Cyclic Spaces for Grassmann Derivatives and Additive Theory

Let A be a finite subset of Z_p (where p is a prime). Erdösand Heilbronn conjectured (1964) that the set of sums of the2-subsets of A has cardinality at least min(p, 2|A| —3). We show here that the set of sums of all m-subsets of Ahas cardinality at least min {p,m(|A| — m)+ 1}. In particular,we answer affirmatively the above conjecture. We apply thisresult to the problem of finding the smallest n such that forevery subset 5 of cardinality n and every xZ_p there is a subsetof S with sum equal to x. On this last problem we improve theknown results due to Erdös and Heilbronn and to Olson. The above result will be derived from the following generalproblem on Grassmann spaces. Let F be a field and let V be afinite dimensional vector space of dimension d over F. Let pbe the characteristic of F in nonzero characteristic and otherwise. Let Df be the derivative of a linear operatorfon V, restrictedto the mth Grassmann space ^mV. We show that there is a cyclicsubspace for the derivative with dimension at least min {p,m(n–m)+ 1}, where n is the maximum dimension of the cyclic subspacesof f. This bound is sharp and is reached when f has d distincteigenvalues forming an arithmetic progression.     

Complex Ginzburg–Landau Equation with Absorption: Existence,Uniqueness and Localization Properties

In this paper we study the time-dependent complex Ginzburg–Landau equation with a nonlinear absorbing term in ${\Omega \times(0,T),\, \Omega }$ open bounded set in ${\mathbb{R}^{n}}$ . We prove global existence and uniqueness of solutions for the initial and boundary-value problem and study the properties of localization and extinction of solutions in some special cases.     

Aromaticity and cyclic conjugation of three pairs of strongly subspectral series of conjugated molecules as models for graphene armchair and zigzag edges

It is shown that armchair edges possess greater aromaticity and cyclic conjugation than do zigzag edges in model nanoribbons. These results are consistent with the zigzag graphene edges being more prone to rapid oxidation when oxygen is present than armchair graphene edges. These results were obtained using Aihara's BRE and Bosanac and Gutman's CCE methods for measuring aromaticity of individual rings. New numerical results are given for three pairs of strongly subspectral series.     

Charge storage behavior of nanostructures based on SiGe nanocrystals embedded in Al<Subscript>2</Subscript>O<Subscript>3</Subscript> matrix

The charge storage behavior of nanostructures based on Si_1?x Ge _x (0 ≤ x ≤ 1) nanocrystals (NCs) in an Al₂O₃ matrix was investigated. The structures have been grown by RF magnetron sputtering and subsequently annealed at temperatures ranging from 700 °C to 1000 °C for 30 min in nitrogen ambient. The stoichiometry of the SiGe NCs and the alumina crystalline structure were found to be significantly dependent on the RF power and the annealing temperature. The sizes of the SiGe NCs and their distribution were investigated by grazing incidence small angle X-ray scattering (GISAXS). The capacitance-voltage (C-V) and conductance-voltage (G-V) measurements were performed to investigate the charge trapping characteristics of the memory structures. The C-V hysteresis width depends on variations in the crystalline structure resulting from different annealing temperatures. It is also shown that charge injection is governed by the Fowler-Nordheim tunnel mechanism for higher electric fields.     

Optimizing UPLC isocyanate determination through a Taguchi experimental design approach

The development of a chromatographic procedure for an ultra‐performance liquid chromatography can be a very time‐consuming task, as the general approach for finding the appropriate operating conditions has been a trial‐and‐error process. The present study reports a novel approach in the field of ultra‐performance liquid chromatography by using statistical experimental design based on Taguchi's method, which allows a complete separation of nine isocyanates present in a complex matrix. The resolution between two adjacent peaks was considered as a quality characteristic and transformed to a Taguchi signal‐to‐noise ratio. An orthogonal array L₉ (3⁴) was selected to analyze the effect of four chromatographic factors, that is, proportion of solvent, percent triethylamine (v/v), temperature (°C), and flow (mL min⁻¹), with three levels each. The joint analysis performed to the significant factors achieved in the eight analyses of variance allowed to identify two methods to conduct a complete separation of all peaks. Six isocyanates were separated with the first method, with all factors at the lowest level. The remaining three isocyanates were separated with the second method, with the proportion of solvent at the highest level and the other factors at the lowest level. The overall Taguchi experimental design identified the proportion of solvent and the flow rate as major chromatographic factors. Finally, confirmatory experiments were performed with samples prepared with six and three isocyanates, confirming the complete separation of all isocyanates in the study. The Taguchi methods provided a systematic and efficient methodology for this optimization, with considerably less effort than would be required for other optimizations techniques. Copyright © 2013 John Wiley & Sons, Ltd.     

Some existence results for conservation laws with source‐term

We prove some new results concerning the existence and asymptotic behaviour of entropy solutions of hyperbolic conservation laws containing non‐smooth source‐terms. Copyright © 2002 John Wiley & Sons, Ltd.     

Thermal Analyses of Diorganotin dl-Mandelates

The compounds [(LR₂Sn)₂O] {R=CH₃ (Me), n-C₄H₉(Bⁿ); L=C₆H₅CH(OH)COO⁻}were studied by thermogravimetric and differential scanning calorimetry in a dynamic atmosphere of helium. The thermal decomposition mechanisms are similar for both compounds and occur in two consecutive steps. The TG curves of the complexes suggest the liberation of the ligand L in the first step, with probable formation of a tin oxide R₂SnO intermediate. At the end of the second step free tin is obtained in accordance with the stoichiometry of the related compounds. An inverse relation betweenΔH _fusion and solubility of the compounds suggests a polymeric structure for the compound with Bⁿ ligand in relation to the compound with M ligand. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dealing with inconsistent judgments in multiple criteria sorting models

Sorting models consist in assigning alternatives evaluated on several criteria to ordered categories. To implement such models it is necessary to set the values of the preference parameters used in the model. Rather than fixing the values of these parameters directly, a usual approach is to infer these values from assignment examples provided by the decision maker (DM), i.e., alternatives for which (s)he specifies a required category. However, assignment examples provided by DMs can be inconsistent, i.e., may not match the sorting model. In such situations, it is necessary to support the DMs in the resolution of this inconsistency. In this paper, we extend algorithms from mous5ejor03 that calculate different ways to remove assignment examples so that the information can be represented in the sorting model. The extension concerns the possibility to relax (rather than to delete) assignment examples. These algorithms incorporate information about the confidence attached to each assignment example, hence providing inconsistency resolutions that the DMs are most likely to accept. Received: September 2004, Revised: June 2005 AMS classification: 90B50, 91B08, 90C05     

Genetic algorithms for the bus driver scheduling problem: a case study

This paper describes an application of genetic algorithms to the bus driver scheduling problem. The application of genetic algorithms extends the traditional approach of Set Covering/Set Partitioning formulations, allowing the simultaneous consideration of several complex criteria. The genetic algorithm is integrated in a DSS but can be used as a very interactive tool or a stand-alone application. It incorporates the user's knowledge in a quite natural way and produces solutions that are almost directly implemented by the transport companies in their operational planning processes. Computational results with airline and bus crew scheduling problems from real world companies are presented and discussed.