Every multivariate polynomial p(x), x = (x1, . . . , xn) ∈ [0, 1], is enclosed in the interval given by the smallest and the greatest of its coefficients in the Tensorial Bernstein Basis (TBB). Knowing that the total number of these TBB coefficients is exponential with respect to the number of variables n, ∏n i=1(1 + di), even if all partial degrees di equal 1, a combinatorial problem arises: i...

When the coefficients of a linear system are known with interval uncertainty, instead of a single solution, we have the whole set of possible solutions – known as the united set. It is known that in general, computing this united set is NP-hard. There exist several proofs of this NPhardness; all known proofs use examples with intervals of different width – corresponding to different accuracy in...

Mokken’s scalability coefficients take values on the interval (−∞, 1]. The sampling distribution of is skewed near boundary, so Wald-based confidence intervals and significance tests may be biased. We introduce a transformation their standard errors, which can used to construct range-preserving tests. demonstrated that for away from properties this method are similar method, but outperforms whe...

This paper is a continuation of Part I where the authors treated the Fourier analysis of chaotic time series generated by a chaotic interval map. Here, we perform multiresolution analysis by using wavelet coefficients and characterize some necessary and sufficient conditions for the occurrence of chaos by the exponential growth with respect to the number of iterations n of certain sums of the w...

We develop a technique for computing tolerable solution set for interval linear systems with convex polyhedral ties upon its coefficients. The tolerable solution set in the above problem is proved to be the intersection of finite number of hyperstripes, i.e. a solution set to a finite system of two-sided nonstrict linear inequalities. For some specific ties on the coefficients, we propose simpl...

A procedure for evaluation of convergent and discriminant validity coefficients is outlined. The method yields interval estimates of these coefficients in a construct validation study conducted via the multitrait-multimethod approach, as well as permits examination of their population relationships. The procedure is readily employed in behavioral research using the increasingly popular latent v...

In the common Fourier regression model we investigate the optimal design problem for estimating pairs of the coefficients, where the explanatory variable varies in the interval [−π, π]. L-optimal designs are considered and for many important cases L-optimal designs can be found explicitly, where the complexity of the solution depends on the degree of the trigonometric regression model and the o...

We consider the problem of generating the recursion coefficients of orthogonal polynomials for a given weight function. The weight function is assumed to be the weighted sum of weight functions, each supported on its own interval. Some of these intervals may coincide, overlap or are contiguous. We discuss three algorithms. Two of them are based on modified moments, whereas the other is based on...

In this paper, we investigate the polynomial integrand of an integral formula that yields the expected length of the minimal spanning tree of a graph whose edges are uniformly distributed over the interval [0, 1]. In particular, we derive a general formula for the coefficients of the polynomial and use it to express the first few coefficients in terms of the structure of the underlying graph; e...

We prove Bernstein type inequalities for algebraic polynomials on the finite interval I := [−1, 1] and for trigonometric polynomials on R when the roots of the polynomials are outside of a certain domain of the complex plane. The case of real vs. complex coefficients are handled separately. In case of trigonometric polynomials with real coefficients and root restriction, the Lpsituation will al...