We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension are identified with traces of quantum monodromy matrices for specific integrable systems with non-periodic boundary conditions. Applications to the Azbel-Hofs...

We study complementary information set codes of length tn and dimension n of order t called (t−CIS code for short). Quasi-cyclic and quasi-twisted tCIS codes are enumerated by using their concatenated structure. Asymptotic existence results are derived for one-generator and have co-index n by Artin’s conjecture for quasi cyclic and special case for quasi twisted. This shows that there are infin...

Let H be a finite-dimensional quasi-Hopf algebra. We show for each quotient quasibialgebra Q of H that Q is a quasi-Hopf algebra whose dimension divides the dimension of H.

Using certain ideas connected with the entropy theory, several kinds of dimensions are introduced for arbitrary topological spaces. Their properties are examined, in particular, for normal spaces and quasi-discrete ones. One of the considered dimensions coincides, on these spaces, with the Čech-Lebesgue dimension and the height dimension of posets, respectively.

The exactly and quasi-exactly solvable problems for spin one-half in one dimension on the basis of a hidden dynamical symmetry algebra of Hamiltonian are discussed. We take the supergroup, OSP (2|1), as such a symmetry. A number of exactly solvable examples are considered and their spectrum are evaluated explicitly. Also, a class of quasi-exactly solvable problems on the basis of such a symmetr...

Recall that the quasi-isometry group QI(X) of a metric space X is the set of equivalence classes of quasi-isometries f : X → X, where two quasiisometries f1, f2 are equivalent iff supx d(f1(x), f2(x)) <∞ (here we consider G as a metric space with a word metric). One approach to this question, which has been the most successful one, is to find an ‘optimal’ space X quasi-isometric to G and show t...