The approximate numerical solution of boundary value problems by relaxation methods,

"Contract N7 onr-358, T. O. I., NR-041-032."

Relaxation methods for solving linear inequality systems: Converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In [12] an algorithm, called extended relaxation method, that solves the feasibility problem, has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we onsider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.

Oxygen mobility in Bi:Sr:Ca:Cu:O ceramic measured using anelastic relaxation methods

Since the discovery of YBaCuO, experiments have shown that its superconducting properties are strongly affected by the oxygen content. More recently, anelastic relaxation measurements in La2CuO4+δ, showed that the decrease in the oxygen content can be related to two events. One is the decrease in mobility between two adjacent CuO planes, and the other is the increase in the number of tilting patterns of the CuO6 octahedra. In the case of the bismuth-based ceramic, it is known that the oxygen content, within some limits, does not affect its superconducting properties. In order to evaluate the mobility and the effect of the oxygen content on this material we have prepared BSCCO ceramic and tested regarding its internal friction and electrical resistivity as a function of the temperature while the oxygen content was being reduced by a sequence of vacuum annelaing at 620 K. The samples were prepared in the Bi:Sr:Ca:Cu = 2212 and 2223 proportion, using powder obtained by the sol-gel route and conventional solid state reaction. The anelastic relaxation measurements were performed using a torsion pendulum operating with frequency about 15-35 Hz between 77 to 700 K. The diffraction pattern of the as sintered and the vacuum annealed material were also presented. The results have shown complex anelastic relaxation structures that were associated to the jump of interstitial oxygen atoms between two adjacent CuO planes. The vacuum annealing showed to be deleterious to the critical temperature of the superconducting ceramic.

A factorization procedure that is equivalent to successive over relaxation /

"This work was supported in part by the National Science Foundation under Grant No. GJ812."

Variable successive over-relaxation,

Vita.

The use of Chebyshev matrix polynomials in the iterative solution of linear equations compared to the method of successive overrelaxtion /

"(This is being submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, June 1959.)"

Activation of beta(2)-adrenergic receptors hastens relaxation and mediates phosphorylation of phospholamban, troponin I, and C-protein in ventricular myocardium from patients with terminal heart failure

Background-Catecholamines hasten cardiac relaxation through beta-adrenergic receptors, presumably by phosphorylation of several proteins, but it is unknown which receptor subtypes are involved in human ventricle. We assessed the role of beta(1)- and beta(2)-adrenergic receptors in phosphorylating proteins implicated in ventricular relaxation. Methods and Results-Right ventricular trabeculae, obtained from freshly explanted hearts of patients with dilated cardiomyopathy (n=5) or ischemic cardiomyopathy (n=5), were paced at 60 bpm. After measurement of the contractile and relaxant effects of epinephrine (10 mu mol/L) or zinterol (10 mu mol/L), mediated through beta(2)-adrenergic receptors, and of norepinephrine (10 mu mol/L), mediated through beta(1)-adrenergic receptors, tissues were freeze clamped. We assessed phosphorylation of phospholamban, troponin I, and C-protein, as well as specific phosphorylation of phospholamban at serine 16 and threonine 17, Data did not differ between the 2 disease groups and were therefore pooled. Epinephrine, zinterol, and norepinephrine increased contractile force to approximately the same extent, hastened the onset of relaxation by 15+/-3%, 5+/-2%, and 20+/-3%, respectively, and reduced the time to half-relaxation by 26+/-3%, 21+/-3%, and 37+/-3%. These effects of epinephrine, zinterol, and norepinephrine were associated with phosphorylation (pmol phosphate/mg protein) of phospholamban 14+/-3, 12+/-4, and 12+/-3, troponin I 40+/-7, 33+/-7, and 31+/-6; and C-protein 7.2+/-1.9, 9.3 +/- 1.4, and 7.5 +/- 2.0. Phosphorylation of phospholamban occurred at both Ser16 and Thr17 residues through both beta(1)- and beta(2)-adrenergic receptors. Conclusions-Norepinephrine and epinephrine hasten human ventricular relaxation and promote phosphorylation of implicated proteins through both beta(1)- and beta(2)-adrenergic receptors, thereby potentially improving diastolic function.

Developing multiple - choice questions in mathematics

In this paper we wish to illustrate different perspectives used to create Multiple-Choice questions and we will show how we can improve these in the construction of math tests. As it is known, web technologies have a great influence on student’s behaviour. Based on an on-line project beginning at 2007 which has been contributing to help students on their individual work, we would like to share our experience and thoughts with colleagues who have a common concern when they have the task of constructing Multiple-Choice tests. We feel that Multiple-Choice tests play an important and a very useful supporting role in selfevaluation or self-examination of our students. Nonetheless, good Multiple–Choice Test Items are generally more complex and time-consuming to create than other types of tests. It requires a certain amount of skill. However, this skill maybe increases through study, practice and experience. This paper discusses a number of issues related to the use of Multiple-Choice questions, lists the advantages and disadvantages of this question format contrasting it with open questions. Some examples are given in this context.

