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This paper aims to introduce a new class of entire functions whose zeros (zk)k≥1 satisfy ∑k=1∞Im zk=O(1).
This is done by means of a Ritt's formula which is used to prove that every partial sum of the Riemann Zeta function, ζn(z):=∑k=1n1/kz, n≥2, has zeros (snk)k≥1 verifying ∑k=1∞Re snk=O(1) and extending this property to a large class of entire functions denoted by AO.
It is found that this new class AO has a part in common with the class A introduced by Levin but is distinct from it. It is shown that, in particular, AO contains every partial sum of the Riemann Zeta function ζn(iz) and every finite truncation of the alternating Dirichlet series expansion of the Riemann zeta function, Tn(iz):=∑k=1n(−1)k−1/kiz, for all n≥2.
With the exception of the n=2 case, numerical experiences show that all zeros of ζn(z) and Tn(z) are not symmetrically distributed around the imaginary axis. However, the fact consisting of every function ζn(iz) and Tn(iz) to be in the class AO implies the existence of a very precise physical equilibrium between the zeros situated on the left half‐plane and the zeros situated on the right half‐plane of each function. This is a relevant fact and it points out that there is certain internal rule that distributes the zeros of ζn(z) and Tn(z) in such a way that few zeros on the left of the imaginary axis and far away from it, must be compensated with a lot of zeros on the right of the imaginary axis and close to it, and vice versa.
The paper presents an original class of entire functions that provides a new point of view to study the approximants and the alternating Dirichlet truncations of the Riemann zeta function.
Purpose – This chapter provides an overview of issues related to analysing crash data characterised by excess zero responses and/or long tails and how to overcome these…
Purpose – This chapter provides an overview of issues related to analysing crash data characterised by excess zero responses and/or long tails and how to overcome these problems. Factors affecting excess zeros and/or long tails are discussed, as well as how they can bias the results when traditional distributions or models are used. Recently introduced multi-parameter distributions and models developed specifically for such datasets are described. The chapter is intended to guide readers on how to properly analyse crash datasets with excess zeros and long or heavy tails.
Methodology – Key references from the literature are summarised and discussed, and two examples detailing how multi-parameter distributions and models compare with the negative binomial distribution and model are presented.
Findings – In the event that the characteristics of the crash dataset cannot be changed or modified, recently introduced multi-parameter distributions and models can be used efficiently to analyse datasets characterised by excess zero responses and/or long tails. They offer a simpler way to interpret the relationship between crashes and explanatory variables, while providing better statistical performance in terms of goodness-of-fit and predictive capabilities.
Research implications – Multi-parameter models are expected to become the next series of traditional distributions and models. The research on these models is still ongoing.
Practical implications – With the advancement of computing power and Bayesian simulation methods, multi-parameter models can now be easily coded and applied to analyse crash datasets characterised by excess zero responses and/or long tails.
Vector error-correction models (VECMs) have become increasingly important in their application to financial markets. Standard full-order VECM models assume non-zero…
Vector error-correction models (VECMs) have become increasingly important in their application to financial markets. Standard full-order VECM models assume non-zero entries in all their coefficient matrices. However, applications of VECM models to financial market data have revealed that zero entries are often a necessary part of efficient modelling. In such cases, the use of full-order VECM models may lead to incorrect inferences. Specifically, if indirect causality or Granger non-causality exists among the variables, the use of over-parameterised full-order VECM models may weaken the power of statistical inference. In this paper, it is argued that the zero–non-zero (ZNZ) patterned VECM is a more straightforward and effective means of testing for both indirect causality and Granger non-causality. For a ZNZ patterned VECM framework for time series of integrated order two, we provide a new algorithm to select cointegrating and loading vectors that can contain zero entries. Two case studies are used to demonstrate the usefulness of the algorithm in tests of purchasing power parity and a three-variable system involving the stock market.
There is a lack of empirical evidence to support the claim that zero-tolerance policies decrease violent incidents in schools or improve school safety. The message behind…
There is a lack of empirical evidence to support the claim that zero-tolerance policies decrease violent incidents in schools or improve school safety. The message behind the policies clearly indicates that violence in schools is not tolerable under any circumstances; however, there is no correlation between the message and the outcomes from policy implementation. The literature on school order and safety suggests that zero tolerance is the simplest and least effective approach with a myriad of unintentional consequences that have a negative impact on education, not just for an individual student but for the system as a whole (American Psychological Association, 2006; Casella, 2003). This chapter examines the role of the school leader, the historical background of school safety, the role of the school leader as a learner, the legislative events that led to the development of zero-tolerance policies, and outline the unintended consequences of zero-tolerance policies in relation to leadership and learning. An alternative approach to school discipline is proposed – namely a restorative justice approach, which may work towards alleviating many of these unintended consequences.
Recent U.S. Treasury yields have been constrained to some extent by the zero lower bound (ZLB) on nominal interest rates. Therefore, we compare the performance of a…
Recent U.S. Treasury yields have been constrained to some extent by the zero lower bound (ZLB) on nominal interest rates. Therefore, we compare the performance of a standard affine Gaussian dynamic term structure model (DTSM), which ignores the ZLB, to a shadow-rate DTSM, which respects the ZLB. Near the ZLB, we find notable declines in the forecast accuracy of the standard model, while the shadow-rate model forecasts well. However, 10-year yield term premiums are broadly similar across the two models. Finally, in applying the shadow-rate model, we find no gain from estimating a slightly positive lower bound on U.S. yields.
