A Homological Approach to Two Problems on Finite Sets

We propose a homological approach to two conjectures descended from the Erdös-Ko-Rado Theorem, one due to Chvátal and the other to Frankl and Füredi. We apply the method to reprove, and in one case improve, results of these authors related to their conjectures.     

A law of large numbers result for a bifurcating process with an infinite moving average representation

This paper derives a law of large numbers theorem for bifurcating processes defined on a perfect binary tree. This theorem can be viewed as a generalization of some results that have already appeared in the literature. For instance, all that is required of the bifurcating process is an infinite moving average representation with geometrically decaying coefficients and a finite moment assumption. In addition, the summands are assumed to belong to a flexible class of functions that satisfy a generalized Lipschitz type condition. These two criteria allow for an expansive range of applicability. Two examples are given as corollaries to the theorem.     

On the analytic model of a class of semi-hyponormal operators

The analytic model of a class of semi-hyponormal operators is derived using three kernal functions. In addition, explicit forms of the kernal functions are given and the Pincus principal functions of the operators are calculated.     

An inviscid model for vortex shedding from a deforming body

An inviscid vortex sheet model is developed in order to study the unsteady separated flow past a two-dimensional deforming body which moves with a prescribed motion in an otherwise quiescent fluid. Following Jones (J Fluid Mech 496, 405–441, 2003) the flow is assumed to comprise of a bound vortex sheet attached to the body and two separate vortex sheets originating at the edges. The complex conjugate velocity potential is expressed explicitly in terms of the bound vortex sheet strength and the edge circulations through a boundary integral representation. It is shown that Kelvin’s circulation theorem, along with the conditions of continuity of the normal velocity across the body and the boundedness of the velocity field, yields a coupled system of equations for the unknown bound vortex sheet strength and the edge circulations. A general numerical treatment is developed for the singular principal value integrals arising in the solution procedure. The model is validated against the results of Jones (J Fluid Mech 496, 405–441, 2003) for computations involving a rigid flat plate and is subsequently applied to the flapping foil experiments of Heathcote et al. (AIAA J, 42, 2196–2204, 2004) in order to predict the thrust coefficient. The utility of the model in simulating aquatic locomotion is also demonstrated, with vortex shedding suppressed at the leading edge of the swimming body.      

Assessing the exchange coupling in binuclear lanthanide(iii) complexes and the slow relaxation of the magnetization in the antiferromagnetically coupled Dy2 derivative

We report here the synthesis and the investigation of the magnetic properties of a series of binuclear lanthanide complexes belonging to the metallacrown family. The isostructural complexes have a core structure with the general formula [Ga₄Ln₂(shi^3–)₄(Hshi^2–)₂(H₂shi^–)₂(C₅H₅N)₄(CH₃OH)_x(H₂O)_x]·xC₅H₅N·xCH₃OH·xH₂O (where H₃shi = salicylhydroxamic acid and Ln = Gd^III1; Tb^III2; Dy^III3; Er^III4; Y^III5; Y^III_0.9Dy^III_0.16). Apart from the Er-containing complex, all complexes exhibit an antiferromagnetic exchange coupling leading to a diamagnetic ground state. Magnetic studies, below 2 K, on a single crystal of 3 using a micro-squid array reveal an opening of the magnetic hysteresis cycle at zero field. The dynamic susceptibility studies of 3 and of the diluted DyY 6 complexes reveal the presence of two relaxation processes for 3 that are due to the excited ferromagnetic state and to the uncoupled Dy^III ions. The antiferromagnetic coupling in 3 was shown to be mainly due to an exchange mechanism, which accounts for about 2/3 of the energy gap between the antiferro- and the ferromagnetic states. The overlap integrals between the Natural Spin Orbitals (NSOs) of the mononuclear fragments, which are related to the magnitude of the antiferromagnetic exchange, are one order of magnitude larger for the Dy₂ than for the Er₂ complex.     

Thermal sensor allocation for 3DICs using three dimensional thermal sensors

Stacking active layers leads to increased power density and overall higher temperatures in a three dimensional integrated circuit (3DIC). Thermal sensors are therefore crucial for run-time thermal management of 3DICs. A thermal sensor allocation method customized for 3DICs that utilizes ring oscillator based 3D sensors is introduced in this paper. A new 3D thermal map modeling method that facilitates efficient and very fast analyses is embodied in this thermal sensor distribution algorithm. Our results indicate that for a 4-layer stacked 3DIC, consisting of two layers of quad-core processors and one layer of L2 cache and one layer of main memory, less than 3.58% in maximum sensor reading error can be accomplished with a 53× speedup in the thermal evaluation time and thermal sensor distribution algorithm implementation.     

All-acrylic film-forming colloidal polymer/silica nanocomposite particles prepared by aqueous emulsion polymerization

The efficient synthesis of all-acrylic, film-forming, core-shell colloidal nanocomposite particles via in situ aqueous emulsion copolymerization of methyl methacrylate with n-butyl acrylate in the presence of a glycerol-functionalized ultrafine silica sol using a cationic azo initiator at 60 °C is reported. It is shown that relatively monodisperse nanocomposite particles can be produced with typical mean weight-average diameters of 140-330 nm and silica contents of up to 39 wt %. The importance of surface functionalization of the silica sol is highlighted, and it is demonstrated that systematic variation of parameters such as the initial silica sol concentration and initiator concentration affect both the mean particle diameter and the silica aggregation efficiency. The nanocomposite morphology comprises a copolymer core and a particulate silica shell, as determined by aqueous electrophoresis, X-ray photoelectron spectroscopy, and electron microscopy. Moreover, it is shown that films cast from n-butyl acrylate-rich copolymer/silica nanocomposite dispersions are significantly more transparent than those prepared from the poly(styrene-co-n-butyl acrylate)/silica nanocomposite particles reported previously. In the case of the aqueous emulsion homopolymerization of methyl methacrylate in the presence of ultrafine silica, a particle formation mechanism is proposed to account for the various experimental observations made when periodically sampling such nanocomposite syntheses at intermediate comonomer conversions.