Orbifold cup products and ring structures on Hochschild cohomologies

In this paper we study the Hochschild cohomology ring of convolution algebras associated to orbifolds, as well as their deformation quantizations. In the first case the ring structure is given in terms of a wedge product on twisted polyvectorfields on the inertia orbifold. After deformation quantization, the ring structure defines a product on the cohomology of the inertia orbifold. We study the relation between this product and an $S^1$-equivariant version of the Chen--Ruan product. In particular, we give a de Rham model for this equivariant orbifold cohomology

Reaching Approximate Byzantine Consensus with Multi-hop Communication

We address the problem of reaching consensus in the presence of Byzantine faults. In particular, we are interested in investigating the impact of messages relay on the network connectivity for a correct iterative approximate Byzantine consensus algorithm to exist. The network is modeled by a simple directed graph. We assume a node can send messages to another node that is up to $l$ hops away via forwarding by the intermediate nodes on the routes, where $l\in \mathbb{N}$ is a natural number. We characterize the necessary and sufficient topological conditions on the network structure. The tight conditions we found are consistent with the tight conditions identified for $l=1$, where only local communication is allowed, and are strictly weaker for $l>1$. Let $l^*$ denote the length of a longest path in the given network. For $l\ge l^*$ and undirected graphs, our conditions hold if and only if $n\ge 3f+1$ and the node-connectivity of the given graph is at least $2f+1$ , where $n$ is the total number of nodes and $f$ is the maximal number of Byzantine nodes; and for $l\ge l^*$ and directed graphs, our conditions is equivalent to the tight condition found for exact Byzantine consensus. Our sufficiency is shown by constructing a correct algorithm, wherein the trim function is constructed based on investigating a newly introduced minimal messages cover property. The trim function proposed also works over multi-graphs.Comment: 24 pages, 1 figure. arXiv admin note: text overlap with arXiv:1203.188

Heteroepitaxy of deposited amorphous layer by pulsed electron-beam irradiation

We demonstrate that a single short pulse of electron irradiation of appropriate energy is capable of recrystallizing epitaxially an amorphous Ge layer deposited on either or Si single-crystal substrate. The primary defects observed in the case were dislocations, whereas stacking faults were observed in samples

Epitaxial growth of deposited amorphous layer by laser annealing

We demonstrate that a single short pulse of laser irradiation of appropriate energy is capable of recrystallizing in open air an amorphous Si layer deposited on a (100) single-crystal substrate into an epitaxial layer. The laser pulse annealing technique is shown to overcome the interfacial oxide obstacle which usually leads to polycrystalline formation in normal thermal annealing

Production of large-particle-size monodisperse latexes

The research program achieved two objectives: (1) it has refined and extended the experimental techniques for preparing monodisperse latexes in quantity on the ground up to a particle diameter of 10 microns; and (2) it has demonstrated that a microgravity environment can be used to grow monodisperse latexes to larger sizes, where the limitations in size have yet to be defined. The experimental development of the monodisperse latex reactor (MLR) and the seeded emulsion polymerizations carried out in the laboratory prototype of the flight hardware, as a function of the operational parameters is discussed. The emphasis is directed towards the measurement, interpretation, and modeling of the kinetics of seeded emulsion polymerization and successive seeded emulsion polymerization. The recipe development of seeded emulsion polymerization as a function of particle size is discussed. The equilibrium swelling of latex particles with monomers was investigated both theoretically and experimentally. Extensive studies are reported on both the type and concentration of initiators, surfactants, and inhibitors, which eventually led to the development of the flight recipes. The experimental results of the flight experiments are discussed, as well as the experimental development of inhibition of seeded emulsion polymerization in terms of time of inhibition and the effect of inhibitors on the kinetics of polymerization

Simultaneous dense and nondense orbits for commuting maps

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.We show that, for two commuting automorphisms of the torus and for two elements of the Cartan action on compact higher rank homogeneous spaces, many points have drastically different orbit structures for the two maps. Specifically, using measure rigidity, we show that the set of points that have dense orbit under one map and nondense orbit under the second has full Hausdorff dimension.V. B. acknowledges support received from the National Science Foundation via Grant DMS-1162073 M. E. acknowledges support by the SNF (200021-152819). J. T. acknowledges the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. 291147

Simultaneous dense and nondense orbits for commuting maps

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.We show that, for two commuting automorphisms of the torus and for two elements of the Cartan action on compact higher rank homogeneous spaces, many points have drastically different orbit structures for the two maps. Specifically, using measure rigidity, we show that the set of points that have dense orbit under one map and nondense orbit under the second has full Hausdorff dimension.V. B. acknowledges support received from the National Science Foundation via Grant DMS-1162073 M. E. acknowledges support by the SNF (200021-152819). J. T. acknowledges the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. 291147

The first products made in space: Monodisperse latex particles

The preparation of large particle size 3 to 30 micrometer monodisperse latexes in space confirmed that original rationale unequivocally. The flight polymerizations formed negligible amounts of coagulum as compared to increasing amounts for the ground-based polymerizations. The number of offsize large particles in the flight latexes was smaller than in the ground-based latexes. The particle size distribution broadened and more larger offsize particles were formed when the polymerizations of the partially converted STS-4 latexes were completed on Earth. Polymerization in space also showed other unanticipated advantages. The flight latexes had narrower particle size distributions than the ground-based latexes. The particles of the flight latexes were more perfect spheres than those of the ground-based latexes. The superior uniformity of the flight latexes was confirmed by the National Bureau of Standards acceptance of the 10 micrometer STS-6 latex and the 30 micrometer STS-11 latexes as Standard Reference Materials, the first products made in space for sale on Earth. The polymerization rates in space were the same as those on Earth within experimental error. Further development of the ground-based polymerization recipes gave monodisperse particles as large as 100 micrometer with tolerable levels of coagulum, but their uniformity was significantly poorer than the flight latexes. Careful control of the polymerization parameters gave uniform nonspherical particles: symmetrical and asymmetrical doublets, ellipsoids, egg-shaped, ice cream cone-shaped, and popcorn-shaped particles

NbSe3: Effect of Uniaxial Stress on the Threshold Field and Fermiology

We have measured the effect of uniaxial stress on the threshold field ET for the motion of the upper CDW in NbSe3. ET exhibits a critical behavior, ET ~ (1 - e/ec)^g, wher e is the strain, and ec is about 2.6% and g ~ 1.2. This ecpression remains valid over more than two decades of ET, up to the highest fields of about 1.5keV/m. Neither g nor ec is very sensitive to the impurity concentraction. The CDW transition temperature Tp decreases linearly with e at a rate dTp/de = -10K/%, and it does not show any anomaly near ec. Shubnikov de-Haas measurements show that the extremal area of the Fermi surface decreases with increasing strain. The results suggest that there is an intimate relationship between pinning of the upper CDW and the Fermiology of NbSe3.Comment: 4 pages, 5 figure