Resolution-scale relativistic formulation of non-differentiable mechanics

This article motivates and presents the scale relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. It stems from the scale relativity proposal to extend the principle of relativity to resolution-scale transformations, which leads to considering non-differentiable dynamical paths. We first define a complex scale-covariant time-differential operator and show that mechanics of non-differentiable paths is implemented in the same way as classical mechanics but with the replacement of the time derivative and velocity with the time-differential operator and associated complex velocity. With this, the generalized form of Newton's fundamental relation of dynamics is shown to take the form of a Langevin equation in the case of stationary motion characterized by a null average classical velocity. The numerical integration of the Langevin equation in the case of a harmonic oscillator taken as an example reveals the same statistics as the stationary solutions of the Schrodinger equation for the same problem. This motivates the rest of the paper, which shows Schrodinger's equation to be a reformulation of Newton's fundamental relation of dynamics as generalized to non-differentiable geometries and leads to an alternative interpretation of the other axioms of standard quantum mechanics in a coherent picture. This exercise validates the scale relativistic approach and, at the same time, it allows to envision macroscopic chaotic systems observed at resolution time-scales exceeding their horizon of predictability as candidates in which to search for quantum-like dynamics and structures.Comment: 30 pages, 4 figure

What Causes the Volatility of the Balancing Item?

This paper analyzes the impacts of timing errors, capital flows and economic openness on the behavior of the balancing item. We choose Norway, Sweden, Philippines and South Africa as sample countries where the size of the balancing item is often excess the IMF's criterion of ‘smallness'. The empirical results show that the sources of the volatility of the balancing item are different among these four countries.Balancing item, Balance of payments

An analysis of the change in financial position of the construction industry in Hong Kong

The purpose of this report is to find out the relationship between Hong Kong construction industry and the market condition of Hong Kong in the past 5 years (1993-97). Prior research showed that construction industry is an important contributor to the economic development of Singapore by helping to establish the infrastructure required for sustaining socioeconomic development (Ofori 1988). Although a number of researches were on the prediction of solvency, none was related to the construction industry in Hong Kong. Recently, Hong Kong has been facing economy difficulty, concern is aroused in the healthiness of Hong Kong business. Construction industry, being an important industry, deserves to study. To determine the relationship between market condition and the industry, we use the Capital Asset Pricing Model (CAPM). The results of CAPM showed that the financial performance of construction companies follow the movement of the market. We determine the change of financial position of Hong Kong construction companies by using the industrial average of the construction sector in Hong Kong and applying financial statement analysis techniques. We found from the financial statement analysis that most construction companies were not profitable and most of them had high gearing ratios. Questionnaires are sent to 22 listed construction companies to identify the possible factors that affect the their performance. According to the view of these construction companies, their performance was much affected by the economic condition. These results are consistent in the way that the construction companies are not profitable during the periods. Long Debtor’s Day and high gearing position are norms in construction industry. Most sample companies in our study follow these norms. The result shows that most sample companies follow the market to grow but the growth rate is not as rapid as the market. We recommend that the construction companies should better control their debt and expenses with great care so as to improve profitability and financial leverage. Through value management to achieve an effective management of change

Asymptotic distributions of the signal-to-interference ratios of LMMSE detection in multiuser communications

Let ${\mathbf{s}}_k=\frac{1}{\sqrt{N}}(v_{1k},...,v_{Nk})^T,$ $k=1,...,K$, where $\{v_{ik},i,k$ $=1,...\}$ are independent and identically distributed random variables with $Ev_{11}=0$ and $Ev_{11}^2=1$. Let ${\mathbf{S}}_k=({\mathbf{s}}_1,...,{\mathbf{s}}_{k-1},$ ${\mathbf{s}}_{k+1},...,{\mathbf{s}}_K)$, ${\mathbf{P}}_k=\operatorname {diag}(p_1,...,$ $p_{k-1},p_{k+1},...,p_K)$ and \beta_k=p_k{\mathbf{s}}_k^T({\mathb f{S}}_k{\mathbf{P}}_k{\mathbf{S}}_k^T+\sigma^2{\mathbf{I}})^{-1}{\math bf{s}}_k, where $p_k\geq 0$ and the $\beta_k$ is referred to as the signal-to-interference ratio (SIR) of user $k$ with linear minimum mean-square error (LMMSE) detection in wireless communications. The joint distribution of the SIRs for a finite number of users and the empirical distribution of all users' SIRs are both investigated in this paper when $K$ and $N$ tend to infinity with the limit of their ratio being positive constant. Moreover, the sum of the SIRs of all users, after subtracting a proper value, is shown to have a Gaussian limit.Comment: Published at http://dx.doi.org/10.1214/105051606000000718 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

DOES PRIVACY THREAT MATTER IN MOBILE HEALTH SERVICE? FROM HEALTH BELIEF MODEL PERSPECTIVE

A lot of mobile health (mHealth) service apps have been launched in the market with advances in technology. When people decide to use these mHealth service apps, they have to provide their personal data or personal health data more or less to the service providers. However, the health data is more sensitive data than general personal data. In addition, the behaviour of using mHealth service apps includes technology use behaviour and health promotion behaviour. Therefore, we employed HBM to be the theory foundation to find out what factors will impact on the intention to upload personal health data via a mHealth service app. Online questionnaires were distributed and 133 valid questionnaires were returned. The results showed the perceived benefits is the only factor to influence an individual intention to upload personal health data. The specific information privacy concerns has no significant effect on the behaviour intention. That means people value the benefits that the mhealth service app can bring more than the threat of privacy they perceived. The construct, disposition to value privacy (DTVP), have strong effects on perceived vulnerability, perceived severity, and specific information privacy concerns. Future studies will be recommended

Speeds of invasion for models with Allee effects

Models that describe the spread of invading organisms often assume no Allee effect. In contrast, abundant observational data provide evidence for Allee effects. In chapter 1, I study an invasion model based on an integrodifference equation with an Allee effect. I derive a general result for the sign of the speed of invasion. I then examine a special, linear-constant, Allee growth function and introduce a numerical scheme that allows me to estimate the speed of traveling wave solutions. In chapter 2, I study an invasion model based on a reaction-diffusion equation with an Allee effect. I use a special, piecewise-linear, Allee population growth rate. This function allows me to obtain traveling wave solutions and to compute wave speeds for a full range of Allee effects, including weak Allee effects. Some investigators claim that linearization fails to give the correct speed of invasion if there is an Allee effectI show that the minimum speed for a sufficiently weak Allee may be the same as that derived by means of linearization. In chapters 3 and 4, I extend a discrete-time analog of the Lotka-Volterra competition equations to an integrodifference-competition model and analyze this model by investigating traveling wave solutions. The speed of wave is calculated as a function of the model parameters by linearization. I also show that the linearization may fail to give the correct speed for the competition model with strongly interacting competitors because of the introduction of a weak Allee effect . A linear-constant approximation to the resulting Allee growth function is introduced to estimate the speed under this weak Allee effect. I also analyze the back of the wave for the competition model. Some sufficient conditions that guarantee no oscillation behind the wave are given