Non-linear representations of inhomogeneous groups

1978 ◽  
Vol 2 (6) ◽  
pp. 499-504 ◽  
Author(s):  
Georges Pinczon ◽  
Jacques Simon
Keyword(s):  
Linear Representations ◽  
Non Linear

scholarly journals Non-linear representations of extended supersymmetry with central charges

1983 ◽  
Vol 19 (3) ◽  
pp. 267-273 ◽  
Author(s):  
S. Ferrara ◽  
L. Maiani ◽  
P. C. West
Keyword(s):  
Extended Supersymmetry ◽  
Linear Representations ◽  
Non Linear

The analysis of Westphalian German Spirantization

Diachronica ◽  
2014 ◽  
Vol 31 (2) ◽  
pp. 223-266 ◽  
Author(s):  
T. Alan Hall
Keyword(s):  
Present Article ◽  
Short Vowel ◽  
Linear Representations ◽  
Crucial Component ◽  
Non Linear ◽  
New Treatment

Westphalian German Spirantization refers to the change from an original prevocalic long vowel to the corresponding short vowel plus fricative (i.e. [ɣ]). For example, the [ɪɣ] sequence in the Westphalian word [klɪɣə] “bran” derived historically from [iː]. The present article offers a new treatment for the historical shift from [iː] to [ɪɣ] — as well as similar ones involving other vowels — which breaks the process down into five separate changes. It is argued that each of these changes modified non-linear representations involving syllables, moras and segmental features. A crucial component of the proposed analysis is that each of the five changes is seen as a repair to a constraint.

scholarly journals Reflected ray retrieval from radio occultation data using radio holographic filtering of wave fields in ray space

2017 ◽  
Author(s):  
Michael E. Gorbunov ◽  
Estel Cardellach ◽  
Kent B. Lauritsen
Keyword(s):  
Radio Occultation ◽  
Wigner Distribution ◽  
Fourier Integral ◽  
Automatic Identification ◽  
Fourier Integral Operators ◽  
Reflection Index ◽  
Wave Fields ◽  
Linear Representations ◽  
Non Linear ◽  
Occultation Data

Abstract. Linear and non-linear representations of wave fields constitute the basis of modern algorithms for analysis of radio occultation (RO) data. Linear representations are implemented by Fourier Integral Operators, which allow for high-resolution retrieval of bending angles. Non-linear representations include Wigner Distribution Function (WDF), which equal the pseudo-density of energy in the ray space. Representations allow for filtering wave fields by suppressing some areas of the ray space and mapping the field back from the transformed space to the initial one. We apply this technique to the retrieval of reflected rays from RO observations. The use of reflected rays may increase the accuracy of the retrieval of the atmospheric refractivity. Reflected rays can be identified by the visual inspection of WDF or spectrogram plots. Numerous examples from COSMIC data indicate that reflections are mostly observed over oceans or snow, in particular, over Antarctica. We introduce the reflection index that characterizes the relative intensity of the reflected ray with respect to the direct ray. The index allows for the automatic identification of events with reflections. We use the radio holographic estimate of the errors of the retrieved bending angle profiles of reflected rays. A comparison of indices evaluated for a large base of events including the visual identification of reflections indicated a good agreement.

scholarly journals Non linear representations of Lie groups

1977 ◽  
Vol 10 (3) ◽  
pp. 405-418 ◽  
Author(s):  
Moshé Flato ◽  
Georges Pinczon ◽  
Jacques Simon
Keyword(s):  
Lie Groups ◽  
Linear Representations ◽  
Non Linear ◽  
Representations Of Lie Groups

scholarly journals Reflected ray retrieval from radio occultation data using radio holographic filtering of wave fields in ray space

2018 ◽  
Vol 11 (2) ◽  
pp. 1181-1191 ◽  
Author(s):  
Michael E. Gorbunov ◽  
Estel Cardellach ◽  
Kent B. Lauritsen
Keyword(s):  
Radio Occultation ◽  
Wigner Distribution ◽  
Fourier Integral ◽  
Automatic Identification ◽  
Fourier Integral Operators ◽  
Reflection Index ◽  
Wave Fields ◽  
Linear Representations ◽  
Non Linear ◽  
Occultation Data

