Reversed-Phase Thin-Layer Chromatography of Some Foodstuff Dyes

JPC – Journal of Planar Chromatography – Modern TLC - The chromatographic behavior of nine frequently used water-soluble food dyes has been studied by TLC on RP-18 silica gel....     

A novel procedure for the aromatization of ring a in 19-nortestosterone

A convenient, 40% overall yield synthesis of 2,3,17β-triacetoxy-1,3,5(10)-estratriene is described, which involves epoxidation of 19-nortestosterone and subsequent acetylation, lead tetra-acetate acetoxylation of the so-formed 17β-acetoxy-4β,5-epoxy-5β-estran-3-one, and aromatization of ring A, by means of acidic alumina, of the resulting 2α and 2β epimers of 2,17β-diacetoxy-4β,5-epoxy-5β-estran-3-one.     

Positive values of non-homogeneous indefinite quadratic forms of type (1, 4)

Let Г_r,n—r denote the infimum of all number Г > 0 such that for any real indefinite quadratic form inn variables of type (r, n—r), determinantD ≠ 0 and real numbers c₁; c₂,…, c_n, there exist integersx ₁,x₂,…,x_n satisfying 0 < Q(x₁+c₁,x₂ + c₂,…,x_n + c_n) ≤(Г|Z > |)^1/n. All the values of Г_r,n—r are known except for г_1,4. Earlier it was shown that 8 ≤Г_1,4 ≤16. Here we improve the upper bound to get Г_1,4 < 12.     

Chemical surface composition of the polyethylene implanted by Ag ions studied by phase imaging atomic force microscopy

High density polyethylene (HDPE) has been modified by Ag⁺ ion implantation with the energy of 60 keV. The total amount of implanted silver ions was 1, 5 and 12 × 10¹⁵ ions/cm². The surface topography was observed by atomic force microscopy (AFM), while the surface composition changes were detected using phase imaging AFM. Surface topography changes were studied in detail using 3D surface parameters analyses. The average roughness decreased for the implanted HDPE indicating the flattening of the surface. Phase AFM images indicated the homogenization of the polyethylene during ion implantation, while histogram analyses confirmed the change in surface composition.     

The error bounds of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szegő type

We consider the Gauss-Kronrod quadrature formulae for the Bernstein-Szeg? weight functions consisting of any one of the four Chebyshev weights divided by the polynomial \(\rho (t)=1-\frac {4\gamma }{(1+\gamma )^{2}}\,t^{2},\quad t\in (-1,1),\ -1<\gamma \le 0\). For analytic functions, the remainder term of this quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points ? 1 and sum of semi-axes ρ > 1, for the given quadrature formula. Starting from the explicit expression of the kernel, we determine the locations on the ellipses where maximum modulus of the kernel is attained. So we derive effective error bounds for this quadrature formula. An alternative approach, which has initiated this research, has been proposed by S. Notaris (Numer. Math. 103, 99–127, 2006).