On Existence of L1L^1-solutions for Coupled Boltzmann Transport Equation and Radiation Therapy Treatment Optimization

The paper considers a linear system of Boltzmann transport equations modelling the evolution of three species of particles, photons, electrons and positrons. The system is coupled because of the collision term (an integral operator). The model is intended especially for dose calculation (forward problem) in radiation therapy. It, however, does not apply to all relevant interactions in its present form. We show under physically relevant assumptions that the system has a unique solution in appropriate ($L^1$-based) spaces and that the solution is non-negative when the data (internal source and inflow boundary source) is non-negative. In order to be self-contained as much as is practically possible, many (basic) results and proofs have been reproduced in the paper. Existence, uniqueness and non-negativity of solutions for the related time-dependent coupled system are also proven. Moreover, we deal with inverse radiation treatment planning problem (inverse problem) as an optimal control problem both for external and internal therapy (in general $L^p$-spaces). Especially, in the case $p=2$ variational equations for an optimal control related to an appropriate differentiable convex object function are verified. Its solution can be used as an initial point for an actual (global) optimization.Comment: Corrected typos. Added a new section 3. Revised the argument of Example 7.

Self-employment duration in urban and rural locations

Previous research has shown that local environment is important for self-employment. Self-employment dynamics varies between areas characterized by different labour market conditions, entrepreneurial tradition and other structural factors. Alternation between different labour market states (self-employment, paid-employment, non-employment) is also likely to increase if employment opportunities remain low in local labour market markets. This paper analyses the factors influencing the duration of self-employment spells in Finland with a large registered-based data set from the period of 1987-2002. It is evident that rates of exit out of self-employment and the length of self-employment spells depend upon personal characteristics and cyclical trends in the economy. The main aim is to analyse the role of region-specific factors as compared with individual specific and other factors on the duration of self-employment spells. Self-employment duration is modelled by using discrete survival analysis. First, descriptive analysis is done. Second, simple Cox proportional hazard models are estimated. Third, more complex hazard models e.g. with competing risks are used.

Intergenerational mobility in self-employment: a regional approach

Self-employment is an important option in the work careers of many. It may be seen as a learning process illustrated for example in the social development model by Gibb and Ritchie (1982) and in the model of entrepreneurial careers by Dyer (1994). In the former, entrepreneurship is mainly seen in terms of the situations which individuals encounter and the social groups to which they relate. Among many others, family background, education and work experience have an effect directly, or indirectly through intentions (see Krueger and Carsrud 1993)on becoming self-employed. The children of parents owned a business are more likely to see such a career as more acceptable than working for someone else. An individual who has a self-employed parent possess a kind of 'entrepreneurial human capital'. Family background may provide self-confidence and social support, a supply of resources needed by the business, and strategic capacity to learn and organise for new activities. The movement to self-employment may also simply arise because children tend to inherit family firms. This paper analyses self-employment among children with parents owned a business based on the Finnish Longitudinal Census data and the Longitudinal Employment statistics from the period of 1970 to 1995 (1998). This exceptionally wide register based data makes possible the examination of intergenerational mobility in different regions. In the data file, individuals belonging to age-group 0-14 years as of 1970 have the socio-economic status, industry and occupational status of their household reference person, mostly the father, included in their record. Our sample is consisted of those children in 1970 who are from families of self-employed. The aim of this paper is to describe and model the swift into self-employment among children of self-employed parents. The explanatory variables are divided into three categories: family background, individual characteristics, and regional features. The analysis refers to the year 1995, and when possible, to the year 1998. Follow-up of individuals throughout the study period will also be made. Main questions concern the role of family background, sex, education, industry and region in the inheritance of entrepreneurship. The results are also compared with the results based on a sample of individuals belonging to the same age group but with non self-employed parents.

Does the compositional effect explain the association between rates of in-migration and out-migration?

A common empirical observation obtained in many countries is that regions with a high gross out-migration per capita also tend to have a high gross in-migration per capita, and vice versa. Another common and curious observation is a positive correlation between out-migration rate and net-migration rate. This has been interpreted to mean that out-migration is independent of the economic characteristics of the region. A number of explanations has been suggested to explain the positive relationship between the rates of out-migration and in-migration. According to the compositional effect- explanation, a region that attracts migrants grow to have a population which is more migration prone, thus also increasing out-migration from the region. Another explanation is related to the idea of "vacancy chain": the departure of residents leaves vacated positions such as jobs and houses for new-comers, thus increasing in-migration. The economic activities that make an area attractive may also increase turnover and thus out-migration. If jobs are easily available, this attracts in-migrants, but may also make workers to leave the jobs easily, thus adding out-migration. This paper analyses the relationships between the components of migration in Finland in the 1990s, and their development since 1975. Inter-regional migration, and regional concentration with it, accelerated pronouncedly in Finland after the mid 1990s. Migration research, which also gained popularity, is dominated by the analysis of net-migration and analyses based on micro-data, but the analysis related to gross migration is few in number. Therefore, we have only limited understanding on the behaviour and relationships of the out-, in- and net-migration rates in Finland. The results show that the rate of out-migration is positively related to the rate of in- migration, but negatively related to the rate of net-migration. The first result is in accordance with the common result, but the second is not. Out-migration seems to be related with the economic characteristics of the region in Finland, and therefore the correlation between the rates of out- and net-migration is negative. The push factors work in Finland, which result has also been obtained from migration studies based on micro-data. In analysing the relationship between the out- and in-migration rates, this paper also analyses the significance of the compositional effect by utilizing micro-based data from the period of 1987-96. In this analysis, the population is divided into two parts, those who have moved before and those who have not, and the relationships between the components of migration are analysed separately in these two groups. Accordingly, we swift from the use of microdata to the use of macro (regional) data in this analysis.

