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  system
This implies that a system is algebraically integrable (i.e., its eigenvalue problem is explicitly solvable in quadratures) if and only if the differential Galois group is commutative for generic eigenvalues.
      
We apply this criterion of algebraic integrability to two examples: finite-zone potentials and the elliptic Calogero-Moser system.
      
In the second example, we obtain a proof of the Chalyh-Veselov conjecture that the Calogero-Moser system with integer parameter is algebraically integrable, using the results of Felder and Varchenko.
      
The least upper bound for the degrees of elements in a system of generators turns out to be independent of the number of vector variables.
      
We consider 3-parametric polynomialsPμ*(x; q, t, s) which replace theAn-series interpolation Macdonald polynomialsPμ*(x; q, t) for theBCn-type root system.
      
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  the system
In this paper, the random weighting method is applied to the exponential system, and we construct the approximation to the estimates of the system parameters with an accuracy ofo(n-1/2) asn→∞.
      
A system receives shocks at successive random points of discrete time, and each shock causes a positive integer-valued random amount of damage which accumulates on the system one after another.
      
The system is subject to failure and it fails once the total cumulative damage level first exceeds a fixed threshold.
      
Upon failure the system must be replaced by a new and identical one and a cost is incurred.
      
If the system is replaced before failure, a smaller cost is incurred.
      
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  systems
Quantum integrable systems and differential Galois theory
      
This paper is devoted to a systematic study of quantum completely integrable systems (i.e., complete systems of commuting differential operators) from the point of view of algebraic geometry.
      
We investigate the eigenvalue problem for such systems and the correspondingD-module when the eigenvalues are in generic position.
      
We give explicit systems of generators of the algebras of invariant polynomials in arbitrary many vector variables for the classical reflection groups (including the dihedral groups).
      
We show that manifolds which parameterize values of first integrals of integrable finite-dimensional bihamiltonian systems carry a geometric structure which we call aKronecker web.
      
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  system of
The least upper bound for the degrees of elements in a system of generators turns out to be independent of the number of vector variables.
      
Fourier transforms related to a root system of rank 1
      
Explicit bounds on the number of type V variables in a complete system of typical separating invariants are given for the binary polyhedral groups, and this is applied to the invariant theory of binary
      
We extend to general finite groups a well-known relation used for checking the orthogonality of a system of vectors as well as for orthogonalizing a nonorthogonal one.
      
We extend to general finite groups a well-known relation used for checking the orthogonality of a system of vectors as well as for orthogonalizing a nonorthogonal one.
      
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