Construction of confidence intervals for a variance component corresponding to the random factor in mixed linear models with two variance components is considered. At first, attention is drawn to an approximate confidence interval suggested by El-Bassiouni (1994), which is an extension of the well known Williams-Tukey interval. Though the stated interval has some nice properties, it is not very...

This paper deals with systems of parametric equations over the reals, in the framework of interval constraint programming. As parameters vary within intervals, the solution set of a problem may have a non null volume. In these cases, an inner box (i.e., a box included in the solution set) instead of a single punctual solution is of particular interest, because it gives greater freedom for choos...

The purpose of this paper is to analyze the convergence of interval-type algorithms for solving the generalized fractional program. They are characterized by an interval [LBk, UBk] including A*, and the length of the interval is reduced at each iteration. A closer analysis of the bounds LBk and UBk allows to modify slightly the best known interval-type algorithm NEWMODM accordingly to prove its...

We introduce a generalization of intervals over compact matrix Lie groups. Interval group elements are defined using a midpoint-radius representation. Furthermore, we define the respective group operations and the action of interval group elements on vector spaces. We developed structures and operations are implemented for the special case of orthogonal matrices in the matrix library of the COC...

Recently generalized interval probability was proposed as a new mathematical formalism of imprecise probability. It provides a simplified probabilistic calculus based on its definitions of conditional probability and independence. The Markov property can be described in a form similar to classical probability. In this paper, an expectation-maximization approach is developed to train generalized...

Anyone who has listened to a piece of music and tried to anticipate the next few measures understands that music is full of recognizable patterns. For centuries, theorists have attempted to analyze these patterns in order to better appreciate musical works. Only in the last century, however, has music theory been significantly extended into the world of mathematics. One of the primary figures b...

Modal interval theory is an extension of classical interval theory which provides richer interpretations (including in particular inner and outer approximations of the ranges of real functions). In spite of its promising potential, modal interval theory is not widely used today because of its original and complicated construction. The present paper proposes a new formulation of modal interval t...

The work of interval arithmetic was originally introduced by Dwyer [3] in 1951. The development of interval arithmetic as a formal system and evidence of its value as a computational device was provided by Moore [15] and Moore and Yang [16]. Furthermore, Moore and others [3]; [4]; [10] and [17] have developed applications to differential equations. Chiao in [2] introduced sequence of interval n...

In 1999 in [J. Difference Equ. Appl. 5, 355–377], Noonan and Zeilberger extended the Goulden-Jackson Cluster Method to find generating functions of word factors. Then in 2009 in [Electron. J. Combin. 16(2), RZZ], Kitaev, Liese, Remmel and Sagan found generating functions for word embeddings and proved several results on Wilf-equivalence in that setting. In this article, the authors focus on gen...