Parametric rigidity of real families of conformal diffeomorphisms tangent to x→−x

2018 ◽  
Vol 149 (1) ◽  
pp. 261-277
Author(s):  
Waldo Arriagada
Keyword(s):  
Fixed Points ◽  
Crucial Importance ◽  
Siegel Domain ◽  
Siegel Domains ◽  
Points Of View

We prove that one-parameter families of real germs of conformal diffeomorphisms tangent to the involution x ↦−x are rigid in the parameter. We establish a connection between the dynamics in the Poincaré and Siegel domains. Although repeatedly employed in the literature, the dynamics in the Siegel domain does not explain the intrinsic real properties of these germs. Rather, these properties are fully elucidated in the Poincaré domain, where the fixed points are linearizable. However, a detailed study of the dynamics in the Siegel domain is of crucial importance. We relate both points of view on the intersection of the Siegel normalization domains.

KORÁNYI’S LEMMA FOR HOMOGENEOUS SIEGEL DOMAINS OF TYPE II. APPLICATIONS AND EXTENDED RESULTS

2014 ◽  
Vol 90 (1) ◽  
pp. 77-89 ◽  
Author(s):  
DAVID BÉKOLLÉ ◽  
HIDEYUKI ISHI ◽  
CYRILLE NANA
Keyword(s):  
Functional Analysis ◽  
Bergman Kernel ◽  
Atomic Decomposition ◽  
Bergman Spaces ◽  
Decomposition Theorem ◽  
Interpolation Theorem ◽  
Type Ii ◽  
Siegel Domain ◽  
Homogeneous Case ◽  
Siegel Domains

AbstractWe show that the modulus of the Bergman kernel $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}B(z, \zeta )$ of a general homogeneous Siegel domain of type II is ‘almost constant’ uniformly with respect to $z$ when $\zeta $ varies inside a Bergman ball. The control is expressed in terms of the Bergman distance. This result was proved by A. Korányi for symmetric Siegel domains of type II. Subsequently, R. R. Coifman and R. Rochberg used it to establish an atomic decomposition theorem and an interpolation theorem by functions in Bergman spaces $A^p$ on these domains. The atomic decomposition theorem and the interpolation theorem are extended here to the general homogeneous case using the same tools. We further extend the range of exponents $p$ via functional analysis using recent estimates.

scholarly journals On classification of quasi-symmetric domains

1976 ◽  
Vol 62 ◽  
pp. 1-12 ◽  
Author(s):  
I. Satake
Keyword(s):  
Bounded Domain ◽  
Siegel Domain ◽  
The Third ◽  
Siegel Domains

The notion of “Siegel domains” was introduced by [8]. It was then shown that every homogeneous bounded domain is holomorphically equivalent to a Siegel domain (of the second kind) determined uniquely up to an affine isomorphism ([15], cf. also [2], [4], [9b]). In a recent note [10b], I have shown that among (homogeneous) Siegel domains the symmetric domains can be characterized by three conditions (i), (ii), (iii) on the data (U, V, Ω, F) defining the Siegel domain (see Theorem in § 2 of this paper). The class of homogeneous Siegel domains satisfying partial conditions (i), (ii), which we propose to call “quasi-symmetric”, seems to be of some interest, since for instance the fibers appearing in the expressions of symmetric domains as Siegel domains of the third kind fall in this class ([10b], [16]).

scholarly journals Homogeneous Siegel domains

1982 ◽  
Vol 86 ◽  
pp. 39-83 ◽  
Author(s):  
Josef Dorfmeister
Keyword(s):  
Explicit Form ◽  
General Problem ◽  
Symmetric Domain ◽  
Bounded Symmetric Domain ◽  
Bounded Domains ◽  
Higher Dimension ◽  
Siegel Domain ◽  
Siegel Domains ◽  
Infinitesimal Automorphisms ◽  
Holomorphic Automorphisms

