Divisibility of Trinomials by Irreducible Polynomials over F_2

Irreducible trinomials of given degree n over F_2 do not always exist and in the cases that there is no irreducible trinomial of degree n it may be effective to use trinomials with an irreducible factor of degree n. In this paper we consider some conditions under which irreducible polynomials divide trinomials over F_2. A condition for divisibility of self-reciprocal trinomials by irreducible polynomials over F_2 is established. And we extend Welch's criterion for testing if an irreducible polynomial divides trinomials x^m + x^s + 1 to the trinomials x^am + x^bs + 1.

... Algebraic numbers. Report of the Committee on Algebraic Numbers, National Research Council,

Cover-title.

Tables of logarithms of numbers and of sines and tangents for every ten seconds of the quadrant, with other useful tables.

Mode of access: Internet.

Sperner's theorem on maximal-sized antichains and its generation /

Includes bibliographical references.

The rhythm of fountains: The length and time scales of rise height fluctuations at low and high Froude numbers

The magnitude and frequency of vertical fluctuations of the top of an axisymmetric miscible Boussinesq fountain forms the focus of this work. We present measurements of these quantities for saline-aqueous fountains in uniform quiescent surroundings. Our results span source Froude numbers 0.3 ≤ Fr 0 ≤ 40 and, thereby, encompass very weak, weak, intermediate and forced classes of fountain. We identify distinct scalings, based on known quantities at the fountain source, for the frequency of fountain height fluctuations which collapse our data within bands of Fr0. Notably, our scalings reveal that the (dimensionless) frequency takes a constant value within each band. These results highlight characteristic time scales for the fluctuations which we decompose into a single, physically apparent, length scale and velocity scale within each band. Moreover, within one particular band, spanning source Froude numbers towards the lower end of the full range considered, we identify unexpectedly long-period fluctuations indicating a near balance of inertia and (opposing) buoyancy at the source. Our analysis identifies four distinct classes of fluctuation behaviour (four bands of Fr 0) and this classification matches well with existing classifications of fountains based on rise heights. As such, we show that an analysis of the behaviour of the fountain top alone, rather than the entire fountain, provides an alternative approach to classifying fountains. The similarity of classifications based on the two different methods confirms that the boundaries between classes mark tangible changes in the physics of fountains. For high Fr0 we show that the dominant fluctuations occur at the scale of the largest eddies which can be contained within the fountain near its top. Extending this, we develop a Strouhal number, Strtop, based on experimental measures of the fountain top, defined such that Strtop = 1 would suggest the dominant fluctuations are caused by a continual cycle of eddies forming and collapsing at this largest physical scale. For high- Fr 0 fountains we find Strtop ≈ 0. 9. © 2013 Cambridge University Press.

The problem of the graphic artist

'The problem of the graphic artist' is a small example of applying elementary mathematics (divisibility of natural numbers) to a real problem which we ourselves have actually experienced. It deals with the possibilities for partitioning a sheet of paper into strips. In this contribution we report on a teaching unit in grade 6 as well as on informal tests with students in school and university. Finally we analyse this example methodologically, summarise our observations with pupils and students, and draw some didactical conclusions.

Quality of work life and turnover intention in primary healthcare organisations : a cross-sectional study of registered nurses in Saudi Arabia

