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We study the basic height conjecture for points on curves defined over number fields and show: On any algebraic curve defined over a number field the set of algebraic points contains an unrestricted subset of infinite cardinality such that for all of its points their canonical height is bounded in terms of a small power of their root discriminant. In addition, if we assume GRH, then the upper bound is, as it is conjectured, linear in the logarithm of the root discriminant.

We study the basic height conjecture for points on curves defined over number fields and show: On any algebraic curve defined over a number field the set of algebraic points contains an unrestricted subset of infinite cardinality such that for all of its points their canonical height is bounded in terms of a small power of their root discriminant. In addition, if we assume GRH, then the upper bound is, as it is conjectured, linear in the logarithm of the root discriminant.

Traditionally, game theorists have contented themselves with specifying a single numerical payoff function for each player. They do so without any consideration of the units in which utility is measured, or what alternative profiles of payoff functions can be regarded as equivalent. This paper will have succeeded if it leaves the reader with the impression that considering such measurement issues can considerably enrich our understanding of the decision-theoretic foundations of game theory. A useful byproduct is identifying which games can be treated as equivalent to especially simple games, such as two-person zero-sum games, or team games.

Finally, it is pointed out that the usual utility concepts in single-person decision theory can be derived by considering different players’ objectives in the whole class of consequentialist game forms, rather than just in one particular game.

We study the basic height conjecture for points on curves defined over number fields and show: On any algebraic curve defined over a number field the set of algebraic points contains an unrestricted subset of infinite cardinality such that for all of its points their canonical height is bounded in terms of a small power of their root discriminant. In addition, if we assume GRH, then the upper bound is, as it is conjectured, linear in the logarithm of the root discriminant.

We have presented equivalence scales derived from a survey where subjects have been asked to assess the income needs of different hypothetical households given five levels of reference income of a reference household. We find that equivalence scales obtained negatively depend on the level of reference income. This finding strongly questions the results of previous studies where equivalence scales have been assumed to be constant. Obviously, this constancy assumption either means an overestimation of the needs of “rich” or the underestimation of the needs of “poor” multi-person households or the mis-specification of the needs of both. Second, the number of adults in the household turns out to be an important criterion for the evaluation of children needs. According to our respondents, the income needs of children are an increasing function of the number of adult household members. It is, therefore, necessary to broaden economic models with respect to this interaction.

We study the basic height conjecture for points on curves defined over number fields and show: On any algebraic curve defined over a number field the set of algebraic points contains an unrestricted subset of infinite cardinality such that for all of its points their canonical height is bounded in terms of a small power of their root discriminant. In addition, if we assume GRH, then the upper bound is, as it is conjectured, linear in the logarithm of the root discriminant.

We study the basic height conjecture for points on curves defined over number fields and show: On any algebraic curve defined over a number field the set of algebraic points contains an unrestricted subset of infinite cardinality such that for all of its points their canonical height is bounded in terms of a small power of their root discriminant. In addition, if we assume GRH, then the upper bound is, as it is conjectured, linear in the logarithm of the root discriminant.

We have presented equivalence scales derived from a survey where subjects have been asked to assess the income needs of different hypothetical households given five levels of reference income of a reference household. We find that equivalence scales obtained negatively depend on the level of reference income. This finding strongly questions the results of previous studies where equivalence scales have been assumed to be constant. Obviously, this constancy assumption either means an overestimation of the needs of “rich” or the underestimation of the needs of “poor” multi-person households or the mis-specification of the needs of both. Second, the number of adults in the household turns out to be an important criterion for the evaluation of children needs. According to our respondents, the income needs of children are an increasing function of the number of adult household members. It is, therefore, necessary to broaden economic models with respect to this interaction.

We study the basic height conjecture for points on curves defined over number fields and show: On any algebraic curve defined over a number field the set of algebraic points contains an unrestricted subset of infinite cardinality such that for all of its points their canonical height is bounded in terms of a small power of their root discriminant. In addition, if we assume GRH, then the upper bound is, as it is conjectured, linear in the logarithm of the root discriminant.

We study the basic height conjecture for points on curves defined over number fields and show: On any algebraic curve defined over a number field the set of algebraic points contains an unrestricted subset of infinite cardinality such that for all of its points their canonical height is bounded in terms of a small power of their root discriminant. In addition, if we assume GRH, then the upper bound is, as it is conjectured, linear in the logarithm of the root discriminant.