On the Fekete-Szego problem for concave univalent functions

We consider the Fekete-Szego problem with real parameter lambda for the class Co(alpha) of concave univalent functions. (C) 2010 Elsevier Inc. All rights reserved.

Uniformly valid analytical solution to the problem of a decaying shock wave

An explicit representation of an analytical solution to the problem of decay of a plane shock wave of arbitrary strength is proposed. The solution satisfies the basic equations exactly. The approximation lies in the (approximate) satisfaction of two of the Rankine-Hugoniot conditions. The error incurred is shown to be very small even for strong shocks. This solution analyses the interaction of a shock of arbitrary strength with a centred simple wave overtaking it, and describes a complete history of decay with a remarkable accuracy even for strong shocks. For a weak shock, the limiting law of motion obtained from the solution is shown to be in complete agreement with the Friedrichs theory. The propagation law of the non-uniform shock wave is determined, and the equations for shock and particle paths in the (x, t)-plane are obtained. The analytic solution presented here is uniformly valid for the entire flow field behind the decaying shock wave.

Noncommutative Quantum Field Theory : Problem of Time and Some Applications

In this thesis the current status and some open problems of noncommutative quantum field theory are reviewed. The introduction aims to put these theories in their proper context as a part of the larger program to model the properties of quantized space-time. Throughout the thesis, special focus is put on the role of noncommutative time and how its nonlocal nature presents us with problems. Applications in scalar field theories as well as in gauge field theories are presented. The infinite nonlocality of space-time introduced by the noncommutative coordinate operators leads to interesting structure and new physics. High energy and low energy scales are mixed, causality and unitarity are threatened and in gauge theory the tools for model building are drastically reduced. As a case study in noncommutative gauge theory, the Dirac quantization condition of magnetic monopoles is examined with the conclusion that, at least in perturbation theory, it cannot be fulfilled in noncommutative space.

Solution of a Boundary-Value Problem associated with Diffraction of Water Waves by a Nearly Vertical Barrier

An exact solution is derived for a boundary-value problem for Laplace's equation which is a generalization of the one occurring in the course of solution of the problem of diffraction of surface water waves by a nearly vertical submerged barrier. The method of solution involves the use of complex function theory, the Schwarz reflection principle, and reduction to a system of two uncoupled Riemann-Hilbert problems. Known results, representing the reflection and transmission coefficients of the water wave problem involving a nearly vertical barrier, are derived in terms of the shape function.

Steady incompressible flow of cohesionless granular materials through a wedge-shaped hopper: Frictional 14kinetic solution to the smooth wall, radial gravity problem

Hybrid frictional-kinetic equations are used to predict the velocity, grain temperature, and stress fields in hoppers. A suitable choice of dimensionless variables permits the pseudo-thermal energy balance to be decoupled from the momentum balance. These balances contain a small parameter, which is analogous to a reciprocal Reynolds number. Hence an approximate semi-analytical solution is constructed using perturbation methods. The energy balance is solved using the method of matched asymptotic expansions. The effect of heat conduction is confined to a very thin boundary layer near the exit, where it causes a marginal change in the temperature. Outside this layer, the temperature T increases rapidly as the radial coordinate r decreases. In particular, the conduction-free energy balance yields an asymptotic solution, valid for small values of r, of the form T proportional r-4. There is a corresponding increase in the kinetic stresses, which attain their maximum values at the hopper exit. The momentum balance is solved by a regular perturbation method. The contribution of the kinetic stresses is important only in a small region near the exit, where the frictional stresses tend to zero. Therefore, the discharge rate is only about 2.3% lower than the frictional value, for typical parameter values. As in the frictional case, the discharge rate for deep hoppers is found to be independent of the head of material.

