Simple and double integrals on an algebraic surface

AbstractUp to an orientation-preserving symmetry, photographic images are produced by a central projection of a restricted area in the space into the image plane. To obtain reliable information about physical objects and the environment through the process of recording is the basic problem of photogrammetry. We present a reconstruction process based on distances from the center of projection and incidence relations among the points to be projected. For any triplet of collinear points in the space, we construct a surface of revolution containing the center of the projection. It is a generalized conic that can be represented as an algebraic surface. The rotational symmetry allows us to restrict the investigations to the defining polynomial of the profile curve in the image plane. An equivalent condition for the boundedness is given in terms of the input parameters, and it is shown that the defining polynomial of the profile curve is irreducible.

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A Characterization of Bergman Spaces on the Unit Ball of ℂn. II

Canadian Mathematical Bulletin ◽

10.4153/cmb-2011-047-6 ◽

2012 ◽

Vol 55 (1) ◽

pp. 146-152 ◽

Cited By ~ 5

Author(s):

Songxiao Li ◽

Hasi Wulan ◽

Kehe Zhu

Keyword(s):

Holomorphic Function ◽

Unit Ball ◽

Bergman Space ◽

Bergman Spaces ◽

Weighted Bergman Space ◽

Double Integrals

AbstractIt has been shown that a holomorphic function f in the unit ball of ℂn belongs to the weighted Bergman space , p > n + 1 + α, if and only if the function | f(z) – f(w)|/|1 – 〈z, w〉| is in Lp( × , dvβ × dvβ), where β = (p + α – n – 1)/2 and dvβ(z) = (1 – |z|2)βdv(z). In this paper we consider the range 0 < p < n + 1 + α and show that in this case, f ∈ (i) if and only if the function | f(z) – f(w)|/|1 – hz, wi| is in Lp( × , dvα × dvα), (ii) if and only if the function | f(z)– f(w)|/|z–w| is in Lp( × , dvα × dvα). We think the revealed difference in the weights for the double integrals between the cases 0 < p < n + 1 + α and p > n + 1 + α is particularly interesting.

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The period-index problem for the Brauer group of an algebraic surface

Duke Mathematical Journal ◽

10.1215/s0012-7094-04-12313-9 ◽

2004 ◽

Vol 123 (1) ◽

pp. 71-94 ◽

Cited By ~ 39

Author(s):

A. J. de Jong

Keyword(s):

Algebraic Surface ◽

Brauer Group ◽

Index Problem

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On the Generalized Weighted Integral Inequality for Double Integrals

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/aicu-2014-0008 ◽

2015 ◽

Vol 61 (1) ◽

pp. 169-179 ◽

Cited By ~ 1

Author(s):

Mehmet Zeki Sarikaya

Keyword(s):

Integral Inequality ◽

Independent Variables ◽

Elementary Analysis ◽

Weighted Integral ◽

Function Of Two Variables ◽

Two Independent Variables ◽

Double Integrals

Abstract In this paper, we obtain weighted Montgomery’s identities for function of two variables and apply them to give new generalization weighted integral inequality for double integrals involving functions of two independent variables by using fairly elementary analysis.

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