Interlacing of zeros of orthogonal polynomials under modification of the measure

We investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure dμ (x), supported on the interval (a, b) and the other with respect to the measure |x -c|τ|x -d|γdμ (x), where c and d are outside (a, b) We prove that the zeros of these polynomials, if they are of equal or consecutive degrees, interlace when either 0 < τ, γ ≤ 1 or γ = 0 and 0 < τ ≤ 2. This result is inspired by an open question of Richard Askey and it generalizes recent results on some families of orthogonal polynomials. Moreover, we obtain further statements on interlacing of zeros of specific orthogonal polynomials, such as the Askey-Wilson ones. © 2013 Elsevier Inc.

Problems of optimal transportation on the circle and their mechanical applications

We consider a mechanical problem concerning a 2D axisymmetric body moving forward on the plane and making slow turns of fixed magnitude about its axis of symmetry. The body moves through a medium of non-interacting particles at rest, and collisions of particles with the body's boundary are perfectly elastic (billiard-like). The body has a blunt nose: a line segment orthogonal to the symmetry axis. It is required to make small cavities with special shape on the nose so as to minimize its aerodynamic resistance. This problem of optimizing the shape of the cavities amounts to a special case of the optimal mass transfer problem on the circle with the transportation cost being the squared Euclidean distance. We find the exact solution for this problem when the amplitude of rotation is smaller than a fixed critical value, and give a numerical solution otherwise. As a by-product, we get explicit description of the solution for a class of optimal transfer problems on the circle.

Investigating the impact of a leadership development program for nurse unit managers on the satisfaction of nursing staff

