An econometric analysis of international tourism demand in Hong Kong : a cointegration and error correction approach

The purpose of this study is to develop econometric models to better understand the economic factors affecting inbound tourist flows from each of six origin countries that contribute to Hong Kong’s international tourism demand. To this end, we test alternative cointegration and error correction approaches to examine the economic determinants of tourist flows to Hong Kong, and to produce accurate econometric forecasts of inbound tourism demand. Our empirical findings show that permanent income is the most significant determinant of tourism demand in all models. The variables of own price, weighted substitute prices, trade volume, the share price index (as an indicator of changes in wealth in origin countries), and a dummy variable representing the Beijing incident (1989) are also found to be important determinants for some origin countries. The average long-run income and own price elasticity was measured at 2.66 and – 1.02, respectively. It was hypothesised that permanent income is a better explanatory variable of long-haul tourism demand than current income. A novel approach (grid search process) has been used to empirically derive the weights to be attached to the lagged income variable for estimating permanent income. The results indicate that permanent income, estimated with empirically determined relatively small weighting factors, was capable of producing better results than the current income variable in explaining long-haul tourism demand. This finding suggests that the use of current income in previous empirical tourism demand studies may have produced inaccurate results. The share price index, as a measure of wealth, was also found to be significant in two models. Studies of tourism demand rarely include wealth as an explanatory forecasting long-haul tourism demand. However, finding a satisfactory proxy for wealth common to different countries is problematic. This study indicates with the ECM (Error Correction Models) based on the Engle-Granger (1987) approach produce more accurate forecasts than ECM based on Pesaran and Shin (1998) and Johansen (1988, 1991, 1995) approaches for all of the long-haul markets and Japan. Overall, ECM produce better forecasts than the OLS, ARIMA and NAÏVE models, indicating the superiority of the application of a cointegration approach for tourism demand forecasting. The results show that permanent income is the most important explanatory variable for tourism demand from all countries but there are substantial variations between countries with the long-run elasticity ranging between 1.1 for the U.S. and 5.3 for U.K. Price is the next most important variable with the long-run elasticities ranging between -0.8 for Japan and -1.3 for Germany and short-run elasticities ranging between – 0.14 for Germany and -0.7 for Taiwan. The fastest growing market is Mainland China. The findings have implications for policies and strategies on investment, marketing promotion and pricing.

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Mathematical and numerical modelling of dispersion-managed solitons, autosolitons and self-similar optical pulses

This thesis presents theoretical investigation of three topics concerned with nonlinear optical pulse propagation in optical fibres. The techniques used are mathematical analysis and numerical modelling. Firstly, dispersion-managed (DM) solitons in fibre lines employing a weak dispersion map are analysed by means of a perturbation approach. In the case of small dispersion map strengths the average pulse dynamics is described by a perturbation approach (NLS) equation. Applying a perturbation theory, based on the Inverse Scattering Transform method, an analytic expression for the envelope of the DM soliton is derived. This expression correctly predicts the power enhancement arising from the dispersion management.Secondly, autosoliton transmission in DM fibre systems with periodical in-line deployment of nonlinear optical loop mirrors (NOLMs) is investigated. The use of in-line NOLMs is addressed as a general technique for all-optical passive 2R regeneration of return-to-zero data in high speed transmission system with strong dispersion management. By system optimisation, the feasibility of ultra-long single-channel and wavelength-division multiplexed data transmission at bit-rates ³ 40 Gbit s-1 in standard fibre-based systems is demonstrated. The tolerance limits of the results are defined.Thirdly, solutions of the NLS equation with gain and normal dispersion, that describes optical pulse propagation in an amplifying medium, are examined. A self-similar parabolic solution in the energy-containing core of the pulse is matched through Painlevé functions to the linear low-amplitude tails. The analysis provides a full description of the features of high-power pulses generated in an amplifying medium.

