bases were introduced in [Smy77] where they are called “R-structures”. Examples of abstract bases are concrete bases of continuous domains, of course, where the relation≺ is the restriction of the order of approximation. Axiom (INT) is satisfied because of Lemma 2.2.15 and because we have required bases in domains to have directed sets of approximants for each element. Other examples are partially ordered sets, where (INT) is satisfied because of reflexivity. We will shortly identify posets as being exactly the bases of compact elements of algebraic domains. In what follows we will use the terminology developed at the beginning of this chapter, even though the relation ≺ on an abstract basis need neither be reflexive nor antisymmetric. This is convenient but in some instances looks more innocent than it is. An idealA in a basis, for example, has the property (following from directedness) that for everyx ∈ A there is another element y ∈ A with x ≺ y. In posets this doesn’t mean anything but here it becomes an important feature. Sometimes this is stressed by using the expression ‘ A is a round ideal’. Note that a set of the form↓x is always an ideal because of (INT) but that it need not contain x itself. We will refrain from calling ↓x ‘principal’ in these circumstances. Definition 2.2.21. For a basis〈B,≺〉 let Idl(B) be the set of all ideals ordered by inclusion. It is called theideal completionof B. Furthermore, leti : B → Idl(B) denote the function which maps x ∈ B to ↓x. If we want to stress the relation with whichB is equipped then we write Idl(B,≺) for the ideal completion. Proposition 2.2.22.Let 〈B,≺〉 be an abstract basis.

Domain theory

A method and an apparatus to analyze two measured signals that are modeled as containing desired and undesired portions such as noise, FM and AM modulation. Coefficients relate the two signals according to a model defined in accordance with the present invention. In one embodiment, a transformation is used to evaluate a ratio of the two measured signals in order to find appropriate coefficients. The measured signals are then fed into a signal scrubber which uses the coefficients to remove the unwanted portions. The signal scrubbing is performed in either the time domain or in the frequency domain. The method and apparatus are particularly advantageous to blood oximetry and pulserate measurements. In another embodiment, an estimate of the pulserate is obtained by applying a set of rules to a spectral transform of the scrubbed signal. In another embodiment, an estimate of the pulserate is obtained by transforming the scrubbed signal from a first spectral domain into a second spectral domain. The pulserate is found by identifying the largest spectral peak in the second spectral domain.

Signal processing apparatus and method

Ordered magnetic nanostructures: fabrication and properties

The rapid development of electron tomography, in particular the introduction of novel tomographic imaging modes, has led to the visualization and analysis of three-dimensional structural and chemical information from materials at the nanometre level. In addition, the phase information revealed in electron holograms allows electrostatic and magnetic potentials to be mapped quantitatively with high spatial resolution and, when combined with tomography, in three dimensions. Here we present an overview of the techniques of electron tomography and electron holography and demonstrate their capabilities with the aid of case studies that span materials science and the interface between the physical sciences and the life sciences.

Electron tomography and holography in materials science

Light beams can be engineered to carry orbital angular momentum, with application as, for instance, optical 'spanners' — essentially a 'twisted' variant of the more familiar optical tweezers Here it is shown that it is, in principle, possible to engineer similar behaviour into an electron beam Such a beam could find use in a variety of spectroscopy and microscopy techniques

Generation of electron beams carrying orbital angular momentum

Ni-rich Ni-Fe and Ni evaporated polycrystalline films, the thickness of which is larger than a critical value, were found to be composed of stripe domains running parallel to the field previously applied to the films. B-H loops and magnetoresistance effect revealed that the magnetization in each domain points in one sense and deflects from the plane of the film upwards and downwards alternately. This type of domain structure is to be caused by the anisotropy whose easy axis is normal to the plane of the film, the origin of which is attributed to the magnetostrictive effect due to strains or defects in the film. The width of the domain increases with the thickness of the film, but does not depend sensitively on substrate temperatures and compositions. The critical thickness increases with an elevation of substrate temperatures and with decreasing Ni concentration. The stripe domain is no longer observable for the film containing Ni less than 80% where the magnetostriction constant is positive. The relation...

A New Type of Magnetic Domain Structure in Negative Magnetostriction Ni-Fe Films

In this experiment, an electron- and optical-holographic technique is employed with small toroidal ferromagnets each forming a magnetic-flux closure. The holographic interferometry proves that a phase difference between two electron beams having passed through the field-free regions agrees well with the fundamental relation known as the Aharonov-Bohm effect. It is also confirmed from the same hologram that flux leakage from the toroids does not affect the conclusion.

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Observation of Aharonov-Bohm effect by electron holography

The coercivity and permeability of Fe‐Si films can be improved by laminating several layers with either nonmagnetic (SiO2, Al2O3, Al or Mo) or ferromagnetic (Ni, Fe, Co or 20‐wt. % Fe–Ni) spacers. It is also found that films made with soft magnetic laminations have an advantage over nonmagnetic or hard magnetic ones. Such behavior is concluded to be attributed to the smaller grain size, and pinhole or exchange coupling of multilayered Fe‐Si films by observing domain and grain structures.

Magnetic properties of multilayered Fe‐Si films

A magneto-optical recording medium in which the inside of grooves formed along recording tracks is a signal recording area in groove recording, and the domain wall displacement detection method is employed; and a curvature radius R 1 , in the cross section perpendicular to the recording tracks, of a shoulder portion of a land separating the grooves that is adjacent to the groove is 30 nm or less and a curvature radius R 2 , in the cross section perpendicular to the recording tracks, of the inside edge portion of the groove for the recording that is adjacent to the land is 20 nm or more, so that a wide recording power margin can be obtained, the jitter can be improved, and the error rate can also be improved.

Hideo Fujiwara

Papers

A New Type of Magnetic Domain Structure in Negative Magnetostriction Ni-Fe Films

Observation of Aharonov-Bohm effect by electron holography

Magnetic properties of multilayered Fe‐Si films

Magneto-optical recording medium

A New Type of Magnetic Domain in Thin Ni-Fe Films