Background and significance: Nurses' job dissatisfaction is associated with negative nursing and patient outcomes. One of the most powerful reasons for nurses to stay in an organisation is satisfaction with leadership. However, nurses are frequently promoted to leadership positions without appropriate preparation for the role. Although a number of leadership programs have been described, none have been tested for effectiveness, using a randomised control trial methodology. Aims: The aims of this research were to develop an evidence based leadership program and to test its effectiveness on nurse unit managers' (NUMs') and nursing staff's (NS's) job satisfaction, and on the leader behaviour scores of nurse unit managers. Methods: First, the study used a comprehensive literature review to examine the evidence on job satisfaction, leadership and front-line manager competencies. From this evidence a summary of leadership practices was developed to construct a two component leadership model. The components of this model were then combined with the evidence distilled from previous leadership development programs to develop a Leadership Development Program (LDP). This evidence integrated the program's design, its contents, teaching strategies and learning environment. Central to the LDP were the evidence-based leadership practices associated with increasing nurses' job satisfaction. A randomised controlled trial (RCT) design was employed for this research to test the effectiveness of the LDP. A RCT is one of the most powerful tools of research and the use of this method makes this study unique, as a RCT has never been used previously to evaluate any leadership program for front-line nurse managers. Thirty-nine consenting nurse unit managers from a large tertiary hospital were randomly allocated to receive either the leadership program or only the program's written information about leadership. Demographic baseline data were collected from participants in the NUM groups and the nursing staff who reported to them. Validated questionnaires measuring job satisfaction and leader behaviours were administered at baseline, at three months after the commencement of the intervention and at six months after the commencement of the intervention, to the nurse unit managers and to the NS. Independent and paired t-tests were used to analyse continuous outcome variables and Chi Square tests were used for categorical data. Results: The study found that the nurse unit managers' overall job satisfaction score was higher at 3-months (p = 0.016) and at 6-months p = 0.027) post commencement of the intervention in the intervention group compared with the control group. Similarly, at 3-months testing, mean scores in the intervention group were higher in five of the six "positive" sub-categories of the leader behaviour scale when compared to the control group. There was a significant difference in one sub-category; effectiveness, p = 0.015. No differences were observed in leadership behaviour scores between groups by 6-months post commencement of the intervention. Over time, at three month and six month testing there were significant increases in four transformational leader behaviour scores and in one positive transactional leader behaviour scores in the intervention group. Over time at 3-month testing, there were significant increases in the three leader behaviour outcome scores, however at 6-months testing; only one of these leader behaviour outcome scores remained significantly increased. Job satisfaction scores were not significantly increased between the NS groups at three months and at six months post commencement of the intervention. However, over time within the intervention group at 6-month testing there was a significant increase in job satisfaction scores of NS. There were no significant increases in NUM leader behaviour scores in the intervention group, as rated by the nursing staff who reported to them. Over time, at 3-month testing, NS rated nurse unit managers' leader behaviour scores significantly lower in two leader behaviours and two leader behaviour outcome scores. At 6-month testing, over time, one leader behaviour score was rated significantly lower and the nontransactional leader behaviour was rated significantly higher. Discussion: The study represents the first attempt to test the effectiveness of a leadership development program (LDP) for nurse unit managers using a RCT. The program's design, contents, teaching strategies and learning environment were based on a summary of the literature. The overall improvement in role satisfaction was sustained for at least 6-months post intervention. The study's results may reflect the program's evidence-based approach to developing the LDP, which increased the nurse unit managers' confidence in their role and thereby their job satisfaction. Two other factors possibly contributed to nurse unit managers' increased job satisfaction scores. These are: the program's teaching strategies, which included the involvement of the executive nursing team of the hospital, and the fact that the LDP provided recognition of the importance of the NUM role within the hospital. Consequently, participating in the program may have led to nurse unit managers feeling valued and rewarded for their service; hence more satisfied. Leadership behaviours remaining unchanged between groups at the 6 months data collection time may relate to the LDP needing to be conducted for a longer time period. This is suggested because within the intervention group, over time, at 3 and 6 months there were significant increases in self-reported leader behaviours. The lack of significant changes in leader behaviour scores between groups may equally signify that leader behaviours require different interventions to achieve change. Nursing staff results suggest that the LDP's design needs to consider involving NS in the program's aims and progress from the outset. It is also possible that by including regular feedback from NS to the nurse unit managers during the LDP that NS's job satisfaction and their perception of nurse unit managers' leader behaviours may alter. Conclusion/Implications: This study highlights the value of providing an evidence-based leadership program to nurse unit managers to increase their job satisfaction. The evidence based leadership program increased job satisfaction but its effect on leadership behaviour was only seen over time. Further research is required to test interventions which attempt to change leader behaviours. Also further research on NS' job satisfaction is required to test the indirect effects of LDP on NS whose nurse unit managers participate in LDPs.

Pilot study evaluating the effect of massage therapy on stress, anxiety and aggression in a young adult psychiatric inpatient unit

Objective: The aim of the present pilot study was to examine the effectiveness of a relaxation massage therapy programme in reducing stress, anxiety and aggression on a young adult psychiatric inpatient unit. Method: This was a prospective, non-randomized intervention study comparing treatment as usual (TAU) with TAU plus massage therapy intervention (MT) over consecutive 7 week blocks (May–August 2006). MT consisted of a 20 min massage therapy session offered daily to patients during their period of hospitalization. The Kennedy Nurses’ Observational Scale for Inpatient Evaluation (NOSIE), the Symptom Checklist-90–Revised (SCL-90-R), the State–Trait Anxiety Inventory (STAI) and stress hormone (saliva cortisol) levels were used to measure patient outcomes at admission and discharge from the unit. The Staff Observation Aggression Scale–Revised (SOAS-R) was used to monitor the frequency and severity of aggressive incidents on the unit. Results: There was a significant reduction in self-reported anxiety (p < 0.001), resting heart rate (p < 0.05) and cortisol levels (p < 0.05) immediately following the initial and final massage therapy sessions. Significant improvements in hostility (p = 0.007) and depression scores (p < 0.001) on the SCL-90-R were observed in both treatment groups. There was no group×time interaction on any of the measures. Poor reliability of staff-reported incidents on the SOAS-R limited the validity of results in this domain. Conclusions: Massage therapy had immediate beneficial effects on anxiety-related measures and may be a useful de-escalating tool for reducing stress and anxiety in acutely hospitalized psychiatric patients. Study limitations preclude any definite conclusions on the effect of massage therapy on aggressive incidents in an acute psychiatric setting. Randomized controlled trials are warranted.

