Mathematical aspects of Feynman integrals

In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals.rnrnThe integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph.rnrnStarting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative step to an abstract combinatorial problem, known as Hironaka's polyhedra game. We present a publicly available implementation of the improved algorithm. Furthermore we explain the relationship of the sector decomposition method with the resolution of singularities of a variety, given by a sequence of blow-ups, in algebraic geometry.rnrnMotivated by the connection between Feynman integrals and topics of algebraic geometry we consider the set of periods as defined by Kontsevich and Zagier. This special set of numbers contains the set of multiple zeta values and certain values of polylogarithms, which in turn are known to be present in results for Laurent coefficients of certain dimensionally regularized Feynman integrals. By use of the extended sector decomposition algorithm we prove a theorem which implies, that the Laurent coefficients of an arbitrary Feynman integral are periods if the masses and kinematical invariants take values in the Euclidean momentum region. The statement is formulated for an even more general class of integrals, allowing for an arbitrary number of polynomials in the integrand.

Distribution feeder loads classification and decomposition

Load in distribution networks is normally measured at the 11kV supply points; little or no information is known about the type of customers and their contributions to the load. This paper proposes statistical methods to decompose an unknown distribution feeder load to its customer load sector/subsector profiles. The approach used in this paper should assist electricity suppliers in economic load management, strategic planning and future network reinforcements.

The Chinese state enterprise sector: Labour market reform and the impact on male–female wage structure

The paper examines the wage structure in the Chinese state enterprise sector between 1981 and 1987. This period is of particular interest given the introduction of major labour market reforms in China during the early 1980s. In essence the reforms represented a movement away from administratively determined prices towards a market–oriented system combined with a relatively flexible system of labour allocation. The Juhn, Murphy and Pierce (1991) decomposition is employed to shed light on the role of changing labour market institutions over the period.

Decomposition of toxic chemical substance management in three U.S. manufacturing sectors from 1991 to 2008

This study analyzes toxic chemical substance management in three U.S. manufacturing sectors from 1991 to 2008. Decomposition analysis applying the logarithmic mean Divisia index is used to analyze changes in toxic chemical substance emissions by the following five factors: cleaner production, end-of-pipe treatment, transfer for further management, mixing of intermediate materials, and production scale. Based on our results, the chemical manufacturing sector reduced toxic chemical substance emissions mainly via end-of-pipe treatment. In the meantime, transfer for further management contributed to the reduction of toxic chemical substance emissions in the metal fabrication industry. This occurred because the environmental business market expanded in the 1990s, and the infrastructure for the recycling of metal and other wastes became more efficient. Cleaner production is the main contributor to toxic chemical reduction in the electrical product industry. This implies that the electrical product industry is successful in developing a more environmentally friendly product design and production process.

Decomposition of energy-related CO2 emissions in Australia: Challenges and policy implications

Changes in energy-related CO2 emissions aggregate intensity, total CO2 emissions and per-capita CO2 emissions in Australia are decomposed by using a Logarithmic Mean Divisia Index (LMDI) method for the period 1978-2010. Results indicate improvements in energy efficiency played a dominant role in the measured 17% reduction in CO2 emissions aggregate intensity in Australia over the period. Structural changes in the economy, such as changes in the relative importance of the services sector vis-à-vis manufacturing, have also played a major role in achieving this outcome. Results also suggest that, without these mitigating factors, income per capita and population effects could well have produced an increase in total emissions of more than 50% higher than actually occurred over the period. Perhaps most starkly, the results indicate that, without these mitigating factors, the growth in CO2 emissions per capita could have been over 150% higher than actually observed. Notwithstanding this, the study suggests that, for Australia to meet its Copenhagen commitment, the relative average per annum effectiveness of these mitigating factors during 2010-2020 probably needs to be almost three times what it was in the 2005-2010 period-a very daunting challenge indeed for Australia's policymakers.