In 1935 E. Cartan classified all symmetric bounded domains [6]. At that time he proved that a bounded symmetric domain is homogeneous with respect to its group of holomorphic automorphisms. Thus the more general problem of investigating homogeneous bounded domains arose. It was known to E. Cartan that all homogeneous bounded domains of dimension ≤3 are symmetric [6]. For domains of higher dimension little was known. The first example of a 4-dimensional, homogeneous, non-symmetric bounded domain was provided by I. Piatetsky-Shapiro [41]. In several papers he investigated homogeneous bounded domains [20], [21], [41], [42], [43]. One of the main results is that all such domains have an unbounded realization of a certain type, as a so-called Siegel domain. But many questions still remained open. Amongst them the question for the structure and explicit form of the infinitesimal automorphisms of a homogeneous Siegel domain.

scholarly journals On symmetric Siegel domains

1975 ◽  
Vol 59 ◽  
pp. 9-44 ◽  
Author(s):  
Masaru Takeuchi
Keyword(s):  
Fixed Point ◽  
Vector Space ◽  
Holomorphic Automorphism ◽  
Complex Vector Space ◽  
Siegel Domain ◽  
Real Vector ◽  
Complex Vector ◽  
Fixed Point Set ◽  
Siegel Domains ◽  
Point Set

Let V be a convex cone in a real vector space X, F: Y × Y → Xc a V-positive hermitian map on a complex vector space Y, andthe Siegel domain associated to V and F. D(V,F) is said to be symmetric, if for each point p ∈ D(V, F) there exists an involutive holomorphic automorphism σp of D(V,F) such that the fixed point set of σp consists of only the point p. Satake [6] showed that the symmetric Siegel domain D(V, F) is characterized by the following three conditions (i), (ii) and (iii).

scholarly journals Siegel domains over self-dual cones and their automorphisms

1974 ◽  
Vol 55 ◽  
pp. 33-80 ◽  
Author(s):  
Tadashi Tsuji
Keyword(s):  
Lie Algebra ◽  
Vector Fields ◽  
Polynomial Vector ◽  
Siegel Domain ◽  
Polynomial Vector Fields ◽  
Siegel Domains ◽  
Dual Cones ◽  
Graded Lie Algebra ◽  
Infinitesimal Automorphisms ◽  
Affine Part

The Lie algebra gr of all infinitesimal automorphisms of a Siegel domain in terms of polynomial vector fields was investigated by Kaup, Matsushima and Ochiai [6]. It was proved in [6] that gr is a graded Lie algebra; gr = g-1 + g-1/2 + g0 + g1/2 + g1 and the Lie subalgebra ga of all infinitesimal affine automorphisms is given by the graded subalgebra; ga = g-1 + g-1/2 + g0. Nakajima [9] proved without the assumption of homogeneity that the non-affine parts g1/2 and g1 can be determined from the affine part ga.

High Resolution Specimen Area Imaged Under Negligible Field Aberrations

1970 ◽  
Vol 28 ◽  
pp. 540-541 ◽  
Author(s):  
T. Yanaka ◽  
K. Shirota
Keyword(s):  
High Resolution ◽  
Field Distribution ◽  
Image Space ◽  
Beam Deflection ◽  
Objective Lens ◽  
Resolution Limit ◽  
Leakage Flux ◽  
Specimen Area ◽  
Points Of View ◽  
Aberration Theory

It is significant to note field aberrations (chromatic field aberration, coma, astigmatism and blurring due to curvature of field, defined by Glaser's aberration theory relative to the Blenden Freien System) of the objective lens in connection with the following three points of view; field aberrations increase as the resolution of the axial point improves by increasing the lens excitation (k2) and decreasing the half width value (d) of the axial lens field distribution; when one or all of the imaging lenses have axial imperfections such as beam deflection in image space by the asymmetrical magnetic leakage flux, the apparent axial point has field aberrations which prevent the theoretical resolution limit from being obtained.