On the maximal rate of non-square STBCs from complex orthogonal designs

A Linear Processing Complex Orthogonal Design (LPCOD) is a p x n matrix epsilon, (p >= n) in k complex indeterminates x(1), x(2),..., x(k) such that (i) the entries of epsilon are complex linear combinations of 0, +/- x(i), i = 1,..., k and their conjugates, (ii) epsilon(H)epsilon = D, where epsilon(H) is the Hermitian (conjugate transpose) of epsilon and D is a diagonal matrix with the (i, i)-th diagonal element of the form l(1)((i))vertical bar x(1)vertical bar(2) + l(2)((i))vertical bar x(2)vertical bar(2)+...+ l(k)((i))vertical bar x(k)vertical bar(2) where l(j)((i)), i = 1, 2,..., n, j = 1, 2,...,k are strictly positive real numbers and the condition l(1)((i)) = l(2)((i)) = ... = l(k)((i)), called the equal-weights condition, holds for all values of i. For square designs it is known. that whenever a LPCOD exists without the equal-weights condition satisfied then there exists another LPCOD with identical parameters with l(1)((i)) = l(2)((i)) = ... = l(k)((i)) = 1. This implies that the maximum possible rate for square LPCODs without the equal-weights condition is the same as that or square LPCODs with equal-weights condition. In this paper, this result is extended to a subclass of non-square LPCODs. It is shown that, a set of sufficient conditions is identified such that whenever a non-square (p > n) LPCOD satisfies these sufficient conditions and do not satisfy the equal-weights condition, then there exists another LPCOD with the same parameters n, k and p in the same complex indeterminates with l(1)((i)) = l(2)((i)) = ... = l(k)((i)) = 1.

On the maximal rate of (n+1) x n and (n+2) x n complex orthogonal designs

For p x n complex orthogonal designs in k variables, where p is the number of channels uses and n is the number of transmit antennas, the maximal rate L of the design is asymptotically half as n increases. But, for such maximal rate codes, the decoding delay p increases exponentially. To control the delay, if we put the restriction that p = n, i.e., consider only the square designs, then, the rate decreases exponentially as n increases. This necessitates the study of the maximal rate of the designs with restrictions of the form p = n+1, p = n+2, p = n+3 etc. In this paper, we study the maximal rate of complex orthogonal designs with the restrictions p = n+1 and p = n+2. We derive upper and lower bounds for the maximal rate for p = n+1 and p = n+2. Also for the case of p = n+1, we show that if the orthogonal design admit only the variables, their negatives and multiples of these by root-1 and zeros as the entries of the matrix (other complex linear combinations are not allowed), then the maximal rate always equals the lower bound.

Stabilization of Collective Motion in Synchronized, Balanced and Splay Phase Arrangements on a Desired Circle

This paper proposes a design methodology to stabilize collective circular motion of a group of N-identical agents moving at unit speed around individual circles of different radii and different centers. The collective circular motion studied in this paper is characterized by the clockwise rotation of all agents around a common circle of desired radius as well as center, which is fixed. Our interest is to achieve those collective circular motions in which the phases of the agents are arranged either in synchronized, in balanced or in splay formation. In synchronized formation, the agents and their centroid move in a common direction while in balanced formation, the movement of the agents ensures a fixed location of the centroid. The splay state is a special case of balanced formation, in which the phases are separated by multiples of 2 pi/N. We derive the feedback controls and prove the asymptotic stability of the desired collective circular motion by using Lyapunov theory and the LaSalle's Invariance principle.

