Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “inequality”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Griffiths' inequalities for Ashkin-Teller model

The two Griffiths' (1967) inequalities for the correlation functions of Ising ferromagnets with two-body interactions, and two other inequalities obtained by Kelly and Sherman (1968) and by Sherman (1969) are shown to hold not only for the Ashkin-Teller (1943) model but also for a generalized Ashkin-Teller model (Kihara et al., 1954) with many-body interactions involving arbitrary clusters of particles. A cluster of particles is understood to mean a collection of pairs of particles rather than a group of particles. The four generalized inequalities under consideration are presented in the form of theorems, and a new inequality is obtained.

Lee, C. T.↗
NASA NTRS1973

An Evaluation of an Algorithm for Linear Inequalities and Its Applications

An algorithm is presented for obtaining a solution alpha to a set of inequalities (A alpha) 0 where A is an N x m-matrix and alpha is an m-vector. If the set of inequalities is consistant, then the algorithm is guaranteed to arrive at a solution in a finite number of steps. Also, if in the iteration, a negative vector is obtained, then the initial set of inequalities is inconsistant, and the iteration is terminated.

Jurgensen, J.↗
NASA NTRS1972

Effect of stratified inequality of blood flow on gas exchange in liquid-filled lungs.

This investigation set out to answer two questions: (1) are the distal alveoli in the terminal lung units less well perfused than the proximal alveoli, i.e., is there stratification of blood flow; and (2) if so, does this enhance gas exchange in the presence of stratified inequality of ventilation. Excised dog lungs were ventilated with saline and perfused with blood. Following single inspirations of xenon 133 in saline and various periods of breath holding, the expired xenon concentration against volume was measured and it confirmed marked stratified inequality of ventilation under these conditions. By measuring the rate of depletion of xenon from alveoli during a period of blood flow, we showed that the alveoli which emptied at the end of expiration had 16% less blood flow than those exhaling earlier. However, by measuring the xenon concentration in pulmonary venous blood, we found that about 10% less tracer was transferred from the alveoli into the blood when the inspired xenon was stratified within the respiratory zone. Thus while stratification of blood flow was confirmed, it was shown to impair rather than enhance the efficiency of gas transfer.

West, J. B.↗
NASA NTRS1973

A result on differential inequalities and its application to higher order trajectory derivatives

A result on differential inequalities is obtained by considering the adjoint differential equation of the variational equation of the right side of the inequality. The main theorem is proved using basic results on differentiability of solutions with respect to initial conditions. The result is then applied to the problem of determining solution behavior using comparison techniques.

Gunderson, R. W.↗
NASA NTRS1965

Necessary conditions for a multistage bolza- mayer problem involving control variables and having inequality and finite equation constraints

A multiplier rule and analogues of the Weierstrass and Clebsch conditions are developed for a multistage Bolza-Meyer calculus of variations problems. The number of stages is fixed, but partition points defining state boundaries are variable. Discontinuities are allowed in variables finite equations and inequalities, as well as differential equations, all of which involve control variables. An appendix summarizes some of the results obtained by C. H. Denbow, as modified by R. W. hunt, for a generalized Bolza problem. The appendix is independent of the rest of the paper.

Differential equation↗