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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.
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We apply this criterion of algebraic integrability to two examples: finite-zone potentials and the elliptic Calogero-Moser system.
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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.
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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.
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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 least upper bound for the degrees of elements in a system of generators turns out to be independent of the number of vector variables.
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Fourier transforms related to a root system of rank 1
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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
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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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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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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→∞.
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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.
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The system is subject to failure and it fails once the total cumulative damage level first exceeds a fixed threshold.
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Upon failure the system must be replaced by a new and identical one and a cost is incurred.
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If the system is replaced before failure, a smaller cost is incurred.
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The authors used testimonies of students on the dominant motives of joining a higher education institution as the behavioral model that prefers a high probability of the attainment of a goal or its subjective value.
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They compared the features of the motivation sphere related to the choice of profession with the psychophysiological data of 38 students of a sports higher education institution.
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The authors analyzed physical development and training, nonspecific immunity, free-radical oxidation, hemodynamic indices, and autonomic regulation in pupils from the first to ninth grade levels of a new educational institution (gymnasium).
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The chief institution was the Institute of Mathematics, Academy of Sciences of the Ukrainian SSR.
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The institution of the authors has developed the so-called 3MA-approach (micromagnetic, multiple-parameter, microstructure, and stress analysis) in the last decade.
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