On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach

We investigate the problem of determining the stationary temperature field on an inclusion from given Cauchy data on an accessible exterior boundary. On this accessible part the temperature (or the heat flux) is known, and, additionally, on a portion of this exterior boundary the heat flux (or temperature) is also given. We propose a direct boundary integral approach in combination with Tikhonov regularization for the stable determination of the temperature and flux on the inclusion. To determine these quantities on the inclusion, boundary integral equations are derived using Green’s functions, and properties of these equations are shown in an L2-setting. An effective way of discretizing these boundary integral equations based on the Nystr¨om method and trigonometric approximations, is outlined. Numerical examples are included, both with exact and noisy data, showing that accurate approximations can be obtained with small computational effort, and the accuracy is increasing with the length of the portion of the boundary where the additionally data is given.

On an indirect integral equation approach for stationary heat transfer in semi-infinite layered domains in R3 with cavities

Regions containing internal boundaries such as composite materials arise in many applications.We consider a situation of a layered domain in IR3 containing a nite number of bounded cavities. The model is stationary heat transfer given by the Laplace equation with piecewise constant conductivity. The heat ux (a Neumann condition) is imposed on the bottom of the layered region and various boundary conditions are imposed on the cavities. The usual transmission (interface) conditions are satised at the interface layer, that is continuity of the solution and its normal derivative. To eciently calculate the stationary temperature eld in the semi-innite region, we employ a Green's matrix technique and reduce the problem to boundary integral equations (weakly singular) over the bounded surfaces of the cavities. For the numerical solution of these integral equations, we use Wienert's approach [20]. Assuming that each cavity is homeomorphic with the unit sphere, a fully discrete projection method with super-algebraic convergence order is proposed. A proof of an error estimate for the approximation is given as well. Numerical examples are presented that further highlights the eciency and accuracy of the proposed method.

An alternating potential based approach for a Cauchy problem for the Laplace equation in a planar domain with a cut

We consider a Cauchy problem for the Laplace equation in a bounded region containing a cut, where the region is formed by removing a sufficiently smooth arc (the cut) from a bounded simply connected domain D. The aim is to reconstruct the solution on the cut from the values of the solution and its normal derivative on the boundary of the domain D. We propose an alternating iterative method which involves solving direct mixed problems for the Laplace operator in the same region. These mixed problems have either a Dirichlet or a Neumann boundary condition imposed on the cut and are solved by a potential approach. Each of these mixed problems is reduced to a system of integral equations of the first kind with logarithmic and hypersingular kernels and at most a square root singularity in the densities at the endpoints of the cut. The full discretization of the direct problems is realized by a trigonometric quadrature method which has super-algebraic convergence. The numerical examples presented illustrate the feasibility of the proposed method.

Fokker-Planck equation approach to the description of soliton statistics in optical fiber transmission systems

We derive rigorously the Fokker-Planck equation that governs the statistics of soliton parameters in optical transmission lines in the presence of additive amplifier spontaneous emission. We demonstrate that these statistics are generally non-Gaussian. We present exact marginal probability-density functions for soliton parameters for some cases. A WKB approach is applied to describe the tails of the probability-density functions. © 2005 Optical Society of America.

Free energy functional expansion as the generalized approach to the equation of state of dense fluids

A version of the thermodynamic perturbation theory based on a scaling transformation of the partition function has been applied to the statistical derivation of the equation of state in a highpressure region. Two modifications of the equations of state have been obtained on the basis of the free energy functional perturbation series. The comparative analysis of the experimental PV T- data on the isothermal compression for the supercritical fluids of inert gases has been carried out. © 2012.

Inverse forecasting:a new approach for predictive modelling

In the last two decades there have been substantial developments in the mathematical theory of inverse optimization problems, and their applications have expanded greatly. In parallel, time series analysis and forecasting have become increasingly important in various fields of research such as data mining, economics, business, engineering, medicine, politics, and many others. Despite the large uses of linear programming in forecasting models there is no a single application of inverse optimization reported in the forecasting literature when the time series data is available. Thus the goal of this paper is to introduce inverse optimization into forecasting field, and to provide a streamlined approach to time series analysis and forecasting using inverse linear programming. An application has been used to demonstrate the use of inverse forecasting developed in this study. © 2007 Elsevier Ltd. All rights reserved.

