Covering of differentiable manifolds with open disks

Summary The aim of this paper is to prove that every open (i.e. noncompaet without boundary) manifold of dimensionn can be covered with exactlyn open disks. This is a generalization of a theorem of E. Luft [3] concerning the case of any open 2-dimensional manifold. It is then proved that every compact manifold of dimensionn with nonempty boundary can also be covered with exactlyn open disks. The proofs of the theorems are in the spirit of Morse theory [1].     

Functionalized iminium salt systems for catalytic asymmetric epoxidation

A range of dihydroisoquinolinium salts containing alcohol, ether, and acetal functionalities in the nitrogen substituent has been prepared and tested as asymmetric epoxidation catalysts, providing ee's of up to ca. 60%.     

Biologically relevant conformational features of linear and cyclic proteolipid protein (PLP) peptide analogues obtained by high-resolution nuclear magnetic resonance and molecular dynamics

Proteolipid protein (PLP) is one of the main proteins of myelin sheath that are destroyed during the progress of multiple sclerosis (MS). The immunodominant PLP_139–151 epitope is known to induce experimental autoimmune encephalomyelitis (EAE, animal model of MS), wherein residues 144 and 147 are recognized by T cell receptor (TCR) during the formation of trimolecular complex with peptide-antigen and major histocompability complex. The conformational behavior of linear and cyclic peptide analogues of PLP, namely PLP_139–151 and cyclic (139–151) (L¹⁴⁴, R¹⁴⁷) PLP_139–151, have been studied in solution by means of nuclear magnetic resonance (NMR) methods in combination with unrestrained molecular dynamics simulations. The results indicate that the side chains of mutated amino acids in the cyclic analogue have different spatial orientation compared with the corresponding side chains of the linear analogue, which can lead to reduced affinity to TCR. NMR experiments combined with theoretical calculations pave the way for the design and synthesis of potent restricted peptides of immunodominant PLP_139–151 epitope as well as non peptide mimetics that rises as an ultimate goal.     

Zinc(II) binding ability of tri-, tetra- and penta-peptides containing two or three histidyl residues

Macroscopic and microscopic protonation processes and zinc(II) complexes of a series of multihistidine peptides (Ac-HGH-OH, Ac-HGH-NHMe, Ac-HHGH-OH, Ac-HHGH-NHMe, Ac-HVGDH-NH(2), Ac-HHVGD-NH(2), Ac-HVHAH-NH(2), Ac-HAHVH-NH(2), Ac-HPHAH-NH(2) and Ac-HAHPH-NH(2)) were studied by potentiometric, NMR and ESI-MS spectroscopic techniques. Protonations of histidyl imidazole-N donor functions were not much affected by the number and location of histidyl residues, but the presence of C-terminal carboxylate groups had a significant impact on the basicities of the neighbouring histidyl sites. The formation of 2N(im) and 3N(im) macrochelates with the stoichiometry of [ZnL] was the major process in the complexation reactions of all peptides followed by the formation of hydroxo or amide bonded species. Thermodynamic stabilities of the zinc(II) complexes were primarily determined by the number of histidyl residues, but the presence of C-terminal carboxylate functions has also a significant contribution to metal binding. The stabilizing effect of the aspartyl beta-carboxylate group was also observed, but its extent is much weaker than that of the C-terminal carboxylate with a neighbouring histidyl residue. Zinc(II) promoted peptide amide deprotonation and co-ordination was observed only in the zinc(II)-Ac-HHVGD-NH(2) system above pH 8.     

A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES＊

Using a fixed-point method,we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation:f(kx + y) + f(kx - y) =kf(x + y) + kf(x -y) + 2f(kx) - 2kf(x) in Banach modules o...     

A New Generalization of a Theorem of Jung for the Orthogonality Equation

The main result of this paper states as follows: Assume that for a closed ball D @ 0 and with center at the origin, a mapping T : D M D satisfies $$ T(0) = 0\ \hbox{and}\ \vert \langle Tx, Ty \rangle - \langle x, y \rangle \vert \leq \varepsilon \eqno (1) $$ for some 0 h l < min { 1/4, d 2 /17} and for all x , y ] D . Then, there exists an isometry I : D M D with $$ \vert Tx - Ix \vert \le \left\{ {\matrix{ {13\sqrt \varepsilon } \hfill &{{\rm for}\; d     

Asymmetric epoxidation using iminium salt organocatalysts featuring dynamically controlled atropoisomerism

Introduction of a pseudoaxial substituent at a stereogenic center adjacent to the nitrogen atom in binaphthyl- and biphenyl-derived azepinium salt organocatalysts affords improved enantioselectivities and yields in the epoxidation of unfunctionalized alkenes. In the biphenyl-derived catalysts, the atropoisomerism at the biphenyl axis is controlled by the interaction of this substituent with the chiral substituent at nitrogen.     

One-pot synthesis of highly crystalline mesoporous TiO2 nanoparticle assemblies with enhanced photocatalytic activity

We report an unprecedented formation of mesoporous titania via a surfactant-assisted aggregating assembly of TiO(2) nanoparticles. These mesostructures possess a highly crystalline anatase phase, large and accessible pore surface area, and exhibit superior photocatalytic performance.