Crystal structure images of large gold clusters and growing crystals by HRTEM

1984 ◽  
Vol 42 ◽  
pp. 428-429
Author(s):  
L.R. Wallenberg ◽  
J.-O. Bovin ◽  
G. Schmid
Keyword(s):  
Crystal Structure ◽  
Nucleation And Growth ◽  
Close Packing ◽  
Gold Clusters ◽  
Molecular Weight Determination ◽  
Growth Mechanisms ◽  
Starting Point ◽  
Different Types ◽  
Nucleation And Growth Mechanisms ◽  
Points Of View

Metallic clusters are interesting from various points of view, e.g. as a mean of spreading expensive catalysts on a support, or following heterogeneous and homogeneous catalytic events. It is also possible to study nucleation and growth mechanisms for crystals with the cluster as known starting point.Gold-clusters containing 55 atoms were manufactured by reducing (C6H5)3PAuCl with B2H6 in benzene. The chemical composition was found to be Au9.2[P(C6H5)3]2Cl. Molecular-weight determination by means of an ultracentrifuge gave the formula Au55[P(C6H5)3]Cl6 A model was proposed from Mössbauer spectra by Schmid et al. with cubic close-packing of the 55 gold atoms in a cubeoctahedron as shown in Fig 1. The cluster is almost completely isolated from the surroundings by the twelve triphenylphosphane groups situated in each corner, and the chlorine atoms on the centre of the 3x3 square surfaces. This gives four groups of gold atoms, depending on the different types of surrounding.

Conflict Detection Techniques for Preserving Privacy in Social Media

2018 ◽  
pp. 78-85
Author(s):  
Fulpagare Priya K. ◽  
Nitin N. Patil
Keyword(s):  
Social Media ◽  
Privacy Management ◽  
Crucial Importance ◽  
Network Integration ◽  
Critical Problem ◽  
Detection Techniques ◽  
Privacy Preferences ◽  
Content Sharing ◽  
Privacy Settings ◽  
Relationship Network

Social Network is an emerging e-service for Content Sharing Sites (CSS). It is an emerging service which provides reliable communication. Some users over CSS affect user’s privacy on their personal contents, where some users keep on sending annoying comments and messages by taking advantage of the user’s inherent trust in their relationship network. Integration of multiple user’s privacy preferences is very difficult task, because privacy preferences may create conflict. The techniques to resolve conflicts are essentially required. Moreover, these methods need to consider how users would actually reach an agreement about a solution to the conflict in order to offer solutions acceptable by all of the concerned users. The first mechanism to resolve conflicts for multi-party privacy management in social media that is able to adapt to different situations by displaying the enterprises that users make to reach a result to the conflicts. Billions of items that are uploaded to social media are co-owned by multiple users. Only the user that uploads the item is allowed to set its privacy settings (i.e. who can access the item). This is a critical problem as users’ privacy preferences for co-owned items can conflict. Multi-party privacy management is therefore of crucial importance for users to appropriately reserve their privacy in social media.

مشروعية نكاح المتعة عند الإمامية الإثنى عشرية وموقف المذاهب الإسلامية منها

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
fithriah wardi
Keyword(s):  
Analytical Methods ◽  
Points Of View

Both fuqaha (Moslem jurists) of the Sunni and the Shi’ah are in agreement that Mut’ah marriage was permitted at the beginning of Islam, based on Al-quran verses and Rasulullah (pbuh) hadiths. However, they disagree as to the annulment and permissibility. The Shi’as considered Mut’ah marriage as permitted until the Day of Resurrection, meanwhile the Sunni viewed it as forbidden. The execution of Mut’ah marriage has always been singled out as one of the specific features of the Shi’ite doctrine in which denying it means denial of the religion. They also believe that woman who practised Mut’ah marriage will result in her sins being forgiven. According to the Shi’ites, Mut’ah marriage is one of the biggest reasons for someone to be granted heaven, and his status be elevated to the rank of the Holy Prophet PBUH. Hence, it can be said that practicing Mut’ah marriage is one of the most crucial issues among the Shi’ite community which is totally contradicted to the Sunni doctrine which believed it is unlawful marriage and equalized to Zina (adultery). There is no doubt that this is one of the most important topics that lead to the dispute between the two schools of thought. Using the descriptive and analytical methods, this study aims to elaborate the views on the issue from Shi’ite and Sunni points of view based on various proofs (adillah) and their argumentations in supporting the views.

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