Projection constants of symmetric spaces and variants of Khintchine's inequality

1999 ◽  
Vol 1999 (511) ◽  
pp. 1-42 ◽  
Author(s):  
Hermann König ◽  
Carsten Schütt ◽  
Nicole Tomczak-Jaegermann
Keyword(s):  
Symmetric Spaces ◽  
Dimensional Space ◽  
Complex Case ◽  
Real Case ◽  
The Real ◽  
Symmetric Basis ◽  
Projection Constant ◽  
Khintchine’S Inequality ◽  
Averaging Techniques

Abstract The projection constants of the lpn-spaces for 1 ≦ p ≦ 2 satisfy with in the real case and in the complex case. Further, there is c < 1 such that the projection constant of any n-dimensional space Xn with 1-symmetric basis can be estimated by . The proofs of the results are based on averaging techniques over permutations and a variant of Khintchine's inequality which states that

scholarly journals Generalized Givens Rotations Applied to Complex Joint Eigenvalue Decomposition

2021 ◽  
Vol 1 (1) ◽  
pp. 58-62
Author(s):  
Ammar Mesloub
Keyword(s):  
Complex Case ◽  
Eigenvalue Decomposition ◽  
Real Case ◽  
Joint Diagonalization ◽  
The Real ◽  
Givens Rotation ◽  
Givens Rotations ◽  
Simulation Results ◽  
Complex Joint

This paper shows the different ways of using generalized Givens rotations in complex joint eigenvaluedecomposition (JEVD) problem. It presents the different schemes of generalized Givens rotation, justifies the introducedapproximations and focuses on the process of extending an algorithm developed for real JEVD to the complex JEVD.Several Joint Diagonalization problem use generalized Givens rotations to achieve the solution, many algorithmsdeveloped in the real case exist in the literature and are not generalized to the complex case. Hence, we show herein asimple and not trivial way to get the complex case from the real one. Simulation results are provided to highlight theeffectiveness and behaviour of the proposed techniques for different scenarios.

On quadrics through five real points

1967 ◽  
Vol 63 (2) ◽  
pp. 369-388
Author(s):  
R. H. F. Denniston
Keyword(s):  
Projective Space ◽  
Fixed Points ◽  
Complex Case ◽  
Real Case ◽  
Quadric Surface ◽  
Real Projective Space ◽  
The Real ◽  
Homology Groups

Let Q1,…, Q5 be five fixed points (no four coplanar) of the real projective space S3: let s be a variable quadric surface through these points. The set of all such quadrics can be represented by the points of a real S4, in which there is a quartic primal that represents cones. The geometry of this threefold is well known in the complex case, but has hardly been considered at all in the real case: and one object of the present paper is to describe the real threefold and determine its homology groups.

Affine cubic functions

1980 ◽  
Vol 87 (1) ◽  
pp. 1-14 ◽  
Author(s):  
C. T. C. Wall
Keyword(s):  
Complex Case ◽  
Real Case ◽  
Dynamic Approach ◽  
Cubic Curves ◽  
The Real ◽  
Level Curves ◽  
Cubic Curve

The classification of affine cubic functions in the real case is a fairly easy corollary of that in the complex case (9). However as the results can be easily interpreted by diagrams, one can obtain a much richer understanding. For example, the question of which types of cubic curve occur as level curves of which types of function is now much less trivial. This will lead us first to re-examine the classification of cubic curves going back to Newton (4). Next the ‘dynamic’ approach of considering these curves as members of families leads to the diagrams associated with the umbilic catastrophes of Thorn (8). However the consideration of functions rather than of curves gives a 1-dimensional foliation of these diagrams which we describe next. We conclude by placing the results back in a protective setting.

A successful example of citizen science within the PRISMA network applied to the 15th March 2021 bolide over Italy

2021 ◽  
Author(s):  
Daniele Gardiol ◽  
Tiberio Cuppone ◽  
Giovanni Ascione ◽  
Dario Barghini ◽  
Albino Carbognani ◽  
...  
Keyword(s):  
Citizen Science ◽  
Video Recording ◽  
Real Case ◽  
The Real ◽  
The City

&lt;p&gt;PRISMA is the italian fireball network dedicated to observation of bright meteors and recovery of freshly fallen meteorites. Since the very beginning of the project, we experienced an increasing enthusiastic participation of non-professionals, starting from amateur astronomers and reaching an ever wider audience among citizens. Nowadays PRISMA has become an established italian stakeholder in the field of meteors and meteorites, being the reference for visual warnings, video recording of fireballs and report of suspect meteorite finds.&lt;/p&gt; &lt;p&gt;In this contribution we will describe our experience on this topic and the methodologies we have developed to capitalize such potential, by actively training and involving citizens in activities focused on meteorite/meteorwrong identification and organized on-field search campaigns. We will show an application to the real case of the 15&lt;sup&gt;th&lt;/sup&gt; march 2021 meteorite-dropping bolide in sourthern Italy, near the city of Isernia.&lt;/p&gt;

scholarly journals About estimation of base station output power in GSM like systems under real conditions

2020 ◽  
Vol 30 (1) ◽  
pp. 109-119
Author(s):  
Aleksandar Lebl ◽  
Dragan Mitic ◽  
Zarko Markov ◽  
Verica Vasiljevic
Keyword(s):  
Computer Simulation ◽  
Output Power ◽  
Mobile User ◽  
Base Station ◽  
Cumulative Distribution ◽  
Real Case ◽  
The Real ◽  
The Mean

The output power of traffic channels in one cell of GSM like systems is estimated in this paper. We consider the real case: the number of users is much higher than the number of channels, the output power of one channel depends on the cube of the distance between a mobile user and the base station, and the distribution of users in the cell is uniform. We derive the expressions for cumulative distribution of output power of one channel and for the mean output power of the whole base station. Results of the calculation are confirmed by computer simulation.

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