sigma11-045. 428KB Jun 04 2011 12:10:52 AM
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![Figure 1.This diagram represents the degeneration diagram for the surfaces of initial conditions ofmultiplicative type [23].](https://thumb-ap.123doks.com/thumbv2/123dok/914158.900807/6.612.112.515.455.533/figure-diagram-represents-degeneration-diagram-surfaces-conditions-ofmultiplicative.webp)
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Then we can calculate the correlation functions of arbitrary element of density matrix using these algebraic relations, although the calculation become complicated... Unknowns are
It was found in [ 7 ] that the correlation functions of the eight-vertex model can be obtained by using the free field realization of the vertex operators in the eight-vertex SOS
The first is to give an orbital description of the decomposition of τ into irreducibles, in the case when G is a connected, simply connected one-parameter metabelian nilpotent
ˇ Cap generalized to arbitrary parabolic geometries a bijective correspondence between conformal vector fields and adjoint tractors (sections of the associated bundle to the
The parameter differentiation formulae given in [ 5 ] are derivatives for associated Legendre functions of the first and second kind with respect to the degree, evaluated
The types of anisotropic evaporation coefficient are found for which the evaporation-condensation evolution does or does not have solutions that are analogous to the basic solutions
In the three-dimensional flat space, a classical Hamiltonian, which has five functionally independent integrals of motion, including the Hamiltonian, is characterized
We have presented new structured canonical forms for matrices that are symmetric or skew-symmetric with respect to the main diagonal as well as the anti-diagonal, and
