Propertime Quantum Mechanics for Confined Multi-Quark System and Covariant Hadron-Classification Scheme[1]

The general features of the degeneracy structure of (p = 2) parasupersymmetric quantum mechanics are employed to yield a classification scheme for the form of the parasupersymmetric Hamiltonians. The method is applied to parasupersymmetric systems whose Hamiltonian is the square root of a fourth order polynomial in the generators of the parasupersymmetry. These systems are interesting to study for they lead to the introduction of a set of topological invariants very similar to the Witten indices of ordinary supersymmetric quantum mechanics. The topological invariants associated with parasupersymmetry are shown to be related to a pair of Fredholm operators satisfying two compatibility conditions. An explicit algebraic expression for the topological invariants of a class of parasupersymmetric systems is provided.

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Statistical analysis of classification

Symposium - International Astronomical Union ◽

10.1017/s0074180900053420 ◽

1966 ◽

Vol 24 ◽

pp. 188-189

Author(s):

T. J. Deeming

Keyword(s):

Multivariate Analysis ◽

Statistical Analysis ◽

Classification Scheme ◽

Analytical Procedure ◽

Narrow Band ◽

Scientific Research ◽

Maximum Amount ◽

Amount Of Information

If we make a set of measurements, such as narrow-band or multicolour photo-electric measurements, which are designed to improve a scheme of classification, and in particular if they are designed to extend the number of dimensions of classification, i.e. the number of classification parameters, then some important problems of analytical procedure arise. First, it is important not to reproduce the errors of the classification scheme which we are trying to improve. Second, when trying to extend the number of dimensions of classification we have little or nothing with which to test the validity of the new parameters.Problems similar to these have occurred in other areas of scientific research (notably psychology and education) and the branch of Statistics called Multivariate Analysis has been developed to deal with them. The techniques of this subject are largely unknown to astronomers, but, if carefully applied, they should at the very least ensure that the astronomer gets the maximum amount of information out of his data and does not waste his time looking for information which is not there. More optimistically, these techniques are potentially capable of indicating the number of classification parameters necessary and giving specific formulas for computing them, as well as pinpointing those particular measurements which are most crucial for determining the classification parameters.

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Introductory paper

Symposium - International Astronomical Union ◽

10.1017/s0074180900053031 ◽

1966 ◽

Vol 24 ◽

pp. 3-5

Author(s):

W. W. Morgan

Keyword(s):

Line Intensity ◽

Classification Scheme ◽

Two Dimensional ◽

Spectral Classification ◽

Dimensional Array ◽

Rr Lyrae ◽

Metallic Line ◽

Introductory Paper ◽

Parameter Varying ◽

Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

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A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

International Astronomical Union Colloquium ◽

10.1017/s025292110010805x ◽

1988 ◽

Vol 102 ◽

pp. 343-347

Author(s):

M. Klapisch

Keyword(s):

Perturbation Theory ◽

Small Parameter ◽

Classification Scheme ◽

Sum Rules ◽

Energy Levels ◽

Natural Classification ◽

Quantum Numbers ◽

Formal Expansion ◽

Atomic Energy Levels ◽

As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

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The value of Electron Microscope studies of imperfect natural diamonds

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100174102 ◽

1990 ◽

Vol 48 (4) ◽

pp. 194-195

Author(s):

J C Walmsley ◽

A R Lang

Keyword(s):

Electron Microscope ◽

Classification Scheme ◽

Natural Diamond ◽

Sudden Change ◽

Growth Conditions ◽

Diamond Growth ◽

Major Constituent ◽

Natural Diamonds ◽

Type Ia ◽

Platelet Defects

Interest in the defects and impurities in natural diamond, which are found in even the most perfect stone, is driven by the fact that diamond growth occurs at a depth of over 120Km. They display characteristics associated with their origin and their journey through the mantle to the surface of the Earth. An optical classification scheme for diamond exists based largely on the presence and segregation of nitrogen. For example type Ia, which includes 98% of all natural diamonds, contain nitrogen aggregated into small non-paramagnetic clusters and usually contain sub-micrometre platelet defects on {100} planes. Numerous transmission electron microscope (TEM) studies of these platelets and associated features have been made e.g. . Some diamonds, however, contain imperfections and impurities that place them outside this main classification scheme. Two such types are described.First, coated-diamonds which possess gem quality cores enclosed by a rind that is rich in submicrometre sized mineral inclusions. The transition from core to coat is quite sharp indicating a sudden change in growth conditions, Figure 1. As part of a TEM study of the inclusions apatite has been identified as a major constituent of the impurity present in many inclusion cavities, Figure 2.

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