Endothelium-dependent relaxation in response to poly-L-arginine in canine coronary arteries: implications about hyperpolarization as a mechanism of vasodilatation

OBJECTIVE: To study the mechanism by which poly-L-arginine mediates endothelium-dependent relaxation. METHODS: Vascular segments with and without endothelium were suspended in organ chambers filled with control solution maintained at 37ºC and bubbled with 95% O2 / 5% CO2. Used drugs: indomethacin, acetycholine, EGTA, glybenclamide, ouabain, poly-L-arginine, methylene blue, N G-nitro-L-arginine, and verapamil and N G-monomethyl-L-arginine. Prostaglandin F2á and potassium chloride were used to contract the vascular rings. RESULTS: Poly-L-arginine (10-11 to 10-7 M) induced concentration-dependent relaxation in coronary artery segments with endothelium. The relaxation to poly-L-arginine was attenuated by ouabain, but was unaffected by glybenclamide. L-NOARG and oxyhemoglobin caused attenuation, but did not abolish this relaxation. Also, the relaxations was unaffected by methylene blue, verapamil, or the presence of a calcium-free bathing medium. The endothelium-dependent to poly-L-arginine relaxation was abolished only in vessels contracted with potassium chloride (40 mM) in the presence of L-NOARG and indomethacin. CONCLUSION: These experiments indicate that poly-L-arginine induces relaxation independent of nitric oxide.

Equivalence of piecewise-linear approximation and Lagrangian relaxation for network revenue management

The network revenue management (RM) problem arises in airline, hotel, media,and other industries where the sale products use multiple resources. It can be formulatedas a stochastic dynamic program but the dynamic program is computationallyintractable because of an exponentially large state space, and a number of heuristicshave been proposed to approximate it. Notable amongst these -both for their revenueperformance, as well as their theoretically sound basis- are approximate dynamic programmingmethods that approximate the value function by basis functions (both affinefunctions as well as piecewise-linear functions have been proposed for network RM)and decomposition methods that relax the constraints of the dynamic program to solvesimpler dynamic programs (such as the Lagrangian relaxation methods). In this paperwe show that these two seemingly distinct approaches coincide for the network RMdynamic program, i.e., the piecewise-linear approximation method and the Lagrangianrelaxation method are one and the same.

Effects of stress relaxation in beta-titanium orthodontic loops

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Clinical validation of electromyography and acceleromyography as sensors for muscle relaxation

BACKGROUND AND OBJECTIVE: The aim of this study was to determine which of two clinically applied methods, electromyography or acceleromyography, was less affected by external disturbances, had a higher sensitivity and which would provide the better input signal for closed loop control of muscle relaxation. METHODS: In 14 adult patients, anaesthesia was induced with intravenous opioids and propofol. The response of the thumb to ulnar nerve stimulation was recorded on the same arm. Mivacurium was used for neuromuscular blockade. Under stable conditions of relaxation, the infusion-rate was decreased and the effects of turning the hand were investigated. RESULTS: Electromyography and acceleromyography both reflected the change of the infusion rate (P = 0.015 and P < 0.001, respectively). Electromyography was significantly less affected by the hand-turn (P = 0.008) than acceleromyography. While zero counts were detected with acceleromyography, electromyography could still detect at least one count in 51.1%. CONCLUSIONS: Electromyography is more reliable for use in daily practice as it is less influenced by external disturbances than acceleromyography.

Influence of left ventricular relaxation on the pressure half time of aortic regurgitation

BACKGROUND The severity of aortic regurgitation can be estimated using pressure half time (PHT) of the aortic regurgitation flow velocity, but the correlation between regurgitant fraction and PHT is weak. AIM To test the hypothesis that the association between PHT and regurgitant fraction is substantially influenced by left ventricular relaxation. METHODS In 63 patients with aortic regurgitation, subdivided into a group without (n = 22) and a group with (n = 41) left ventricular hypertrophy, regurgitant fraction was calculated using the difference between right and left ventricular cardiac outputs. Left ventricular relaxation was assessed using the early to late diastolic Doppler tissue velocity ratio of the mitral annulus (E/ADTI), the E/A ratio of mitral inflow (E/AM), and the E deceleration time (E-DT). Left ventricular hypertrophy was assessed using the M mode derived left ventricular mass index. RESULTS The overall correlation between regurgitant fraction and PHT was weak (r = 0.36, p < 0.005). In patients without left ventricular hypertrophy, there was a significant correlation between regurgitant fraction and PHT (r = 0.62, p < 0.005), but not in patients with left ventricular hypertrophy. In patients with a left ventricular relaxation abnormality (defined as E/ADTI< 1, E/AM< age corrected lower limit, E-DT >/= 220 ms), no associations between regurgitant fraction and PHT were found, whereas in patients without left ventricular relaxation abnormalities, the regurgitant fraction to PHT relations were significant (normal E/AM: r = 0.57, p = 0.02; E-DT< 220 ms: r = 0.50, p < 0.001; E/ADTI < 1: r = 0.57, p = 0.02). CONCLUSIONS Only normal left ventricular relaxation allows a significant decay of PHT with increasing aortic regurgitation severity. In abnormal relaxation, which is usually present in left ventricular hypertrophy, wide variation in prolonged backward left ventricular filling may cause dissociation between the regurgitant fraction and PHT. Thus the PHT method should only be used in the absence of left ventricular relaxation abnormalities.

Sequential and parallel synchronous alternating iterative methods

The so-called parallel multisplitting nonstationary iterative Model A was introduced by Bru, Elsner, and Neumann [Linear Algebra and its Applications 103:175-192 (1988)] for solving a nonsingular linear system Ax = b using a weak nonnegative multisplitting of the first type. In this paper new results are introduced when A is a monotone matrix using a weak nonnegative multisplitting of the second type and when A is a symmetric positive definite matrix using a P -regular multisplitting. Also, nonstationary alternating iterative methods are studied. Finally, combining Model A and alternating iterative methods, two new models of parallel multisplitting nonstationary iterations are introduced. When matrix A is monotone and the multisplittings are weak nonnegative of the first or of the second type, both models lead to convergent schemes. Also, when matrix A is symmetric positive definite and the multisplittings are P -regular, the schemes are also convergent.

Stability and convergence of general multistep and multivalue methods with variable step size.

Thesis--University of Illinois.