In the reactions of N,N 0 -bis(2-hydroxyethyl)oxamide (BHEOD) with an excess of ethylene carbonate (EC) and N,N 0 -bis(2-hydroxypropyl)oxamide (BHPOD) with an excess of propylene carbonate (PC), the hydroxyethoxy and hydroxypropoxy derivatives of oxamide (OD) were obtained, respectively, distinguished by an increased thermal stability. First time, these derivatives were used as polyol components to obtain foamed polyurethane plastics with the contribution of 4,4 0 -diisocyanate diphenylmethane (MDI). The rigid polyurethane foams of a slight water uptake, good stability of dimensions, enhanced thermal stability, and compression strength were obtained.
We analyse the exact solution of the eigenproblem for the Heisenberg Hamiltonian of magnetic heptagon, i.e. the ring of N = 7 nodes, each with spin 1/2, within the XXX model with nearest neighbour interactions, from the point of view of finite extensions of the field Q of rationals. We point out, as the main result, that the associated arithmetic structure of these extensions makes natural an introduction of some Galois qubits. They are two-dimensional subspaces of the Hilbert space of the model, which admit a quantum informatic interpretation as elementary memory units for a (hypothetical) computer, based on their distinctive properties with respect to the action of related Galois group for indecomposable factors of the secular determinant.These Galois qubits are nested on the lattice of subfields which involves several minimal fields for determination of eigenstates (the complex Heisenberg field), spectrum (the real Heisenberg field), and Fourier transforms of magnetic configurations (the cyclotomic field, based on the simple 7th root of unity). The structure of the corresponding lattice of Galois groups is presented in terms of Kummer theory, and its physical interpretation is indicated in terms of appropriate permutations of eigenstates, energies, and density matrices.
Exemplary OSID style[J. Milewski et al., Galois actions on the eigenproblem of the Heisenberg heptagon] 2 Kummer theory.
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