Purpose: The purpose of this study was to improve the retention of primary healthcare (PHC) nurses through exploring and assessing their quality of work life (QWL) and turnover intention. Design and methods: A cross-sectional survey design was used in this study. Data were collected using a questionnaire comprising four sections (Brooks’ survey of Quality of Nursing Work Life [QNWL], Anticipated Turnover Intention, open-ended questions and demographic characteristics). A convenience sample was recruited from 143 PHC centres in Jazan, Saudi Arabia. A response rate of 87% (n = 508/585) was achieved. The SPSS v17 for Windows and NVivo 8 were used for analysis purposes. Procedures and tests used in this study to analyse the quantitative data were descriptive statistics, t-test, ANOVA, General Linear Model (GLM) univariate analysis, standard multiple regression, and hierarchical multiple regression. Qualitative data obtained from responses to the open-ended questions were analysed using the NVivo 8. Findings: Quantitative findings suggested that PHC nurses were dissatisfied with their work life. Respondents’ scores ranged between 45 and 218 (mean = 139.45), which is lower than the average total score on Brooks’ Survey (147). Major influencing factors were classified under four dimensions. First, work life/home life factors: unsuitable working hours, lack of facilities for nurses, inability to balance work with family needs and inadequacy of vacations’ policy. Second, work design factors: high workload, insufficient workforce numbers, lack of autonomy and undertaking many non-nursing tasks. Third, work context factors: management practices, lack of development opportunities, and inappropriate working environment in terms of the level of security, patient care supplies and unavailability of recreation room. Finally, work world factors: negative public image of nursing, and inadequate payment. More positively, nurses were notably satisfied with their co-workers. Conversely, 40.4% (n = 205) of the respondents indicated that they intended to leave their current employment. The relationships between QWL and demographic variables of gender, age, marital status, dependent children, dependent adults, nationality, ethnicity, nursing tenure, organisational tenure, positional tenure, and payment per month were significant (p < .05). The eta squared test for these demographics indicates a small to medium effect size of the variation in QWL scores. Using the GLM univariate analysis, education level was also significantly related to the QWL (p < .05). The relationships between turnover intention and demographic variables including gender, age, marital status, dependent children, education level, nursing tenure, organisational tenure, positional tenure, and payment per month were significant (p < .05). The eta squared test for these demographics indicates a small to moderate effect size of the variation in the turnover intention scores. Using the GLM univariate analysis, the dependent adults’ variable was also significantly related to turnover intention (p < .05). Turnover intention was significantly related to QWL. Using standard multiple regression, 26% of the variance in turnover intention was explained by the QWL F (4,491), 43.71, p < .001, with R² = .263. Further analysis using hierarchical multiple regression found that the total variance explained by the model as a whole (demographics and QWL) was 32.1%, F (17.433) = 12.04, p < .001. QWL explained an additional 19% of the variance in turnover intention, after controlling for demographic variables, R squared change =.19, F change (4, 433) = 30.190, p < .001. The work context variable makes the strongest unique contribution (-.387) to explain the turnover intention, followed by the work design dimension (-.112). The qualitative findings reaffirmed the quantitative findings in terms of QWL and turnover intention. However, the home life/work life and work world dimensions were of great important to both QWL and turnover intention. The qualitative findings revealed a number of new factors that were not included in the survey questionnaire. These included being away from family, lack of family support, social and cultural aspects, accommodation facilities, transportation, building and infrastructure of PHC, nature of work, job instability, privacy at work, patients and community, and distance between home and workplace. Conclusion: Creating and maintaining a healthy work life for PHC nurses is very important to improve their work satisfaction, reduce turnover, enhance productivity and improve nursing care outcomes. Improving these factors could lead to a higher QWL and increase retention rates and therefore reinforcing the stabilisation of the nursing workforce. Significance of the research: Many countries are examining strategies to attract and retain the health care workforce, particularly nurses. This study identified factors that influence the QWL of PHC nurses as well as their turnover intention. It also determined the significant relationship between QWL and turnover intention. In addition, the present study tested Brooks’ survey of QNWL on PHC nurses for the first time. The qualitative findings of this study revealed a number of new variables regarding QWL and turnover intention of PHC nurses. These variables could be used to improve current survey instruments or to develop new research surveys. The study findings could be also used to develop and appropriately implement plans to improve QWL. This may help to enhance the home and work environments of PHC nurses, improve individual and organisational performance, and increase nurses’ commitment. This study contributes to the existing body of research knowledge by presenting new data and findings from a different country and healthcare system. It is the first of its kind in Saudi Arabia, especially in the field of PHC. It has examined the relationship between QWL and turnover intention of PHC nurses for the first time using nursing instruments. The study also offers a fresh explanation (new framework) of the relationship between QWL and turnover intention among PHC nurses, which could be used or tested by researchers in other settings. Implications for further research: Review of the extant literature reveals little in-depth research on the PHC workforce, especially in terms of QWL and organisational turnover in developing countries. Further research is required to develop a QWL tool for PHC nurses, taking into consideration the findings of the current study along with the local culture. Moreover, the revised theoretical framework of the current study could be tested in further research in other regions, countries or healthcare systems in order to identify its ability to predict the level of PHC nurses’ QWL and their intention to leave. There is a need to conduct longitudinal research on PHC organisations to gain an in-depth understanding of the determents of and changes in QWL and turnover intention of PHC nurses at various points of time. An intervention study is required to improve QWL and retention among PHC nurses using the findings of the current study. This would help to assess the impact of such strategies on reducing turnover of PHC nurses. Focusing on the location of the current study, it would be valuable to conduct another study in five years’ time to examine the percentage of actual turnover among PHC nurses compared with the reported turnover intention in the current study. Further in-depth research would also be useful to assess the impact of the local culture on the perception of expatriate nurses towards their QWL and their turnover intention. A comparative study is required between PHC centres and hospitals as well as the public and private health sector agencies in terms of QWL and turnover intention of nursing personnel. Findings may differ from sector to sector according to variations in health systems, working environments and the case mix of patients.

