geometries are compared with the experimental photoelectron spectra (Huber et al 2009 Phys. Rev. B 80 235425; Kostko et al 2007 Phys. Rev. Lett.98 043401) for N > 41. The agreement between theory and experiment is good for almost all the clusters and the changes in the spectrum with size correlate very well with the changes in the shapes as observed in the evolutionary trend of the ground state geometries.     

Indecomposable decomposition of tensor products of modules over Drinfeld doubles of Taft algebras

In this paper, we study the tensor product structure of the category of finite dimensional modules over Drinfeld doubles of Taft Hopf algebras. Tensor product decomposition rules for all finite dimensional indecomposable modules are explicitly given.