Properties of chains of prime ideals in an amalgamated algebra along an ideal

Let f:A→B be a ring homomorphism and let J be an ideal of B. In this paper, we study the amalgamation of A with B along J with respect to f (denoted by A?^fJ), a construction that provides a general frame for studying the amalgamated duplication of a ring along an ideal, introduced and studied by D’Anna and Fontana in 2007, and other classical constructions (such as the A+XB[X], the A+XB?X? and the D+M constructions). In particular, we completely describe the prime spectrum of the amalgamated duplication and we give bounds for its Krull dimension.     

Optimising a general repair kit problem with a service constraint

Field services are a particular type of after-sales service performed at the customer’s location where technicians repair malfunctioning machines. The inventory decisions about which spare part types to take to the repair site and in what quantities is called the repair kit problem. This problem is characterized by an order-based performance measure since a customer is only satisfied when all required spare parts are available to fix the machine. As a result, the service level in the decision making process is defined as a job fill rate. In this paper we derive a closed-form expression for the expected service level and total costs for the repair kit problem in a general setting, where multiple units of each part type can be used in a multi-period problem. Such an all-or-nothing strategy is a new characteristic to investigate, but commonly used in practice. Namely, items are only taken from the inventory when all items to perform the repair are available in the right quantity. We develop a new algorithm to determine the contents of the repair kit both for a service and cost model while incorporating this new expression for the job fill rate. We show that the algorithm finds solutions which differ on average 0.2% from optimal costs. We perform a case study to test the performance of the algorithm in practice. Our approach results in service level improvements of more than 30% against similar holding costs.     

The Shapley value for arbitrary families of coalitions

We address the problem of finding a suitable definition of a value similar to that of Shapley’s, when the games are defined on a subfamily of coalitions with no structure. We present two frameworks: one based on the familiar efficiency, linearity and null player axioms, and the other on linearity and the behavior on unanimity games. We give several properties and examples in each case, and give necessary and sufficient conditions on the family of coalitions for the approaches to coincide.     

On the Lebesgue constant for the Xu interpolation formula

In the paper [Y. Xu, Lagrange interpolation on Chebyshev points of two variables, J. Approx. Theory 87 (1996) 220–238], the author introduced a set of Chebyshev-like points for polynomial interpolation (by a certain subspace of polynomials) in the square [-1,1]², and derived a compact form of the corresponding Lagrange interpolation formula. In [L. Bos, M. Caliari, S. De Marchi, M. Vianello, A numerical study of the Xu polynomial interpolation formula in two variables, Computing 76(3–4) (2005) 311–324], we gave an efficient implementation of the Xu interpolation formula and we studied numerically its Lebesgue constant, giving evidence that it grows like , n being the degree. The aim of the present paper is to provide an analytic proof to show that the Lebesgue constant does have this order of growth.     

Experimental test of two-way quantum key distribution in the presence of controlled noise

We describe the experimental test of a quantum key distribution performed with a two-way protocol without using entanglement. An individual incoherent eavesdropping is simulated and induces a variable amount of noise on the communication channel. This allows a direct verification of the agreement between theory and practice.     

A Three-component Extension of the Camassa–Holm Hierarchy

We introduce a bi-Hamiltonian hierarchy on the loop-algebra of endowed with a suitable Poisson pair. It gives rise to the usual Camassa–Holm (CH) hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a three-component extension of the CH equation.     

Anisotropic multiplicative elastoplasticity for the prediction of earings in sheet forming

In this work, the simulation of earings in cup drawing by means of a recently developed anisotropic combined hardening material model is discussed. The model represents a multiplicative formulation of anisotropic elastoplasticity in the finite strain regime with nonlinear kinematic and isotropic hardening. Plastic anisotropy is described by the use of second-order structure tensors as additional arguments in the representation of the yield function and the plastic flow rule. The evolution equations are integrated by a form of the exponential map that preserves the plastic volume and the symmetry of the internal variables. Finite element simulations of cylindrical cup drawing processes are performed by means of ABAQUS/Standard where the discussed material model has been implemented into a user-defined reduced integration solid-shell element. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Remanent quantum correlations in dissipative qubits

Starting from the exact evolution of a Markovian dissipative quantum walk, a non-Markovian decoherence of two qubits interacting with a phonon thermal bath has been investigated analytically using quantum information tools. Concurrence and quantum discord are affected in a complex way, showing that entanglement decreases with dissipation. At the limit where dissipation dominates, quantum correlations survive in time as ∝t^−1/2$\propto t^{-1/2}$. Thus, even under the influence of dissipation, two qubits retain their quantumness for a long time. Quantum correlations could be therefore observed for a long time in related photonic experiments.