The number of planar central configurations for the 4-body problem is finite when 3 mass positions are fixed

In the n{body problem a central con guration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n = 3 and for n > 4 that if n ? 1 masses are located at xed points in the plane, then there are only a nite number of ways to position the remaining nth mass in such a way that they de ne a central con guration. Lindstrom leaves open the case n = 4. In this paper we prove the case n = 4 using as variables the mutual distances between the particles.

The Effect of a Physical Activity Program on the Total Number of Primary Care Visits in Inactive Patients: A 15-Month Randomized Controlled Trial

Abstract Background: Effective promotion of exercise could result in substantial savings in healthcare cost expenses in terms of direct medical costs, such as the number of medical appointments. However, this is hampered by our limited knowledge of how to achieve sustained increases in physical activity. Objectives: To assess the effectiveness of a Primary Health Care (PHC) based physical activity program in reducing the total number of visits to the healthcare center among inactive patients, over a 15-month period. Research Design: Randomized controlled trial. Subjects: Three hundred and sixty-two (n = 362) inactive patients suffering from at least one chronic condition were included. One hundred and eighty-three patients (n = 183; mean (SD); 68.3 (8.8) years; 118 women) were randomly allocated to the physical activity program (IG). One hundred and seventy-nine patients (n = 179; 67.2 (9.1) years; 106 women) were allocated to the control group (CG). The IG went through a three-month standardized physical activity program led by physical activity specialists and linked to community resources. Measures: The total number of medical appointments to the PHC, during twelve months before and after the program, was registered. Self-reported health status (SF-12 version 2) was assessed at baseline (month 0), at the end of the intervention (month 3), and at 12 months follow-up after the end of the intervention (month 15). Results: The IG had a significantly reduced number of visits during the 12 months after the intervention: 14.8 (8.5). The CG remained about the same: 18.2 (11.1) (P = .002). Conclusions: Our findings indicate that a 3-month physical activity program linked to community resources is a shortduration, effective and sustainable intervention in inactive patients to decrease rates of PHC visits. Trial Registration: ClinicalTrials.gov NCT00714831

Influence of "historic" photoperiod during stem elongation on the number of fertile florets in wheat

Extending the duration of the late reproductive phase in wheat has been proposed as a possible avenue to improve spike fertility. There is a positive correlation between the number of fertile florets and the duration of the stem elongation phase when this phase is varied by extended photoperiod. Photoperiod treatments imposed during the vegetative period also influence the duration of stem elongation. The present study analysed the effect of long photoperiod (19 h) of different duration (10, 12, 14, 18 or 22 d) imposed before the onset of stem elongation on floret fertility in wheat. It was found that the length of the stem elongation phase was modified by earlier ‘historic ’ photoperiod treatments imposed during previous phases. However, neither the number of fertile florets per spike nor the spikelet fertility was affected significantly by these historic treatments. The results of the study therefore showed that an increased duration of the late reproductive phase was ineffective in increasing the number of fertile florets, unless the length of that phase was directly altered by current photoperiod.

Complexation to macromolecules with a large number of sites

This paper presents an approach based on the saddle-point approximation to study the equilibrium interactions between small molecules and macromolecules with a large number of sites. For this case, the application of the Darwin–Fowler method results in very simple expressions for the stoichiometric equilibrium constants and their corresponding free energies in terms of integrals of the binding curve plus a correction term which depends on the first derivatives of the binding curve in the points corresponding to an integer value of the mean occupation number. These expressions are simplified when the number of sites tends to infinity, providing an interpretation of the binding curve in terms of the stoichiometric stability constants. The formalism presented is applied to some simple complexation models, obtaining good values for the free energies involved. When heterogeneous complexation is assumed, simple expressions are obtained to relate the macroscopic description of the binding, given by the stoichiomeric constants, with the microscopic description in terms of the intrinsic stability constants or the affinity spectrum. © 1999 American Institute of Physics.

Application of Information Statistical Theory to the Description of the Effect of Heat Conduction on the Chemical Reaction Rate in Gases

The effect of the heat flux on the rate of chemical reaction in dilute gases is shown to be important for reactions characterized by high activation energies and in the presence of very large temperature gradients. This effect, obtained from the second-order terms in the distribution function (similar to those obtained in the Burnett approximation to the solution of the Boltzmann equation), is derived on the basis of information theory. It is shown that the analytical results describing the effect are simpler if the kinetic definition for the nonequilibrium temperature is introduced than if the thermodynamic definition is introduced. The numerical results are nearly the same for both definitions

Evaluating the impact of filming on the number of errors committed by nursing students to determine the efficacy of simulated clinical situations

Clinic simulation as a training and knowledge method allows people experiment a real event representation with the aim of acquiring knowledge, abilities and aptitudes. The filming of the staging represents a useful tool to review the decisions taken and the actions they did, with the purpose to highlight the strengths, weaknesses and the areas for improvement. The article describes a study carried out by a group of students in second course of nursing, and it tries to evaluate if there is any influence if somebody is filming you during the clinic simulation, does it make you do more errors or not?