External Inversion, Internal Inversion, and Reflection Invariance

Having in mind that physical systems have different levels of structure we develop the concept of external, internal and total improper Lorentz transformation (space inversion and time reversal). A particle obtained from the ordinary one by the application of internal space inversion or time reversal is generally a different particle. From this point of view the intrinsic parity of a nuclear particle (`elementary particle') is in fact the external intrinsic parity, if we take into account the internal structure of a particle. We show that non-conservation of the external parity does not necessarily imply non-invariance of nature under space inversion. The conventional theory of beta-decay can be corrected by including the internal degrees of freedom to become invariant under total space inversion, though not under the external one.Comment: 15 pages. An early proposal of "mirror matter", published in 1974. This is an exact copy of the published paper. I am posting it here because of the increasing interest in the "exact parity models" and its experimental consequence

Inversion improves the recognition of facial expression in thatcherized images

The Thatcher illusion provides a compelling example of the face inversion effect. However, the marked effect of inversion in the Thatcher illusion contrasts to other studies that report only a small effect of inversion on the recognition of facial expressions. To address this discrepancy, we compared the effects of inversion and thatcherization on the recognition of facial expressions. We found that inversion of normal faces caused only a small reduction in the recognition of facial expressions. In contrast, local inversion of facial features in upright thatcherized faces resulted in a much larger reduction in the recognition of facial expressions. Paradoxically, inversion of thatcherized faces caused a relative increase in the recognition of facial expressions. Together, these results suggest that different processes explain the effects of inversion on the recognition of facial expressions and on the perception of the Thatcher illusion. The grotesque perception of thatcherized images is based on a more orientation-sensitive representation of the face. In contrast, the recognition of facial expression is dependent on a more orientation-insensitive representation. A similar pattern of results was evident when only the mouth or eye region was visible. These findings demonstrate that a key component of the Thatcher illusion is to be found in orientation-specific encoding of the features of the face

Negative inversion, negative concord and sentential negation in the history of English

It is claimed in van Kemenade (2000: 62) that clauses with initial negative constituents are a context in which subject–verb inversion occurs throughout the history of English. However, different patterns of negative inversion are seen at different periods of English. I argue that changes in the availability of negative inversion reflect changes in the way sentential scope for negation is marked in negative concord constructions. Thus, negative concord involving Middle and Early Modern English not does not co-occur with negative inversion, but negative concord involving Middle English ne does. Changes to negative inversion can be seen to parallel changes in the way sentential scope negation is expressed at successive stages of the Middle English Jespersen Cycle. I propose that the changes to negative inversion and Jespersen's Cycle should both be analysed as changes in the ability of negative items to mark sentential scope for negation. This observation can be formalised within a Minimalist framework as variation in the LF-interpretability of negative features, following the account of Jespersen's Cycle proposed by Wallage (2008)

Inversion of Parahermitian matrices

Parahermitian matrices arise in broadband multiple-input multiple-output (MIMO) systems or array processing, and require inversion in some instances. In this paper, we apply a polynomial eigenvalue decomposition obtained by the sequential best rotation algorithm to decompose a parahermitian matrix into a product of two paraunitary, i.e.lossless and easily invertible matrices, and a diagonal polynomial matrix. The inversion of the overall parahermitian matrix therefore reduces to the inversion of auto-correlation sequences in this diagonal matrix. We investigate a number of different approaches to obtain this inversion, and and assessment of the numerical stability and complexity of the inversion process

Seismic Ray Impedance Inversion

This thesis investigates a prestack seismic inversion scheme implemented in the ray parameter domain. Conventionally, most prestack seismic inversion methods are performed in the incidence angle domain. However, inversion using the concept of ray impedance, as it honours ray path variation following the elastic parameter variation according to Snell’s law, shows the capacity to discriminate different lithologies if compared to conventional elastic impedance inversion. The procedure starts with data transformation into the ray-parameter domain and then implements the ray impedance inversion along constant ray-parameter profiles. With different constant-ray-parameter profiles, mixed-phase wavelets are initially estimated based on the high-order statistics of the data and further refined after a proper well-to-seismic tie. With the estimated wavelets ready, a Cauchy inversion method is used to invert for seismic reflectivity sequences, aiming at recovering seismic reflectivity sequences for blocky impedance inversion. The impedance inversion from reflectivity sequences adopts a standard generalised linear inversion scheme, whose results are utilised to identify rock properties and facilitate quantitative interpretation. It has also been demonstrated that we can further invert elastic parameters from ray impedance values, without eliminating an extra density term or introducing a Gardner’s relation to absorb this term. Ray impedance inversion is extended to P-S converted waves by introducing the definition of converted-wave ray impedance. This quantity shows some advantages in connecting prestack converted wave data with well logs, if compared with the shearwave elastic impedance derived from the Aki and Richards approximation to the Zoeppritz equations. An analysis of P-P and P-S wave data under the framework of ray impedance is conducted through a real multicomponent dataset, which can reduce the uncertainty in lithology identification.Inversion is the key method in generating those examples throughout the entire thesis as we believe it can render robust solutions to geophysical problems. Apart from the reflectivity sequence, ray impedance and elastic parameter inversion mentioned above, inversion methods are also adopted in transforming the prestack data from the offset domain to the ray-parameter domain, mixed-phase wavelet estimation, as well as the registration of P-P and P-S waves for the joint analysis. The ray impedance inversion methods are successfully applied to different types of datasets. In each individual step to achieving the ray impedance inversion, advantages, disadvantages as well as limitations of the algorithms adopted are detailed. As a conclusion, the ray impedance related analyses demonstrated in this thesis are highly competent compared with the classical elastic impedance methods and the author would like to recommend it for a wider application