Models for capacitated lot-sizing problem with backlogging,setup carryover and crossover

Setup operations are significant in some production environments. It is mandatory that their production plans consider some features, as setup state conservation across periods through setup carryover and crossover. The modelling of setup crossover allows more flexible decisions and is essential for problems with long setup times. This paper proposes two models for the capacitated lot-sizing problem with backlogging and setup carryover and crossover. The first is in line with other models from the literature, whereas the second considers a disaggregated setup variable, which tracks the starting and completion times of the setup operation. This innovative approach permits a more compact formulation. Computational results show that the proposed models have outperformed other state-of-the-art formulation.     

Stability and convergence of the spectral Lagrange-Galerkin method for mixed periodic/non-periodic convection-dominated diffusion problems

We present a convergence analysis of the spectral Lagrange-Galerkinmethod for mixed periodic/non-periodic convection-diffusionproblems. The scheme is unconditionally stable, independentof the diffusion coefficient, even in the case when numericalquadrature is used. The theoretical predictions are illustratedby a series of numerical experiments. For the periodic case,our results present a significant improvement on those givenby Süli & Ware (1991) SIAM J. Numer.Anal.28, 423-445).     

Elementary-particle treatment of the radiative muon capture in 12C

We consider radiative muon capture to a definite nuclear final state. The example chosen is the ${}^{12}\text{C}\text{(0}{}^{\mathrm{+}}\text{T = 0)(μ}{}^{\mathrm{?}}\text{, γν)}{}^{12}\text{B}\text{(1}{}^{\mathrm{+}}\text{T = 1)}$ transition. The elementary particle treatment adopted in this work discloses several aspects of the reaction mechanism, which remain hidden in the usual impulse approximation calculations. In particular, one sees a considerable enhancement of the capture rate when the q² dependence of the weak form factors F_A(q²) and F_P(q²) is taken into account. The branching ratio of the radiative capture in the region sensitive to the possibly non-zero mass m_νμ of the muon-neutrino is estimated to be ≈1.36 × 10^?10.     

Coupled channel method for the π-4He elastic and inelastic scattering

Equations of the coupled channel method written in the momentum space are solved in the K-matrix approach. In this way we are able to consider simultaneously the elastic and inelastic pion-nuclear reactions. Calculated total elastic and total inelastic cross sections are given for several outgoing channels of the reaction⁴He(π ^?,π ^?)⁴He^*. The single-charge-exchange reaction on⁴He is discussed.     

Giant M2 and transversal E1 resonances in light nuclei

The cross section for inelastic backward electron scattering on 1p shell nuclei at incident energy E_e = 70 MeV is calculated in the shell model. Comparison is made with radiative pion capture and muon capture. It is shown that the T_> branch of the M2 resonance in (e, e') and the main maxima in the (π^?, γ) response function are formed by identical partial transitions. We consider the basic features of the M2 resonance excitation in 1p shell nuclei and predict configurational and isospin splitting of this mode.     

Rapid photometric determination of phosphorus in iron ores and related materials as phosphomolybdenum-blue

A rapid, simple and accurate method for determining phosphorus photometrically in iron ores and related materials, obviating the use of perchloric acid, is described. The sample is fused with sodium peroxide in a zirconium crucible and the melt dissolved in hydrochloric acid. The molybdenum-blue complex is developed by the addition of ammonium molybdate and hydrazine sulphate and the absorbance is measured at 725 nm. The range of the method is from 0.005 to 1.0% P. A batch of 6 samples can be analysed in about 2 hr.