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.

Contamination routes and control of Listeria monocytogenes in Food Production

Listeria monocytogenes is the causative agent of the severe foodborne infection listeriosis. The number of listeriosis cases in recent years has increased in many European countries, including Finland. Contamination of the pathogen needs to be minimized and growth to high numbers in foods prevented in order to reduce the incidence of human cases. The aim of this study was to evaluate contamination routes of L. monocytogenes in the food chain and to investigate methods for control of the pathogen in food processing. L. monocytogenes was commonly found in wild birds, the pig production chain and in pork production plants. It was found most frequently in birds feeding at landfill site, organic farms, tonsil samples, and sites associated with brining. L. monococytogenes in birds, farms, food processing plant or foods did not form distinct genetic groups, but populations overlapped. The majority of genotypes recovered from birds were also detected in foods, food processing environments and other animal species and birds may disseminate L. monocytogenes into food chain. Similar genotypes were found in different pigs on the same farm, as well as in pigs on farms and later in the slaughterhouse. L. monocytogenes contamination spreads at farm level and may be a contamination source into slaughterhouses and further into meat. Incoming raw pork in the processing plant was frequently contaminated with L. monocytogenes and genotypes in raw meat were also found in processing environment and in RTE products. Thus, raw material seems to be a considerable source of contamination into processing facilities. In the pork processing plant, the prevalence of L. monocytogenes increased in the brining area, showing that the brining was an important contamination site. Recovery of the inoculated L. monocytogenes strains showed that there were strain-specific differences in the ability to survive in lettuce and dry sausage. The ability of some L. monocytogenes strains to survive well in food production raises a challenge for industry, because these strains can be especially difficult to remove from the products and raises a need to use an appropriate hurdle concept to control most resistant strains. Control of L. monocytogenes can be implemented throughout the food chain. Farm-specific factors affected the prevalence of L. monocytogenes and good farm-level practices can therefore be utilized to reduce the prevalence of this pathogen on the farm and possibly further in the food chain. Well separated areas in a pork production plant had low prevalences of L. monocytogenes, thus showing that compartmentalization controls the pathogen in the processing line. The food processing plant, especially the brining area, should be subjected to disassembling, extensive cleaning and disinfection to eliminate persistent contamination by L. monocytogenes, and replacing brining with dry-salting should be considered. All of the evaluated washing solutions decreased the populations of L. monocytogenes on precut lettuce, but did not eliminate the pathogen. Thus, the safety of fresh-cut produce cannot rely on washing with disinfectants, and high-quality raw material and good manufacturing practices remain important. L. monocytogenes was detected in higher levels in sausages without the protective culture than in sausages with this protective strain, although numbers of L. monocytogenes by the end of the ripening decreased to the level of < 100 MPN/g in all sausages. Protective starter cultures provide an appealing hurdle in dry sausage processing and assist in the control of L. monocytogenes.

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.

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.

Analysis of co-current hydraircooling of food products in bulk

A mathematical model is developed to describe the hydraircooling process when the water and air are flowing in the same direction. The governing equations for the simultaneous heat and mass transfer are solved using finite-difference numerical methods. The half cooling time of the food products is correlated as a function of the dimensionless process parameters. It is observed that a process time of approximately double the half cooling time will result in the food products attaining almost a steady state. The process times of the bulk hydraircooling process and the bulk air precooling process are compared.

Consumers' attitudes towards food prices

High food prices can be a barrier to healthy eating because some of the food products may be perceived as expensive. Understanding the role of price in food purchase situations is important, but only a few studies document attitudes towards expensiveness or cheapness in foods. In this thesis, the role of food price in food choice and consumers attitudes towards food prices were investigated and the aim was to measure the food price attitudes. Food price attitudes were hypothesized to have an impact on consumers willingness to pay judgements and their willingness to buy premium-priced food products. First, using qualitative data consisting of 40 thematic interviews the experiences of the expensiveness and cheapness in foods were explored by using functional food products as a target product category. Second, a Food Price Attitude Scale was developed using four quantitative surveys representing Finnish consumers (2001 N=1158; 2002 N=1156; 2004a N=1113; 2004b N=1027). Food price attitudes were confirmed to compose a multidimensional construct and consumers may perceive positive and negative attitudes towards both high and low food prices. Finnish consumers were clustered into four groups based on their food price attitudes. In the first group, 29% of respondents were negative towards high food prices and they were willing to seek low food prices, whereas respondents in another group (22%) were positive towards high food prices. Additionally, in the third group consumers (17%) were willing to pay for high quality but still looked for low food prices. In the fourth group, consumers (32%) were willing to look for low food prices, unwilling to pay for high quality, but high-priced food was appreciated if offered to others. It was found in qualitative data that consumers willingness to accept high prices in foods was connected to price fairness and to justifications. Feelings of fairness or unfairness might be a core element of food price attitudes. Using quantitative methods, it was confirmed that positive attitudes towards high food prices in terms of high quality enhanced consumers willingness to buy food products with certain benefits (e.g., a health claim). Additionally, the favourable attitude towards low food prices lowered the willingness to pay estimates. This type of tendency, however, can create a possible bias in small convenient samples. In the food price-related research, it is advisable to take into account food price attitudes as possible background variables. The Food Price Attitude Scale needs further development to increase construct validity even though, in the present study, it was shown to be a reliable measure with good predictive and discriminant validity. The theoretical and managerial implications of the results for a better understanding of the role of price in consumers food purchases are discussed.

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.

A New Approach to the Problem of Scattering of Water Waves by Vertical Barriers

Using a modified Green's function technique the two well-known basic problems of scattering of surface water waves by vertical barriers are reduced to the problem of solving a pair of uncoupled integral equations involving the “jump” and “sum” of the limiting values of the velocity potential on the two sides of the barriers in each case. These integral equations are then solved, in closed form, by the aid of an integral transform technique involving a general trigonometric kernel as applicable to the problems associated with a radiation condition.