Cycle-maximal triangle-free graphs

We conjecture that the balanced complete bipartite graph _{K⌊n/2⌋,⌈n/2⌉}$K_{\lfloor n/2\rfloor ,\lceil n/2\rceil }$ contains more cycles than any other n$n$-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and use the bounds to show that among regular graphs, the conjecture holds. We also consider graphs that are close to being regular, with the minimum and maximum degrees differing by at most a positive integer k$k$. For k=1$k=1$, we show that any such counterexamples have n≤91$n\le 91$ and are not homomorphic to _C5$C_5$; and for any fixed k$k$ there exists a finite upper bound on the number of vertices in a counterexample. Finally, we describe an algorithm for efficiently computing the matrix permanent (a #P$\#P$-complete problem in general) in a special case used by our bounds.     

Extinction time and the total mass of the continuous-state branching processes with competition

Consider a general continuous-state branching process with additional interaction, which destroys the branching property. We give precise conditions on the interaction term, in order to decide whether the extinction time of the process remains or not bounded as the initial value tends to infinity, and similarly for the total mass of the process.     

A comparison of lower bounds for the symmetric circulant traveling salesman problem

When the matrix of distances between cities is symmetric and circulant, the traveling salesman problem (TSP) reduces to the so-called symmetric circulant traveling salesman problem (SCTSP), that has applications in the design of reconfigurable networks, and in minimizing wallpaper waste. The complexity of the SCTSP is open, but conjectured to be NP-hard, and we compare different lower bounds on the optimal value that may be computed in polynomial time. We derive a new linear programming (LP) relaxation of the SCTSP from the semidefinite programming (SDP) relaxation in [E. de Klerk, D.V. Pasechnik, R. Sotirov, On semidefinite programming relaxation of the traveling salesman problem, SIAM Journal of Optimization 19 (4) (2008) 1559-1573]. Further, we discuss theoretical and empirical comparisons between this new bound and three well-known bounds from the literature, namely the Held-Karp bound [M. Held, R.M. Karp, The traveling salesman problem and minimum spanning trees, Operations Research 18 (1970) 1138-1162], the 1-tree bound, and the closed-form bound for SCTSP proposed in [J.A.A. van der Veen, Solvable cases of TSP with various objective functions, Ph.D. Thesis, Groningen University, The Netherlands, 1992].     

Field-induced thermal metal-to-insulator transition in underdoped La(2-x)Sr(x)CuO(4+delta)

The transport of heat and charge in cuprates was measured in single crystals of La(2-x)Sr(x)CuO(4+delta) (LSCO) across the doping phase diagram at low temperatures. In underdoped LSCO, the thermal conductivity is found to decrease with increasing magnetic field in the T-->0 limit, in striking contrast to the increase observed in all superconductors, including cuprates at higher doping. In heavily underdoped LSCO, where superconductivity can be entirely suppressed with an applied magnetic field, we show that a novel thermal metal-to-insulator transition takes place upon going from the superconducting state to the field-induced normal state.     

Infrared camera based on a curved retina

Design of miniature and light cameras requires an optical design breakthrough to achieve good optical performance. Solutions inspired by animals' eyes are the most promising. The curvature of the retina offers several advantages, such as uniform intensity and no field curvature, but this feature is not used. The work presented here is a solution to spherically bend monolithic IR detectors. Compared to state-of-the-art methods, a higher fill factor is obtained and the device fabrication process is not modified. We made an IR eye camera with a single lens and a curved IR bolometer. Images captured are well resolved and have good contrast, and the modulation transfer function shows better quality when comparing with planar systems.     

Tunable optical vortex arrays from a single nematic topological defect

We report on the generation of tunable structured light fields endowed with various sets of phase singularities from a single topological defect in a nematic liquid crystal mesophase. The experimental demonstration relies on the use of electric field-induced nonsingular topological defects called "umbilics."     

Etude de proprietes physico-chimiques de l'hydrure d'aluminium

Journal of Thermal Analysis and Calorimetry - L'hydrure d'aluminium exempt de solvant a pu Être préparé avec une bonne pureté, et sa stabilité thermique a...     

Phosphine-mediated [4 + 2] annulation of bis(enones): a Lewis base catalyzed "mock Diels-Alder" reaction

Lewis-base-catalyzed cycloisomerization of bis(enones) to decalins has been demonstrated as an alternative to the traditional Lewis acid catalyzed Diels-Alder cycloaddition. In this process, a trialkylphosphine mediates both bond formation steps in two distinct catalytic cycles. The single-pot operation generates two carbon-carbon bonds and up to five contiguous stereocenters in one step, starting from achiral, aliphatic substrates; eight examples are provided. [reaction: see text]     

The preparation and intra- and intermolecular addition reactions of acyclic N-acylimines: application to the synthesis of (+/-)-sertraline

Intramolecular endo-cyclization reactions of N-acyliminium ions have seen wide application for the synthesis of heterocyclic compounds. The corresponding exocyclic variant, which would provide 1-aminotetralin derivatives, for example, has little precedent. We have discovered that acyclic N-acylcarbamates can be readily reduced to the corresponding N-acylhemiaminal derivatives in high yield using DIBAL as the reducing agent. These intermediates are remarkably stable and, if desired, can be purified and stored. The acyclic N-acylhemiaminals undergo both intra- and intermolecular nucleophilic addition reactions mediated by strong Lewis acids, such as TiCl(4). Diastereoselectivity, induced either by a substituent on the newly formed ring, or by utilizing a chiral ester on the carbamic acid, was disappointingly low. This methodology was successfully applied to the synthesis of the racemic form of the marketed antidepressant sertraline.