title: Linear law for the logarithms of the Riemann periods at simple critical zeta zeros

authors: Broughan, Kevin A.

subjects: mathematics

abstract: Each simple zero 1/2 + iγn of the Riemann zeta function on the critical line with γn > 0 is a center for the flow s˙ = ξ(s) of the Riemann xi function with an associated period Tn. It is shown that, as γn →∞, log Tn ≥ π/4 γn + O(log γn).
Numerical evaluation leads to the conjecture that this inequality can be replaced by an equality. Assuming the Riemann Hypothesis and a zeta zero separation conjecture γn+1 − γn≥ γn-θ for some exponent θ > 0, we obtain the upper bound log Tn ≤ γn2 + θ Assuming a weakened form of a conjecture of Gonek, giving a bound for the reciprocal of the derivative of zeta at each zero, we obtain the expected upper bound for the periods so, conditionally, log Tn = π/ 4 γn +O(log γn). Indeed, this linear relationship is equivalent to the given weakened conjecture, which implies the zero separation conjecture, provided the exponent is sufficiently large. The frequencies corresponding to the periods relate to natural eigenvalues for the Hilbert–Polya conjecture. They may provide a goal for those seeking a self-adjoint operator related to the Riemann hypothesis.

text: Linear law for the logarithms of the Riemann periods at simple critical zeta zeros Each simple zero 1/2 + iγn of the Riemann zeta function on the critical line with γn > 0 is a center for the flow s˙ = ξ(s) of the Riemann xi function with an associated period Tn. It is shown that, as γn →∞, log Tn ≥ π/4 γn + O(log γn).
Numerical evaluation leads to the conjecture that this inequality can be replaced by an equality. Assuming the Riemann Hypothesis and a zeta zero separation conjecture γn+1 − γn≥ γn-θ for some exponent θ > 0, we obtain the upper bound log Tn ≤ γn2 + θ Assuming a weakened form of a conjecture of Gonek, giving a bound for the reciprocal of the derivative of zeta at each zero, we obtain the expected upper bound for the periods so, conditionally, log Tn = π/ 4 γn +O(log γn). Indeed, this linear relationship is equivalent to the given weakened conjecture, which implies the zero separation conjecture, provided the exponent is sufficiently large. The frequencies corresponding to the periods relate to natural eigenvalues for the Hilbert–Polya conjecture. They may provide a goal for those seeking a self-adjoint operator related to the Riemann hypothesis.

year: 2006

title: Lessons from literature: How to manage staff turnover in hotels?

authors: Mohsin, Asad

subjects: staff turnover

abstract: The aim of this study is to review research and discusses the phenomenon of staff turnover generally, its impact and how it has been managed in the hotel industry specifically? As stated by Step Business Builders (2010) “... once businesses determined the future of the workforce, now the workforce determines the future of the business”. It might be beyond the scope of this study to capture all the literature on staff turnover hence the focus is on that in last 25 years, how the research has helped to understand this phenomenon? And what lessons the hotel industry could learn to manage this process? To make an effective analysis some information is drawn from the literature prior to 1990 with a multidisciplinary approach.  In order to effectively meet the objectives of the study, a critical analysis is undertaken with regard to turnover culture in hospitality industry, factors and issues that impact staff turnover globally with specificity of the situation in New Zealand.  The study notes that staff turnover is not just a management issue from a micro-environment perspective of a company, but it is also affected by macro-environmental factors outside the organization such as economic conditions.  For example in New Zealand’s domestic market and in the international market, since 2007 the staff turnover rates have slightly dropped due to the economic recession.  Employees are not feeling confident in ‘actively’ seeking a better job. Current study attempts to understand the turnover issues from both the industry and the personnel perspective and makes suggestions for future practice and research.

text: Lessons from literature: How to manage staff turnover in hotels? The aim of this study is to review research and discusses the phenomenon of staff turnover generally, its impact and how it has been managed in the hotel industry specifically? As stated by Step Business Builders (2010) “... once businesses determined the future of the workforce, now the workforce determines the future of the business”. It might be beyond the scope of this study to capture all the literature on staff turnover hence the focus is on that in last 25 years, how the research has helped to understand this phenomenon? And what lessons the hotel industry could learn to manage this process? To make an effective analysis some information is drawn from the literature prior to 1990 with a multidisciplinary approach.  In order to effectively meet the objectives of the study, a critical analysis is undertaken with regard to turnover culture in hospitality industry, factors and issues that impact staff turnover globally with specificity of the situation in New Zealand.  The study notes that staff turnover is not just a management issue from a micro-environment perspective of a company, but it is also affected by macro-environmental factors outside the organization such as economic conditions.  For example in New Zealand’s domestic market and in the international market, since 2007 the staff turnover rates have slightly dropped due to the economic recession.  Employees are not feeling confident in ‘actively’ seeking a better job. Current study attempts to understand the turnover issues from both the industry and the personnel perspective and makes suggestions for future practice and research.

year: 2013

title: Learning in later life: a bicultural perspective from Aotearoa/New Zealand

authors: Findsen, Brian

abstract: This article is concerned with how learning in later life has been constructed and practised by the two most numerous ethnic groups in Aotearoa/New Zealand, Pākėhā (Europeans) and Māori (Indigenous people). It is argued that learning is heavily influenced by historic features of interaction between these two groups; Pākehā as the dominant cultural and economic group and Māori as subordinate. While contemporary perspectives are necessarily interpreted in the light of historical trends and events, fresh interpretations of what constitutes biculturalism in this country allow for more nuanced understanding of possibilities for and obstacles to older adult learning/education. Themes from lifelong learning are analysed with special reference to older people’s learning, the consequences of Māori sovereignty on pedagogy and trends identified for older adult education. Two linked case studies of Pākehā and Māori older adult education in a New Zealand university are described to illustrate complexities and tensions in provision in a bicultural context.

text: Learning in later life: a bicultural perspective from Aotearoa/New Zealand This article is concerned with how learning in later life has been constructed and practised by the two most numerous ethnic groups in Aotearoa/New Zealand, Pākėhā (Europeans) and Māori (Indigenous people). It is argued that learning is heavily influenced by historic features of interaction between these two groups; Pākehā as the dominant cultural and economic group and Māori as subordinate. While contemporary perspectives are necessarily interpreted in the light of historical trends and events, fresh interpretations of what constitutes biculturalism in this country allow for more nuanced understanding of possibilities for and obstacles to older adult learning/education. Themes from lifelong learning are analysed with special reference to older people’s learning, the consequences of Māori sovereignty on pedagogy and trends identified for older adult education. Two linked case studies of Pākehā and Māori older adult education in a New Zealand university are described to illustrate complexities and tensions in provision in a bicultural context.

year: 2016