We prove that, for any quantum evolution in`2 (Z D), there exist arbitrarily long time scales on which the qth moment of the position operator increases at least as fast as a power of time given by q=D times the packing dimension of the spectral measure. Packing dimensions of measures and their connections to scaling exponents and box-counting dimensions are also discussed.

We give asymptotic expressions for the number of words containing a given number of occurrences of a pattern for two families of patterns with two parameters each. One is the family of classical patterns in the form 22 · · · 212 · · · 22 and the other is a family of partially ordered patterns. The asymptotic expressions are in terms of the number of solutions to an equation, and for one subfami...

Swanson was partially motivated by the analogous question for “Frobenius powers”, which has important applications to the theory of tight closure (the so-called “localization problem;” see [HH, Section 4]). Suppose now that R has prime characteristic p > 0 and q is a power of p. The Frobenius power I [q] of an ideal I is the ideal generated by all the qth powers of the elements (equivalently, t...

We discuss the converse of a theorem of Potter stating that if the matrix equation AB = ωBA is satisfied with ω a primitive qth root of unity, then Aq+Bq = (A+B)q. We show that both conditions have to be modified to get a converse statement and we present a characterization when the converse holds for these modified conditions and q = 3 and a conjecture for the general case. We also present som...

This paper proposes that cognitive humour can be modelled using the mathematical framework of quantum theory, suggesting that a Quantum Theory of Humour (QTH) is a viable approach. We begin with brief overviews of both research on humour, and the generalized quantum framework. We show how the bisociation of incongruous frames or word meanings in jokes can be modelled as a linear superposition o...

The aim of this in vitro study was to evaluate the influence of light-curing units and different sample thicknesses on the microhardness of a composite resin. Composite resin specimens were randomly prepared and assigned to nine experimental groups (n = 5): considering three light-curing units (conventional quartz tungsten halogen [QTH]: 550 mW/cm(2) - 20 s; high irradiance QTH: 1160 mW/cm(2) -...

In linear regression, an important role is played by the least quantile of squares (LQS) estimate, which involves the minimization of the qth smallest squared residual for a given set of data. This function is nondifferentiable and nonconvex and may have a large number of local minima. This paper is mainly concerned with the efficient calculation of the global solution, and some different appro...

This paper provides a solution to the fundamental linear fractional order differential equation, namely, cdtqx(t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the induct...

and Applied Analysis 3 the autoregressive coefficient estimator. For the nonstationary of continuous-valued time series, we often need to examine whether the characteristic polynomial of AR(1) process has a unit root. Thus, we want to see if we can find the limiting distribution of the autoregressive coefficient estimator. Let us present a result that is needed later on. Lemma 3. Suppose that Z...