Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [29]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.

COMPARISON RESULTS FOR CONJUGATE AND FOCAL POINTS IN SEMI-RIEMANNIAN GEOMETRY VIA MASLOV INDEX

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.

Improved Prediction of Hydrocarbon Flash Points from Boiling Point Data

Flash points (T(FP)) of hydrocarbons are calculated from their flash point numbers, N(FP), with the relationship T(FP) (K) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901 In turn, the N(FP) values can be predicted from experimental boiling point numbers (Y(BP)) and molecular structure with the equation N(FP) = 0.987 Y(BP) + 0.176D + 0.687T + 0.712B - 0.176 where D is the number of olefinic double bonds in the structure, T is the number of triple bonds, and B is the number of aromatic rings. For a data set consisting of 300 diverse hydrocarbons, the average absolute deviation between the literature and predicted flash points was 2.9 K.

Calculating Flash Point Numbers from Molecular Structure: An Improved Method for Predicting the Flash Points of Acyclic Alkanes

We report a novel method for calculating flash points of acyclic alkanes from flash point numbers, N(FP), which can be calculated from experimental or calculated boiling point numbers (Y(BP)) with the equation N(FP) = 1.020Y(BP) - 1.083 Flash points (FP) are then determined from the relationship FP(K) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901 For it data set of 102 linear and branched alkanes, the correlation of literature and predicted flash points has R(2) = 0.985 and an average absolute deviation of 3.38 K. N(FP) values can also be estimated directly from molecular structure to produce an even closer correspondence of literature and predicted FP values. Furthermore, N(FP) values provide a new method to evaluate the reliability of literature flash point data.

Simple Method to Evaluate and to Predict Flash Points of Organic Compounds

Flash points (T(FP)) of organic compounds are calculated from their flash point numbers, N(FP), with the relationship T(FP) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901. In turn, the N(FP) values can be predicted from boiling point numbers (Y(BP)) and functional group counts with the equation N(FP) = 0.974Y(BP) + Sigma(i)n(i)G(i) + 0.095 where G(i) is a functional group-specific contribution to the value of N(FP) and n(i) is the number of such functional groups in the structure. For a data set consisting of 1000 diverse organic compounds, the average absolute deviation between reported and predicted flash points was less than 2.5 K.

Electrochemical Control of the Time-Dependent Intensity Fluctuations in Surface-Enhanced Raman Scattering (SERS)

Time-dependent fluctuations in surface-enhanced Raman scattering (SERS) intensities were recorded from a roughened silver electrode immersed in diluted solutions of rhodamine 6G (R6G) and congo red (CR). These fluctuations were attributed to a small number of SERS-active molecules probing regions of extremely high electromagnetic field (hot spots) at the nanostructured surface. The time-dependent distribution of SERS intensities followed a tailed statistics at certain applied potentials, which has been linked to single-molecule dynamics. The shape of the distribution was reversibly tuned by the applied voltage. Mixtures of both dyes, R6G and CR, at low concentrations were also investigated. Since R6G is a cationic dye and CR is an anionic dye, the statistics of the SERS intensity distribution of either dye in a mixture were independently controlled by adjusting the applied potential. The potential-controlled distribution of SERS intensities was interpreted by considering the modulation of the surface coverage of the adsorbed dye by the interfacial electric field. This interpretation was supported by a two-dimensional Monte Carlo simulation that took into account the time evolution of the surface configuration of the adsorbed species and their probability to populate a hypothetical hot spot. The potential-controlled SERS dynamics reported here is a first step toward the spectroelectrochemical investigation of redox processes at the single-molecule level by SERS.

