Convexity and variation diminishing property of multidimensional Bernstein polynomials

A necessary and sufficient condition for the convexity of the Bézier surface over the k-dimensional simplex is presented. We also consider a multidimensional version of the variation diminishing property of the Bernstein polynomials.     

(Liquid + liquid) equilibria of (water + propionic acid + cyclohexanone) at several temperatures

(Liquid + liquid) equilibrium (LLE) data for (water + propionic acid + cyclohexanone) were measured under atmospheric pressure and at T = (293.2, 298.2 and 303.2) K. Phase diagrams were obtained by determining solubility and tie-line data. The LLE data of the ternary systems were predicted by UNIFAC method. Distribution coefficients and separation factors were evaluated over the immiscibility regions.     

Extraction of lead with nitrobenzene solution of strontium bis-1,2-dicarbollylcobaltate in the presence of 15-crown-5

From extraction experiments and γ-activity measurements, the extraction constant corresponding to the equilibrium Pb²⁺(aq)+SrL₂ ²⁺(nb)⇆PbL₂ ²⁺(nb)+Sr²⁺(aq) taking place in the two-phase water-nitrobenzene system (L=15-crown-5; aq = aqueous phase, nb = nitrobenzene phase) was evaluated: logK _ex (Pb²⁺,SrL₂ ²⁺)=3.0. Further, the stability constant of the PbL₂ ²⁺ complex in nitrobenzene saturated with water was calculated: log β_nb(PbL ₂ ²⁺ )=17.8     

HPTLC and HPLC Determination of Alkaloids in Poppies Subjected to Stress

JPC – Journal of Planar Chromatography – Modern TLC - Papaver somniferum produces secondary metabolites which have important roles in self-defense processes, in plant biochemistry, and...     

Set-theoretic constructions of nonshrinking open covers

A family {M_α|α?A} is a shrinking of a cover {O_α|α?A} of a topological space if {M_α|α?A} also covers and M_α?O_α for all α?A.?⁺⁺ implies that there is a normal space such that every increasing open cover of it has a clopen shrinking but there is an open cover having no closed shrinking.? implies that there is a P-space (i.e. a space having a normal product with every metric space), which has an increasing open cover having no closed shrinking. This space is used in [17] to show that any space which has a normal product with every P-space is metrizable.     

High-pressure (2+2)cycloaddition of toluene-4-sulphonyl isocyanate to glycals

High-pressure (2+2)cycloaddition of toluene-4-sulphonyl isocyanate to glycals is examined. Reactions proceed regiospecifically to afford single products in case of all 3-substituted glycals. Upon heating or even after standing at room temperature adducts undergo retro-addition to give starting glycals. Various aspects of the cycloaddition are discussed, especially ret-ro-reaction and rearrangement of β-lactams to α,β-unsaturated amides.     

Conductivity of Sodium Chloride in Water + 1,4-Dioxane Mixtures from 5 to 35°C II. Concentrated Solution

Conductivity data of sodium chloride in binary mixtures of water and 1,4-dioxanefrom 5 to 35°C were measured, covering an electrolyte concentration range upto the limit of solubility in the solvent mixtures and up to 5 mol-dm^–3 inpure water. Data analysis is based on the mean spherical approximation (MSA).Comparison is made with the data representation by the empirical Casteel-Amisequation. The association constants of the MSA are compared with those fromchemical model calculations at low concentrations (lcCM).