Optimizing reserves in school choice: A dynamic programming approach

We introduce a new model of school choice with reserves in which asocial planner is constrained by a limited supply of reserve seats and tries to find the matching that is optimal according to a social welfare function. We construct the optimal distribution of reserves via a quartic-time dynamic programming algorithm. Due to the modular nature of the algorithm, the resulting mechanism is strategy-proof for reserve-eligible students.     

Solving multiple facilities location problems with separated clusters

This paper examines a special case of multi-facility location problems where the set of demand points is partitioned into a given number of subsets or clusters that can be treated as smaller independent sub-problems once the number of facilities allocated to each cluster is determined. A dynamic programming approach is developed to determine the optimal allocation of facilities to clusters. The use of clusters is presented as a new idea for designing heuristics to solve general multi-facility location problems.     

Efectos torsionales en estructuras sobre suelo blando

In this work the torsional vibrations of structures on soft soil caused by the combined effects of structural asymmetry and base rotation are evaluated. A simplified soil-structure system with five degrees of freedom is analyzed. The foundation is considered to be embedded into a uniform layer resting on an elastic half-space, under the incidence of inclined SH waves. Instead of matching the maximum torsional moments due to the independent effects of structural asymmetry and base rotation, a new approach for computing the design eccentricity is applied. Specifically, torsional eccentricity coefficients compatible with the peak coupled lateral-torsional response are obtained, using an ensemble of narrow-band earthquake motions typical of soft-soil sites in Mexico City. It is shown that these coefficients are not constant along the principal axes, but they depend on the position of the resistant element. Hence, it is necessary to compute them without assuming a linear variation, as is done nowadays. The torsional eccentricity coefficients can significantly differ from the currently codified values, particularly for torsionally flexible structures for which both coefficients may be negative. This implies that the lateral displacement is reduced by the effects of torsion.     

Dynamic modelling and input-energy comparison for the elevator system

The elevator system driven by a permanent magnet synchronous motor (PMSM) is studied in this paper. The mathematical model of the elevator system includes the electrical and mechanical equations, and the dimensionless forms are derived for the purpose of practicable upward and downward movement. In this paper, the trapezoidal, cycloidal, five-degree (5-D) and seven-degree (7-D) polynomial and industry trajectories are designed and compared numerically in various motion and the absolute input energies. From numerical simulations, it is found that the trapezoidal trajectory consumes the minimum energy; the 7-D polynomial trajectory consumes the maximum one. The less end-point constraints are required, the less energy is consumed. Finally, the proposed sliding mode controller (SMC) is employed to demonstrate the robustness and well tracking control performance numerically.     

Dynamic modeling of copper flash smelting process at a Smelter in China

Due to the highly dynamic characteristic in copper smelting process at a Copper Smelter in China, it is difficult to maintain high performance level control. As a key process indicator to evaluate smelting performance, matte grade is in urgent need of being monitored online. Thus, a real-time dynamic model of predicting matte grade was developed and validated with data collected at an actual plant. Based on desulfurization ratio of copper concentrate, the model couples dynamic mass balances on each species with equilibrium relationships for major component (Cu, Fe, S, SiO₂, et al.) to form a system of differential and algebraic equations. The simulation results illustrate that the maximum relative error and average relative error of matte grade between measured values and predicted value of the model proposed is 3.3%, and the average relative error is 0.54%, which verify the effectiveness of the model developed in providing the guidance for controlling the copper flash smelting process.     

A class of dual fuzzy dynamic programs

In this paper we propose a large class of fuzzy dynamic programs. By use of the notion of dual binary relation we define a dual fuzzy dynamic program in the class. We establish two duality theorems between primal and dual fuzzy dynamic programs. One is for the two-parametric recursive equations. The other is for the nonparametric. We specify maximum–minimum process and minimum–minimum process in fuzzy environment and multiplicative–multiplicative process in quasi-stochastic environment. It is shown that the duality theorems hold between primal and dual programs.     

The generalized four-peg tower of hanoi problem

The generalized ρ-peg Tower of Hanoi problem with ρ  4 is considered in this paper. Denoting by M(n, p) the minimum number of (legal) moves required to transfer the tower of n( 1) discs from the pegP ₁, to the pegP _ρ, the dynamic programming formulation has heen employed to find the optimality equations and some local-value relationships satisfied hy M(n, p). These results are then exploited to solve the 4-peg Tower of Hanoi problem completely     

Finite-stage stochastic decision processes with recursive reward structure I: optimality equations and deterministic strategies

In this paper we examine an N-stage stochastic decision model with a recursive reward structure whose state and action spaces are standard Borel ones. The central results relate to the validity of the optimality equations and to the sufficiency of deterministic strategies. The results expand statements known for classical dynamic programming problems with additive total rewards to a wide class of recursive reward functions under certain monotonicity and continuity assumptions. The existence of an expected utility representation of the total rewards is generally not presupposed     

Modelling of off-road wheeled vehicles for real-time dynamic simulation

Simulation of wheel-ground and vehicle-ground interactions is very important in many applications. Achieving accuracy and efficiency is challenging for both soft and hard terrains. This is not only because of the simulation and numerical challenges, but also due to the questionable nature of the existing terrain models. For example, the most widely used terramechanics model is not a representative constitutive relation for a full range of dynamic conditions and applications, but rather a parametrization of steady state conditions. In general, the selection and development of the proper constitutive model and the parametrization of the ground properties are very challenging. Here, we present a unified framework for general wheel-ground interaction which can be used with different terramechanics models. The framework is based on a complementarity formulation and also uses the concept of kinematic constitutive relations, beside the other known concepts for modelling and parametrizing the soil properties. The framework makes it possible to consider the appropriate modelling of the terrain for a broad range of dynamic behaviours and simulation conditions. We will illustrate the material with several examples for off-road conditions.     

Advanced numerical analyses by the Non-Smooth Contact Dynamics method of an ancient masonry bell tower

Advanced numerical analyses were carried out in order to assess the nonlinear dynamical behaviour of the bell tower of Pomposa Abbey in Codigoro, in the province of Ferrara (Italy), by means of the Non-Smooth Contact Dynamics (NSCD) method. The main purpose of the work is to investigate the capacity of the main mechanical parameter used in the analyses, namely, the friction coefficient, to have effects on the mechanical response of ancient masonry structures undergoing seismic actions. Therefore, the tower was modelled following the discrete element method (DEM) and assembling the masonry texture as rigid bodies tied by frictional joints. Thus a discontinuous approach was used to assess the dynamic properties and the vulnerability of the masonry structure, through large deformations regulated by the Signorini's law, concerning the impenetrability between the rigid bodies; and by the Coulomb's law, regarding the dry-friction model. Afterward, different values were assigned to the friction coefficient of the models, and a variety of real seismic shocks have been applied in the nonlinear analyses. Finally, it is possible to see different failure mechanisms resulting for each friction value and types of dynamic actions used, as expected.