The schur subgroup of an imaginary field

1974 ◽  
pp. 132-142
Author(s):  
Toshihiko Yamada
Keyword(s):  
Imaginary Field

scholarly journals -ADIC EISENSTEIN SERIES AND -FUNCTIONS OF CERTAIN CUSP FORMS ON DEFINITE UNITARY GROUPS

2014 ◽  
Vol 15 (3) ◽  
pp. 471-510 ◽  
Author(s):  
Ellen Eischen ◽  
Xin Wan
Keyword(s):  
Positive Integer ◽  
Eisenstein Series ◽  
Constant Term ◽  
Unitary Groups ◽  
Cusp Forms ◽  
Imaginary Field

We construct$p$-adic families of Klingen–Eisenstein series and$L$-functions for cusp forms (not necessarily ordinary) unramified at an odd prime$p$on definite unitary groups of signature$(r,0)$(for any positive integer$r$) for a quadratic imaginary field${\mathcal{K}}$split at$p$. When$r=2$, we show that the constant term of the Klingen–Eisenstein family is divisible by a certain$p$-adic$L$-function.

Radio frequency properties of a plane grid capacitor immersed in a hot collision-free plasma

1968 ◽  
Vol 2 (3) ◽  
pp. 339-351 ◽  
Author(s):  
R. Buckley
Keyword(s):  
Plasma Frequency ◽  
Real Component ◽  
Hot Plasma ◽  
Capacitive Component ◽  
Longitudinal Plasma ◽  
Imaginary Field ◽  
Complex Admittance ◽  
Frequency Properties ◽  
Plane Grid ◽  
Made In

A pair of plane parallel grids is inserted in a hot plasma, and an oscillatory voltage is applied across them. The electric field excited in the plasma, and the complex admittance of the grid/plasma system, are computed for applied frequencies high enough to justify neglect of ion response. The grids are electrically, but not mechanically, coupled to the plasma, which is assumed to be in a spatially uniform collision free Maxwellian equilibrium state. The field is computed as a function of distance from the grid plates over a range of frequencies covering the plasma frequency, and the complex admittance of the system is computed as a function of frequency at various grid separation distances. The real component of the field and the capacitive component of the admittance are subject to three major effects: cold plasma dielectric behaviour, oscillatory Debye sheaths on the grids, and (above the plasma frequency), longitudinal plasma waves. The imaginary field component and the conductive admittance component are produced by spatial Landau damping. In an accompanying paper (Freeston 1968), the computed admittance is compared with laboratory measurements made in a situation approximating well to the idealized problem considered here.

scholarly journals Frobenius fields for Drinfeld modules of rank 2

2008 ◽  
Vol 144 (4) ◽  
pp. 827-848 ◽  
Author(s):  
Alina Carmen Cojocaru ◽  
Chantal David
Keyword(s):  
Quadratic Field ◽  
Galois Representations ◽  
Rational Functions ◽  
Galois Representation ◽  
Field Extension ◽  
Imaginary Quadratic Field ◽  
Drinfeld Module ◽  
Rank 2 ◽  
Imaginary Field ◽  
Square Sieve

AbstractLet ϕ be a Drinfeld module of rank 2 over the field of rational functions $F=\mathbb {F}_q(T)$, with $\mathrm {End}_{\bar {F}}(\phi ) = \mathbb {F}_q[T]$. Let K be a fixed imaginary quadratic field over F and d a positive integer. For each prime $\mathfrak {p}$ of good reduction for ϕ, let $\pi _{\mathfrak {p}}(\phi )$ be a root of the characteristic polynomial of the Frobenius endomorphism of ϕ over the finite field $\mathbb {F}_q[T] / \mathfrak {p}$. Let Πϕ(K;d) be the number of primes $\mathfrak {p}$ of degree d such that the field extension $F(\pi _{\mathfrak {p}}(\phi ))$ is the fixed imaginary quadratic field K. We present upper bounds for Πϕ(K;d) obtained by two different approaches, inspired by similar ones for elliptic curves. The first approach, inspired by the work of Serre, is to consider the image of Frobenius in a mixed Galois representation associated to K and to the Drinfeld module ϕ. The second approach, inspired by the work of Cojocaru, Fouvry and Murty, is based on an application of the square sieve. The bounds obtained with the first method are better, but depend on the fixed quadratic imaginary field K. In our application of the second approach, we improve the results of Cojocaru, Murty and Fouvry by considering projective Galois representations.