Purpose: This study explores the Zero Waste lifestyle trend through the lens of user-generated content posted on Instagram. The aim is to investigate consumer-driven…
Purpose: This study explores the Zero Waste lifestyle trend through the lens of user-generated content posted on Instagram. The aim is to investigate consumer-driven activities and shared beliefs associated with the Zero Waste lifestyle movement from a consumer culture perspective.
Method: Data were collected from 313 public posts associated with the #zerowaste hashtag from 313 individual users on Instagram. A textual analysis of user biographies and a thematic analysis of both visual and textual posts were carried out.
Findings: Findings suggest a female-led consumer lifestyle movement that seems to believe in the power of community to cause an environmentally significant impact. Zero Waste seems to be regarded as a long-term goal rather than an immediate radical action by members of the social media community. This study also identifies an emergence of Zero Waste product/brand influencers which could be categorised as follows: (1) Product promoters, (2) Product critics, (3) Sponsored brand promoters and (4) Non-sponsored brand admirers.
Originality/Value of Paper: This study provides a richer understanding of the Zero Waste lifestyle phenomenon which has grown in popularity through social media during recent years. Besides, findings allow for a better understanding of the role of consumer activists and social media influencers in promoting the Zero Waste lifestyle within online communities.
The purpose of this paper is to introduce the zero‐modified distributions in the calculation of operational value‐at‐risk.
The purpose of this paper is to introduce the zero‐modified distributions in the calculation of operational value‐at‐risk.
This kind of distributions is preferred when excess of zeroes is observed. In operational risk, this phenomenon may be due to the scarcity of data, the existence of extreme values and/or the threshold from which banks start to collect losses. In this article, the paper focuses on the analysis of damage to physical assets.
The results show that basic Poisson distribution underestimates the dispersion, and then leads to the underestimation of the capital charge. However, zero‐modified Poisson distributions perform well the frequency. In addition, basic negative binomial and its related zero‐modified distributions, in their turn, offer a good prediction of count events. To choose the distribution that suits better the frequency, the paper uses the Vuong's test. Its results indicate that zero‐modified Poisson distributions, basic negative binomial and its related zero‐modified distributions are equivalent. This conclusion is confirmed by the capital charge calculated since the differences between the six aggregations are not significant except that of basic Poisson distribution.
Recently, the zero‐modified formulations are widely used in many fields because of the low frequency of the events. This article aims to describe the frequency of operational risk using zero‐modified distributions.
Gives an in depth view of the strategies pursued by the world’s leading chief executive officers in an attempt to provide guidance to new chief executives of today…
Gives an in depth view of the strategies pursued by the world’s leading chief executive officers in an attempt to provide guidance to new chief executives of today. Considers the marketing strategies employed, together with the organizational structures used and looks at the universal concepts that can be applied to any product. Uses anecdotal evidence to formulate a number of theories which can be used to compare your company with the best in the world. Presents initial survival strategies and then looks at ways companies can broaden their boundaries through manipulation and choice. Covers a huge variety of case studies and examples together with a substantial question and answer section.
Briefly reviews previous literature by the author before presenting an original 12 step system integration protocol designed to ensure the success of companies or…
Briefly reviews previous literature by the author before presenting an original 12 step system integration protocol designed to ensure the success of companies or countries in their efforts to develop and market new products. Looks at the issues from different strategic levels such as corporate, international, military and economic. Presents 31 case studies, including the success of Japan in microchips to the failure of Xerox to sell its invention of the Alto personal computer 3 years before Apple: from the success in DNA and Superconductor research to the success of Sunbeam in inventing and marketing food processors: and from the daring invention and production of atomic energy for survival to the successes of sewing machine inventor Howe in co‐operating on patents to compete in markets. Includes 306 questions and answers in order to qualify concepts introduced.
According to European Union Open Internet Regulation, commercial practices of internet access service providers (IASP) should not restrict end-users’ choice regarding…
According to European Union Open Internet Regulation, commercial practices of internet access service providers (IASP) should not restrict end-users’ choice regarding services, applications or contents. This paper aims to analyze the effects of Zero Rating (ZR) on freedom of choice translating this regulatory criterion into a formal expression: providing a ZR offer on a content or application provider (CAP) restricts end-users’ choice if it reduces the volume or provision of others usages.
The analysis is made in two steps. First, the authors assess the direct effect of introducing zero rating on non-ZR usages, all other things equal. Second, the paper studies the knock-on effect of ZR on IASP offers and the supply of CAP.
In the short term, zero rating does not restrict end-users’ choice increasing both ZR and non-ZR usages. In the long term, in the case of pure ZR, IASPs may adapt their offer to support ZR costs impacting negatively other usages. However, in practice, these effects are compensated or diluted by competitive forces or if the ZR traffic is small relatively to the data allowance. In the case of SD, the CAP covers the cost which prevents cross-subsidies and protects freedom of choice if SD is open to all CAPs.
The economic literature on zero rating is scarce and assesses this practice from the general economic criterion of social or consumer welfare. This paper is the first one to use economic analysis to analyze whether Zero Rating is compatible with the EU regulatory criterion of freedom of choice.