Three-factor interaction for the two-level, three-level, and four-level factorial designs was studied. A new technique and formula based on the coefficients of orthogonal polynomial contrast were proposed to calculate the effect of the three-factor interaction The results show that the proposed technique was in agreement with the least squares method. The advantages of the new technique are 1) ...

The method of orthogonal polynomials is a powerful technique for the non perturbative integration of matrix models over one [1] or more matrices [2] in particular with even potential, i.e. with vertices with an even number of legs. Indeed, with even potential, the calculation simplifies both because the integrals are well defined and, as we shall see, the number of equations needed to solve the...

In this paper we present the theory of oscillation numbers and dual for continuous Lagrangian paths in $${\mathbb {R}}^{2n}$$ . Our main results include a connection given path with Lidskii angles special symplectic orthogonal matrix. We also Sturmian type comparison separation theorems difference two paths. These results, as well definition number itself, are based on comparative index (Elysee...

This paper contains a computational analysis and comparison of various representations of a general rigid body spatial screw displacement. Point transformations and line transformations are treated separately. In the context of point transformations, only a brief summary of the known techniques (i.e., homogeneous transforms and quaternion/vector pairs) and their computational behavior is given....

For a Type T ∈ {I, II, III, IV} and length N where there exists no self-dual Type T code of length N , upper bounds on the minimum weight of the dual code of a self-orthogonal Type T code of length N are given, allowing the notion of dual extremal codes. It is proven that the Hamming weight enumerator of a dual extremal maximal self-orthogonal code of a given length is unique.

The Pfaff lattice was introduced by us in the context of a Lie algebra splitting of gl (∞) into sp (∞) and an algebra of lower-triangular matrices. The Pfaff lattice is equivalent to a set of bilinear identities for the wave functions, which yield the existence of a sequence of “τ -functions”. The latter satisfy their own set of bilinear identities, which moreover characterize them. In the semi...

Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We investigate new orthogonal polynomials by adding to the Jacobi matrix r new rows and columns, so that the original Jacobi matrix is shifted downward. The r new...