Stability of the multifractal spectra by transformations of discrete series

2007 ◽  
Author(s):  
A. Corvalán ◽  
E. Serrano
Keyword(s):  
Discrete Series ◽  
Multifractal Spectra

Hard Objects in George Oppen's Discrete Series

2018 ◽  
Vol 13 (4) ◽  
pp. 496-517
Author(s):  
Ned Hercock
Keyword(s):  
Twentieth Century ◽  
Ludwig Wittgenstein ◽  
Discrete Series ◽  
Human Experience ◽  
John Ruskin ◽  
Gerard Manley Hopkins ◽  
Marcel Duchamp ◽  
The World ◽  
Production History ◽  
History Of

This essay examines the objects in George Oppen's Discrete Series (1934). It considers their primary property to be their hardness – many of them have distinctively uniform and impenetrable surfaces. This hardness and uniformity is contrasted with 19th century organicism (Gerard Manley Hopkins and John Ruskin). Taking my cue from Kirsten Blythe Painter I show how in their work with hard objects these poems participate within a wider cultural and philosophical turn towards hardness in the early twentieth century (Marcel Duchamp, Adolf Loos, Ludwig Wittgenstein and others). I describe the thinking these poems do with regard to industrialization and to human experience of a resolutely object world – I argue that the presentation of these objects bears witness to the production history of the type of objects which in this era are becoming preponderant in parts of the world. Finally, I suggest that the objects’ impenetrability offers a kind of anti-aesthetic relief: perception without conception. If ‘philosophy recognizes the Concept in everything’ it is still possible, these poems show, to experience resistance to this imperious process of conceptualization. Within thinking objects (poems) these are objects which do not think.

Study of the structural degradation of steel 15Kh5M upon continuous duty

2020 ◽  
Vol 86 (1) ◽  
pp. 38-43
Author(s):  
Vladimir A. Kim ◽  
Valeriya V. Lysenko ◽  
Anna A. Afanaseva ◽  
Khasan I. Turkmenov
Keyword(s):  
Grain Boundaries ◽  
Structural Changes ◽  
Structural Transformations ◽  
Structural Degradation ◽  
Structural Arrangement ◽  
Dispersed Particles ◽  
Complex Process ◽  
Multifractal Spectra ◽  
Steel 15Kh5m ◽  
Complex Indicators

Structural degradation of the material upon long-term thermal and force impacts is a complex process which includes migration of the grain boundaries, diffusion of the active elements of the external and technological environment, hydrogen embrittlement, aging, grain boundary corrosion and other mechanisms. Application of the fractal and multifractal formalism to the description of microstructures opens up wide opportunities for quantitative assessment of the structural arrangement of the material, clarifies and reveals new aspects of the known mechanisms of structural transformations. Multifractal parameterization allows us to study the processes of structural degradation from the images of microstructures and identify structural changes that are hardly distinguishable visually. Any quantitative structural indicator can be used to calculate the multifractal spectra of the microstructure, but the most preferable is that provides the maximum range of variation in the numerical values of the multifractal components. The results of studying structural degradation of steel 15Kh5M upon continuous duty are presented. It is shown that structural degradation of steel during operation under high temperatures and stresses is accompanied by enlargement of the microstructural objects, broadening of the grain boundaries and allocation of the dispersed particles which are represented as point objects in the images. The processes of structural degradation lead to an increase in the range of changes in the components of the multifractal spectra. High values of complex indicators of structural arrangement indicate to an increase in heterogeneity and randomness at the micro-scale level, but at the same time, to manifestation of the ordered combinations of individual submicrostructures. Those structural transformations adapt the material to external impacts and provide the highest reliability and fracture resistance of the material.

Representations induced from the Zelevinsky segment and discrete series in the half-integral case

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ivan Matić
Keyword(s):  
Linear Group ◽  
Local Field ◽  
General Linear Group ◽  
Discrete Series ◽  
Series Representation ◽  
General Linear ◽  
Composition Series ◽  
Induced Representations ◽  
Discrete Series Representation

AbstractLet {G_{n}} denote either the group {\mathrm{SO}(2n+1,F)} or {\mathrm{Sp}(2n,F)} over a non-archimedean local field of characteristic different than two. We study parabolically induced representations of the form {\langle\Delta\rangle\rtimes\sigma}, where {\langle\Delta\rangle} denotes the Zelevinsky segment representation of the general linear group attached to the segment Δ, and σ denotes a discrete series representation of {G_{n}}. We determine the composition series of {\langle\Delta\rangle\rtimes\sigma} in the case when {\Delta=[\nu^{a}\rho,\nu^{b}\rho]} where a is half-integral.

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