Algorithms for cardinal interpolation using box splines and radial basis functions

Summary We describe an algorithm for (bivariate) cardinal interpolation which can be applied to translates of basis functions which include box splines or radial basis functions. The algorithm is based on a representation of the Fourier transform of the fundamental interpolant, hence Fast Fourier Transform methods are available. In numerical tests the 4-directional box spline (transformed to the characteristical submodule of ²), the thin plate spline, and the multiquadric case give comparably equal and good results.     

Loss of H2O from M + t-Butyl Complex Ions of Benzyl Alcohol in Isobutane Chemical Ionization Mass Spectrometry

In isobutane chemical ionization mass spectrometry benzyl alcohol exhibits ions at m/z 147 (‘M + 39’) that arise by a loss of H₂O from [M + C₄H₉]⁺, i.e. ‘M + 57’ complex ions. Electrophilic aromatic substitution of a proton at an ortho-position of neutral C₆H₅CH₂OH with [t-C₄H₉]⁺ and, alternatively, nucleophilic substitution of H₂O at the benzylic carbon in \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm C_6 H_5 CH_2}\mathop {\rm O}\limits^+ {\rm H}_2 $\end{document} with CH₂?C (CH₃)₂ are discussed as possible pathways. Evidence in favor of the latter is derived from the analysis of C₆D₅CH₂OH and C₆H₅CD₂OH for the origin of the H-atoms lost in H₂O. The inferred ion structure of m/z 147 is verified by mass-analyzed ion kinetic energy (MIKE.) measurements of its collision-activated (CA.) decomposition. MIKE./CA. spectra of mass-selected m/z 147 ions, once generated by (CI(i-C₄H₁₀) from benzyl alcohol and, once, from 2-methyl-4-phenyl-2-butanol match closely and, thus, reflect identical ion structures. With reference to the simple genesis of this ion from the latter precursor, the structure in question can be concluded to be \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm C_6 H_5 CH_2 CH_2}\mathop {\rm C}\limits^+ ({\rm CH}_3)_2 $\end{document} .     

Synthesis of β-Glucuronides of Estradiol,Ethynylestradiol and Estrone

ABSTRACT

Improved syntheses for the 3-β-D-glucuronides of the steroidal sex hormones 17β-estradiol, 17α-ethynylestradiol and estrone are reported employing boron trifluoride diethyl etherate catalysis with tetraacetylated glucuronic acid or the corresponding imidate.     

Schatten properties,nuclearity and minimality of phase shift invariant spaces

We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator $\mathrm{Op}(a)$ is a Schatten-q operator from $M^{\infty }$ to $M^p$ and r-nuclear operator from $M^{\infty }$ to $M^r$ when $a\in M^r$ for suitable p, q and r in $(0,\infty ]$.     

α-Diphenylphosphino-N-(pyrazin-2-yl)glycine as a ligand in Ni-catalyzed ethylene oligomerization

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Backstepping-based output regulation for systems with infinite-dimensional actuator and sensor dynamics

The output regulation problem is solved for an ODE plant driven by a parabolic actuator with spatially varying coefficients. Applying the backstepping transformation to the actuator allows the solution of the regulator equations in closed-form and thus the formulation of the solvability condition. An output feedback regulator is obtained by designing a disturbance observer using delayed measurement and a reference observer that both achieve finite-time convergence. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)