Effect of the dispersibility of ZrO2 nanoparticles in Ni-ZrO2 electroplated nanocomposite coatings on the mechanical properties of nanocomposite coatings

ZrO₂ nanoparticles was uniformly co-deposited into a nickel matrix by electroplating of nickel from a Watts bath containing particles in suspension which were monodispersed with dispersant under DC electrodeposition condition. It was found that morphology, orientation and hardness of the nanocomposite coatings with monodispersed ZrO₂ nanoparticles had lots of difference from the nanocomposite coatings with agglomerated ZrO₂ nanoparticles and pure nickel coatings. Especially, the result of hardness showed that only a very low volume percent (less than 1 wt.%) of monodispered ZrO₂ nanoparticles in Ni-ZrO₂ nanocomposite coatings would result in higher hardness of the coatings. The hardness of Ni-ZrO₂ nanocomposite coatings with monodispersed and agglomerated ZrO₂ nanoparticles were 529 and 393 HV, respectively. The hardness value of the former composite coatings was over 1.3 times higher than that of the later. All these composite coatings were two-three times higher than that of pure nickel plating (207 HV) prepared under the same condition. The strengthening mechanisms of the Ni-ZrO₂ nanocomposite coatings based on a combination of grain refinement strengthening from nickel matrix grain refining and dispersion strengthening from dispersion state of ZrO₂ nanoparticles in the coatings.     

Products of residue currents of Cauchy–Fantappiè–Leray type

With a given holomorphic section of a Hermitian vector bundle, one can associate a residue current by means of Cauchy–Fantappiè–Leray type formulas. In this paper we define products of such residue currents. We prove that, in the case of a complete intersection, the product of the residue currents of a tuple of sections coincides with the residue current of the direct sum of the sections.     

An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings

In this paper,we will establish several strong convergence theorems for the approximation ofcommon fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banachspaces using the modiied implicit iteration sequence with errors,and prove the necessary and sufficient conditionsfor the convergence of the sequence.Our results generalize,extend and improve the recent work,in thistopic.     

A Penrose-like inequality for maximal asymptotically flat spin initial data sets

We prove a Penrose-like inequality for the mass of a large class of constant mean curvature (CMC) asymptotically flat n-dimensional spin manifolds which satisfy the dominant energy condition and have a future converging, or past converging compact and connected boundary of non-positive mean curvature and of positive Yamabe invariant. We prove that for every n ≥ 3 the mass is bounded from below by an expression involving the norm of the linear momentum, the volume of the boundary, dimensionless geometric constants and some normalized Sobolev ratio.     

Dynamic programming in cricket: optimizing batting order for a sticky wicket

In cricket, a rain-affected pitch can make batting more difficult than normal. Several other conditions such as poor light or an initially lively pitch, may also result in difficulties for the batsmen. In this note, we refer to all of them as ‘sticky wickets’. On sticky wickets, lower order batsmen are often sent into ‘hold the fort’ until conditions improve. In this paper, a stochastic dynamic programming model is used to examine the appropriateness of this policy. The model suggests that the tactic is often optimal when the sticky wicket persists until the end of the day's play, but not often when the sticky wicket is transitory. In some circumstances, it is worthwhile, on a normal wicket near the end of the day, to send in a lower order batsman to hold the fort (a night watchman): when the wicket is sticky, this tactic is even more worthwhile.     

Characteristics of transmission of electrons in a quantum wire tangentially attached to a superconductor ring threaded by magnetic flux

We present numerical investigations of the transmission properties of electrons in a normal quantum wire tangentially attached to a superconductor ring threaded by magnetic flux. A point scatterer with a δ -function potential is placed at node to model scattering effect. We find that the transmission characteristics of electrons in this structure strongly depend on the normal or superconducting state of the ring. The transmission probability as a function of the energy of incident electrons, in the case of a superconductor ring threaded by one quantum magnetic flux, emerges one deep dip, imposed upon the first broad bump in spectrum. This intrinsic conductance dip originates from the superconductor state of the ring. When increasing the magnetic flux from one quantum magnetic flux to two, the spectrum shifts toward higher energy region in the whole. This conductance dip accordingly shifts and appears in the second bump. In the presence of a point-scatterer at the node, the spectrum is substantially modified. Based on the condition of the formation of the standing wave functions in the ring and the broken of the time-reserve symmetry of Schr?dinger equation after switching magnetic flux, the characteristics of transmission of electrons in this structure can be well understood. Received 6 November 2001