The curse of dimensionality for the class of monotone functions and for the class of convex functions

We study the integration and approximation problems for monotone or convex bounded functions that depend on $d$ variables, where $d$ can be arbitrarily large. We consider the worst case error for algorithms that use finitely many function values. We prove that these problems suffer from the curse of dimensionality. That is, one needs exponentially many (in $d$) function values to achieve an error $\epsilon$.     

Ring current and anisotropy effects on OH chemical shifts in resonance-assisted intramolecular H-bonds

Ring current effects on resonance-assisted and intramolecularly bridged hydrogen bond protons for 10-hydroxybenzo[h]quinoline 1 and a number of related compounds were calculated and the through-space NMR shieldings (TSNMRS) obtained hereby visualized as iso-chemical-shielding surfaces (ICSS) of various size and direction. These calculations revealed that this through-space effect is comparably large (up to 2?ppm) dependent on the position of the intramolecularly bridged OH proton, and therefore, contribute considerably to the chemical shift of the latter making it questionable to use δ(OH)/ppm in the estimation of intramolecular hydrogen bond strength without taking this into account. Furthermore, the anisotropy effects of additional groups on the aromatic moiety (e.g. the carbonyl group in salicylaldehyde or in o-hydroxyacetophenone of ca. 0.6?ppm deshielding) should also be considered. These through-space effects need to be taken into account when using OH chemical shifts to estimate hydrogen bond strength.     

Simultaneous determination of capecitabine and its metabolite 5-fluorouracil by column switching and liquid chromatographic/tandem mass spectrometry

A liquid chromatographic/tandem mass spectrometric method was developed and validated for the quantitation of capecitabine and its metabolite 5-fluorouracil in human plasma. The simultaneous determination of both analytes was achieved by a column switching method using a trapping column and two analytical columns with different stationary phases. Isocratic elution was used for the separation of capecitabine on a C18 column whereas 5-fluorouracil was separated using gradient elution on an non-polar carbon phase. The calibration curves were linear for both compounds with a correlation factor (R2) > 0.9993 for 5-fluorouracil and >0.9942 for capecitabine. The assay was validated in the concentration range 5.00-1000 ng ml(-1) for both compounds. The intra-day precision was better than 10% for 5-fluorouracil and better than 11% for capecitabine whereas the inter-day precision was better than 8% for 5-fluorouracil and better than 14% for capecitabine.     

Electronic influences on 3J(C,H) coupling constants via -S-, -S(O)- and -SO2-: their determination, calculation and comparison of detection methods

3J(C,H) coupling constants via a sulfur atom in two series of compounds, both including a sulfide, a sulfoxide and a sulfone, were detected experimentally and calculated by quantum mechanical methods. In the first series (1-3) the coupling between a hydrogen, bonded to an sp3 carbon, and an sp2 carbon is treated; the second series (4-6) deals with the coupling between a hydrogen, bonded to an sp3 carbon, and an sp3 carbon. Different pulse sequences (broadband HMBC, SelJres, 1D HSQMBC, J-HMBC-2, selective J-resolved long-range experiment and IMPEACH-MBC) proved to be useful in determining the long-range 3J(C,H) coupling constants. However, the dynamic behaviour of two of the compounds (4 and 6) led to weighted averages of the two coupling constants expected (concerning equatorial and axial positions of the corresponding hydrogens). DFT calculations proved to be useful to calculate not only the 3J(C,H) coupling constants but also the different contributions of FC, PSO, DSO and SD terms; the calculation of the Fermi contact term (FC) was found to be sufficient for the correct estimation of 3J(C,H) coupling constants.     

Quantification of the push-pull character of azo dyes and a basis for their evaluation as potential nonlinear optical materials

The push-pull characters of a large series of donor-acceptor substituted azo dyes—71 structures in all—have been quantified by the NN double bond lengths, d_NN, the ¹⁵N NMR chemical shift differences, Δδ_15N, of the two nitrogen atoms and the quotient, π^∗/π, of the occupations of the antibonding π^∗, and bonding π orbitals of this partial NN double bond. The excellent correlation of the occupation quotients with the bond lengths strongly infers that both π^∗/π and d_NN are excellent parameters for quantifying charge alternation in the push-pull chromophore and the molecular hyperpolarizability, β₀, of these compounds. By this approach, selected compounds can be appropriately considered as viable candidates for nonlinear optical (NLO) applications.     

Visualization of homoaromaticity in cations, neutral molecules and anions by spatial magnetic properties (through space NMR shieldings)—an H/C NMR chemical shift study

Prototypes for homoaromaticity in cations, neutral molecules, and anions are theoretically studied at the MP2 level of theory. For the global minimum structures on the potential energy surface both ¹H/¹³C chemical shifts and spatial magnetic properties as through space NMR shieldings (TSNMRS) were calculated by the GIAO perturbation method. The TSNMRS are visualized as iso-chemical-shielding surfaces (ICSS) of different sign and size. Coincident experimental and computed ¹H/¹³C chemical shifts afforded the possibility to decide from the TSNMRSs at hand on both the existence and the size of homoaromaticity in the molecules studied.     

Probing the exohedral magnetic properties of C20 derivatives by through space NMR shieldings (TSNMRS)

The through space NMR shieldings (TSNMRS) of dodecahedrane C₂₀H₂₀, of the isomeric hydrocarbons C₂₀H₁₂, of the ions C₂₀H₁₂²⁺ and C₂₀H₁₂^2?, of the fluxional fullerene C₂₀ and of its dication C₂₀²⁺ have been ab initio calculated employing the NICS concept on basis of MP2/6-31G1 geometries and visualized as iso-chemical-shielding/deshielding surfaces (ICSSs). TSNMRS values were employed to study the exohedral magnetic properties of the compounds studied. Hereby, the curved π-conjugation in the compounds studied could be quantified.     

Chiral stationary phases for separation of intermedine and lycopsamine enantiomers from Symphytum uplandicum

Enantioseparation of the pyrrolizidine alkaloid isomers intermedine and lycopsamine, isolated from Symphytum uplandicum, is discussed. The separatory power of two immobilized carbohydrate‐based chiral HPLC columns, Chiralpak IA and IC, in different chromatographic conditions is compared. The study demonstrated the importance of solvent and column selection while developing such chiral HPLC separation methods. The baseline HPLC separation of the two alkaloid isomers in preparatory scale is reported for the first time. The optimized separations were achieved on a Chiralpak IA column with mobile phases of ACN/methanol (80:20) and methanol/methyl‐t‐butyl ether (90:10), both containing 0.1% diethylamine.