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.     

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.     

Positive Harmonic Functions that Vanish on a Subset of a Cylindrical Surface

This paper investigates positive harmonic functions on domains that are complementary to a subset of a cylindrical surface. It characterizes, both in terms of harmonic measure and of a Wiener-type criterion, those domains that admit minimal harmonic functions with exponential growth. Illustrative examples are provided. Two applications are also given. The first of these concerns minimal harmonic functions associated with an irregular boundary point, and amplifies a recent construction of Gardiner and Hansen. The second concerns the possible non-approximability of positive harmonic functions by integrable positive harmonic functions. This research was supported by Science Foundation Ireland under Grant 06/RFP/MAT057, and is also part of the programme of the ESF Network “Harmonic and Complex Analysis and Applications” (HCAA).     

Large time behavior of solutions to degenerate parabolic equations with weights

We study the degenerate parabolic equation t_∂u=a(δ(x))upΔu−g(u) in Ω×(0,∞), where Ω⊂RN (N?1) is a smooth bounded domain, p?1, δ(x)=dist(x,∂Ω) and a is a continuous nondecreasing function such that a(0)=0. Under some suitable assumptions on a and g we prove the existence and the uniqueness of a classical solution and we study its asymptotic behavior as t→∞.     

Rank-two vector bundles on Hirzebruch surfaces

We survey some parts of the vast literature on vector bundles on Hirzebruch surfaces, focusing on the rank-two case.     

Tunable ultrafast nonlinear optofluidic coupler

We present an optofluidic nonlinear coupler fabricated by selective filling of two strands of a photonic crystal fiber with the liquid CCl4 which exhibits a large ultrafast Kerr nonlinearity. We demonstrate power dependent switching in this novel optofluidic device. The large thermo-optical effect of liquids enables us to tune the behavior of the nonlinear coupler by changing the coupling strength with temperature. This opens the road towards flexible designs and realization of a new class of tunable ultrafast nonlinear couplers with switching times below 1 ps.