scholarly journals Projective Cross-ratio on Hypercomplex Numbers

2012 ◽  
Vol 23 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Sky Brewer
Keyword(s):  
Cross Ratio ◽  
Hypercomplex Numbers

Projector calibration based on cross ratio invariance

2020 ◽  
Vol 13 (6) ◽  
pp. 1-9
Author(s):  
YANG Jian-bai ◽  
◽  
ZHAO Jian ◽  
SUN Qiang ◽  
Keyword(s):  
Cross Ratio ◽  
Projector Calibration

Suggested Notation for Ratios and Cross-Ratios

1912 ◽  
Vol 6 (98) ◽  
pp. 294-296
Author(s):  
Alfred Lodge
Keyword(s):  
Cross Ratio ◽  
The Cross

I wish to call attention to the value, for some purposes, ot the notation for the ratio ; and for the cross-ratio . For instance: in Menelaus’ theorem for the property of a transversal meeting the sides of a triangle ABC in the points P, Q, R, the first mentioned notation makes the property shine out very clearly The equation in the form is , which conspicuously separates the points on the transversal from the angular points of the triangle.

scholarly journals Time-dependent cross ratio estimation for bivariate failure times

Biometrika ◽  
2011 ◽  
Vol 98 (2) ◽  
pp. 341-354 ◽  
Author(s):  
T. Hu ◽  
B. Nan ◽  
X. Lin ◽  
J. M. Robins
Keyword(s):  
Cross Ratio ◽  
Time Dependent ◽  
Ratio Estimation ◽  
Failure Times

Equivariant Forms: Structure and Geometry

2013 ◽  
Vol 56 (3) ◽  
pp. 520-533 ◽  
Author(s):  
Abdelkrim Elbasraoui ◽  
Abdellah Sebbar
Keyword(s):  
Riemann Surface ◽  
Line Bundle ◽  
Modular Forms ◽  
Differential Forms ◽  
Cross Ratio ◽  
Canonical Line Bundle ◽  
The Cross

Abstract.In this paper we study the notion of equivariant forms introduced in the authors' previous works. In particular, we completely classify all the equivariant forms for a subgroup of SL2(ℤ) by means of the cross-ratio, weight 2 modular forms, quasimodular forms, as well as differential forms of a Riemann surface and sections of a canonical line bundle.

scholarly journals Hypothesis of the Hidden Multiverse Explains Dark Matter and Dark Energy

2017 ◽  
Vol 9 (2) ◽  
pp. 30 ◽  
Author(s):  
Alexander Alexandrovich Antonov
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Special Theory ◽  
Physical Reality ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Hypercomplex Numbers ◽  
Distant Future ◽  
Parallel Universes ◽  
Quaternion Structure

There are currently a large number of Multiverse hypotheses, which are, however, non-verifiable, i.e. they can be neither confirmed nor refuted experimentally even in the distant future. In contrast, the hypothesis of the hidden Multiverse considered in the article is verifiable and therefore has a right to be called a theory. The theory uses the principle of physical reality of imaginary numbers discovered 500 years ago, including complex and hypercomplex numbers, as fundamental and proved by the author theoretically and experimentally. This principle has allowed revealing a number of serious mistakes in the special theory of relativity. An adjusted version of the special theory of relativity has been proposed and the theory of the hidden Multiverse has been developed on its basis. The Multiverse has been referred to as hidden, because parallel universes it contains are mutually invisible. The nature of their invisibility is explained in the article. It is shown that dark matter and dark energy are other universes of the hidden Multiverse apart from ours. Analysis of data from WMAP and Planck spacecrafts has shown that the hidden Multiverse has quaternion structure comprising four pairs of universes and antiverses (i.e., four pairs of matter and antimatter).

Sign in / Sign up

Export Citation Format

Share Document