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.
We shall construct a generating set of a nonfinitely generated Ga-invariant ring given in Freudenburg's counterexample by making use of an integral sequence which was constructed inductively by Freudenburg.
Based on it the authors establish inhomogeneous discrete Calderón reproducing formulas for spaces of homogeneous type, making use of Calderón-Zygmund operators.
A class of constrained semi-infinite minimax problem is transformed into a simple constrained problem, by means of discretization decomposition and maximum entropy method, making use of surrogate constraint.
In this paper the reaction-diffusion systems and the damped wave systems with non-linear terms of gradient form are studied, and the conditions for making them to be gradient systems are given.
By making use of the 3-D zerotree structure, a simple method for region of interest (ROI) mask generation is put forward.
Sulphuric acid limited the formation of bio-oil more effectively than hydrochloric acid and phosphoric acid.
Extraction of molybdenum(V) as its ferron complex with trioctylamine in chloroform from a sulphuric acid medium
The method is based on the extraction of a Mo(V)-ferron (7-iodo-8-hydroxyquinoline-5-sulphonic acid) complex into trioctylamine-chloroform in a sulphuric acid medium using ascorbic acid as a reductant.
Key parameters (pyrrole, aniline, dopant and sulphuric acid concentrations and deposition potential) influencing the coating's mechanical stability and surface homogeneity were optimised and thermostability of the coating was investigated.
In the method one and three the samples were leached in low concentrated nitric and sulphuric acid.