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.     

Is the Conventional Interpretation of the Anisotropic Effects of CC Double Bonds and Aromatic Rings in NMR Spectra in Terms of the π‐Electron Shielding/Deshielding Contributions Correct?

Based on the nucleus‐independent chemical shift (NICS) concept, isotropic magnetic shielding values have been computed along the three Cartesian axes for ethene, cyclobutadiene, benzene, naphthalene, and benzocyclobutadiene, starting from the molecular/ring center up to 10 Å away. These through‐space NMR spectroscopic shielding (TSNMRS) values, which reflect the anisotropic effects, have been broken down into contributions from localized‐ and canonical molecular orbitals (LMOs and CMOs); these contributions revealed that the proton NMR spectroscopic chemical shifts of nuclei that are spatially close to the C?C double bond or the aromatic ring should not be explained in terms of the conventionally accepted π‐electron shielding/deshielding effects. In fact, these effects followed the predictions only for the antiaromatic cyclobutadiene ring.     

Synthesis and stereochemical studies of 1- and 2-phenyl-substituted 1,3-oxazino[4,3-a]isoquinoline derivatives

Starting from the 1′- or 2′-phenyl-substituted 1-(2′-hydroxyethyl)-6,7-dimethoxy-1,2,3,4-tetrahydroisoquinoline diastereomers 3 and 6, 4-unsubstituted and 4-(p-nitrophenyl)- and 4-oxo-substituted 1-phenyl- and 2-phenyl-9,10-dimethoxy-2H,4H-1,6,7,11b-tetrahydro-1,3-oxazino[4,3-a]isoquinolines (7-12) were prepared. The relative configurations and the predominant conformations of the products were determined by NMR spectroscopy, by quantum chemical calculations and, for (2R^∗,4S^∗,11bR^∗)-9,10-dimethoxy-4-(p-nitrophenyl)-2-phenyl-2H,4H-1,6,7,11b-tetrahydro-1,3-oxazino[4,3-a]isoquinoline (11), by X-ray diffraction.     

The four-electron diamagnetic ring current of porphycene

Porphycene, an isomer that can replace porphin in chemical and biochemical contexts, is predicted by ab initio calculation to exhibit a global diatropic pi ring current with bifurcation across the four pyrrole units of the macrocycle. Analysis of the orbital contributions to the current density in porphycene reveals that the global current, with its bifurcation feature, is attributable to the four electrons of the near-degenerate HOMO levels, the same set of active electrons that feature in the well-known four-orbital model of the electronic spectra of porphyrins. Integration of the current density gives 1H, 13C and 15N NMR shieldings that are compatible with the observed low-field shifts of peripheral and bridge protons and high-field shift of the internal NH protons, assignment of the 13C NMR spectrum and the single average 15N chemical shift resulting from rapid NH tautomerism. Geometries were calculated with the DFT B3LYP functional, the current density maps were calculated with the ipsocentric coupled-Hartree-Fock CTOCD-DZ method, and the shieldings with the CTOCD-PZ2 variant, all in the same 6-31G** basis.     

Solution- and bound-state conformational study of N,N',N"-triacetyl chitotriose and other analogous potential inhibitors of hevamine: application of trNOESY and STD NMR spectroscopy

The solution-state conformations of N,N',N"-triacetyl chitotriose (1) and other potential chitinase inhibitors 2-4 were studied using a combination of NMR spectroscopy (NOESY) and molecular mechanics calculations. Determination solely of the global energy minimum conformation was found to be insufficient for an agreement with the NMR results. An appropriate consistency between the NMR experimental data and theoretical calculations was only reached by assessing the structures as population-weighted average conformers based on Boltzmann distributions derived from the calculated relative energies. Analogies, but also particular differences, between the synthetic compounds 2-4 and the naturally-occurring N,N',N"-triacetyl chitotriose were found. Furthermore, the conformation of compounds 1 and 2 when bound to hevamine was also studied using transferred NOESY experiments and the binding process was found to impart a level of conformational restriction on the ligands. The preferred conformation as determined for 1 in the bound state to hevamine belonged to one of the conformational families found for the compound when free in solution, although full characterisation of the bound-state conformations was impeded due to severe signal overlap. Saturation transfer difference NMR experiments were also employed to analyse the binding epitopes of the bound compounds. We thus determined that it is mainly the acetyl amido groups of the trisaccharide and the heterocyclic moiety which are in close contact with hevamine.     

