Search results for " formulation"
showing 10 items of 221 documents
Formulations and valid inequalities for the capacitated dispersion problem
2023
This work focuses on the capacitated dispersion problem for which we study several mathematical formulations in different spaces using variables associated with nodes, edges, and costs. The relationships among the presented formulations are investigated by comparing the projections of the feasible sets of the LP relaxations onto the subspace of natural variables. These formulations are then strengthened with families of valid inequalities and variable-fixing procedures. The separation problems associated with the valid inequalities that are exponential in number are shown to be polynomially solvable by reducing them to longest path problems in acyclic graphs. The dual bounds obtained from s…
The Mathematicians’ Happy Hunting Ground: Einstein’s General Theory of Relativity
2004
There is hardly any doubt that for physics special relativity theory is of much greater consequence than the general theory. The reverse situation prevails with respect to mathematics: there special relativity theory had comparatively little, general relativity theory very considerable, influence, above all upon the development of a general scheme for differential geometry. —Hermann Weyl, “Relativity as a Stimulus to Mathematical Research,” pp. 536–537.
Seeing reality through Einstein's eyes: a teaching proposal for special relativity
2021
The teaching of Special Relativity is still a critical issue not only for students but also for teachers. In this paper, we describe the trial of a learning unit on the Special Relativity topic based on Minkowski's approach through spacetime diagrams, following the results in pedagogical researches in this field. The main innovation of our project consists of a mechanical instrument: it allows to physically and mechanically represent Lorentz’s transformations by hands, exploring the effects of a change of the reference frame. Teachers and students can deal “by eye” with unusual phenomena as the loss of simultaneity, time dilation, length contraction, relativistic addition of velocities and …
Thermoconvective instability and local thermal non-equilibrium in a porous layer with isoflux-isothermal boundary conditions
2014
The effects of lack of local thermal equilibrium between the solid phase and the fluid phase are taken into account for the convective stability analysis of a horizontal porous layer. The layer is bounded by a pair of plane parallel walls which are impermeable and such that the lower wall is subject to a uniform flux heating, while the upper wall is isothermal. The local thermal non-equilibrium is modelled through a two-temperature formulation of the energy exchange between the phases, resulting in a pair of local energy balance equations: one for each phase. Small-amplitude disturbances of the basic rest state are envisaged to test the stability. Then, the standard normal mode procedure is…
Qualità della didattica universitaria e sviluppo della capacità decisionale. Il modello ADVP per garantire i passaggi da L-19 a LM-85bis.
2020
Il presente contributo intende offrire una riflessione sulle competenze attese individuate attraverso la formulazione dei descrittori di Dublino dei CdS in Scienze dell’Educazione (L-19) e Scienze della Formazione Primaria (LM-85bis) istituiti presso l’Ateneo di Palermo e nello stesso tempo proporre un modello per lo sviluppo della maturità professional e necessaria a garantire scelte consapevoli, mature e responsabili. L’analisi condotta ci ha permesso, in una seconda fase di individuare gli obiettivi formativi finali scelti seguendo il modello proposto dalle Linee Guida dell ’Anvur, e di scegliere il modello dell’Activaction du Developpement Vocationnel et Personnel quale strumento per lo…
Finite element method for a nonlocal Timoshenko beam model
2014
A finite element method is presented for a nonlocal Timoshenko beam model recently proposed by the authors. The model relies on the key idea that nonlocal effects consist of long-range volume forces and moments exchanged by non-adjacent beam segments, which contribute to the equilibrium of a beam segment along with the classical local stress resultants. The long-range volume forces/moments are linearly depending on the product of the volumes of the interacting beam segments, and their relative motion measured in terms of the pure beam deformation modes, through appropriate attenuation functions governing the spatial decay of nonlocal effects. In this paper, the beam model is reformulated wi…
FIA-fluorimetric determination of thiamine.
1990
A flow injection-fluorimetric determination of thiamine is reported. The procedure is based on the oxidation of the analyte with potassium hexacyanoferrate(III) immobilized on an anionic exchange resin; the fluorescence is monitored in aqueous basic solution. Concentrations of the vitamin of 0.1-4 ppm have been determined; the relative standard deviation was 1.8%. The injection rate was 28 samples/h. The influence of other substances and the determination of the drug in a pharmaceutical formulation are also reported.
Effect of different dispersing additives on the morphology and the properties of polyethylene-based nanocomposite films
2011
In this work, the use of a polar wax, e.g. amphiphilic Tegomer ® E 525 (TEG) is investigated with the aim of mod- ifying, and possibly improving, the dispersion of an organically modified nanoclay (OMMT), loaded at 5 wt%, in a poly- ethylene matrix (PE) at relatively low loading levels. We have indeed found that the incorporation of low loadings, e.g. 0.5 wt%, of TEG, an amphiphilic block co-polymer, into a PE/OMMT sample results in a substantial improvement of the clay dispersion in the nanocomposite and, consequently, of the mechanical and thermomechanical properties of the films. The achieved results are comparable to those obtained for systems containing traditional dispersing agents su…
A branch-and-cut algorithm for the Team Orienteering Problem
2017
The Team Orienteering Problem aims at maximizing the total amount of profit collected by a fleet of vehicles while not exceeding a predefined travel time limit on each vehicle. In the last years, several exact methods based on different mathematical formulations were proposed. In this paper, we present a new two-index formulation with a polynomial number of variables and constraints. This compact formulation, reinforced by connectivity constraints, was solved by means of a branch-and-cut algorithm. The total number of instances solved to optimality is 327 of 387 benchmark instances, 26 more than any previous method. Moreover, 24 not previously solved instances were closed to optimality.