Thermomagnetic hysteresis and electrical transport in amorphous films

We report resistivity and magnetization measurements on an amorphous Ni₇₄Mn₂₄Pt₂ thin film in the temperature range of 3–300 K. Two significant features are apparent in both the magnetic susceptibility and electrical resistivity. A low-temperature (low-T) anomaly is observed at about 40 K, where a cusp appears in the resistivity, while a concomitant step-like increase in zero-field-cooled (ZFC) magnetization (M) appears with increasing temperature. The low-T anomaly is attributed to a crossover from a pure re-entrant spin-glass within individual domains to a mixed ferro-spin-glass regime at lower temperatures. By contrast, the high-temperature (high-T) anomaly, signaled by the appearance of hysteresis below 250 K, corresponds to the freezing of transverse spins in individual domains acting independently. Between the low-T and high-T anomalies a small but discernable magnetic hysteresis is observed for warming vs. cooling in the field-cooled (FC) case. This behavior clearly indicates the presence of domain structure in the sample, while the disappearance of this hysteresis at lower temperatures indicates the complete freezing of the spin orientation of these domains. According to these results, we have divided the magnetic state of this sample into three regions: at temperatures above 250 K, the sample behaves like a soft ferromagnet, exhibiting M vs. H loops with very small hysteresis (less than 5 Oe). As the temperature is lowered into the intermediate region (the range 40–250 K), spins become frozen randomly and progressively within the individual domains. These domains behave independently, rather than as a cooperative behavior of the sample. Weak irreversibility sets in, indicating the onset of transverse spin freezing within the domains. At temperatures below 40 K, the M vs. H loops exhibit larger hysteresis, for both the ZFC and FC cases, as in a pure spin-glass. We have also demonstrated giant noise in the resistivity at temperatures just below 250 K. Such noise can originate from fluctuations of the domains near the film surface because of competing effective bulk and surface anisotropy fields. The large observed amplitude may be explained by means of a large ferromagnetic anisotropy in the resistivity due to the large spin–orbit effect seen in NiMn systems. Finally, the low-T peak in the resistivity has been analyzed using Fisher and Langer's expression based on the Friedel Model proposed for critical transitions in transition metals (s–d systems). The fitted results are in satisfactory agreement with the predictions of this model.     

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