The forms of azeotropic rule for multidimensional diagrams of equilibrium distillation

Linear independent forms of the azeotropy rule applicable to diagrams of distillation (reaction distillation) and their fragments are established and presented as simple polyhedra of arbitrary dimensions.     

On cardinal characteristics of Yorioka ideals

Yorioka introduced a class of ideals (parametrized by reals) on the Cantor space to prove that the relation between the size of the continuum and the cofinality of the strong measure zero ideal on the real line cannot be decided in . We construct a matrix iteration of c.c.c. posets to force that, for many ideals in that class, their associated cardinal invariants (i.e., additivity, covering, uniformity and cofinality) are pairwise different. In addition, we show that, consistently, the additivity and cofinality of Yorioka ideals does not coincide with the additivity and cofinality (respectively) of the ideal of Lebesgue measure zero subsets of the real line.     

Besov continuity of pseudo-differential operators on compact Lie groups revisited

In this note we present some results on the action of global pseudo-differential operators on Besov spaces on compact Lie groups.     

Stereocomplementary Routes to Hydroxylated Nitrogen Heterocycles: Total Syntheses of Casuarine,Australine, and 7‐epi‐Australine

Addition of lithiated 1‐benzyloxyallene to a D ‐arabinose‐derived cyclic nitrone occurred with perfect diastereoselectivity furnishing a bicyclic 1,2‐oxazine derivative, which is an excellent precursor for pyrrolizidine alkaloids hydroxylated at C‐7 with optional configuration at this stereogenic center. Depending on the stage of the N? O bond cleavage and ring re‐closure, 7‐hydroxypyrrolizidines with 7R or 7S configuration were obtained, as a result of completely selective addition reactions occurring complementarily at the bottom or top face of the endocyclic C? C double bond in six‐ and five‐membered B rings, respectively. Applicability of these stereodivergent routes to obtain polyhydroxy pyrrolizidine alkaloids is demonstrated by the efficient syntheses of casuarine and australine as examples of the two classes of diversely configured 7‐hydroxypyrrolizidine alkaloids. An alternative synthesis of australine and two strategies for the preparation of 7‐epi‐australine are also reported, which demonstrate that the stereoselectivity of hydride reduction of an exocyclic C? O double bond is independent of the ring size, occurring preferentially from the top face either in a six‐ or five‐membered ring.     

Synthesis and spectrophotometric studies of water-soluble amino[bis(ethanesulfonate)] azobenzene pH indicators

Three azobenzene pH indicators with amino[bis(ethanesulfonate)] substituents were synthesized and studied by UV–visible absorption spectroscopy in aqueous solution. The indicators exhibit brilliant and distinct colour changes with transitions between pH 1 and 4. Significant changes were observed in the UV–visible spectra on titration with acid with pK_a values ranging from 2.2 to 2.8. The indicators demonstrate individual changes in colour as a function of pH. These novel pH indicators complement the existing library of azobenzene indicator dyes and may be useful for environmental situations with high proton concentrations.     

On identifiability for chemical systems from measurable variables

The dynamics of the composition of chemical species in reacting systems can be characterized by a set of autonomous differential equations derived from mass conservation principles and some elementary hypothesis related to chemical reactivity. These sets of ordinary differential equations (ODEs) are basically non-linear, their complexity grows as much increases the number of substances present in the reacting media and can be characterized by a set of phenomenological constants (kinetic rate constants) which contains all the relevant information about the physical system. The determination of these kinetic constants is critical for the design or control of chemical systems from a technological point of view but the non-linear nature of the ODEs implies that there are hidden correlations between the parameters which maybe can be revealed with a identifiability analysis.     

Theoretical investigation of the molecular structure,vibrational spectra,and molecular docking of tramadol using density functional theory

The optimized molecular structures, harmonic vibrational wavenumbers, and the corresponding vibrational assignments of (1S,2S)-tramadol and (1R,2R)-tramadol are computationally examined using the B3LYP density functional theory method together with the standard 6–311++G(d,p) and def2-TVZP basis sets. The optimized structures show that phenolic rings of both 1R,2R and 1S,2S tramadol adopt planar geometry, which are slightly distorted due to the substitution at the meta-position; and the six-membered cyclohexane adopts a slightly distorted chair conformation. The 1S,2S enantiomer is energetically more favorable than 1R,2R with the energy differences of 1.32 and 1.03 kcal/mol obtained at B3LYP/6–311++G(d,p) and B3LYP/Def2-TVZP levels, respectively. The analysis of the binding pocket in the silico molecular docking with the m-opioid receptor shows that it originated two clusters with the 1S,2S enantiomer and one cluster with the 1R,2R enantiomer of tramadol. The results point to a more stable complex of the m-opioid receptor with the 1R,2R enantiomer of tramadol.     

Splitting of the conduction bands of GaAs for k along [110]

The splitting of the spin degeneracy of the lowest conduction band of GaAs for $\text{k}$ along [110] is calculated by $\text{k}$·$\text{p}$ perturbation theory as well as by means of the self-consistent LMTO method. The magnitude and the sign of the calculated splitting agree with recent measurements of the spin precession in spin- polarized photoemission from GaAs [110] surfaces.