We decompose the problem of the optimal multi-degree reduction of Bézier curves with corners constraint into two simpler subproblems, namely making high order interpolations at the two endpoints without degree reduction, and doing optimal degree reduction without making high order interpolations at the two endpoints. Further, we convert the second subproblem into multi-degree reduction of Jacob...

In the analysis of the structure of totally categorical first order theories, the second author showed that certain combinatorial counting functions play an important role. Those functions are invariants of the structures and are always polynomials in one or many variables, depending on the number of independent dimensions of the theory in question. The first author introduced the notion of gra...

The method of symmetric polynomials (MSP) was developed for computation analytical functions of matrices, in particular, integer powers of matrix. MSP does not require for its realization finding eigenvalues of the matrix. A new type of recurrence relations for symmetric polynomials of order n is found. Algorithm for the numerical calculation of high powers of the matrix is proposed.This comput...

In this paper, the Fourier series expansion of Tangent polynomials higher order is derived using Cauchy residue theorem. Moreover, some variations higher-order are defined by mixing concept with that Bernoulli and Genocchi polynomials, Tangent–Bernoulli Tangent–Genocchi polynomials. Furthermore, expansions these also