Optimization on the orthogonal group for independent component analysis

This paper derives a new algorithm that performs independent component analysis (ICA) by optimizing the contrast function of the RADICAL algorithm. The core idea of the proposed optimization method is to combine the global search of a good initial condition with a gradient-descent algorithm. This new ICA algorithm performs faster than the RADICAL algorithm (based on Jacobi rotations) while still preserving, and even enhancing, the strong robustness properties that result from its contrast. © Springer-Verlag Berlin Heidelberg 2007.

Effect of copolymerized ethylene unit on the crystallization behavior of poly(propylene-co-ethylene)s

The crystallization behavior of two kinds of commercial poly(propylene-co-ethylene)s (PPE1, PPE2) with similar average molecular weight and molecular weight distribution, isotacticity and copolymerized ethylene unit content and their fractions was investigated by differential scanning calorimetry (DSC), transmission electron microscopy (TEM) and polarized optical microscopy (POM) techniques. The results indicate that the PPE1 isothermally crystallized films possess thicker and less cross-hatched lamellar structure than those of the PPE2. As for the fractionated samples, the thin films of low temperature (less than or equal to 90 degreesC) fractions (PPE1-80, PPE2-80) of both PPE1 and PPE2 exhibit similar crystallization behavior, while for the high temperature ( greater than or equal to 95 degreesC) fractions (PPE1-108, PPE2-108), the crystalline morphology has marked differences. Compared with PPE2-108, the PPE1-108 isothermally crystallized thin films possess thicker lamellae and less crosshatched lamellar structure, while for the fibrous crystal number, the former is less than that of the latter. The main reason to create the crystallization behavior differences between the two PPEs and their fractions is due to the effect of molecular chain structure, i.e. the different distribution of copolymerized ethylene unit in polypropylene chains.

Cardo polyarylethersulfones and polyaryletherketones bearing alkyl substituents on the phenylene unit

A series of cardo polyaryletherketones and polyaryletersulfones containing alkyl substituents of a different kind, number and volume were synthesized from bis(4-nitrophenyl)ketone or bis(4-fluorophenyl)sulfone with various alkyl substituted phenolphthaleins by polycondensation using K2CO3 as catalyst. Their chemical and aggregation structures were confirmed by FT-IR, H-1-NMR and WAXD. The resulting polymers were soluble in a variety of common polar solvents and, transparent, colorless, and tough films could be easily cast from 1,1,2-trichluoroethane solution. Their tensile strength, elongation at break and tensile modulis were in the range of 70.5 similar to 97.1MPa, 4.49%similar to7.81%, and 1.69 similar to2.27GPa, respectively. The prepared polymers had reasonably high glass transition temperatures at 207 to 269 degreesC, and showed fairly good thermal stability with 5% thermal decomposition loss above 410 degreesC.

Studies on the hemolytic activity of tentacle extracts of jellyfish Rhopilema esculentum Kishinouye: Application of orthogonal test

The present work is first reporting the hemolytic activity of venom from jellyfish Rhopilema esculentum Kishinouye extracted by different phosphate buffer solutions and incubated at different temperature according to the orthogonal test L6(1) x 3(6). Of the seven controllable independent variables, incubated temperature and phenylmethylsulfonyl fluoride (PMSF) had strongest effect on the hemolytic activity. (c) 2006 Elsevier B.V. All rights reserved.

Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

The unit ball of the complex P(3H)

Let H be a two-dimensional complex Hilbert space and P(3H) the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, P(3H), from which we deduce that the unit sphere of P(3H) is the disjoint union of the sets of its extreme and smooth points. We also show that an extreme point of P(3H) remains extreme as considered as an element of L(3H). Finally we make a few remarks about the geometry of the unit ball of the predual of P(3H) and give a characterization of its smooth points.