Symplectic integration of nonlinear Hamiltonian systems

There exist several standard numerical methods for integrating ordinary differential equations. However, if one is interested in integration of Hamiltonian systems, these methods can lead to wrong results. This is due to the fact that these methods do not explicitly preserve the so-called ‘symplectic condition’ (that needs to be satisfied for Hamiltonian systems) at every integration step. In this paper, we look at various methods for integration that preserve the symplectic condition.     

A study of the thermal properties of bamboo knitted fabrics

In this research, the thermal properties of bamboo single jersey knitted fabrics have been studied in relation to stitch length and yarn linear density in tex. The objective was to determine the influence of fabric factors like stitch length and the constituent yarn linear density on fabric properties, such as air permeability, thermal conductivity, thermal resistance and relative water vapour permeability. Yarns with linear densities of 19.6, 23.6, 29.5 tex and with the same twist level were used to construct the fabrics of single jersey structure with stitch lengths of 0.27, 0.29 and 0.31 cm. The anticipated increase in air permeability and relative water vapour permeability with decrease in yarn linear density and increase in stitch length was observed. The thermal conductivity and thermal resistance tended in general to increase with constituent yarn linear density but decreased with increase in stitch length.     

Maximal stable sets of two-player games

If a connected component of perfect equilibria of a two-player game contains a stable set as defined by Mertens, then the component is itself stable. Thus the stable sets maximal under inclusion are connected components of perfect equilibria. Received: October 1999/Revised: February 2001     

Invariant metric for nonlinear symplectic maps

In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree (≥3). The homogeneous polynomials specify a nonlinear symplectic map which in turn represents a Hamiltonian system. By minimizing the norm constructed out of this metric as a function of system parameters, we demonstrate that the performance of a nonlinear Hamiltonian system is enhanced.     

Spontaneous resolution through helical association of a Cu-azamacrocyclic complex with Lindqvist-type isopolyanion

Anionic metathesis reaction between the perchlorate salt of a copper-tetraazamacrocycle complex and the tetrabutylammonium salt of Lindqvist-type isopolyoxometalates in acetonitrile leads to the formation of two new inorganic-organic hybrid solids formulated as [Cu(L)(MeCN)][W(6)O(19)] (1) and [Cu(L)(MeCN)][Mo(6)O(19)] (2). Interestingly, both ion-pair complexes crystallize in a chiral space group P2(1)2(1)2(1). Crystallographic analysis of the obtained compounds reveals the occurrence of spontaneous resolution during crystallization. Both the enantiomorphs of compound 1 have been structurally characterized, whereas the resolution of compound 2 is rather poor.     

An incentive model for closed-loop supply chain under the EPR law

Motivated by the collection outsourcing phenomena under Extended Producer Responsibility (EPR), this paper studies a contract design problem for a manufacturer who consigns the used product collection to a collector, while the manufacturer only has incomplete information on the collector's cost. On the basis of the incentive theory, optimal contracts are developed to minimize the cost and satisfy the collection constraints prescribed by EPR. Properties of the contract parameters are derived, and issues such as information rent and information value are also explored. The impacts of EPR are analysed by comparing whether or not EPR law is implemented, and more managerial insights are further obtained through numerical examples.     

The impact of consumer returns policies on consignment contracts with inventory control

We consider a consignment contract with consumer non-defective returns behavior. In our model, an upstream vendor contracts with a downstream retailer. The vendor decides his consignment price charged to the retailer for each unit sold and his refund price for each returned item, and then the retailer sets her retail price for selling the product. The vendor gets paid based on net sold units and salvages unsold units as well as returned items in a secondary market. Under the framework, we study and compare two different consignment arrangements: the retailer/vendor manages consignment inventory (RMCI/VMCI) programs. To study the impact of return policy, we discuss a consignment contract without return policy as a benchmark. We show that whether or not the vendor offers a return policy, it is always beneficial for the channel to delegate the inventory decision to the vendor. We find that the vendor’s return policy depends crucially on the salvage value of returns. If the product has no salvage value, the vendor’s optimal decision is not to offer a return policy; otherwise, the vendor can gain more profit by offering a return policy when the salvage value turns out to be positive.