Covalent formation of nanoscale fullerene and dendrimer patterns

Localized patterns of amine-terminated monolayers obtained via the surface modification of a monolayer with the biased probe of an atomic force microscope were used to covalently attach buckminsterfullerene or dendrimers to the surface, affording lines as narrow as 20 nm.     

How to Pack Trees

In a virtual memory system, the address space is partitioned into pages, and the main memory serves as a cache to the disk. In this setting, we address the following problem: Given a tree, find an allocation of its nodes to pages, so-called a packing, which optimizes the cache performance for some access pattern to the tree nodes. We investigate a model for tree access in which a node is accessed only via the path leading to it from the root. Two cost functions are considered: the total number of different pages visited in the search, and the number of page faults incurred. It is shown that both functions can be optimized simultaneously. An efficient dynamic programming algorithm to find an optimal packing is presented. The problem of finding an optimal packing which also uses the minimum number of pages is shown to be NP-complete. However, an efficient approximation algorithm is presented. This algorithm finds a packing that uses the minimum number of pages and requires at most one extra page fault per search. Finally, we study this problem in the context of dynamic trees which allow insertions and deletions.     

Radially symmetric minimizers for a p-Ginzburg Landau type energy in {\mathbb R^2}

We consider the minimization of a p-Ginzburg-Landau energy functional over the class of radially symmetric functions of degree one. We prove the existence of a unique minimizer in this class, and show that its modulus is monotone increasing and concave. We also study the asymptotic limit of the minimizers as p ?? ??. Finally, we prove that the radially symmetric solution is locally stable for 2?<?p????4.     

Nobiletin: a citrus flavonoid displaying potent physiological activity

Nobiletin [systematic name: 2‐(3,4‐dimethoxyphenyl)‐5,6,7,8‐tetramethoxy‐4H‐chromen‐4‐one; C₂₁H₂₂O₈] is a flavonoid found in citrus peels, and has been reported to show a wide range of physiological properties, including anti‐inflammatory, anticancer and antidementia activities. We have solved the crystal structure of nobiletin, which revealed that the chromene and arene rings of its flavone moiety, as well as the two methoxy groups bound to its arene ring, were coplanar. In contrast, the C atoms of the four methoxy groups bound to the chromene ring are out of the plane, making the molecule conformationally chiral. A comparison of the crystal structures of nobiletin revealed that it could adopt a variety of different conformations through rotation of the covalent bond between the chromene and arene rings, and the orientations of methoxy groups bound to the chromene ring.     

A decidualized endometrial cyst in a pregnant woman: a case observed with a steady-state free precession imaging sequence

Decidual changes of the ectopic endometrial stroma during pregnancy are well known among pathologists and obstetricians. However, they appear very similar to endometrial cysts with malignant transformation when imaged. Balanced fast field echo (BFFE) is a steady-state free precession imaging sequence and its contrast is decided by the T1/T2 ratio. The authors report a case of a decidualized endometrial cyst in which mural nodules were isointense with the nomotopic decidualized endometrium on T1- and T2-weighted images and BFFE. Isointensity with the nomotopic endometrium is an MR characteristic that can differentiate a decidualized endometrial cyst from malignant transformation. BFFE is a good alternative sequence during pregnancy because of its shorter acquisition time and lower radiofrequency absorption.     

Harmonic functions on planar and almost planar graphs and manifolds,via circle packings

The circle packing theorem is used to show that on any bounded valence transient planar graph there exists a non constant, harmonic, bounded, Dirichlet function. If is a bounded circle packing in whose contacts graph is a bounded valence triangulation of a disk, then, with probability , the simple random walk on converges to a limit point. Moreover, in this situation any continuous function on the limit set of extends to a continuous harmonic function on the closure of the contacts graph of ; that is, this Dirichlet problem is solvable. We define the notions of almost planar graphs and manifolds, and show that under the assumptions of transience and bounded local geometry these possess non constant, harmonic, bounded, Dirichlet functions. Let us stress that an almost planar graph is not necessarily roughly isometric to a planar graph. Oblatum 4-I-1995 & 23-IV-1996     

Expanders are not hyperbolic

We bound from above the number of vertices of a graph in terms of the Cheeger constant and the δ-hyperbolicity of the graph. As a corollary we get that expanders are not uniformly hyperbolic.     

Breakage mechanics—Part II: Modelling granular materials

The compression of granular materials has been traditionally modelled with the limitations of classical elasto-plasticity. The energy was implicitly assumed to dissipate from the frictional interaction of particles. However, the fact that brittle granular materials crush suggests that energy must also be dissipated from the fracturing of the grains, as in fracture mechanics. The concept of breakage as a thermomechanical internal variable was introduced in Part I [Einav, I., 2006. Breakage mechanics—Part I: theory. J. Mech. Phys. Solids 00,000-000] to describe the fracturing mechanisms. The theory allows to treat ideal theoretical materials that undergo dissipation purely from breakage with no other mechanism allowed for the energy consumption. However, as accounted for in elasto-plasticity, dissipation must also occur from the frictional rearrangement of grains. The combination of the two dissipative mechanisms of breakage and plasticity must therefore be investigated, as we do in this paper. Those two mechanisms are generally coupled, in the sense that one inevitably appears when the other develops. Plastic dissipation emerges as a by-product of breakage dissipation because after grains crush, local rearrangement must occur. This scenario may be termed an ‘active breakage mechanism’, and typifies compression deformations. In shear the plastic dissipation is dominant but breakage appears inevitably from grains abrasion. This scenario may be called a ‘passive breakage mechanism’. Based on the coupling assumption, models are developed for granular materials. In particular, we show that in compression isotropic hardening of sands may appear without involving plastic strains, i.e., independent of frictional dissipation. This interpretation of hardening is different from the one used in classical critical state soil mechanics. However, frictional dissipation leads to plastic straining that are necessary for the models to be predictive in unloading.     

Stereoselective Access to Fully Substituted Aldehyde-Derived Silyl Enol Ethers by Iridium-Catalyzed Alkene Isomerization

An in situ generated cationic Ir-catalyst isomerizes simple allylic silyl ethers into valuable, fully substituted aldehyde-derived silyl enol ethers. Importantly, by judicious choice of substrate, either of the two possible stereoisomers of a given enolate derivative is accessible with complete stereoselectivity. One-pot isomerization-aldol and isomerization-allylation processes illustrate the synthetic utility of this method.