A multi-objective capacitated rural school bus routing problem with heterogeneous fleet and mixed loads

Four multi-objective meta-heuristic algorithms are presented to solve a multi-objective capacitated rural school bus routing problem with a heterogeneous fleet and mixed loads. Three objectives are considered: the total weighted traveling time of the students, the balance of routes among drivers, and the routing costs. The proposed methods were compared with one from the literature, and their performance assessed observing three multi-objective metrics: cardinality, coverage, and hyper-volume. All four devised methods outperformed the one from the literature. The algorithm with a path relinking procedure embedded during the crowding distance selection scheme had the best overall performance.     

Martingales on Frame Bundles

Let M be a smooth manifold endowed with a symmetric connection . There are two important ways of lift the connection of M to the frame bundle BM, the canonical lift and the horizontal lift . The aim of this work is determine the -martingales and the -martingales on BM. Our results allow to establish new characterizations of harmonic maps from Riemannian manifolds to frame bundles. The research of P. Catuogno is supported in part by FAPESP 01/13158-4 and S. Stelmastchuk is fully supported by FAPESP 02/12154-8.     

Complete orthonormal sets of polynomial solutions of the Riesz and Moisil-Teodorescu systems in ℝ3

As it is well-known, the generalization of the classical Cauchy-Riemann system to higher dimensions leads to the so-called Riesz and Moisil-Teodorescu systems. Rewriting these systems in quaternionic language and taking advantage of the underlying algebra, we construct complete sets of polynomials solutions of both systems that are orthonormal with respect to a certain inner product. The restrictions of those polynomials to the unit sphere can be viewed as analogues to the complex case of the Fourier exponential functions $\{e^{i n \theta}\}_{n\geq 0}$ on the unit circle and constitute a refinement of the well-known spherical harmonics.     

The multisublinear maximal type operators in Banach function lattices

The main aim of this paper is to study a general multisublinear operators generated by quasi-concave functions between weighted Banach function lattices. These operators, in particular, generalize the Hardy–Littlewood and fractional maximal functions playing an important role in harmonic analysis. We prove that under some general geometrical assumptions on Banach function lattices two-weight weak type and also strong type estimates for these operators are true. To derive the main results of this paper we characterize the strong type estimate for a variant of multilinear averaging operators. As special cases we provide boundedness results for fractional maximal operators in concrete function spaces.