New a posteriori error estimates for singular boundary value problems

In this paper, we discuss the asymptotic properties and efficiency of several a posteriori estimates for the global error of collocation methods. Proofs of the asymptotic correctness are given for regular problems and for problems with a singularity of the first kind. We were also strongly interested in finding out which of our error estimates can be applied for the efficient solution of boundary value problems in ordinary differential equations with an essential singularity. Particularly, we compare estimates based on the defect correction principle with a strategy based on mesh halving. AMS subject classification 65L05Supported in part by the Austrian Research Fund (FWF) grant P-15072-MAT and SFB Aurora.     

Coloring-flow duality of embedded graphs

Let be a directed graph embedded in a surface. A map is a tension if for every circuit , the sum of on the forward edges of is equal to the sum of on the backward edges of . If this condition is satisfied for every circuit of which is a contractible curve in the surface, then is a local tension. If holds for every , we say that is a (local) -tension. We define the circular chromatic number and the local circular chromatic number of by and , respectively. The invariant is a refinement of the usual chromatic number, whereas is closely related to Tutte's flow index and Bouchet's biflow index of the surface dual .

From the definitions we have . The main result of this paper is a far-reaching generalization of Tutte's coloring-flow duality in planar graphs. It is proved that for every surface and every 0$">, there exists an integer so that holds for every graph embedded in with edge-width at least , where the edge-width is the length of a shortest noncontractible circuit in .

In 1996, Youngs discovered that every quadrangulation of the projective plane has chromatic number 2 or 4, but never 3. As an application of the main result we show that such `bimodal' behavior can be observed in , and thus in for two generic classes of embedded graphs: those that are triangulations and those whose face boundaries all have even length. In particular, if is embedded in some surface with large edge-width and all its faces have even length , then . Similarly, if is a triangulation with large edge-width, then . It is also shown that there exist Eulerian triangulations of arbitrarily large edge-width on nonorientable surfaces whose circular chromatic number is equal to 5.

     

Physics of size selectivity

We demonstrate that two mechanisms used by biological ion channels to select particles by size are driven by entropy. With uncharged particles in an infinite cylinder, we show that a channel that attracts particles is small-particle selective and that a channel that repels water from the wall is large-particle selective. Comparing against the extensive density-functional theory calculations of our model, we find that the main physics can be understood with surprisingly simple bulk models that neglect the confining geometry of the channel completely.     

Experimental observation of universality in depolarized light scattering

Experimental results on light depolarization due to multimode scattering are reported. By means of polarization tomography, we characterize the depolarizing power and the polarization entropy of a broad class of optically scattering media and confirm the recently predicted universal behavior of these two quantities [Phys. Rev. Lett. 94, 090406 (2005)].     

Ring-closing alkyne metathesis approach toward the synthesis of alkyne mimics of thioether A-, B-, C-, and DE-ring systems of the lantibiotic nisin Z

[reaction: see text] Ring-closing alkyne metathesis toward the synthesis of the alkyne-brigded A-, B-, C-, and (D)E-ring mimics of the peptide antibiotic nisin Z is described. We have successfully synthesized alkyne-bridged cyclic peptides containing 4-7 amino acid residues in yields ranging from 18 to 82%.     

Evolutionary chemistry approach toward finding novel inhibitors of the type 2 diabetes target glucose-6-phosphate translocase

A genetic algorithm (GA), driven by experimentally determined biological activities as a feedback fitness function, was used to propose novel small molecules as inhibitors of glucose-6-phosphate translocase (G6PT) in iterative rounds of evolutionary optimization. A straightforward polymer-supported synthetic sequence was implemented to synthesize molecules proposed by the GA, and the biological activities of the compounds were determined by a microsomal assay. Additional compound design strategies were integrated, such as Tanimoto similarity-based selection of starting materials and transfer of favored structure elements into a new chemical scaffold to identify more active and selective inhibitors.     

Identification of Tmem10/Opalin as a novel marker for oligodendrocytes using gene expression profiling

Background  

During the development of the central nervous system, oligodendrocytes generate large amounts of myelin, a multilayered insulating membrane that ensheathes axons, thereby allowing the fast conduction of the action potential and maintaining axonal integrity. Differentiation of oligodendrocytes to myelin-forming cells requires the downregulation of RhoA GTPase activity.     

Mesophase behaviour and thermal stability of octa-alkoxy substituted phthalocyaninatocobalt (II) complexes

Cobalt (II) phthalocyanines substituted with eight alkoxy chains in the peripheral (2, 3, 9, 10, 16, 17, 23, 24) positions were prepared. The alkoxy chain length was varied between n-butyloxy (C₄H₉O) and n-octadecyloxy (C₁₈H₃₇O). Studies by polarizing optical microscopy and high temperature X-ray diffraction revealed that all the complexes are liquid crystalline and that they exhibit a hexagonal columnar mesophase (Col_h). Transition enthalpies were determined by differential scanning calorimetry. The clearing point could only be observed for compounds with a chain length longer than C₁₃H₂₇O. Both the melting and clearing points decrease with increasing chain length. The transition temperatures of these discotic metallomesogens are higher than those of the corresponding metal-free phthalocyanines, but are comparable with those of the corresponding copper (II) compounds. The thermal decomposition of the compounds was studied by thermogravimetry.