scholarly journals The quarter median

Metrika ◽  
2021 ◽  
Author(s):  
Ludwig Baringhaus ◽  
Rudolf Grübel
Keyword(s):  
Asymptotic Normality ◽  
Orthogonal Basis

AbstractWe introduce and discuss a multivariate version of the classical median that is based on an equipartition property with respect to quarter spaces. These arise as pairwise intersections of the half-spaces associated with the coordinate hyperplanes of an orthogonal basis. We obtain results on existence, equivariance, and asymptotic normality.

Asymptotic normality of processes with a branching structure

1998 ◽  
Vol 14 (4) ◽  
pp. 833-848
Author(s):  
Malcolm P. Quine ◽  
Władysław Szczotka
Keyword(s):  
Asymptotic Normality

Detection of signals with the orthogonal basis of the Gauss–Hermite functions

2018 ◽  
Vol 1 (1) ◽  
pp. 48-61
Author(s):  
D. A. Balakin ◽  
◽  
S. S. Churkin ◽  
V. V. Shtykov ◽  
◽  
...  
Keyword(s):  
Orthogonal Basis ◽  
Hermite Functions ◽  
Detection Of Signals

scholarly journals New ideas for handling of loop and angular integrals in D-dimensions in QCD

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Valery E. Lyubovitskij ◽  
Fabian Wunder ◽  
Alexey S. Zhevlakov
Keyword(s):  
Computer Algebra ◽  
Cross Sections ◽  
Orthogonal Basis ◽  
Computer Algebra Systems ◽  
Covariant Formalism ◽  
Linear Combinations ◽  
Recursion Relations ◽  
New Ideas ◽  
Rotational Invariant ◽  
Geometric Picture

Abstract We discuss new ideas for consideration of loop diagrams and angular integrals in D-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of linear combinations of external momenta. It gives a very simple representation for the final results and is more convenient for calculations on computer algebra systems. In case of angular integrals we demonstrate how to simplify the integration of differential cross sections over polar angles. Also we derive the recursion relations, which allow to reduce all occurring angular integrals to a short set of basic scalar integrals. All order ε-expansion is given for all angular integrals with up to two denominators based on the expansion of the basic integrals and using recursion relations. A geometric picture for partial fractioning is developed which provides a new rotational invariant algorithm to reduce the number of denominators.

A model for random instantaneous growth on an interval

1991 ◽  
Vol 28 (3) ◽  
pp. 529-538
Author(s):  
M. P. Quine
Keyword(s):  
Asymptotic Normality ◽  
Instantaneous Growth ◽  
Mean And Variance ◽  
The Mean

Points arrive in succession on an interval and immediately ‘cover' a region of length ½ to each side (less if they are close to the boundary or to a covered part). The location of a new point is uniformly distributed on the uncovered parts. We study the mean and variance of the total number of points ever formed, in particular as a → 0, in which case we also establish asymptotic normality.

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