Extremal Properties of Some Geometric Processes

1987 ◽  
pp. 61-69
Author(s):  
J. Mecke
Keyword(s):  
Geometric Processes ◽  
Extremal Properties

scholarly journals Permutation Matrices, Their Discrete Derivatives and Extremal Properties

2020 ◽  
Vol 48 (4) ◽  
pp. 719-740
Author(s):  
Richard A. Brualdi ◽  
Geir Dahl
Keyword(s):  
Permutation Matrix ◽  
Permutation Matrices ◽  
Discrete Derivative ◽  
The Relationship ◽  
Derivatives Of ◽  
Extremal Properties

AbstractFor a permutation π, and the corresponding permutation matrix, we introduce the notion of discrete derivative, obtained by taking differences of successive entries in π. We characterize the possible derivatives of permutations, and consider questions for permutations with certain properties satisfied by the derivative. For instance, we consider permutations with distinct derivatives, and the relationship to so-called Costas arrays.

Extremal Properties of an Intermittent Poisson Process Generating 1/f Noise

2016 ◽  
Vol 15 (04) ◽  
pp. 1650028 ◽  
Author(s):  
Ferdinand Grüneis
Keyword(s):  
Stochastic Processes ◽  
Poisson Process ◽  
Total Power ◽  
Spectral Features ◽  
Active Period ◽  
Quiescent Period ◽  
The Family ◽  
Random Intervals ◽  
Theoretical Results ◽  
Extremal Properties

It is well-known that the total power of a signal exhibiting a pure [Formula: see text] shape is divergent. This phenomenon is also called the infrared catastrophe. Mandelbrot claims that the infrared catastrophe can be overcome by stochastic processes which alternate between active and quiescent states. We investigate an intermittent Poisson process (IPP) which belongs to the family of stochastic processes suggested by Mandelbrot. During the intermission [Formula: see text] (quiescent period) the signal is zero. The active period is divided into random intervals of mean length [Formula: see text] consisting of a fluctuating number of events; this is giving rise to so-called clusters. The advantage of our treatment is that the spectral features of the IPP can be derived analytically. Our considerations are focused on the case that intermission is only a small disturbance of the Poisson process, i.e., to the case that [Formula: see text]. This makes it difficult or even impossible to discriminate a spike train of such an IPP from that of a Poisson process. We investigate the conditions under which a [Formula: see text] spectrum can be observed. It is shown that [Formula: see text] noise generated by the IPP is accompanied with extreme variance. In agreement with the considerations of Mandelbrot, the IPP avoids the infrared catastrophe. Spectral analysis of the simulated IPP confirms our theoretical results. The IPP is a model for an almost random walk generating both white and [Formula: see text] noise and can be applied for an interpretation of [Formula: see text] noise in metallic resistors.

Extremal properties associated with univalent subordination chains in $$\mathbb {C}^n$$ C n

2013 ◽  
Vol 359 (1-2) ◽  
pp. 61-99 ◽  
Author(s):  
Ian Graham ◽  
Hidetaka Hamada ◽  
Gabriela Kohr ◽  
Mirela Kohr
Keyword(s):  
Extremal Properties

scholarly journals Combinatorial Constructions of Weight Bases: The Gelfand-Tsetlin Basis

10.37236/305 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Patricia Hersh ◽  
Cristian Lenart
Keyword(s):  
Lie Algebras ◽  
Simple Algorithm ◽  
Irreducible Representations ◽  
Combinatorial Proof ◽  
Young Tableaux ◽  
Constructive Approach ◽  
Function Identity ◽  
New Interpretation ◽  
Combinatorial Constructions ◽  
Extremal Properties

This work is part of a project on weight bases for the irreducible representations of semisimple Lie algebras with respect to which the representation matrices of the Chevalley generators are given by explicit formulas. In the case of $\mathfrak{ sl}$$_n$, the celebrated Gelfand-Tsetlin basis is the only such basis known. Using the setup of supporting graphs developed by Donnelly, we present a new interpretation and a simple combinatorial proof of the Gelfand-Tsetlin formulas based on a rational function identity (all the known proofs use more sophisticated algebraic tools). A constructive approach to the Gelfand-Tsetlin formulas is then given, based on a simple algorithm for solving certain equations on the lattice of semistandard Young tableaux. This algorithm also implies certain extremal properties of the Gelfand-Tsetlin basis.

scholarly journals Extremal properties of a class of slit conformal mappings.

1978 ◽  
Vol 25 (2) ◽  
pp. 223-232 ◽  
Author(s):  
W. E. Kirwan ◽  
Richard Pell
Keyword(s):  
Conformal Mappings ◽  
Extremal Properties
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