Gaussian partitions

Let V=V(n,q) denote the finite vector space of dimension n over the finite field with q elements. A subspace partition of V is a collection Π of subspaces of V such that each 1-dimensional subspace of V is in exactly one subspace of Π. In a recent paper, we proved some strong connections between the lattice of the subspace partitions of V and the lattice of the set partitions of n={1,…,n}. We now define a Gaussian partition of [n] _q =(q ⁿ −1)/(q−1) to be a nonincreasing sequence of positive integers formed by ordering all elements of some multiset {dim(W):W∈Π}, where Π is a subspace partition of V. The Gaussian partition function gp(n,q) is then the number of all Gaussian partitions of [n] _q , and is naturally analogous to the classical partition function p(n). In this paper, we initiate the study of gp(n,q) by exhibiting all Gaussian partitions for small n. In particular, we determine gp(n,q) as a polynomial in q for n≤5, and find a lower bound for gp(6,q).     

A fourth/second order accurate collocation method for singularly perturbed two-point boundary value problems using tension splines

Summary.   The collocation tension spline is considered as a numerical solution of a singularly perturbed two-point boundary value problem: . The collocation points are chosen as a generalization of the classical Gaussian points. Unlike the traditional approach, we employ the B-spline representation in the analysis. This leads to global quadratic convergence of the method for small perturbation parameters, and, for large values, the order of convergence is four. Received October 4, 1996 / Revised version received September 23, 1999 / Published online October 16, 2000     

Metal-insulator transition tuned by external gates in Hall systems with constrictions

The nature of a metal-insulator transition tuned by external gates in quantum Hall systems with point constrictions, as reported in recent experiments [S. Roddaro, Phys. Rev. Lett. 95, 156804 (2005)10.1103/PhysRevLett.95.156804], is examined. We attribute this phenomenon to a splitting of the integer edge into conducting and insulating stripes, the latter wide enough to allow for the stability of the edge structure. Interchannel impurity scattering and interchannel Coulomb interactions do not destabilize this picture.     

Collinear improvement of the BFKL kernel in the electroproduction of two light vector mesons

The use of the BFKL kernel improved by the inclusion of subleading terms generated by renormalization group (RG) analysis has been suggested to cure the instabilities in the behavior of the BFKL Green’s function in the next-to-leading approximation (NLA). We test the performance of a RG-improved kernel in the determination of the amplitude of a physical process, the electroproduction of two light vector mesons, in the BFKL approach in the NLA. We find that a smooth behavior of the amplitude with the center-of-mass energy can be achieved, setting the renormalization and energy scales appearing in the subleading terms to values much closer to the kinematical scales of the process than in the approaches based on the unimproved kernel.     

Preparation, characterization and catalytic behavior of Pt-Cu nanoparticles in methane combustion

Fine and well dispersed Pt-Cu bimetallic nanoparticles stabilized by polyvinyl pyrrolidone (PVP) were synthesized by alkaline polyol method. The molar ratio of Pt to Cu was 1 : 1. Further, the Pt-Cu bimetallic nanoparticles were supported on alumina and their catalytic behavior in methane combustion was investigated. The as-prepared as well as the supported Pt-Cu nanoparticles were characterized by transmission elec-tron microscopy (TEM), X-ray photoelectron spectroscopy (XPS), fractal analysis and X-ray diffraction (XRD). The dependence of methane combustion on the morphology and surface composition of Pt-Cu nanoparticles was analyzed based on the experimental results.     

Proximal point method for minimizing quasiconvex locally Lipschitz functions on Hadamard manifolds

In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex locally Lipschitz objective functions on Hadamard manifolds. To reach this goal, we use the concept of Clarke subdifferential on Hadamard manifolds and assuming that the function is bounded from below, we prove the global convergence of the sequence generated by the method to a critical point of the function.     

Four algorithms to solve symmetric multi-type non-negative matrix tri-factorization problem

Journal of Global Optimization - In this paper, we consider the symmetric multi-type non-negative matrix tri-factorization problem (SNMTF), which attempts to factorize several symmetric...     

Total oxidation of benzene using Cu-Cr mixed oxide as catalyst

Benzene total oxidation on a Cu-Cr supported catalyst was investigated using the work function method. Above 300°C, the majority of the oxygen species on the surface was O²⁻ in the absence or in the presence of hydrocarbon.     

New Self-Concordant Barrier for the Hypercube

We introduce a new barrier function to build new interior-point algorithms to solve optimization problems with bounded variables. First, we show that this function is a (3/2)n-self-concordant barrier for the unitary hypercube [0,1] ⁿ , assuring thus the polynomial property of related algorithms. Second, using the Hessian metric of that barrier, we present new explicit algorithms from the point of view of Riemannian geometry applications. Third, we prove that the central path defined by the new barrier to solve a certain class of linearly constrained convex problems maintains most of the properties of the central path defined by the usual logarithmic barrier. We present also a primal long-step path-following algorithm with similar complexity to the classical barrier. Finally, we introduce a new proximal-point Bregman type algorithm to solve linear problems in [0,1] ⁿ and prove its convergence. P.R. Oliveira was partially supported by CNPq/Brazil.