In this paper, the Lie group analysis method is applied to the geometric average Asian option pricing equation in financial problems. Firstly, the complete Lie symmetry group and infinitesimal generators of this equation are derived. Then the optimal system with one parameter for the Lie symmetry algebra are obtained, which gives the possibility to describe a complete set of invariant solutions...

We have solved completely the problem of the description of quasi-linear hyperbolic differential equations in two independent variables that are invariant under three-parameter Lie groups. The problem of group classification of differential equations is one of the central problems of modern symmetry analysis of differential equations[1]. One of the important classes of hyperbolic equations. The...

The complete symmetry groups of systems of linear second order ordinary differential equations are considered in the context of the simple harmonic oscillator. One finds that in general the representation of the complete symmetry group is not unique and in the particular case of a four-dimensional system there are two distinct complete symmetry groups. The results for general second order linea...

We analyze gauge symmetry enhancements SO(16) → E8 on eight D7-branes and SO(14) × U(1) → E8 on seven D7-branes from open strings. String configurations which we present in this paper are closely related to the ones given by Gaberdiel and Zwiebach. Our construction is based on SO(8)×SO(8) decomposition and its relation to the D8-brane case via T-duality is clearer. Then we study supersymmetric ...

We consider the p-spin spherical spin-glass model in the presence of an external magnetic field as a general example of a mean-field system where a one-step replica symmetry breaking (1-RSB) occurs. In this context we compute the complexity of the Thouless–Anderson– Palmer states, performing a quenched computation. We find what the general connection is between this method and the standard stat...

Any Coxeter group Γ, with string diagram, is the symmetry group of a (possibly infinite) regular polytope P. When Γ is crystallographic, we may reduce its standard real representation modulo an odd prime p, thereby obtaining a finite representation in some orthogonal space over Zp. In many cases, the latter group will be the symmetry group of a finite regular polytope. In this paper, we investi...

Generalizing previous results for orbifolds, in this paper we describe the compactification of Matrix model on an orientifold which is a quotient space R/Γ as a Yang-Mills theory living on a quantum space. The information of the compactification is encoded in the action of the discrete symmetry group Γ on Euclidean space Rd and a projective representation U of Γ. The choice of Hilbert space on ...

Commutative algebra of symmetries is not a sufficient condition for the separation of variables. It is necessary for the solvability of system (2) that operators Yμ must meet additional requirements [2]. Let linear differential equation (1) allow a non-Abelian symmetry group G. We shall now investigate the most efficient way how the non-Abelian symmetry group can be used for the integration of ...

Consider the d-dimensional euclidean space E d. Two main results are presented: First, for any N 2 N, the number of types of periodic equivariant tilings (T ; ?) that have precisely N orbits of (2; 4; 6 : : :)-ags with respect to the symmetry group ?, is nite. Second, for any N 2 N, the number of types of convex, periodic equivariant tilings (T ; ?) that have precisely N orbits of tiles with re...

Algebra Interview 1 The first interview began with Edwards asking “What is mathematics?” By asking follow-up questions as needed, Edwards made sure each student said something about the nature and role of definitions in mathematics. After that introductory discussion, each student was handed the following definition. Binary operations were being studied in class, but the definition of group had...