The value of a saved tree : The lifecycle of CO2-emissions associated with the combination of printing paper and electricity production of wood in the U.S. and Sweden

The pulp- and paper production is a very energy intensive industry sector. Both Sweden and the U.S. are major pulpandpaper producers. This report examines the energy and the CO2-emission connected with the pulp- and paperindustry for the two countries from a lifecycle perspective.New technologies make it possible to increase the electricity production in the integrated pulp- andpaper mill through black liquor gasification and a combined cycle (BLGCC). That way, the mill canproduce excess electricity, which can be sold and replace electricity produced in power plants. In thisprocess the by-products that are formed at the pulp-making process is used as fuel to produce electricity.In pulp- and paper mills today the technology for generating energy from the by-product in aTomlinson boiler is not as efficient as it could be compared to the BLGCC technology. Scenarios havebeen designed to investigate the results from using the BLGCC technique using a life cycle analysis.Two scenarios are being represented by a 1994 mill in the U.S. and a 1994 mill in Sweden.The scenariosare based on the average energy intensity of pulp- and paper mills as operating in 1994 in the U.S.and Sweden respectively. The two other scenarios are constituted by a »reference mill« in the U.S. andSweden using state-of-the-art technology. We investigate the impact of varying recycling rates and totalenergy use and CO2-emissions from the production of printing and writing paper. To economize withthe wood and that way save trees, we can use the trees that are replaced by recycling in a biomassgasification combined cycle (BIGCC) to produce electricity in a power station. This produces extra electricitywith a lower CO2 intensity than electricity generated by, for example, coal-fired power plants.The lifecycle analysis in this thesis also includes the use of waste treatment in the paper lifecycle. Both Sweden and theU.S. are countries that recycle paper. Still there is a lot of paper waste, this paper is a part of the countries municipalsolid waste (MSW). A lot of the MSW is landfilled, but parts of it are incinerated to extract electricity. The thesis hasdesigned special scenarios for the use of MSW in the lifecycle analysis.This report is studying and comparing two different countries and two different efficiencies on theBLGCC in four different scenarios. This gives a wide survey and points to essential parameters to specificallyreflect on, when making assumptions in a lifecycle analysis. The report shows that there arethree key parameters that have to be carefully considered when making a lifecycle analysis of wood inan energy and CO2-emission perspective in the pulp- and paper mill in the U.S. and in Sweden. First,there is the energy efficiency in the pulp- and paper mill, then the efficiency of the BLGCC and last theCO2 intensity of the electricity displaced by BIGCC or BLGCC generatedelectricity. It also show that with the current technology that we havetoday, it is possible to produce CO2 free paper with a waste paper amountup to 30%. The thesis discusses the system boundaries and the assumptions.Further and more detailed research, including amongst others thesystem boundaries and forestry, is recommended for more specificanswers.

Acupuncture for labour pain

Background: Acupuncture involves puncturing the skin with thin sterile needles at defined acupuncture points. Previous studies are inconclusive regarding the effect of acupuncture on labour pain, but some studies have found a reduction in the use of pharmacological pain relief when acupuncture is administered. The appropriate dose of acupuncture treatment required to elicit a potential effect on labour pain has not been fully explored. The dose is determined by many different factors, including the number of needles used and the intensity of the stimulation. In Sweden, manual stimulation of the needles is common practice when acupuncture is used for labour pain, but electrical stimulation of the needles, which gives a higher dose, could possibly be more effective. The overall aim of this thesis was to evaluate the effectiveness of acupuncture with manual stimulation (MA) of the needles as well as acupuncture with a combination of manual and electrical stimulation (EA) in reducing labour pain, compared with standard care without any form of acupuncture (SC). Methods: The study was designed as a three-armed randomised controlled trial in which 303 nulliparous women with normal pregnancies were randomised to MA, EA, or SC. The primary outcome was labour pain, assessed using the Visual Analogue Scale (VAS). Secondary outcomes were relaxation during labour, use of obstetric pain relief, and associations between maternal characteristics and labour pain and use of epidural analgesia respectively. Also, labour and infant outcomes, recollection of labour pain, and maternal experiences, such as birth experience and experience of the midwife, were investigated two months after the birth. The sample size calculation was based on the potential to discover a difference of 15 mm on the VAS. Data were collected during labour before the interventions, the day after birth, and two months later. Besides using the VAS, information was collected by means of study specific protocol, questionnaires and medical records. Results: The mean VAS scores were 66.4 in the MA group, 68.5 in the EA group, and 69.0 in the SC group (mean differences: MA vs. SC 2.6 95% CI -1.7 to 6.9, and EA vs. SC 0.6 95% CI -3.6 to 4.8). Other methods of pain relief were used less frequently in the EA group, including epidural analgesia, MA 61.4%, EA 46%, and SC 69.9%. (EA vs. SC OR 0.4 95% CI 0.2 to 0.7). No statistically significant differences were found in the recollection of labour pain between the three groups two months after birth (mean VAS score: MA 69.3, EA 68.7 and SC 70.1). A few maternal characteristics were associated with labour pain (age, dysmenorrhea, and cervix dilatation), but none of the investigated characteristics predicted the outcome of the acupuncture treatment in MA or EA. Women in the EA group experienced acupuncture as being effective for labour pain to a higher extent than women who received MA, MA 44.4%, EA 67.1% (EA vs. MA OR 2.4 95% CI 1.2 to 4.8). Women in the EA group also spent less time in labour (mean 500 min) than those who received MA (mean 619 min) and SC (mean 615 min) (EA vs. MA HR 1.4 95% CI 1.0 to1.9, EA vs. SC HR 1.4, 95% CI 1.1 to 2.0), and had less blood loss than women receiving SC, (EA vs. SC OR 0.1 95% CI 0.3 to 0.7). The women’s assessment of the midwife as being supportive during labour (MA 77.2%, EA 83.5%, SC 80%), overall satisfaction with midwife care (MA 100%, EA 97.5%, SC 98.7%), and having an overall positive childbirth experience (MA 64.6%, EA 61.0%, SC 54.3%) did not differ statistically. No serious side effects of the acupuncture treatment were reported. Conclusion: Acupuncture, regardless of type of stimulation, did not differ from standard care without acupuncture in terms of reducing women’s experience of pain during labour, or their memory of pain and childbirth overall two months after the birth. However, other forms of obstetric pain relief were less frequent in women receiving a combination of manual and electrical stimulation, suggesting that this method could facilitate coping with labour pain.

