We derive the equation linking the Weyl tensor with its Lanczos potential, called the Weyl-Lanczos equation, in 1+3 covariant formalism for perfect fluid Bianchi type I spacetime and find an explicit expression for a Lanczos potential of the Weyl tensor in these spacetimes. To achieve this, we first need to derive the covariant decomposition of the Lanczos potential in this formalism. We also study an example by Novello and Velloso and derive their Lanczos potential in shear-free, irrotational perfect fluid spacetimes from a particular ansatz in 1+3 covariant formalism. The existence of the Lanczos potential is in some ways analogous to the vector potential in electromagnetic theory. Therefore, we also derive the electromagnetic potential equation in 1+3 covariant formalism for a general spacetime.

Asymptotically flat spaces are widely studied because it is one natural way of describing an isolated system in general relativity. In this thesis we study what happens to the Lanczos potential at spacelike infinity in such spacetimes. By transformations of the Weyl-Lanczos equation, we derive expressions for the limiting equations on both the timelike unit hyperboloid, and the timelike unit cylinder. Finally the Newman-Penrose formalism is used to get a component version of the equations..

Objective: The aim of this study was to compare equations used to calculate BMR to values of BMR obtained from measurements in order to determine the most suitable equation to be used on children and adolescents with CF.Design: The participants where children and adolescents with CF. Data was collected from the division of Clinical Nutrition at Uppsala Akademiska Sjukhus. Age, weight, height, BMI, BMR, FFM and FM was recorded from 27 measurements. BMR from the participants collected from the indirect respiratory calorimetry was compared to the results obtained from five equations used to obtain a calculated value of BMR.Results: Tverskayas equation was best correlated with the measured BMR for the whole group. The equation underestimated BMR for the participants with a measured BMR over 1400 kcal/24h and overestimated BMR for participants with a measured BMR under 1400 kcal/24h.

This paper aims to derive the Black-Scholes equation for readers without advanced knowledge in finance and mathematics. To succeed, this paper contains a theoretical chapter in which concepts such as options, interest rate, differential equations and stochastic variable are explained. This paper also presents the theory of stochastic processes such as the Wiener process and Ito process. In the chapter on the Black-Scholes model the Ito process is used to describe price of shares and with the help of Ito's lemma Black-Scholes equation can be derived. In the paper, assumptions are listed that apply to the Black-Scholes model and then uses the Black-Scholes equation to calculate the price of a European call option.

Objective: The aim of this study was to compare equations used to calculate BMR to values of BMR obtained from measurements in order to determine the most suitable equation to be used on children and adolescents with CF.Design: The participants where children and adolescents with CF. Data was collected from the division of Clinical Nutrition at Uppsala Akademiska Sjukhus. Age, weight, height, BMI, BMR, FFM and FM was recorded from 27 measurements. BMR from the participants collected from the indirect respiratory calorimetry was compared to the results obtained from five equations used to obtain a calculated value of BMR.Results: Tverskayas equation was best correlated with the measured BMR for the whole group. The equation underestimated BMR for the participants with a measured BMR over 1400 kcal/24h and overestimated BMR for participants with a measured BMR under 1400 kcal/24h.

This paper aims to derive the Black-Scholes equation for readers without advanced knowledge in finance and mathematics. To succeed, this paper contains a theoretical chapter in which concepts such as options, interest rate, differential equations and stochastic variable are explained. This paper also presents the theory of stochastic processes such as the Wiener process and Ito process. In the chapter on the Black-Scholes model the Ito process is used to describe price of shares and with the help of Ito's lemma Black-Scholes equation can be derived. In the paper, assumptions are listed that apply to the Black-Scholes model and then uses the Black-Scholes equation to calculate the price of a European call option.

During the last decade, there has been an increase in the use of technology-based self-services within the retail sector. The increase is particularly noticeable within the grocery market. The reason behind the increased use of these systems is partially due to the fact that companies within highly competitive retail markets continually look for ways of decreasing costs while upholding efficiency. The problem is that it is difficult to understand the true economical implications of investments relating to these machines. The purpose of this study is to investigate and contribute with new insights regarding the cost-structures of the stationary self-checkout systems and traditional cashier desks, within the retail grocery market.