Platinum complexes of oxopurines: cis‐bis(theophyllinato‐N7)bis(triphenylphosphine)platinum(II) and cis‐chloro(theobrominato‐N1)bis(triphenylphosphine)platinum(II) ethanol hemisolvate

The syntheses and structures of two mixed‐ligand complexes of platinum(II) with deprotonated oxopurine bases and tri­phenyl­phosphine are reported, namely the theophyllinate complex cis‐bis(1,2,3,6‐tetra­hydro‐1,3‐di­methyl­purine‐2,6‐dionato‐κN⁷)­bis(tri­phenyl­phosphine‐κP)­platinum(II), [Pt(C₇H₇N₄O₂)₂(C₁₈H₁₅P)₂], (I), and the theobrominate complex cis‐chloro(1,2,3,6‐tetrahydro‐3,7‐dimethylpurine‐2,6‐dionato‐κN¹)­bis(tri­phenyl­phosphine‐κP)­platinum(II) ethanol hemisolvate, [PtCl(C₇H₇N₄O₂)(C₁₈H₁₅P)₂]·0.5C₂H₅OH, (II). In (I), the coordination geometry of Pt is square planar, formed by the two coordinating N atoms of the theophyl­linate anions in a cis arrangement and two P atoms from the tri­phenyl­phosphine groups. In (II), there are two crystallographically independent mol­ecules. They both exhibit a square‐planar coordination geometry around Pt involving one Cl atom, the coordinating N atom of the theobrominate anion and two P atoms from the tri­phenyl­phosphine groups. The two tri­phenyl­phosphine groups are arranged in a cis configuration in both structures. The heterocyclic rings are rotated with respect to the coordination plane of the metal by 82.99 (8) and 88.09 (8)° in complex (I), and by 85.91 (16) and 88.14 (18)° in complex (II). Both structures are stabilized by intramolecular stacking interactions involving the purine rings and the phenyl rings of adjacent tri­phenyl­phosphine moieties.     

Kristallstruktur und Phasenumwandlung von Betain-Borat, (CH3)3NCH2COO·B(OH)3

Summary Betaine borate undergoes a phase transition of strongly second order at 142.5 K. Crystals below this temperature belong to the ferroelastic Aizu species mmmF2/m. The crystal structures of both phases have been determined. Paraelastic phase: Pmcn,a=7.769(1),b=9.873(2),c=11.974(2)Å,Z=4,T=293K,R=0.041 for 519 unique observed reflections. Ferroelastic phase: P2₁/c,a=7.615(5),b=9.872(3),c=11.947(5)Å, =92.98(8)°,Z=4,T=130K,R=0.083 for 507 unique observed reflections. In both structures the betaine molecules are connected to B(OH)₃-groups via hydrogen bonds to form chains running parallel[001]. These chains are associated to each other by van der Waals forces.

     

On the hypothetical protein F154 of the TTV1 virus/Thermoproteus Tenax. Part II: Synthesis of the trieicosapeptide,corresponding to the protein sequence 79–101

Summary For the identification of a protein predicted by DNA sequence analysis of the TTV1 virus from the archaebacteriumThermoproteus tenax, the trieicosapeptide H-Thr-Pro-Thr-Pro-Thr-Pro-Thr-Tyr-Asp-Ile-Thr-Tyr-Val-Val-Phe-Asp-Val-Thr-Pro-Ser-Pro-Thr-Pro-OH, corresponding to the protein fragment 79–101, was prepared by conventional methods of peptide synthesis. This sequence portion may possibly represent a suitable protein specific immunepitope.

---

Zur Hypothese eines TTV1 Virus/Thermoproteus tenax F154-Proteins. Teil II: Synthese des Protein-fragments 79–101

Zusammenfassung Für den Nachweis der Expression des Proteins F154 — nach einer Sequenzanalyse des Genoms des TTV1 Virus im ArchaebakteriumThermoproteus tenax postuliert — wurde das Peptid H-Thr-Pro-Thr-Pro-Thr-Pro-Thr-Tyr-Asp-Ile-Thr-Tyr-Val-Val-Phe-Asp-Val-Thr-Pro-Ser-Pro-Thr-Pro-OH (Proteinfragment 79–101) mit Hilfe konventioneller Peptidsynthese hergestellt. Diese Peptidsequenz sollte ein geeignetes proteinspezifisches Immunepitop darstellen.

     

Modelling of polymer aggregates in solution

The self-consistent mean field model of Scheutjens and Fleer is used to model spherical aggregates of homopolymers and monomer—polymer particles in solution. For homopolymer aggregates we found that the chain ends are preferentially located at the exterior side of the polymer/solvent interface. The distribution of the end segments may be an important parameter in latex film formation. For monomer—polymer particles a “core-shell” structure is found with an extended core containing a monomer—polymer mixture and a thin shell a few nanometres thick strongly enriched with monomer. The monomer-enriched shell seems to function as a solvating envelope for the dangling chain ends. These results are compared with other simulations based on a single chain in a spherical-cavity model.