Analysis at a Regular Point

2020 ◽  
pp. 21-27
Author(s):  
Yoshishige Haraoka
Keyword(s):  
Regular Point

The coincidence approach to stochastic point processes

1975 ◽  
Vol 7 (1) ◽  
pp. 83-122 ◽  
Author(s):  
Odile Macchi
Keyword(s):  
Poisson Process ◽  
Probability Space ◽  
Point Processes ◽  
Counting Process ◽  
Regular Point ◽  
General Point ◽  
Completely Regular ◽  
Photon Process ◽  
Stochastic Point Processes

The structure of the probability space associated with a general point process, when regarded as a counting process, is reviewed using the coincidence formalism. The rest of the paper is devoted to the class of regular point processes for which all coincidence probabilities admit densities. It is shown that their distribution is completely specified by the system of coincidence densities. The specification formalism is stressed for ‘completely’ regular point processes. A construction theorem gives a characterization of the system of coincidence densities of such a process. It permits the study of most models of point processes. New results on the photon process, a particular type of conditioned Poisson process, are derived. New examples are exhibited, including the Gauss-Poisson process and the ‘fermion’ process that is suitable whenever the points are repulsive.

scholarly journals The Sormani–Wenger intrinsic flat convergence of Alexandrov spaces

2018 ◽  
Vol 12 (03) ◽  
pp. 819-839 ◽  
Author(s):  
Nan Li ◽  
Raquel Perales
Keyword(s):  
Regular Point ◽  
Dimensional Sphere ◽  
Volume Estimate ◽  
Alexandrov Spaces ◽  
Filling Volume ◽  
Integral Current ◽  
Structure Formula ◽  
Intrinsic Flat ◽  
Dimensional Integral ◽  
Uniformly Bounded

We study sequences of integral current spaces [Formula: see text] such that the integral current structure [Formula: see text] has weight [Formula: see text] and no boundary and, all [Formula: see text] are closed Alexandrov spaces with curvature uniformly bounded from below and diameter uniformly bounded from above. We prove that for such sequences either their limits collapse or the Gromov–Hausdorff and Sormani–Wenger Intrinsic Flat limits agree. The latter is done showing that the lower [Formula: see text]-dimensional density of the mass measure at any regular point of the Gromov–Hausdorff limit space is positive by passing to a filling volume estimate. In an appendix, we show that the filling volume of the standard [Formula: see text]-dimensional integral current space coming from an [Formula: see text]-dimensional sphere of radius [Formula: see text] in Euclidean space equals [Formula: see text] times the filling volume of the [Formula: see text]-dimensional integral current space coming from the [Formula: see text]-dimensional sphere of radius [Formula: see text].

The K ‐Function for Nearly Regular Point Processes

Biometrics ◽  
2001 ◽  
Vol 57 (1) ◽  
pp. 224-231 ◽  
Author(s):  
Charles C. Taylor ◽  
Ian L. Dryden ◽  
Rahman Farnoosh
Keyword(s):  
Point Processes ◽  
Regular Point ◽  
K Function

Conformal maps in methods of asymptotic continuation

1987 ◽  
Vol 105 (1) ◽  
pp. 319-335
Author(s):  
H. Gingold
Keyword(s):  
Asymptotic Expansion ◽  
Holomorphic Function ◽  
Taylor Series ◽  
Theoretical Basis ◽  
Regular Point ◽  
Taylor Series Expansion ◽  
Computational Method ◽  
Conformal Map ◽  
Conformal Maps ◽  
Summation Of Divergent Series

SynopsisTake the coefficients of a Taylor series expansion of a holomorphic function about its regular point zR. It is known that the holomorphic function possesses an asymptotic expansion about a possibly singular point zs. We show how to construct and calculate the coefficients in the asymptotic expansion from the coefficient of the Taylor series. The main theorem demonstrates that a suitable conformal map is a decisive step in dealing with the problem above. Therefore, a suitable conformal map is critical to a successful summation of divergent series. Some other methods which utilise orthogonal polynomial and Cesaro summability are also discussed. The paper may serve as a theoretical basis for a new computational method.

scholarly journals New Characterization for Nonlinear Weighted Best Simultaneous Approximation

2009 ◽  
Vol 2009 ◽  
pp. 1-9
Author(s):  
Xianfa Luo ◽  
Delin Wu ◽  
Jinsu He
Keyword(s):  
Wide Class ◽  
Simultaneous Approximation ◽  
Regular Point ◽  
Linear Spaces ◽  
Characterization Result ◽  
Normed Linear Spaces ◽  
Best Simultaneous Approximation

This paper is concerned with the problem of a wide class of weighted best simultaneous approximation in normed linear spaces, and it establishes a new characterization result for the class of approximation by virtue of the notion of simultaneous regular point.

Marking the Boundaries between the Community, the State and History in the Andes

1990 ◽  
Vol 22 (3) ◽  
pp. 575-594 ◽  
Author(s):  
Sarah A. Radcliffe
Keyword(s):  
Regular Point ◽  
The State ◽  
The Andes ◽  
Peasant Community ◽  
Multiple References

This paper attempts to draw out the significance and meaning of the recorreo [sic] (recorrido) de los linderos (going around the boundaries), also called linderaje ritual in an Andean peasant community. In villages such as Kallarayan which lie in the crop and pastureland regions of Cuzco department, Peru, the recorreo is a regular point in the ritual calendar, occurring as part of the lead-up to Lent.1 The event, which occurs on the Tuesday before Ash Wednesday, contains multiple references to the Peruvian nation, to surrounding haciendas, to local apus (spiritual powers embodied in mountain peaks), and to the community: as such it is a ‘polyvalent’ ritual,2 juxtaposing and inter-mingling symbols and meanings which otherwise are kept separate.

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