Optimal repair-cost limit for a consumer following expiry of a warranty

This paper develops a methodology for obtaining the optimalrepair-cost limit for the repair-replace decision that a consumerfaces on the expiry of a product warranty, where the producthas been minimally repaired on failure during the warranty.Three cases are considered; (i) an exponentially distributedtime to failure with an arbitrary repair-cost distribution,(ii) an exponentially distributed time to failure with a uniformrepair-cost distribution, and (iii) a Weibull-distributed timeto failure with a beta-distributed repair cost. Numerical optimizationsare performed for the third case, and conclusions drawn as tothe sensitivity of the optimal repair-cost limit on the parametervalues of the distributions involved.     

Crossover from BCS-superconductivity to Bose-condensation

Starting from a model of free Fermions in two dimensions with an arbitrary strong effective interaction, we derive a Ginzburg-Landau theory describing the crossover from BCS-superconductivity to Bose-condensation. We find a smooth crossover from the standard BCS-limit to a Gross-Pitaevski type equation for the order parameter in a Bose superfluid. The mean field transition temperature exhibits a maximum at a coupling strength, where the behaviour crosses over from BCS to Bose like with corresponding values of 2 Δ₀/T_c ≈ 5 which are characteristic for high T_c superconductors.     

Finite temperature infinitesimally deformed classical and quantum gravity

Deformed classical mechanics and gravity is discussed. Infinitesimally deformed quantum field theory is reviewed. Infinitesimally deformed Bose-Einstein distribution is derived. Infinitesimally deformed thermofield dynamics is constructed and applied to a scalar field and string theories.On leave of absence from: Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt     

The automatic conversion of spinor equations to dyad form in MAPLE

A new package in the symbolic algebra system MAPLE is presented for the conversion of complicated spinor equations to their expansions with respect to a normalized spinor dyad. By following a simple index convention, we obtain a powerful computational tool with a straightforward and easy to use syntax. A number of examples, including nontrivial applications of the package to recent research, are provided.     

Conditions for the onset of sliding in a plane system with friction

The problem of the plane motion of a rigid body along a fixed surface in the presence of dry (Coulomb) friction is considered. The constraint is assumed to be non-restraining. It is shown that the validity of a certain system of two inequalities of the same type guarantees that the surfaces maintain contact and that the body will continue to roll without sliding. These conditions are analysed in a few specific cases of mechanical systems.     

Observation of sharp resistance anomalies near Tc in granular superconductors

Granular films prepared from well-defined In clusters embedded in Kr (? 10-40 at % Kr) show sharp resistance anomalies very close to the superconducting transition temperature. The observed resistance peak(s), which go(es) above the normal state resistance R_N and which can be as high as ? 1.5 R_N, can be explained by a “mesoscopic” effect: Superconducting percolation aggregates of size ξ_ρ, larger than the superconducting coherence length ξ_S, but smaller than the quasiparticle relaxation length λ_Q*, have a superconducting gap, but are not yet able to carry a supercurrent.     

Rheology of a mixture of liquid-crystal polymers in solution

The rheological behavior of a mixture of two liquid-crystal polymers, hydroxypropyl cellulose and ethyl cellulose, in acetone solution is studied. The total polymer concentration in the solvent is held constant (40%) as the ratio of the two polymers is varied. The mixtures are anisotropic, isotropic, or biphasic (isotropic/anisotropic), depending on the concentration. Curves of viscosity vs shear rate for all the mixtures studied show three regions of viscosity, as described by Onogi and Asada for liquid-crystal polymers. The viscosity as a function of the weight ratio of the two polymers at constant shear rate exhibits deviations from additivity of viscosities of the two components at all concentrations. In mixtures of two polymers in the melt, deviations are also observed; the negative ones are attributed to phase separation and the positive ones to homogenous mixing (comparison with the phase diagram). All the mixtures studied (anisotropic, isotropic, or biphasic), show ranges of shear rates where the first normal-stress difference is negative, as is generally observed for anisotropic liquid-crystal polymers. It is concluded that the isotropic solutions become anisotropic under shear, as they are not far from the critical concentration. © 1994 John Wiley & Sons, Inc.     

Properties of polystyrene-poly(methylmethacrylate) random and diblock copolymers in dilute and semidilute solutions

Solution properties for random and diblock copolymers of polystyrene (PS) and poly(methyl methacrylate) (PMMA) have been measured by dynamic and total intensity light scattering in solvents of differing quality. The results are compared with the corresponding properties for PS and PMMA homopolymers of similar molecular weight, in order to determine if interactions between unlike monomers are significant. The hydrodynamic radius (R_h) and diffusion second virial coefficient (k_d) for the random copolymer are found to be larger than the corresponding values for the homopolymers in a solvent which is near-theta for the two homopolymers, whereas no such effect is observed for the block copolymer. This suggests that most intrachain interactions occur a relatively short distance along the chain backbone. In a mutual good solvent R_h and k_d of the random copolymer are comparable to the average of the values for the homopolymers, indicating that in a good solvent monomer/solvent interactions dominate over monomer/monomer interactions. For an isolated diblock copolymer in a mutual good solvent, there is no evidence that interactions between unlike monomers lead to additional expansion of the entire molecule, as measured by R_h, nor expansion of the individual blocks as probed by light scattering with one block optically masked. However, at low but finite concentration there is evidence (the coefficients of the binary interaction terms in the viscosity and the mutual diffusion coefficient, and the second and third virial coefficients) that a weak ordering effect may exist in block copolymer solutions, far from the conditions where microphase separation occurs. Finally, measurements of ternary polymer-polymer-solvent solutions show no dependence on monomer composition or monomer distribution for the tracer diffusion of probe PS-PMMA copolymers in a PMMA/toluene matrix. This indicate that the frictional interaction is largely unaffected by interactions between unlike monomers. However, there is evidence that the thermodynamic interaction is more unfavorable between a random copolymer and the homopolymer matrix than between a diblock and the matrix. © 1994 John Wiley & Sons, Inc.     

High-T c superconducting magnetic bearings for rotation-based devices

Summary A Modified-Melt-Powder-Melt-Growth (MMPMG) technique has been developed for the preparation of melt-textured Y-Ba−Cu−O pellets. To test their performances, the samples were characterized with respect to their microstructure, pinning strength and interaction force with permanent magnets. A superconducting magnetic bearing was built and integrated in a levitating flywheel system for energy storage. Paper presented at the “VII Congresso SATT?, Torino, 4–7 October 1994. Under a Fondazione Confalonieri grant.     

Neighborhood unions and the cycle cover number of a graph

For several years, the study of neighborhood unions of graphs has given rise to important structural consequences of graphs. In particular, neighborhood conditions that give rise to hamiltonian cycles have been considered in depth. In this paper we generalize these approaches to give a bound on the smallest number of cycles in G containing all the vertices of G. We show that if for all x, y ? V(G), |N(x) ∩ N(y)| ≧ 2n/5 + 1, then V(G) is coverable by at most two cycles. Several related results and extensions to t cycles are also given.