Abstract. Linear and non-linear representations of wave fields constitute the basis of modern algorithms for analysis of radio occultation (RO) data. Linear representations are implemented by Fourier Integral Operators, which allow for high-resolution retrieval of bending angles. Non-linear representations include Wigner Distribution Function (WDF), which equals the pseudo-density of energy in the ray space. Representations allow for filtering wave fields by suppressing some areas of the ray space and mapping the field back from the transformed space to the initial one. We apply this technique to the retrieval of reflected rays from RO observations. The use of reflected rays may increase the accuracy of the retrieval of the atmospheric refractivity. Reflected rays can be identified by the visual inspection of WDF or spectrogram plots. Numerous examples from COSMIC data indicate that reflections are mostly observed over oceans or snow, in particular over Antarctica. We introduce the reflection index that characterizes the relative intensity of the reflected ray with respect to the direct ray. The index allows for the automatic identification of events with reflections. We use the radio holographic estimate of the errors of the retrieved bending angle profiles of reflected rays. A comparison of indices evaluated for a large base of events including the visual identification of reflections indicated a good agreement with our definition of reflection index.

scholarly journals Non-linear representations of the conformal group and mapping of galileons

2013 ◽  
Vol 2013 (10) ◽  
Author(s):  
Paolo Creminelli ◽  
Marco Serone ◽  
Enrico Trincherini
Keyword(s):  
Conformal Group ◽  
Linear Representations ◽  
Non Linear

scholarly journals The status of extrasyllabic consonants in English and German

2001 ◽  
Vol 21 ◽  
pp. 89-117
Author(s):  
Tracy Alan Hall
Keyword(s):  
Present Article ◽  
Linear Representations ◽  
Non Linear ◽  
The Status

Since the advent of nonlinear phonology many linguists have either assumed or argued explicitly that many languages have words in which one or more segment does not belong structurally to the syllable. Three commonly employed adjectives used to describe such consonants are 'extrasyllabic', 'extrametrical' or 'stray'. Other authors refer to such segments as belonging to the 'appendix'. [...] Various non-linear representations have been proposed to express the 'extrasyllabicity' of segments [...]. The ones I am concerned with in the present article analyze [...] consonants [...] structurally as being outside of the syllable [...]. For transparency I ignore here both subsyllabic constituency as well as higher level prosodic constituents to which the stray consonants are sometimes assumed to attach. For reasons to be made clear below I refer to syllables [...] in which the stray consonant is situated outside of the syllable, as abstract syllables.  

scholarly journals Rhizomatic Learning in Action: A Virtual Exposition for Demonstrating Learning Rhizomes

2021 ◽  
Author(s):  
Alexios Brailas
Keyword(s):  
Academic Research ◽  
Complex Learning ◽  
Learning And Teaching ◽  
Linear Representations ◽  
Non Linear ◽  
Representational Format ◽  
The Creation ◽  
Human Actors ◽  
Practical Implications ◽  
Better Than

In this paper, we developed a virtual exposition as a model to visualize and demonstrate the dynamic and non-linear affordances of a learning rhizome. Virtual expositions are non-linear multimodal web installations that facilitate the creation of interconnections through which the research as practice and the practice as research are highlighted and communicated more effectively. Through a specific virtual exposition platform, we created a visual and performative representation of a rhizomatic learning course, allowing visitors to experience the complexity, multiplicity, unpredictability, and multivoicedness of such an approach in an isomorphic way. A complex learning rhizome is a performative confluence of human and non-human actors that engages people, resources, processes, and contextual parameters. As such, it is impossible to be represented in any representational format. The virtual exposition developed here attempts to offer a fair approximative model of rhizomatic learning which is far better than text-only linear representations. This paper offers a new view to rhizomatic learning as an applied practice that can enhance teaching and catalyze learning through complex synergies and dynamics. The originality of this paper lies in its attempt to bridge linear with non-linear academic research formats in order to offer a multimodal and performative model of rhizomatic learning. Theoretical and practical implications for learning and teaching are discussed.

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