The mitochondrial genome of the Russian wheat aphid Diuraphis noxia : large repetitive sequences between trnE and trnF in aphids

To characterize aphid mitochondrial genome (mitogenome) features, we sequenced the complete mitogenome of the Russian wheat aphid, Diuraphis noxia. The 15,784-bp mitogenome with a high A + T content (84.76%) and strong C skew (− 0.26) was arranged in the same gene order as that of the ancestral insect. Unlike typical insect mitogenomes, D. noxia possessed a large tandem repeat region (644 bp) located between trnE and trnF. Sequencing partial mitogenome of the cotton aphid (Aphis gossypii) further confirmed the presence of the large repeat region in aphids, but with different repeat length and copy number. Another motif (58 bp) tandemly repeated 2.3 times in the control region of D. noxia. All repeat units in D. noxia could be folded into stem-loop secondary structures, which could further promote an increase in copy numbers. Characterization of the D. noxia mitogenome revealed distinct mitogenome architectures, thus advancing our understanding of insect mitogenomic diversities and evolution.

Onset of transition in mixed convection of a lid-driven trapezoidal enclosure filled with water-Al2O3 nanofluid

A numerical study is carried out to investigate the transition from laminar to chaos in mixed convection heat transfer inside a lid-driven trapezoidal enclosure. In this study, the top wall is considered as isothermal cold surface, which is moving in its own plane at a constant speed, and a constant high temperature is provided at the bottom surface. The enclosure is assumed to be filled with water-Al2O3 nanofluid. The governing Navier–Stokes and thermal energy equations are expressed in non-dimensional forms and are solved using Galerkin finite element method. Attention is paid in the present study on the pure mixed convection regime at Richandson number, Ri = 1. The numerical simulations are carried out over a wide range of Reynolds (0.1 ≤ Re ≤ 103) and Grashof (0.01 ≤ Gr ≤ 106) numbers. Effects of the presence of nanofluid on the characteristics of mixed convection heat transfer are also explored. The average Nusselt numbers of the heated wall are computed to demonstrate the influence of flow parameter variations on heat transfer. The corresponding change of flow and thermal fields is visualized from the streamline and the isotherm contour plots.