Administración en la cadena de suministro y su relación con el desempeño de las PYME del sector agroindustrial

En la actualidad las organizaciones están en búsqueda de una mejora continua, esto lleva a que las empresas hagan una revisión de estrategias que permitan alcanzar una posición de líderes en los diferentes sectores en los que se desempeñan. Una de las estrategias para lograr un alto posicionamiento en las nuevas empresas es la adecuada gestión que hacen de la cadena de suministro. El sector agroindustrial tiene un amplia cadena de suministro desde la obtención de materias primas hasta la llegada al cliente final, por su gran magnitud requiere de una adecuada administración de procesos que permitan ser eficaces y eficientes para alcanzar logros propuestos, aprovechar los recursos limitados con los que cuentan para su cumplimiento y, por último, la capacidad propia para la transformación de sus recursos. Para lograr que las empresas obtengan ventajas competitivas, es necesario que los distintos eslabones de la cadena de suministros cuenten con una capacidad de interacción que les permita, tanto agilizar como asegurar el éxito durante la incorporación de los nuevos productos en el mercado. Por medio de esta investigación se busca esclarecer y analizar la importancia de la administración en la cadena de suministro y la relación con el desempeño, basándose en las Pymes del sector agroindustrial. La intención es evaluar la información de diversos autores quienes han hablado de la relación que existe entre la cadena de suministro y su desempeño, teniendo en cuenta variables como el sector agroindustrial y las Pymes.

The Chinese state enterprise sector: labour market reform and the impact on male-female wage structure

The paper examines the wage structure in the Chinese state enterprise sector between 1981 and 1987. This period is of particular interest given the introduction of major labour market reforms in China during the early 1980s. In essence the reforms represented a movement away from administratively determined prices towards a market–oriented system combined with a relatively flexible system of labour allocation. The Juhn, Murphy and Pierce (1991) decomposition is employed to shed light on the role of changing labour market institutions over the period.

Lipids and polycyclic aromatic hydrocarbons in bottom sediments from the Atlantic sector of the Southern Ocean

Distribution and composition of lipids and contents of alkanes and polycyclic aromatic hydrocarbons(PAHs) in bottom sediments of the Scotia and Weddell seas are discussed. Comparatively low concentrations of organic carbon (average 0.35%) and lipids (average 0.024%) result from rapid decomposition of organic matter in upper layers of the water column. Composition of alkanes indicates that lipids are of autochthonous origin, and stable concentrations of PAHs (average 25.8 ppb, sigma 15.3 ppb) indicate that they represent the background level for bottom sediments. Higher concentrations of PAHs in sediments near the King George Island (252.1 ppb) and different distributions of individual polyarenes are produced there by the heating systems of the Polish Antarctic Station.

Application of factor decomposition techniques to vertical specialisation measurements

The increasing importance of vertical specialisation (VS) trade has been a notable feature of rapid economic globalisation and regional integration. In an attempt to understand countries’ depth of participation in global production chains, many Input-Output based VS indicators have been developed. However, most of them focus on showing the overall magnitude of a country’s VS trade, rather than explaining the roles that specific sectors or products play in VS trade and what factors make the VS change over time. Changes in vertical specialisation indicators are, in fact, determined by mixed and complex factors such as import substitution ratios, types of exported goods and domestic production networks. In this paper, decomposition techniques are applied to VS measurement based on the OECD Input-Output database. The decomposition results not only help us understand the structure of VS at detailed sector and product levels, but also show us the contributions of trade dependency, industrial structures of foreign trade and domestic production system to a country’s vertical specialisation trade.