Post-migratory employment prospect: Evidence from Finland

This paper analyses the role which migration has in augmenting the likelihood of employment, by examining employment status of migrants and nonmigrants at the end of the migration interval on the basis of microdata. The paper continues the analysis of the paper by Tervo (1997) which examined the impact of unemployment on labour force mobility. Together these two papers address the role which interregional migration has as a labour market equilibrating mechanism. The empirical analysis is concerned with the situation of Finland. The data is taken from the Finnish longitudinal census data file from which a 1% sample has been taken. It contains data gathered at the censuses 1970, 1975, 1980, 1985, 1990 and 1995. The analysis is directed at those individuals belonging to the labour force, in which case the sample size is about 20 - 22 000, depending on the time period. The analysis deals with long-distance migration which is defined as occurring where an individual is resident in a different province from that five years earlier. The theoretical framework of the paper is in the job-search-model and human capital model of migration. For both the employed and unemployed, migration should augment the employability of migrants compared with nonmigrants if earnings potential is held constant. The direct impact of migration on re-employment is estimated with the help of logit regression, while holding constant the selectivity factors of migration and the marginal benefits and costs of search. In the estimations, a binary migration variable provides information on the comparative efficiency of job search between migrants and nonmigrants.

Self-employment dynamics in rural and urban labour markets

Only few in-depth studies of the alternation between different labour market states have been published. This paper deals with the alternation between self-employment, paid-employment and non-employment in Finland in 1987-1999, paying special attention to differences in self-employment dynamics between areas characterized by different labour market conditions, viz. rural and urban locations. The analysis is based on a one-percent random sample drawn from panel data on the census and longitudinal employment statistics. The results show differences in the transition processes between the three labour market states by the type of area. The results suggest that alternation between different employment options is likely to increase, if employment opportunities remain low in local labour markets. Five major types of working careers are identified, all of which are more common in rural than urban areas. The type of area is importantly related to alternating working careers even when all the important control variables are included into the models.

Does the compositional effect explain the association between rates of in-migration and out-migration?

A common empirical observation obtained in many countries is that regions with a high gross out-migration per capita also tend to have a high gross in-migration per capita, and vice versa. Another common and curious observation is a positive correlation between out-migration rate and net-migration rate. This has been interpreted to mean that out-migration is independent of the economic characteristics of the region. A number of explanations has been suggested to explain the positive relationship between the rates of out-migration and in-migration. According to the compositional effect- explanation, a region that attracts migrants grow to have a population which is more migration prone, thus also increasing out-migration from the region. Another explanation is related to the idea of "vacancy chain": the departure of residents leaves vacated positions such as jobs and houses for new-comers, thus increasing in-migration. The economic activities that make an area attractive may also increase turnover and thus out-migration. If jobs are easily available, this attracts in-migrants, but may also make workers to leave the jobs easily, thus adding out-migration. This paper analyses the relationships between the components of migration in Finland in the 1990s, and their development since 1975. Inter-regional migration, and regional concentration with it, accelerated pronouncedly in Finland after the mid 1990s. Migration research, which also gained popularity, is dominated by the analysis of net-migration and analyses based on micro-data, but the analysis related to gross migration is few in number. Therefore, we have only limited understanding on the behaviour and relationships of the out-, in- and net-migration rates in Finland. The results show that the rate of out-migration is positively related to the rate of in- migration, but negatively related to the rate of net-migration. The first result is in accordance with the common result, but the second is not. Out-migration seems to be related with the economic characteristics of the region in Finland, and therefore the correlation between the rates of out- and net-migration is negative. The push factors work in Finland, which result has also been obtained from migration studies based on micro-data. In analysing the relationship between the out- and in-migration rates, this paper also analyses the significance of the compositional effect by utilizing micro-based data from the period of 1987-96. In this analysis, the population is divided into two parts, those who have moved before and those who have not, and the relationships between the components of migration are analysed separately in these two groups. Accordingly, we swift from the use of microdata to the use of macro (regional) data in this analysis