Exploring and validating the internal dimensions of occupational stress: Evidence from construction cost estimators in China

A recurring feature of modern practice is occupational stress of project professionals, with both debilitating effects on the people concerned and indirectly affecting project success. Previous research outside the construction industry has involved the use of a psychology perceived stress questionnaire (PSQ) to measure occupational stress, resulting in the identification of one stressor – demand - and three sub-dimensional emotional reactions in terms of worry, tension and joy. The PSQ is translated into Chinese with a back translation technique and used in a survey of young construction cost professionals in China. Principal component analysis and confirmatory factor analysis are used to test the divisibility of occupational stress - little mentioned in previous research on stress in the construction context. In addition, structural equation modelling is used to assess nomological validity by testing the effects of the three dimensions on organizational commitment, the main finding of which is that lack of joy has the sole significant effect. The three-dimensional measurement framework facilitates the standardizing measurement of occupational stress. Further research will establish if the findings are also applicable in other settings and explore the relations between stress dimensions and other managerial concepts.

Low-density koala (Phascolarctos cinereus) populations in the mulgalands of south-west Queensland. IV. Abundance and conservation status

Urban encroachment on dense, coastal koala populations has ensured that their management has received increasing government and public attention. The recently developed National Koala Conservation Strategy calls for maintenance of viable populations in the wild. Yet the success of this, and other, conservation initiatives is hampered by lack of reliable and generally accepted national and regional population estimates. In this paper we address this problem in a potentially large, but poorly studied, regional population in the State that is likely to have the largest wild populations. We draw on findings from previous reports in this series and apply the faecal standing-crop method (FSCM) to derive a regional estimate of more than 59 000 individuals. Validation trials in riverine communities showed that estimates of animal density obtained from the FSCM and direct observation were in close agreement. Bootstrapping and Monte Carlo simulations were used to obtain variance estimates for our population estimates in different vegetation associations across the region. The most favoured habitat was riverine vegetation, which covered only 0.9% of the region but supported 45% of the koalas. We also estimated that between 1969 and 1995 -30% of the native vegetation associations that are considered as potential koala habitat were cleared, leading to a decline of perhaps 10% in koala numbers. Management of this large regional population has significant implications for the national conservation of the species: the continued viability of this population is critically dependent on the retention and management of riverine and residual vegetation communities, and future vegetation-management guidelines should be cognisant of the potential impacts of clearing even small areas of critical habitat. We also highlight eight management implications.

Mathematical Aspects of Financial Markets with Frictions

Frictions are factors that hinder trading of securities in financial markets. Typical frictions include limited market depth, transaction costs, lack of infinite divisibility of securities, and taxes. Conventional models used in mathematical finance often gloss over these issues, which affect almost all financial markets, by arguing that the impact of frictions is negligible and, consequently, the frictionless models are valid approximations. This dissertation consists of three research papers, which are related to the study of the validity of such approximations in two distinct modeling problems. Models of price dynamics that are based on diffusion processes, i.e., continuous strong Markov processes, are widely used in the frictionless scenario. The first paper establishes that diffusion models can indeed be understood as approximations of price dynamics in markets with frictions. This is achieved by introducing an agent-based model of a financial market where finitely many agents trade a financial security, the price of which evolves according to price impacts generated by trades. It is shown that, if the number of agents is large, then under certain assumptions the price process of security, which is a pure-jump process, can be approximated by a one-dimensional diffusion process. In a slightly extended model, in which agents may exhibit herd behavior, the approximating diffusion model turns out to be a stochastic volatility model. Finally, it is shown that when agents' tendency to herd is strong, logarithmic returns in the approximating stochastic volatility model are heavy-tailed. The remaining papers are related to no-arbitrage criteria and superhedging in continuous-time option pricing models under small-transaction-cost asymptotics. Guasoni, Rásonyi, and Schachermayer have recently shown that, in such a setting, any financial security admits no arbitrage opportunities and there exist no feasible superhedging strategies for European call and put options written on it, as long as its price process is continuous and has the so-called conditional full support (CFS) property. Motivated by this result, CFS is established for certain stochastic integrals and a subclass of Brownian semistationary processes in the two papers. As a consequence, a wide range of possibly non-Markovian local and stochastic volatility models have the CFS property.