Wormhole in 5D Kaluza–Klein cosmology

2017 ◽  
Vol 32 (07) ◽  
pp. 1750023 ◽  
Author(s):  
Gargi Biswas ◽  
B. Modak
Keyword(s):  
Boundary Conditions ◽  
Cosmological Constant ◽  
Dimensional Reduction ◽  
Dimensional Space ◽  
Field Equations ◽  
Positive Cosmological Constant ◽  
Euclidean Field ◽  
Pure Gravity ◽  
Imaginary Field ◽  
Kaluza Klein

We present wormhole as a solution of Euclidean field equations as well as the solution of the Wheeler–deWitt (WD) equation satisfying Hawking–Page wormhole boundary conditions in (4 + 1)-dimensional Kaluza–Klein cosmology. The wormholes are considered in the cases of pure gravity, minimally coupled scalar (imaginary) field and with a positive cosmological constant assuming dynamical extra-dimensional space. In above cases, wormholes are allowed both from Euclidean field equations and WD equation. The dimensional reduction is possible.

The Fundamental Imaginary Dimension of the Real in Merleau-Ponty’s Philosophy

2015 ◽  
Vol 45 (1) ◽  
pp. 33-52 ◽  
Author(s):  
Annabelle Dufourcq
Keyword(s):  
The Other ◽  
The Real ◽  
Other Hand ◽  
Mental Entity ◽  
The Common ◽  
Ontological Model ◽  
Imaginary Field ◽  
Mode Of Being

The common opposition between the imaginary and the real prevents us from genuinely understanding either one. Indeed, the imaginary embodies a certain intuitive presence of the thing and not an empty signitive intention. Moreover it is able to compete with perception and even to offer an increased presence, a sur-real display, of the things, as shown by Merleau-Ponty’s analyses of art in Eye and Mind. As a result, we have to overcome the conception according to which the imaginary field is a mere figment of my imagination, a mental entity that I could still possess in the very absence of its object. On the other hand, the presence of reality is never complete or solid: “The transcendence of the far-off encroaches upon my present and brings a hint of unreality even into the experiences with which I believe myself to coincide.” Therefore, first, the imaginary (initially regarded as a peculiar field constituted by specific phenomena such as artworks, fantasies, pictures, dreams, and so forth) has to be redefined as a special hovering modality of the presence of the beings themselves. Second and furthermore: is not the imaginary always intertwined with perception? Merleau-Ponty advocates the puzzling thesis that there is an “imaginary texture of the real.” What is the meaning of this assertion? To what extent will it be able to blur the classical categories without arousing confusion? Can we avoid reducing reality to illusion? Lastly, consistently followed, this reflection leads as far as to discover, in the imaginary mode of being, an ontological model (the ontological model?), the canon enabling Merleau-Ponty to think Being, an “Oneiric Being.” Thus we will venture the apparently paradoxical contention that the imaginary is the fundamental dimension of the real. The notion of “fundament” becomes indeed problematic and receives an ironical connotation, however this is precisely what is at stake in a non-positivist ontology. Existence “lies” in a ghost-like, sketchy and unsubstantial (absence of) ground, in a restlessly creative being that is open to creative interpretations. And there it finds the principle of the ever-recurring crisis that both tears it apart and makes it rich in future promise.

scholarly journals Development of Media Strike Zone for Pitching Learning Process on Softball

2019 ◽  
Vol 6 (1) ◽  
pp. 23-26
Author(s):  
Roas Irsyada
Keyword(s):  
Learning Process ◽  
Development Research ◽  
Real Form ◽  
Stages Of Development ◽  
Product Testing ◽  
Home Base ◽  
Small Ball ◽  
The Real ◽  
Imaginary Field

Softball games are one form of small ball games learned at school. In the softball game there is strike zone, which is an imaginary field between the elbow and the knee of a batter, and is above the home base. Students find it difficult to find the strike zone so that when throwing pitchers always “ball”. when the game takes place students have difficulty determining between “strike” and “ball”. The need for learning media that can provide a real form of strike zone for students. This research is a development research that uses the stages of development of Borg and Gall. Based on product testing, the target media strike zone is very suitable with the softball game and can effectively provide information about the real shape of the strike zone in the softball game, as well as helping students to set targets and throw accuracy.

scholarly journals A Deep Neural Network-Based Interference Mitigation for MIMO-FBMC/OQAM Systems

2021 ◽  
Vol 2 ◽  
Author(s):  
Abla Bedoui ◽  
Mohamed Et-tolba
Keyword(s):  
Neural Network ◽  
Communication Systems ◽  
Deep Neural Network ◽  
Interference Mitigation ◽  
Multiple Input Multiple Output ◽  
Filter Bank Multicarrier ◽  
Multiple Input ◽  
High Spectral Efficiency ◽  
Input Multiple Output ◽  
Imaginary Field

Offset quadrature amplitude modulation-based filter bank multicarrier (FBMC/OQAM) is among the promising waveforms for future wireless communication systems. This is due to its flexible spectrum usage and high spectral efficiency compared with the conventional multicarrier schemes. However, with OQAM modulation, the FBMC/OQAM signals are not orthogonal in the imaginary field. This causes a significant intrinsic interference, which is an obstacle to apply multiple input multiple output (MIMO) technology with FBMC/OQAM. In this paper, we propose a deep neural network (DNN)-based approach to deal with the imaginary interference, and enable the application of MIMO technique with FBMC/OQAM. We show, by simulations, that the proposed approach provides good performance in terms of bit error rate (BER).

