Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

Health-related quality of life in survivors of childhood cancer: the role of chronic health problems.

INTRODUCTION: The influence of specific health problems on health-related quality of life (HRQoL) in childhood cancer survivors is unknown. We compared HRQoL between survivors of childhood cancer and their siblings, determined factors associated with HRQoL, and investigated the influence of chronic health problems on HRQoL. METHODS: Within the Swiss Childhood Cancer Survivor Study, we sent a questionnaire to all survivors (≥16 years) registered in the Swiss Childhood Cancer Registry, who survived >5 years and were diagnosed 1976-2005 aged <16 years. Siblings received similar questionnaires. We assessed HRQoL using Short Form-36 (SF-36). Health problems from a standard questionnaire were classified into overweight, vision impairment, hearing, memory, digestive, musculoskeletal or neurological, and thyroid problems. RESULTS: The sample included 1,593 survivors and 695 siblings. Survivors scored significantly lower than siblings in physical function, role limitation, general health, and the Physical Component Summary (PCS). Lower score in PCS was associated with a diagnosis of central nervous system tumor, retinoblastoma or bone tumor, having had surgery, cranio-spinal irradiation, or bone marrow transplantation. Lower score in Mental Component Summary was associated with older age. All health problems decreased HRQoL in all scales. Most affected were survivors reporting memory problems and musculoskeletal or neurological problems. Health problems had the biggest impact on physical functioning, general health, and energy and vitality. CONCLUSIONS: In this study, we showed the negative impact of specific chronic health problems on survivors' HRQoL. IMPLICATIONS FOR CANCER SURVIVORS: Therapeutic preventive measures, risk-targeted follow-up, and interventions might help decrease health problems and, consequently, improve survivors' quality of life.

Arithmetical problems in number fields, abelian varieties and modular forms

Number theory, a fascinating area in mathematics and one of the oldest, has experienced spectacular progress in recent years. The development of a deep theoretical background and the implementation of algorithms have led to new and interesting interrelations with mathematics in general which have paved the way for the emergence of major theorems in the area. This report summarizes the contribution to number theory made by the members of the Seminari de Teoria de Nombres (UB-UAB-UPC) in Barcelona. These results are presented in connection with the state of certain arithmetical problems, and so this monograph seeks to provide readers with a glimpse of some specific lines of current mathematical research.

Postmodernism and its problems with science

Lecture given in Helsinki at the invitation of the Finnish Mathematical Society.

Parental post-traumatic reactions after premature birth: implications for sleeping and eating problems in the infant.

BACKGROUND: Progress in perinatal medicine has made it possible to increase the survival of very or extremely low birthweight infants. Developmental outcomes of surviving preterm infants have been analysed at the paediatric, neurological, cognitive, and behavioural levels, and a series of perinatal and environmental risk factors have been identified. The threat to the child's survival and invasive medical procedures can be very traumatic for the parents. Few empirical reports have considered post-traumatic stress reactions of the parents as a possible variable affecting a child's outcome. Some studies have described sleeping and eating problems as related to prematurity; these problems are especially critical for the parents. OBJECTIVE: To examine the effects of post-traumatic reactions of the parents on sleeping and eating problems of the children. DESIGN: Fifty families with a premature infant (25-33 gestation weeks) and a control group of 25 families with a full term infant participated in the study. Perinatal risks were evaluated during the hospital stay. Mothers and fathers were interviewed when their children were 18 months old about the child's problems and filled in a perinatal post-traumatic stress disorder questionnaire (PPQ). RESULTS: The severity of the perinatal risks only partly predicts a child's problems. Independently of the perinatal risks, the intensity of the post-traumatic reactions of the parents is an important predictor of these problems. CONCLUSIONS: These findings suggest that the parental response to premature birth mediates the risks of later adverse outcomes. Preventive intervention should be promoted.

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.

Sequential decisions in allocation problems

[eng] In the context of cooperative TU-games, and given an order of players, we consider the problem of distributing the worth of the grand coalition as a sequentia decision problem. In each step of process, upper and lower bounds for the payoff of the players are required related to successive reduced games. Sequentially compatible payoffs are defined as those allocation vectors that meet these recursive bounds. The core of the game is reinterpreted as a set of sequentally compatible payoffs when the Davis-Maschler reduced game is considered (Th.1). Independently of the reduction, the core turns out to be the intersections of the family of the sets of sequentially compatible payoffs corresponding to the different possible orderings (Th.2), so it is in some sense order-independent. Finally, we analyze advantagenous properties for the first player

Some fundamental aspects of palentological methodology: its problems and incidence

Two trends which presently exist in relation to the concept of Paleontology are analyzed, pointing out some of the aspects which negative influence. Various reflections are made based on examples of some of the principal points of paleontological method, such as the influence of a punctual sampling, the meaning of size-frequency distribution and subjectivity in the identification of fossils. Topics which have a marked repercussion in diverse aspects of Paleontology are discussed.

A donde vamos ahora? : (where are we going now) : a report on the problems of the Spanish surnamed and migrant population in Iowa,1970.

This is an overview of the United States Commission on Civil Rights and the duties of the Iowa State Advisory Committee. It contains a report concerning problems of the Spanish surnamed and migrant population in Iowa.