The problem of conserving amphibians in the Western Ghats, India

Habitat distruction and hunting for dissection specimens have taken their toll. But there may be other, subtle factors causing loss of amphibian populations.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

Leisure-time physical activity, health related functioning and retirement : a prospective cohort study among middle-aged employees

Physical inactivity has become a major threat to public health worldwide. The Finnish health and welfare policies emphasize that the working population should maintain good health and functioning until their normal retirement age and remain in good health and independence later in life. Health behaviours like physical activity potentially play an important role in reaching this target as physical activity contributes to better physical fitness and to reduced risk of major chronic diseases. The aim of this study was to examine first whether the volume and intensity of leisure-time physical activity impacts on subsequent physical health functioning, sickness absence and disability retirement. The second aim was to examine changes in leisure-time physical activity of moderate and vigorous intensity after transition to retirement. This study is part of the ongoing Helsinki Health Study. The baseline data were collected by questionnaires in 2000 - 02 among the employees of the City of Helsinki aged 40 to 60. The follow-up survey data were collected in 2007. Data on sickness absence were obtained from the employer s (City of Helsinki) sickness absence registers and pension data were obtained from the Finnish Centre for Pensions. Leisure-time physical activity was measured in four grades of intensity and classified according to physical activity recommendations considering both the volume and intensity of physical activity. Statistical techniques including analysis of covariance, logistic regression, Cox proportional hazards models and Poisson regression were used. Employees who were vigorously active during leisure time especially had better physical health functioning than those physically inactive. High physical activity in particular contributed to the maintenance of good physical health functioning. High physical activity also reduced the risk of subsequent sickness absences as well as the risk of all-cause disability retirement and retirement due to musculoskeletal and mental causes. Among those transferred to old-age retirement moderate-intensity leisure-time physical activity increased on average by more than half an hour per week and in addition the occurrence of physical inactivity reduced. Such changes were not observed among those remained employed and those transferred to disability retirement. This prospective cohort study provided novel results on the effects of leisure-time physical activity on health related functioning and changes in leisure-time physical activity after retirement. Although the benefits of moderate-intensity physical activity for health are well known these results suggest the importance of vigorous physical activity for subsequent health related functioning. Thus vigorous physical activity to enhance fitness should be given more emphasis from a public health perspective. In addition, physical activity should be encouraged among those who are about to retire.

A Direct Approach to the Problem of Diffraction by a Half-Plane under Mixed Boundary Conditions

A general direct technique of solving a mixed boundary value problem in the theory of diffraction by a semi-infinite plane is presented. Taking account of the correct edge-conditions, the unique solution of the problem is derived, by means of Jones' method in the theory of Wiener-Hopf technique, in the case of incident plane wave. The solution of the half-plane problem is found out in exact form. (The far-field is derived by the method of steepest descent.) It is observed that it is not the Wiener-Hopf technique which really needs any modification but a new technique is certainly required to handle the peculiar type of coupled integral equations which the Wiener-Hopf technique leads to. Eine allgemeine direkte Technik zur Lösung eines gemischten Randwertproblems in der Theorie der Beugung an einer halbunendlichen Ebene wird vorgestellt. Unter Berücksichtigung der korrekten Eckbedingungen wird mit der Methode von Jones aus der Theorie der Wiener-Hopf-Technik die eindeutige Lösung für den Fall der einfallenden ebenen Welle hergeleitet. Die Lösung des Halbebenenproblems wird in exakter Form angegeben. (Das Fernfeld wurde mit der Methode des steilsten Abstiegs bestimmt.) Es wurde bemerkt, daß es nicht die Wiener-Hopf-Technik ist, die wirklich irgend welcher Modifikationen bedurfte. Gewiß aber wird eine neue Technik zur Behandlung des besonderen Typs gekoppelter Integralgleichungen benötigt, auf die die Wiener-Hopf-Technik führt.

Lunch eating patterns during working hours and their social and work-related determinants : Study of Finnish employees

