Congruence of minimal surfaces and higher fundamental forms

 We show that minimal surfaces in space forms are determined, up to ambient isometries, by the induced metric and certain invariants which are defined in terms of the higher fundamental forms and the complex structure. Received: 6 May 2002 / Revised version: 5 July 2002 Current address: Institut für Mathematik, Universit?t Augsburg, Universit?tsstrasse 12, D-86135 Augsburg, Germany. e-mail: Theodoros.Vlachos@Math.Uni-Augsburg.De The author was supported by the Alexander von Humboldt Foundation Mathematics Subject Classification (2000): 53A10, 53C42 Acknowledgements. This work was written during the author's stay at the University of Augsburg as a research fellow of the Alexander von Humboldt Foundation. I wish to express my gratitude to the Alexander von Humboldt Foundation for its generous support. Moreover, I wish to thank Professor J.H. Eschenburg for many fruitful and stimulating conversations.     

Highly Efficient Synthesis of Multiantennary Bisected N‐glycans Based on Imidates

The occurrence of N‐glycans with a bisecting GlcNAc modification on glycoproteins has many implications in developmental and immune biology. However, these particular N‐glycans are difficult to obtain either from nature or through synthesis. We have developed a flexible and general method for synthesizing bisected N‐glycans of the complex type by employing modular TFAc‐protected donors for all antennae. The TFAc‐protected N‐glycans are suitable for the late introduction of a bisecting GlcNAc. This integrated strategy permits for the first time the use of a single approach for multiantennary N‐glycans as well as their bisected derivatives via imidates, with unprecedented yields even in a one‐pot double glycosylation. With this new method, rare N‐glycans of the bisected type can be obtained readily, thereby providing defined tools to decipher the biological roles of bisecting GlcNAc modifications.     

Controlled synthesis of carbon-encapsulated copper nanostructures by using smectite clays as nanotemplates

Rhomboidal and spherical metallic-copper nanostructures were encapsulated within well-formed graphitic shells by using a simple chemical method that involved the catalytic decomposition of acetylene over a copper catalyst that was supported on different smectite clays surfaces by ion-exchange. These metallic-copper nanostructures could be separated from the inorganic support and remained stable for months. The choice of the clay support influenced both the shape and the size of the synthesized Cu nanostructures. The synthesized materials and the supported catalysts from which they were produced were studied in detail by TEM and SEM, powder X-ray diffraction, thermal analysis, as well as by Raman and X-ray photoelectron spectroscopy.     

Reactions of titanocene dihalides with N,N′,N″-chelates: Preparation,X-ray structure and characterization of bis(chloro){2,6-bis[(3,5-dimethyl)pyrazol-1-yl]pyridine}(η-peroxo)titanium(IV)

The reaction of [Ti^IV(Cp)₂Cl₂] (Cp⁻ = η⁵-C₅H₅⁻) and 2,6-bis(3,5-dimethylpyrazolyl-1-yl)pyridine (bdmpp) in Me₂CO has afforded complex [Ti^IVCl₂(O₂)(bdmpp)] (1). The complex can also be prepared from the 1:1:1 [Ti(Cp)₂Cl₂]/bdmpp/H₂O₂ reaction mixture in various solvents. Single-crystal, X-ray crystallography has revealed that the Ti^IV center is in a distorted pentagonal bipyramidal environment in both of the two, crystallographically independent molecules that are present in the asymmetric unit; the equatorial positions are occupied by the two O atoms of the side-on (η²) O₂²⁻ group and the three N-atoms of the tridentate chelate, while the two chloro ligands are on the axial positions. IR, Raman, electronic and ¹H NMR data are discussed in terms of the known structure and the coordination modes of the peroxo and bdmpp ligands.     

Modulation by Phosphonium Ions of the Activity of Mitotropic Agents Based on the Chemiluminescence of Luminols

Mitochondria-targeting drugs and diagnostics are used in the monitoring and treatment of mitochondrial pathologies. In this respect, a great number of functional compounds have been made mitotropic by covalently attaching the active moiety onto a triphenylphosphonium (TPP) cation. Among these compounds, a number of molecular detectors for reactive oxygen species (ROS) are based on fluorescent and chemiluminescent probes. In this regard, luminol (probably the most widely known chemiluminescent molecule) has been employed for a number of biological applications, including ROS detection. Its oxidation under specific conditions triggers a cascade of reactions, ultimately leading to the excited 3-aminophthalate (3AP *), which emits light upon deactivation. Hence, the photophysical interaction between the light-emitting species 3AP * and TPP cations needs to be evaluated, as it can add valuable information on the design of novel emission-based mitotropic systems. We herein investigate the quenching effect of ethyltriphenylphosphonium cation onto substituted 3-aminophthalates. These were prepared in situ upon hydrolysis of the corresponding anhydrides, which were synthesized from 3-aminophthalimides. Steady-state fluorescence and time-resolved experiments were employed for the evaluation of a possible electron transfer quenching by phosphonium ions. Our experimental results confirmed such quenching, suggesting it is mainly dynamic in nature. A minor contribution of static quenching that was also detected is attributed to complex formation in the ground state. Accordingly, the chemiluminescence of luminol was indeed strongly reduced in the presence of phosphonium ions. Our results have to be taken into account during the design of new chemiluminescent mitotropic drugs or diagnostic agents of the luminol family.     

Heteroannulation of naphthoquinones. Studies on the reaction of 2-bromo-2,3-dihydronaphthoquinone derivatives with 1,2-binucleophiles.

Heterocyclic derivatives of naphthoquinones were synthesized via their 2-bromo-2,3-dehydro-intermediates. This new route may lead to the formation of benzo[a]phenothiazin-5-ones, benzo[f]quinoxalin-6-ones as well as their 1,4 (or 7,10) dihydroxy-derivatives in high yields. The possible mechanisms involved in the formation of these compounds are discussed.     

Pseudotetrahedral cobaltate(II) anions with two and three different kinds of ligands

New complexes of the general types HCo(NCS)₃ ·nL, HCoX ₂(NCS) ·nL and HCo(NCS)₂I ·nL (whereX=Cl, Br, I;L=diethyl ether, pyridine, aniline;n=1.5, 2, 3, 3.5) have been prepared and characterized. The magnetic and spectroscopic data indicate that pseudotetrahedral [Co(NCS)₃ L]^?, [CoX ₂(NCS)L]^? and [Co(NCS)₂IL]^? anions are present in the solid pyridine and aniline compounds.     

Extension Principles for Dual Multiwavelet Frames of $$L_2(\mathbb {R}^s)$$ constructed from Multirefinable Generators

In this work we prove that any pair of homogeneous dual multiwavelet frames of \(L_2(\mathbb {R}^s)\) constructed from a pair of refinable function vectors gives rise to a pair of nonhomogeneous dual multiwavelet frames and vice versa. We also prove that the Mixed Oblique Extension Principle characterizes dual multiwavelet frames. Our results extend recent characterizations of affine dual frames derived from scalar refinable functions obtained in [3].