We present powerful recurrence relations of the second and third kind which hold in 7-dimensional Einstein's generalized Riemannian manifold X 7. All considerations in this paper are restricted to the first and second classes of X 7 only since the case of the third class, the simplest case, was already studied by many authors. Einstein's connection in a generalized Riemannian manifold X n has b...

We present an algorithm for finding a system of recurrence relations for the number of k-ary words of length n that satisfy a certain set of conditions. A rewriting of these relations automatically gives a system of functional equations satisfied by the multivariate generating function that counts k-ary words by their length and the indices of the corresponding recurrence relations. We propose ...

In this note we give an explanation for two phenomena mentioned in the concluding remarks of " The matching polynomial of a polygraph " by Babic et al. The following results are obtained: (1) Although three matrices for given polygraphs defined in the above article in general have different orders, they determine the same recurrence relations for the matching polynomial of these polygraphs. (2)...

We study a modified Newton’s method with fifth-order convergence for nonlinear equations in Banach spaces. Wemake an attempt to establish the semilocal convergence of this method by using recurrence relations. The recurrence relations for the method are derived, and then an existenceuniqueness theorem is given to establish the R-order of the method to be five and a priori error bounds. Finally,...

We obtain a new integral formula for solutions of the rational quantum Knizhnik-Zamolodchikov equation associated with Lie algebra slN at level zero. Our formula contains the integral representation of form factors of SU(N) invariant Thirring model constructed by F. Smirnov. We write down recurrence relations arising from the construction of the form factors. We check that the recurrence relati...