The aim of this study was to evaluate different types of volume and taper equations that can be used to predict single-tree stem volume and stem diameter at any given height along the tree stem for plantation grown Sitka spruce (Picea sitchensis (Bong.) Carr.), Norway spruce (Picea abies (L.) Karst) and White spruce (Picea glauca (Mounch) Voss) in Iceland. A number of published tree volume equations were tested and modified to predict the total stem volumes over bark but three logarithmic equations were taken for more in-depth analysis. Three taper equations were tested. Two variable-exponent equations (Kozak 1997, Kozak 2004) and one exponential equation described by Biging (1984). Data from a total of 617 sample trees were used in this study, collected from stands in various parts of the country and present different types of stands growing in different soil types and cover most of the site conditions suitable for forestry in Iceland.

Background: Cerebral Palsy is usually divided into three subgroups: ataxic, spastic and dyskinetic, where children and adolescents can, because of misestimation in nutrition and energy intake, suffer from weight problems.Aim: To compare calculations with equations with the individual's measured RMR in the subgroups, to see if any equation is more suitable. This could be used as a tool to calculate the resting metabolism at times when it is not possible to perform clinical measurements.Method: The RMR has been measured in 37 children and adolescents aged 3-15 years through indirect respiratory calorimetry. Those values have been compared with calculations from five equations. The results were then analyzed in order to find if any equation is better to apply for calculating resting metabolism for each subgroup.Results: The ataxic group was overestimated by 56.5% of the calculated values. WHO/FAO/UNU?s equation indicates a significantly strong correlation between the measured and calculated values (r=0.85, p<0.05).

The aim of the study was to find repetitive behavioral patterns pre calving that could be used as indications of calving in beef cattle. In the study sixteen Standing- and lying down sensors were attached to the leg of sixteen beef cows. Ten of the sixteen beef cows gave birth to calves during the trial period. From these ten cows, data from six cows were used to assess the sensors fitness for use as calving indicators. The analytical part of the experiment was divided into two parts, calculation of divergence of mean lying time within different time intervals, and the number of lying bouts.The first part consisted of optimization of an equation used to highlight divergence in mean lying time within eight different time intervals (3, 6, 9, 12, 15, 18, 21 and 24 hours).

Stage-discharge equations for lakes without disharge measurementsSimon AnderssonIn 2015 all lakes, rivers, coastal water and groundwater should be of good ecological statusaccording to the water framework directive from the European Union. In the process ofimproving the quality of Swedish water bodies, knowledge of where problems occur isneeded in order to utilize the resources optimally. The ability of lakes to store water is animportant factor since it controls the flow of water through the country. A stage-dischargeequation is a mathematical relation between discharge from a lake and its water level. Bybetter understanding of stage-discharge equations for lakes, their storage capacity can bedescribed better in hydrological models.This master thesis aims to evaluate methods for determining stage-discharge equations forlakes where a variable amount of field measurements is available.

The CASA-paradigm, Computers Are Social Actors, was introduced in the book "TheMedia Equation" by Reeves and Nass. One of their experiments concluded that we tend to be polite to computers in the same way as we are to people. In this study I have replicated Reeves and Nass experiment but instead of a text-based interface I have used a virtual agentin order to find out if we are polite to the agents, or still to the computer. Two experimental setups was conducted. The two setups had a common first part that was carried out on onecomputer with one agent.

The purpose with this thesis was to examine the cold rolling mill located at Högskolan Dalarna and to stabilize the rolling process, to achieve steady state. Experiments with cold rolling of an aluminium strip have given results for rolling force, friction, reduction, strip tension and strain hardening. Results show that steady state has been found for the experiments with roll force and strain hardening, and not been found for the experiments with friction and reduction. Results show that increased strip tension gives lower roll forces. The roll force equation of Stone shows comparable results with reality for dry contact with reductions up to 30 %, but starts being incomparable with higher reductions.

Objective: In recent years there has been an increasing interest within the clinical (medical) science in measuring people?s health. When estimating quality of life, present practise is to use the EQ-5D questionnaire and an index which weighs the different questions. The question is what happens if the individuals estimate there own health, would it differ from the public preferences? The aim is to make a new prediction model based on the opinion of patients and compare it to the present model based on public preferences.Method: A sample of 362 patients with unstable coronary artery disease from the Frisc II trial, valued their quality of life in the acute phase and after 3, 6 and 12 months.

Development in spin dynamic occurs in the whole world because of therising demands on fast electronic storage for example hard drivesand RAM (Random Access Memory). Measuring the spin resonance of amaterial gives you the insight of the theoretical speed for amagnetic memory. This means the maximum storage speed is below thefirst resonance. All magnetic materials have different propertiesthat will inflict the resonance frequency which brings that theconstructors of memories need to know which magnetic material theywill use to obtain best results. In the market for normal users themaximum storage speed in a RAM memory is 1.6 GHz.