Michael Coons

Factor structure and psychometric properties of the Pain Anxiety Symptoms Scale-20 in a community physiotherapy clinic sample.

The PASS‐20 was developed to assess pain‐related anxiety among a variety of pain populations. This measure was constructed by extracting 20 items from its 40‐item parent measure (PASS). Initial studies of the PASS‐20 suggest that the psychometric properties have been preserved. The purpose of the present study extended this research and explored the factor structure of the PASS‐20, and its reliability and validity in a sample of pain patients receiving treatment in a community physiotherapy clinic. Patients with current pain (n=201) were asked to complete a battery of self‐report measures related to the experience of pain on two separate occasions (3‐month interval). Results of principal components analyses suggested that a 4‐factor solution representing fear of pain, escape‐avoidance, physiological symptoms, and cognitive symptoms of anxiety provided the best fit to these data. Results also showed that the total and subscale scores of the PASS‐20 have good reliability (internal consistency, test—retest) and validity (construct) correlating greater with other conceptually similar measures than distinct constructs. These results suggest that this measure has good utility for both clinical and research applications. Directions for future evaluation are also discussed.

TRANSCENDENCE OF POWER SERIES FOR SOME NUMBER THEORETIC FUNCTIONS

We give a new proof of Fatous theorem: if an algebraic function has a power series expansion with bounded integer coefficients, then it must be a rational function. This result is applied to show that for any non-trivial completely multiplicative function from N to {-1,1}, the series Σ ∞ n=1 f(n)z n is transcendental over Z(z); in particular, Σ ∞ n=1 λ(n)z n is transcendental, where λ is Liouvilles function. The transcendence of Σ ∞ n=1 μ(n)z n is also proved.

Completely multiplicative functions taking values in (-1,1)

Define the Liouville function for A, a subset of the primes P, by λ A (n) = (-1) ΩA(n) , where Ω A (n) is the number of prime factors of n coming from A counting multiplicity. For the traditional Liouville function, A is the set of all primes. Denote L A (x) := Σ n ≤λ A (n) and R A := l i m L A (n)/n. n→∞ n 0) and λ 3 (3) = 1). For the partial sums of character—like functions we give exact values and asymptotics; in particular, we prove the following theorem. Theorem. If p is an odd prime, then max |∑ λ p (k)|≍ logx. n≤x k≤x This result is related to a question of Erdős concerning the existence of bounds for number-theoretic functions. Within the course of discussion, the ratio φ(n)/σ(n) is considered.

The minimal growth of a \(k\)-regular sequence

We determine a lower gap property for the growth of an unbounded \(\mathbb{Z}\)-valued \(k\)-regular sequence. In particular, if \(f:\mathbb{N}\to\mathbb{Z}\) is an unbounded \(k\)-regular sequence, we show that there is a constant \(c>0\) such that \(|f(n)|>c\log n\) infinitely often. We end our paper by answering a question of Borwein, Choi, and Coons on the sums of completely multiplicative automatic functions. DOI: 10.1017/S0004972714000197

THE TRANSCENDENCE OF SERIES RELATED TO STERN'S DIATOMIC SEQUENCE

We prove various transcendence results regarding the Stern sequence and related functions; in particular, we prove that the generating function of the Stern sequence is transcendental. Transcendence results are also proven for the generating function of the Stern polynomials and for power series whose coefficients arise from some special subsequences of Sterns sequence.

Diophantine approximation of Mahler numbers

Suppose that

Transcendence of generating functions whose coefficients are multiplicative

F(x)\in\mathbb{Z}[[x]]

Regular Sequences and the Joint Spectral Radius

is a Mahler function and that

On the residue class distribution of the number of prime divisors of an integer

1/b

On Some Conjectures Concerning Stern's Sequence and Its Twist

is in the radius of convergence of