Expansive Definition Research Articles

Comments on health indicators: methodological perspectives.

This paper discusses several basic conceptual and methodological problems in the development and use of health indicators. We observe that two tendencies of the health indicators movement may deter progress toward producing informations of health status indexes and the tendency to conceptualize "health" in terms of expansive definitions should measure variables specified by a social system model and should be scaled according to units that are relevant to decision-making criteria.

A topological expansion for high-energy hadronic collisions: (I). General properties and connection with the reggeon calculus

In this and in a companion paper a “topological expansion” for high-energy hadronic processes is proposed and discussed. In this first paper the general properties of the expansion and its connection with Gribov's reggeon calculus are presented. The topological expansion is first defined mathematically for a large class of theories and is shown to be equivalent to a “large N expansion” in some theories which include planar dual models and non-Abelian gauge theories. Next, the definition of the bare parameters is given in terms of graphs on a sphere. The bare pomeron pole and its couplings are thus introduced. The (inclusive) form of s-channel unitarity and its consequences fo the above couplings are recalled. It is then shown how the expansion in the number of “handles” of the graph can be related to Gribov's reggeon calculus and how, with the aid of discontinuity equations in the J-plane, scaling solutions can be obtained and critical indices can be computed to yield known results. Our main new results, including the study of s-channel discontinuities and of positivity constraints as well as the definition of a new fireball expansion, and the discussion of the relevance of this theory at finite (present) energies are presented in the second paper.

Application of the hole line expansion to an exactly solvable model

A purely algebraical definition of the hole line expansion is presented. The predictions of the hole line expansion up to fourth order are then investigated in an exactly solvable model which contains an attractive long-range and a repulsive short-range two-body force. Energies and wave functions are studied in relation to the wound integral and the hole-hole interaction.

Asymptotic Expansions of Integral Functions

The paper falls into three divisions. In the first part, which is very short, Poincare's arithmetic definition of asymptotic expansion is given. The second part emphasises the function theory and the ideas of the theory of functions of a complex variable, and contour integrals are freely used in this part; distinction is made between the different ''orders of the asymptotic series; and integrals which may be taken to be their sums are obtained.