Physiological demands of competitive elite cross-country skiing

Introduction Researchers have, for decades, contributed to an increased collective understanding of the physiological demands in cross-country skiing; however, almost all of these studies have used either non-elite subjects and/or performances that emulate cross-country skiing. To establish the physiological demands of cross-country skiing, it is important to relate the investigated physiological variables to the competitive performance of elite skiers. The overall aim of this doctoral thesis was, therefore, to investigate the external validity of physiological test variables to determine the physiological demands in competitive elite cross-country skiing. Methods The subjects in Study I – IV were elite male (I – III) and female (III – IV) cross-country skiers. In all studies, the relationship between test variables (general and ski-specific) and competitive performances (i.e. the results from competitions or the overall ski-ranking points of the International Ski Federation (FIS) for sprint (FISsprint) and distance (FISdist) races) were analysed. Test variables reflecting the subject’s general strength, upper-body and whole-body oxygen uptake, oxygen uptake and work intensity at the lactate threshold, mean upper-body power, lean mass, and maximal double-poling speed were investigated. Results The ability to maintain a high work rate without accumulating lactate is an indicator of distance performance, independent of sex (I, IV). Independent of sex, high oxygen uptake in whole-body and upper-body exercise was important for both sprint (II, IV) and distance (I, IV) performance. The maximal double-poling speed and 60-s double-poling mean power output were indicators of sprint (IV) and distance performance (I), respectively. Lean mass was correlated with distance performance for women (III), whereas correlations were found between lean mass and sprint performance among both male and female skiers (III). Moreover, no correlations between distance performance and test variables were derived from tests of knee-extension peak torque, vertical jumps, or double poling on a ski-ergometer with 20-s and 360-s durations (I), whereas gross efficiency while treadmill roller skiing showed no correlation with either distance or sprint performance in cross-country skiing (IV). Conclusion The results in this thesis show that, depending on discipline and sex, maximal and peak oxygen uptake, work intensity at the lactate threshold, lean mass, double-poling mean power output, and double-poling maximal speed are all externally valid physiological test variables for evaluation of performance capability among elite cross-country skiers; however, to optimally indicate performance capability different test-variable expressions should be used; in general, the absolute expression appears to be a better indicator of competitive sprint performance whereas the influence of body mass should be considered when evaluating competitive distance performance capability of elite cross-country skiers.