A mathematical model for assembly line balancing model to consider disordering sequence of workstations

Purpose – A binary integer programming model for the simple assembly line balancing problem (SALBP), which is well known as SALBP-1, was formulated more than 30 years ago. Since then, a number of researchers have extended the model for the variants of assembly line balancing problem.The model is still prevalent nowadays mainly because of the lower and upper bounds on task assignment. These properties avoid significant increase of decision variables. The purpose of this paper is to use an example to show that the model may lead to a confusing solution. Design/methodology/approach – The paper provides a remedial constraint set for the model to rectify the disordered sequence problem. Findings – The paper presents proof that the assembly line balancing model formulated by Patterson and Albracht may lead to a confusing solution. Originality/value – No one previously has found that the commonly used model is incorrect.

The development of hard real-time systems using a formal approach

Hard real-time systems are a class of computer control systems that must react to demands of their environment by providing `correct' and timely responses. Since these systems are increasingly being used in systems with safety implications, it is crucial that they are designed and developed to operate in a correct manner. This thesis is concerned with developing formal techniques that allow the specification, verification and design of hard real-time systems. Formal techniques for hard real-time systems must be capable of capturing the system's functional and performance requirements, and previous work has proposed a number of techniques which range from the mathematically intensive to those with some mathematical content. This thesis develops formal techniques that contain both an informal and a formal component because it is considered that the informality provides ease of understanding and the formality allows precise specification and verification. Specifically, the combination of Petri nets and temporal logic is considered for the specification and verification of hard real-time systems. Approaches that combine Petri nets and temporal logic by allowing a consistent translation between each formalism are examined. Previously, such techniques have been applied to the formal analysis of concurrent systems. This thesis adapts these techniques for use in the modelling, design and formal analysis of hard real-time systems. The techniques are applied to the problem of specifying a controller for a high-speed manufacturing system. It is shown that they can be used to prove liveness and safety properties, including qualitative aspects of system performance. The problem of verifying quantitative real-time properties is addressed by developing a further technique which combines the formalisms of timed Petri nets and real-time temporal logic. A unifying feature of these techniques is the common temporal description of the Petri net. A common problem with Petri net based techniques is the complexity problems associated with generating the reachability graph. This thesis addresses this problem by using concurrency sets to generate a partial reachability graph pertaining to a particular state. These sets also allows each state to be checked for the presence of inconsistencies and hazards. The problem of designing a controller for the high-speed manufacturing system is also considered. The approach adopted mvolves the use of a model-based controller: This type of controller uses the Petri net models developed, thus preservIng the properties already proven of the controller. It. also contains a model of the physical system which is synchronised to the real application to provide timely responses. The various way of forming the synchronization between these processes is considered and the resulting nets are analysed using concurrency sets.

Mathematical methods in power system stability studies

In this thesis various mathematical methods of studying the transient and dynamic stabiIity of practical power systems are presented. Certain long established methods are reviewed and refinements of some proposed. New methods are presented which remove some of the difficulties encountered in applying the powerful stability theories based on the concepts of Liapunov. Chapter 1 is concerned with numerical solution of the transient stability problem. Following a review and comparison of synchronous machine models the superiority of a particular model from the point of view of combined computing time and accuracy is demonstrated. A digital computer program incorporating all the synchronous machine models discussed, and an induction machine model, is described and results of a practical multi-machine transient stability study are presented. Chapter 2 reviews certain concepts and theorems due to Liapunov. In Chapter 3 transient stability regions of single, two and multi~machine systems are investigated through the use of energy type Liapunov functions. The treatment removes several mathematical difficulties encountered in earlier applications of the method. In Chapter 4 a simple criterion for the steady state stability of a multi-machine system is developed and compared with established criteria and a state space approach. In Chapters 5, 6 and 7 dynamic stability and small signal dynamic response are studied through a state space representation of the system. In Chapter 5 the state space equations are derived for single machine systems. An example is provided in which the dynamic stability limit curves are plotted for various synchronous machine representations. In Chapter 6 the state space approach is extended to multi~machine systems. To draw conclusions concerning dynamic stability or dynamic response the system eigenvalues must be properly interpreted, and a discussion concerning correct interpretation is included. Chapter 7 presents a discussion of the optimisation of power system small sjgnal performance through the use of Liapunov functions.