In this master?s thesis the problem of simulating conditional Bernoulli distributed stochastic variables, given the sum, is considered. Three simulation methods are considered, namely the acceptance/rejection technique, Bondesson?s method and the Markov chain Monte Carlo method.To compare the three methods the bias and the standard deviations of the simulated variables are evaluated. The results of the simulation study shows that the Markov chain Monte Carlo method is not the best method for this type of simulation.

I detta kandidatexamensarbete studeras ett inverst problem: att för en jämnt fördelad last numeriskt minimera energin som tas upp i en fritt upplagd balk. I detta problem antas balken vara indelad i ett givet antal lika långa stycken med konstant böjstyvhet och minimeringen sker med avseende på dessa styckens böjstyvheter. För en fin indelning av balken riskerar den numeriska metoden att bli instabil. Målet med denna studie är undersöka om Tikhonovregularisering kan stabilisera den numeriska metoden i fallet med en fin indelning. I lösningen av balkproblemet används Bernoulli-Eulers ekvation och Lagranges multiplikatormetod för att härleda den målfunktion som skall minimeras.

The report contains three parts. The first part is a summary and overall presentation of thermalcracks and preventing measures against such cracks. This is a theoretical part where theinterested designer can get acquainted with various alternatives, be guided to more detailedliterature, and receive some practical information regarding the design of the respectivemeasures.The second part deals with calculation of the risk for thermal cracks and design of water coolingas a limiting measure. Two complementary methods are reviewed for efficient calculation:?the handbook method CraX1(by Lulea University of Technology) is used for quickverification?finite differential analysis in the calculationtool ConTeSt Pro for more precise projectingHere is also presented a development of existing standards through design of the cooling systemby means of the Bernoulli equation.