Experimentieren, um zu sehen

2012 ◽  
Vol 57 (2) ◽  
pp. 26-43
Author(s):  
Georges Didi-Huberman
Keyword(s):  
Point Of View ◽  
Literary Field ◽  
Alain Resnais ◽  
Visual Style ◽  
Technical Reproducibility ◽  
Andre Malraux ◽  
Imaginary Field ◽  
Chris Marker

Ausgehend vom Standpunkt eines visuellen und kognitiven Experimentierens beschäftigt sich der Beitrag mit der Arbeit André Malraux’ zu den Illustrationen seines Musée imaginaire. Es handelt sich um eine Arbeit, die explizit vom Benjamin der »technischen Reproduzierbarkeit« und des »Autors als Produzenten« inspiriert ist. Studiert wird die Öffnung des imaginären Feldes, wie sie die Praxis des Kunstbuchs – als einem Album, das von einer Art Expressivität der Rahmung, Beleuchtung und Montage getragen wird – bei Malraux nahelegt. Durch diese Praxis der Montage konstruiert Malraux die Autorität seines visuellen Stils und die Schließung seines literarischen Feldes. Vor allem aber setzt sich der Beitrag – auf kritische Weise – mit dem anti-historischen und anti-politischen Zielpunkt seiner Ästhetik auseinander, die von Benjamin weit entfernt zu stehen kommt. Am Schluss steht der Vergleich zwischen zwei zeitgenössischen Werken, Le Musee imaginaire de la sculpture mondiale von Malraux und Les Statues meurent aussi, einem Film von Chris Marker und Alain Resnais.<br><br>Our paper deals with the work of André Malraux on the illustrations for his Musée imaginaire from the point of view of visual and cognitive experimentation. This work is explicitly inspired by the Benjamin of the »technical reproducibility« and the »author as producer.« We examine the opening of the imaginary field, as it is suggested by the praxis of the art book – an album of images that is supported by a certain kind of expressivity of framing, illumination and montage – in Malraux. Through this praxis of montage, Malraux constructs the authority of his visual style and the closure of the literary field. Above all, however, we discuss critically the anti-historical and anti-political destiny of his aesthetics, which in the end is quite far from Benjamin’s, and we conclude with a comparison between two contemporary artworks, namely Malraux’ Le Musee imaginaire de la sculpture mondiale and Les Statues meurent aussi, a film by Chris Marker and Alain Resnais.

Critical and off-critical conformal analysis of the Ising quantum chain in an imaginary field

1991 ◽  
Vol 24 (22) ◽  
pp. 5371-5399 ◽  
Author(s):  
G von Gehlen
Keyword(s):  
Quantum Chain ◽  
Imaginary Field

scholarly journals Foliations on unitary Shimura varieties in positive characteristic

2018 ◽  
Vol 154 (11) ◽  
pp. 2267-2304 ◽  
Author(s):  
Ehud de Shalit ◽  
Eyal Z. Goren
Keyword(s):  
Tangent Bundle ◽  
Positive Characteristic ◽  
Blow Up ◽  
Level Structure ◽  
Horizontal Component ◽  
Zariski Closure ◽  
Shimura Varieties ◽  
Shimura Variety ◽  
Integral Manifolds ◽  
Imaginary Field

When$p$is inert in the quadratic imaginary field$E$and$m<n$, unitary Shimura varieties of signature$(n,m)$and a hyperspecial level subgroup at$p$, carry a naturalfoliationof height 1 and rank$m^{2}$in the tangent bundle of their special fiber$S$. We study this foliation and show that it acquires singularities at deep Ekedahl–Oort strata, but that these singularities are resolved if we pass to a natural smooth moduli problem$S^{\sharp }$, a successive blow-up of$S$. Over the ($\unicode[STIX]{x1D707}$-)ordinary locus we relate the foliation to Moonen’s generalized Serre–Tate coordinates. We study the quotient of$S^{\sharp }$by the foliation, and identify it as the Zariski closure of the ordinary-étale locus in the special fiber$S_{0}(p)$of a certain Shimura variety with parahoric level structure at$p$. As a result, we get that this ‘horizontal component’ of$S_{0}(p)$, as well as its multiplicative counterpart, are non-singular (formerly they were only known to be normal and Cohen–Macaulay). We study two kinds of integral manifolds of the foliation: unitary Shimura subvarieties of signature$(m,m)$, and a certain Ekedahl–Oort stratum that we denote$S_{\text{fol}}$. We conjecture that these are the only integral submanifolds.

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