Allocation efficiency in China : an extension of the dynamic Olley-Pakes productivity decomposition

This paper develops a quantitative measure of allocation efficiency, which is an extension of the dynamic Olley-Pakes productivity decomposition proposed by Melitz and Polanec (2015). The extended measure enables the simultaneous capture of the degree of misallocation within a group and between groups and parallel to capturing the contribution of entering and exiting firms to aggregate productivity growth. This measure empirically assesses the degree of misallocation in China using manufacturing firm-level data from 2004 to 2007. Misallocation among industrial sectors has been found to increase over time, and allocation efficiency within an industry has been found to worsen in industries that use more capital and have firms with relatively higher state-owned market shares. Allocation efficiency among three ownership sectors (state-owned, domestic private, and foreign sectors) tends to improve in industries wherein the market share moves from a less-productive state-owned sector to a more productive private sector.

Is a little sunshine all we need? On the impact of sunshine regulation on profits, productivity and prices in the Dutch drinking water sector

This paper analyzes the performance of Dutch drinking water utilities before and after the introduction of sunshine regulation, which involves publication of the performance of utilities but no formal price regulation. By decomposing profit change into its economic drivers, our results suggest that, in the Dutch political and institutional context, sunshine regulation was effective in improving the productivity of publicly organised services. Nevertheless, while sunshine regulation did bring about a moderate reduction in water prices, sustained and substantial economic profits suggest that it may not have the potential to fully align output prices with economic costs in the long run. In methodological terms, the DEA based profit decomposition is extended to robust and conditional non-parametric efficiency measures, so as to account better for both uncertainty and differences in operating environment between utilities.

State advances and private retreats? Evidence from the decomposition of the Chinese manufacturing aggregate productivity decomposition in China

This paper is motivated by the recent debate on the existence and scale of China's 'Guo Jin Min Tui' phenomenon, which is often translated as 'the state sector advances and the private sector retreats'. We argue that the profound implication of an advancing state sector is not the size expansion of the state ownership in the economy per se, but the likely retardation of the development of the already financially constrained private sector and the issues around the sustainability of the already weakening Chinese economy growth. Drawing on recent methodological advances, we provide a critical analysis of the contributions of the state and non-state sectors in the aggregate Total Factor Productivity and its growth over the period of 1998-2007 to verify the existence of GJMT and its possible impacts on Chinese economic growth. Overall, we find strong and consistent evidence of a systematic and worsening resource misallocation within the state sector and/or between the state sectors and private sectors over time. This suggests that non-market forces allow resources to be driven away from their competitive market allocation and towards the inefficient state sector. Crown Copyright © 2014.

In Situ Observation of the Thermal Decomposition of Weddelite by Heating Stage Environmental Scanning Electron Microscopy

The morphological and chemical changes occurring during the thermal decomposition of weddelite, CaC2O4·2H2O, have been followed in real time in a heating stage attached to an Environmental Scanning Electron Microscope operating at a pressure of 2 Torr, with a heating rate of 10 °C/min and an equilibration time of approximately 10 min. The dehydration step around 120 °C and the loss of CO around 425 °C do not involve changes in morphology, but changes in the composition were observed. The final reaction of CaCO3 to CaO while evolving CO2 around 600 °C involved the formation of chains of very small oxide particles pseudomorphic to the original oxalate crystals. The change in chemical composition could only be observed after cooling the sample to 350 °C because of the effects of thermal radiation.

Thermal decomposition of the synthetic hydrotalcite iowaite

The thermal stability and thermal decomposition pathways for synthetic iowaite have been determined using thermogravimetry in conjunction with evolved gas mass spectrometry. Chemical analysis showed the formula of the synthesised iowaite to be Mg6.27Fe1.73(Cl)1.07(OH)16(CO3)0.336.1H2O and X-ray diffraction confirms the layered structure. Dehydration of the iowaite occurred at 35 and 79°C. Dehydroxylation occurred at 254 and 291°C. Both steps were associated with the loss of CO2. Hydrogen chloride gas was evolved in two steps at 368 and 434°C. The products of the thermal decomposition were MgO and a spinel MgFe2O4. Experimentally it was found to be difficult to eliminate CO2 from inclusion in the interlayer during the synthesis of the iowaite compound and in this way the synthesised iowaite resembled the natural mineral.