Derivations and Dirichlet forms on fractals

We study derivations and Fredholm modules on metric spaces with a local regular conservative Dirichlet form. In particular, on finitely ramified fractals, we show that there is a non-trivial Fredholm module if and only if the fractal is not a tree (i.e. not simply connected). This result relates Fredholm modules and topology, refines and improves known results on p.c.f. fractals. We also discuss weakly summable Fredholm modules and the Dixmier trace in the cases of some finitely and infinitely ramified fractals (including non-self-similar fractals) if the so-called spectral dimension is less than 2. In the finitely ramified self-similar case we relate the p-summability question with estimates of the Lyapunov exponents for harmonic functions and the behavior of the pressure function.     

A robust metal-organic framework constructed from alkoxo-bridged binuclear nodes and hexamethylenetetramine spacers: crystal structure and sorption studies

A neutral 3D metal-organic framework, (3)(∞)[Cu(2)(mand)(2)(hmt)]·H(2)O (1), was constructed from binuclear Cu(2)O(2) alkoxo-bridged nodes, generated by the doubly deprotonated mandelic acid. The nodes are connected by hexamethylenetetramine (hmt) spacers, which act as biconnective bridging ligands, and by carboxylato groups. Channels are observed along the crystallographic c axis. The water molecules from the channels can be easily removed, preserving the architecture of the crystal, which is stable up to 280 °C. The Langmuir surface area was found to be 610 m(2) g(-1). The sorption ability of 1 was investigated using H(2) and CO(2).     

Multiplicativity of Completely Bounded p-Norms Implies a New Additivity Result

We prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ₁₂) − S(γ₁) is restricted to states of the form . We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L ₁ → L _p for L _p spaces defined by the Schatten p-norm on matrices, and give another proof based on entropy inequalities. Several related multiplicativity results are discussed and proved. In particular, we show that both the usual L ₁ → L _p norm of a CP map and the corresponding completely bounded norm are achieved for positive semi-definite matrices. Physical interpretations are considered, and a new proof of strong subadditivity is presented.     

A variant of the level set method and applications to image segmentation

In this paper we propose a variant of the level set formulation for identifying curves separating regions into different phases. In classical level set approaches, the sign of level set functions are utilized to identify up to phases. The novelty in our approach is to introduce a piecewise constant level set function and use each constant value to represent a unique phase. If phases should be identified, the level set function must approach predetermined constants. We just need one level set function to represent unique phases, and this gains in storage capacity. Further, the reinitializing procedure requested in classical level set methods is superfluous using our approach. The minimization functional for our approach is locally convex and differentiable and thus avoids some of the problems with the nondifferentiability of the Delta and Heaviside functions. Numerical examples are given, and we also compare our method with related approaches.

     

Cluster properties of peptides on (100) semiconductor surfaces

Peptide adhesion on semiconductor surfaces is quantitatively investigated by atomic force microscopy. The selected peptides are shown to cluster at the surface, with the larger, higher, and softer clusters appearing on the surfaces with lower peptide adhesion. Average cluster diameters vary from 40 nm on GaAs (100) to 300 nm on Si (100). Direct adhesion of the peptides to the surface competes with forming molecular aggregates that offer an overall reduced surface contact.     

Color tuning in rhodopsins: the mechanism for the spectral shift between bacteriorhodopsin and sensory rhodopsin II

The mechanism of color tuning in the rhodopsin family of proteins has been studied by comparing the optical properties of the light-driven proton pump bacteriorhodopsin (bR) and the light detector sensory rhodopsin II (sRII). Despite a high structural similarity, the maximal absorption is blue-shifted from 568 nm in bR to 497 nm in sRII. The molecular mechanism of this shift is still a matter of debate, and its clarification sheds light onto the general mechanisms of color tuning in retinal proteins. The calculations employ a combined quantum mechanical/molecular mechanical (QM/MM) technique, using a DFT-based method for ground state properties and the semiempirical OM2/MRCI method and ab initio SORCI method for excited state calculations. The high efficiency of the methodology has allowed us to study a wide variety of aspects including dynamical effects. The absorption shift as well as various mutation experiments and vibrational properties have been successfully reproduced. Our results indicate that several sources contribute to the spectral shift between bR and sRII. The main factors are the counterion region at the extracellular side of retinal and the amino acid composition of the binding pocket. Our analysis allows a distinction and identification of the different effects in detail and leads to a clear picture of the mechanism of color tuning, which is in good agreement with available experimental data.     

Heterotopic helicand for designing heterometallic helicates

A new diazine tetratopic helicand, H4L, is obtained from 3-formylsalicylic acid and hydrazine. The reaction between H4L and cobalt(II) perchlorate, iron(III) perchlorate, and sodium carbonate leads to triple-stranded tetranuclear anionic helicates, [L3Co(II)2Fe(III)2]2-, which are connected through Na ions, resulting in chiral coordination polymers, [L3Na2Fe2Co2(H2O)4(EtOH)2].3H2O.     

Tandem reactions of 6-phenylethynylpyrimidine-5-carbaldehydes with alcohols: regioselective synthesis of 5-alkoxy-(7Z)-7-benzylidene-5,7-dihydrofuro[3,4-d]pyrimidines and 5-alkoxy-7-phenyl-5H-pyrano[4,3-d]pyrimidines

An efficient and versatile tandem processes of acetalisation and cycloisomerization reactions have been developed for the reactions of 6-phenylethynylpyrimidine-5-carbaldehydes. The influence of the catalyst and role of the substituent in the position 4 of the pyrimidine ring have been studied. Regioselective synthesis of 5,7-dihydrofuro[3,4-d]pyrimidine and pyrano[4,3-d]pyrimidine cores is described.