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 ...

The design and analysis ofradar systems that transmit over oceans or smooth terrain for example, airborne radars that spot distant incoming missiles, or coastal radars that fmd drug smugglers reqUires accurate evaluation of radar propagation over a smooth sphere. Analysis of smooth sphere diffraction is equally important for general radar applications; by combining several approximations, compo...

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...

We present near-IR interferometric measurements of the K1.5 giant Arcturus (α Bootis), obtained at the IOTA interferometer with the FLUOR instrument, in four narrow filters with central wavelengths ranging from 2.03μm to 2.39μm. These observations were expected to allow us to quantify the wavelength dependence of the diameter of a typical K giant. They are compared to predictions from both plan...

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 ...

We discuss a Galerkin approximation scheme for the elliptic partial differential equation −∆u+ ω2u = f on Sn ⊂ Rn+1. Here ∆ is the Laplace-Beltrami operator on Sn, ω is a non-zero constant and f belongs to C2k−2(Sn), where k ≥ n/4 + 1, k is an integer. The shifts of a spherical basis function φ with φ ∈ H τ (Sn) and τ > 2k ≥ n/2 + 2 are used to construct an approximate solution. An H1(Sn)error ...

Early-type galaxies are characterized by many scaling relations. One of them, the so-called fundamental plane is a relatively tight correlation between three variables, and has resisted a clear physical understanding despite many years of intensive research. Here, we show that the correlation between the three variables of the fundamental plane can be the artifact of the effect of another param...