Work has a central role in the lives of big share of adult Finns and meals they eat during the workday comprise an important factor in their nutrition, health, and well-being. On workdays, lunch is mainly eaten at worksite canteens or, especially among women, as a packed meal in the workplace s break room. No national-level data is available on the nutritional quality of the meals served by canteens, although the Finnish Institute of Occupational Health laid out the first nutrition recommendations for worksite canteens in 1971. The aim of this study was to examine the contribution of various socio-demographic, socioeconomic, and work-related factors to the lunch eating patterns of Finnish employees during the working day and how lunch eating patterns influence dietary intake. Four different population-based cross-sectional datasets were used in this thesis. Three of the datasets were collected by the National Institute for Health and Welfare (Health Behaviour and Health among the Finnish Adult Population survey from 1979 to 2001, n=24746, and 2005 to 2007, n=5585, the National Findiet 2002 Study, n=261), and one of them by the Finnish Institute of Occupational Health (Work and Health in Finland survey from 1997, 2000, and 2003, n=6369). The Health Behaviour and Health among the Finnish Adult Population survey and the Work and Health in Finland survey are nationally representative studies that are conducted repeatedly. Survey information was collected by self-administered questionnaires, dietary recalls, and telephone interviews. The frequency of worksite canteen use has been quite stable for over two decades in Finland. A small decreasing trend can be seen in all socioeconomic groups. During the whole period studied, those with more years of education ate at worksite canteens more often than the others. The size of the workplace was the most important work-related determinant associated with the use of a worksite canteen. At small workplaces, other work-related determinants, like occupation, physical strain at work, and job control, were also associated with canteen use, whereas at bigger workplaces the associations were almost nonexistent. The major social determinants of worksite canteen availability were the education and occupational status of employees and the only work-related determinant was the size of the workplace. A worksite canteen was more commonly available to employees at larger workplaces and to those with the higher education and the higher occupational status. Even when the canteen was equally available to all employees, its use was nevertheless determined by occupational class and the place of residence, especially among female employees. Those with higher occupational status and those living in the Helsinki capital area ate in canteens more frequently than the others. Employees who ate at a worksite canteen consumed more vegetables and vegetable and fish dishes at lunch than did those who ate packed lunches. Also, the daily consumption of vegetables and the proportion of the daily users of vegetables were higher among those male employees who ate at a canteen. In conclusion, life possibilities, i.e. the availability of a canteen, education, occupational status, and work-related factors, played an important role in the choice of where to eat lunch among Finnish employees. The most basic prerequisite for eating in a canteen was availability, but there were also a number of underlying social determinants. Occupational status and the place of residence were the major structural factors behind individuals choices in their lunch eating patterns. To ensure the nutrition, health, and well-being of employees, employers should provide them with the option to have good quality meals during working hours. The availability of worksite canteens should be especially supported in lower socioeconomic groups. In addition, employees should be encouraged to have lunch at a worksite canteen when one is available by removing structural barriers to its use.

Inverse problem for the wave equation : partial data and novel boundary sources

An inverse problem for the wave equation is a mathematical formulation of the problem to convert measurements of sound waves to information about the wave speed governing the propagation of the waves. This doctoral thesis extends the theory on the inverse problems for the wave equation in cases with partial measurement data and also considers detection of discontinuous interfaces in the wave speed. A possible application of the theory is obstetric sonography in which ultrasound measurements are transformed into an image of the fetus in its mother's uterus. The wave speed inside the body can not be directly observed but sound waves can be produced outside the body and their echoes from the body can be recorded. The present work contains five research articles. In the first and the fifth articles we show that it is possible to determine the wave speed uniquely by using far apart sound sources and receivers. This extends a previously known result which requires the sound waves to be produced and recorded in the same place. Our result is motivated by a possible application to reflection seismology which seeks to create an image of the Earth s crust from recording of echoes stimulated for example by explosions. For this purpose, the receivers can not typically lie near the powerful sound sources. In the second article we present a sound source that allows us to recover many essential features of the wave speed from the echo produced by the source. Moreover, these features are known to determine the wave speed under certain geometric assumptions. Previously known results permitted the same features to be recovered only by sequential measurement of echoes produced by multiple different sources. The reduced number of measurements could increase the number possible applications of acoustic probing. In the third and fourth articles we develop an acoustic probing method to locate discontinuous interfaces in the wave speed. These interfaces typically correspond to interfaces between different materials and their locations are of interest in many applications. There are many previous approaches to this problem but none of them exploits sound sources varying freely in time. Our use of more variable sources could allow more robust implementation of the probing.

Vehicle Routing Problem with Load Compatibility Constraints

The major contribution of this paper is to introduce load compatibility constraints in the mathematical model for the capacitated vehicle routing problem with pickup and deliveries. The employee transportation problem in the Indian call centers and transportation of hazardous materials provided the motivation for this variation. In this paper we develop a integer programming model for the vehicle routing problem with load compatibility constraints. Specifically two types of load compatability constraints are introduced, namely mutual exclusion and conditional exclusion. The model is demonstrated with an application from the employee transportation problem in the Indian call centers.

Neural network approach for the two-dimensional assignment problem

A neural network approach for solving the two-dimensional assignment problem is proposed. The design of the neural network is discussed and simulation results are presented. The neural network obtains 10-15% lower cost placements on the examples considered, than the adjacent pairwise exchange method.