Group invariant classification of separable Hamiltonian systems in the Euclidean plane and the O(4)-symmetric Yang–Mills theories of Yatsun

2002 ◽  
Vol 43 (3) ◽  
pp. 1422-1440 ◽  
Author(s):  
Raymond G. McLenaghan ◽  
Roman G. Smirnov ◽  
Dennis The
Keyword(s):  
Hamiltonian Systems ◽  
Euclidean Plane ◽  
Yang Mills ◽  
Group Invariant

scholarly journals Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Tanki Motsepa ◽  
Chaudry Masood Khalique ◽  
Motlatsi Molati
Keyword(s):  
Option Pricing ◽  
Three Dimensional ◽  
Mathematical Finance ◽  
Group Classification ◽  
Lie Point Symmetries ◽  
Group Invariant ◽  
Black Scholes ◽  
Group Invariant Solutions ◽  
Bond Option

We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.

scholarly journals Doubly Semiequivelar Maps on Torus and Klein Bottle

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Anand K. Tiwari ◽  
Amit Tripathi ◽  
Yogendra Singh ◽  
Punam Gupta
Keyword(s):  
Symmetry Group ◽  
Euclidean Plane ◽  
Klein Bottle ◽  
Universal Cover ◽  
Regular Polygons

A tiling of the Euclidean plane, by regular polygons, is called 2-uniform tiling if it has two orbits of vertices under the action of its symmetry group. There are 20 distinct 2-uniform tilings of the plane. Plane being the universal cover of torus and Klein bottle, it is natural to ask about the exploration of maps on these two surfaces corresponding to the 2-uniform tilings. We call such maps as doubly semiequivelar maps. In the present study, we compute and classify (up to isomorphism) doubly semiequivelar maps on torus and Klein bottle. This classification of semiequivelar maps is useful in classifying a category of symmetrical maps which have two orbits of vertices, named as 2-uniform maps.

GARCH in spinor field

2019 ◽  
Vol 16 (07) ◽  
pp. 1950099
Author(s):  
Richard Pincak ◽  
Kabin Kanjamapornkul
Keyword(s):  
Time Series ◽  
Gauge Group ◽  
Spinor Field ◽  
Mirror Symmetry ◽  
Euclidean Plane ◽  
Financial Time Series ◽  
Equivalent Form ◽  
Yang Mills ◽  
Noise Trader ◽  
Financial Time

We extend generalized autoregressive conditional heteroscedastic (GARCH) errors in the Euclidean plane of the scalar field to the tensor field and to the spinor field [Formula: see text], the so-called spinor garch, S-GARCH. We use the model of S-GARCH to explain the stylized fact in financial time series, the so-called volatility cluster, by using hyperbolic coordinate with induced complex lag of delay time scale in mirror symmetry concept. As the result of this theory, we obtain an equivalent form of Yang–Mills equation for financial time series as the interaction between the behavior of traders, the so-called, fundamentalist, chatlist and noise trader, by using volatility in spinor field with invariant of the gauge group [Formula: see text], the so-called modeling of the financial market in icosahedral supersymmetry gauge group.

Classification of the Yang-Mills anomalies in even and odd dimension

1984 ◽  
Vol 147 (6) ◽  
pp. 430-434 ◽  
Author(s):  
Jean Theirry-Mieg
Keyword(s):  
Yang Mills
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