A symmetric quantum calculus

We introduce the $\alpha,\beta$-symmetric difference derivative and the $\alpha,\beta$-symmetric N\"orlund sum. The associated symmetric quantum calculus is developed, which can be seen as a generalization of the forward and backward $h$-calculus.Comment: Submitted 26/Sept/2011; accepted in revised form 28/Dec/2011; to Proceedings of International Conference on Differential & Difference Equations and Applications, in honour of Professor Ravi P. Agarwal, to be published by Springer in the series Proceedings in Mathematics (PROM

An application of a multicriteria model to assess the quality of local governance

This article presents a method to assess the quality of local governance practices. The multicriteria decision analysis modeling approach is illustrated through a real application (Portuguese municipalities). To define the criteria, performance descriptors, and reference levels in each dimension of local governance, and to account for the differences in preference of scoring in each criterion, the judgments of legitimate stakeholders were considered through decision conferencing. The constructed “Municipal Governance Indicator” is calculated for the case of Lisbon to show the outputs of the model and its potential usefulness

Internal relaxation time in immersed particulate materials

We study the dynamics of the solid to liquid transition for a model material made of elastic particles immersed in a viscous fluid. The interaction between particle surfaces includes their viscous lubrication, a sharp repulsion when they get closer than a tuned steric length and their elastic deflection induced by those two forces. We use Soft Dynamics to simulate the dynamics of this material when it experiences a step increase in the shear stress and a constant normal stress. We observe a long creep phase before a substantial flow eventually establishes. We find that the typical creep time relies on an internal relaxation process, namely the separation of two particles driven by the applied stress and resisted by the viscous friction. This mechanism should be relevant for granular pastes, living cells, emulsions and wet foams

Matrices in A(R,S) with minimum t-term ranks

Fundacao para a Ciencia e a Tecnologia through the projects UID/MAT/00297/2019 and UID/MAT/00212/2019.Let R and S be two sequences of nonnegative integers in nonincreasing order which have the same sum, and let A(R,S) be the class of all (0,1)-matrices which have row sums given by R and column sums given by S. For a positive integer t, the t-term rank of a (0,1)-matrix A is defined as the maximum number of 1's in A with at most one 1 in each column and at most t 1's in each row. In this paper, we address conditions for the existence of a matrix in A(R,S) that realizes all the minimum t-term ranks, for t≥1.authorsversionpublishe

Avaliacao de cultivares de milho: efeito da adubacao de plantio e da adubacao nitrogenada em cobertura.

Foi conduzido no Centro Nacional de Pesquisa de Milho e Sorgo, em Sete Lagoas, MG, um experimento de competicao de cultivares de milho, no qual estudou o comportamento da cultivar CMS 201 X, selecionada para cerrado, juntamente com as cultivares comerciais Ag 401 e C 111, em tres doses de adubacao no plantio: 250 kg/ha, 500 kg/ha e 750 kg/ha da formulacao basica 4-14-8 e tres niveis de adubacao nitrogenada: 200 kg/ha, 400 kg/ha e 600 kg/ha de sulfato de amonio em cobertura. Esse experimento foi conduzido nos anos agricolas de 1982/83 e 1983/84, utilizando um delineamento experimental de blocos casualizados, com parcelas subdivididas, em tres repeticoes. As adubacoes de plantio constituiram as parcelas e as interacoes de cultivar e adubacao de cobertura, as subparcelas. Os resultados obtidos demonstraram que houve efeito do ano agricola sobre a produtividade das cultivares, evidenciando que a distribuicao das chuvas influenciou o rendimento de graos no solo de cerrado. Com distribuicao regular de chuvas, a cultivar Ag 401 mostrou melhor comportamento que a CMS 201 X. Em 1982/1983, a resposta ao N em cobertura foi linear e ocorreu somente no ano de boa distribuicao de chuvas. Somente a cultivar C. 111 respondeu a adubacao de plantio, atraves de efeito quadratico da regressao que alcancou uma producao otima economica de 5.905 kg/ha de graos, com a utilizacao de NPK no plantio