Integrable systems are usually given in terms of functions of continuous variables (on R), in terms of functions of discrete variables (on Z), and recently in terms of functions of q-variables (on Kq). We formulate the Gel’fand-Dikii (GD) formalism on time scales by using the delta differentiation operator and find more general integrable nonlinear evolutionary equations. In particular they yie...

The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients of order three. We prove that this difference equation can be solved in general. Consequently we can find an exact solution to the field equations corresponding to a static spherically symmetric gravitational potential in terms of elementary functions. The metric functions, the energy de...

The aim of the present study is to investigate children’s performance in an analogy-making task involving competing perceptual and relational matches in terms of developmental changes in executive functioning. We hypothesize that the selection of the common relational structure requires the inhibition of more salient perceptual features (such as identical shapes or colors). Most of the results ...

whenever (un) ∞ n=0 is a non-degenerate linear recurrence sequence. Mahler’s proof is not effective in the following sense. Given a positive integer m the proof does not yield a number C(m) which is effectively computable in terms of m, such that |un| > m whenever n > C(m). However, Schmidt [31, 32], Allen [1], and Amoroso and Viada [2] have given estimates in terms of t only for the number of ...

Temporomandibular joint (TMJ) disorder (TMD) is a collection of medical and dental conditions affecting the joint and muscles of mastication, as well as contiguous tissue components. This leads to pain and altered oral function and can lead to a poor quality of life. The majority of the population can be affected to some degree. Management of TMD is often simple in the first instance, but may i...

Several algorithms, namely CubeMiner, Trias, and DataPeeler, have been recently proposed to mine closed patterns in ternary relations. We consider here the specific context where a ternary relation denotes the value of a graph adjacency matrix at different timestamps. Then, we discuss the constraint-based extraction of patterns in such dynamic graphs. We formalize the concept of δ-contiguous cl...

We derive some contiguous relations for very well-poised 8<^7 series and use them to construct two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials. We then use these solutions to find explicit representations of two families of associated Askey-Wilson polynomials. We identify the corresponding continued fractions as quotients of tw...

Let Hn be the number of claw-free cubic graphs on 2n labeled nodes. In an earlier paper we characterized claw-free cubic graphs and derived a recurrence relation for Hn. Here

We investigate second order half-linear Euler type difference equations whose coefficients have mean values. We show that these equations are conditionally oscillatory and we explicitly identify the corresponding oscillation constants given by the coefficients. Our results generalize the known ones concerning equations with positive constant, periodic, or (asymptotically) almost periodic coeffi...