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.

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

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

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.

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.

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.

Relaxation of alternating iterative algorithms for the Cauchy problem associated with the modified Helmholtz equation

We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of ` 12 ` 12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed methods.

A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity

We propose two algorithms involving the relaxation of either the given Dirichlet data (boundary displacements) or the prescribed Neumann data (boundary tractions) on the over-specified boundary in the case of the alternating iterative algorithm of Kozlov et al. [16] applied to Cauchy problems in linear elasticity. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed method.

Nitric Oxide-Induced Vasorelaxation in Response to PnTx2-6 Toxin from Phoneutria nigriventer Spider in Rat Cavernosal Tissue

Introduction. Priapism is one of several symptoms observed in accidental bites by the spider Phoneutria nigriventer. The venom of this spider is comprised of many toxins, and the majority has been shown to affect excitable ion channels, mainly sodium (Na+) channels. It has been demonstrated that PnTx2-6, a peptide extracted from the venom of P. nigriventer, causes erection in anesthetized rats and mice. Aim. We investigated the mechanism by which PnTx2-6 evokes relaxation in rat corpus cavernosum. Main Outcome Measures. PnTx2-6 toxin potentiates nitric oxide (NO)-dependent cavernosal relaxation. Methods. Rat cavernosal strips were incubated with bretylium (3 x 10-5 M) and contracted with phenylephrine (PE; 10-5 M). Relaxation responses were evoked by electrical field stimulation (EFS) or sodium nitroprusside (SNP) before and after 4 minutes of incubation with PnTx2-6 (10-8 M). The effect of PnTx2-6 on relaxation induced by EFS was also tested in the presence of atropine (10-6 M), a muscarinic receptor antagonist, N-type Ca2+ channel blockers (omega-conotoxin GVIA, 10-6 M) and sildenafil (3 x 10-8 M). Technetium99m radiolabeled PnTx2-6 subcutaneous injection was administrated in the penis. Results. Whereas relaxation induced by SNP was not affected by PnTx2-6, EFS-induced relaxation was significantly potentiated by this toxin as well as PnTx2-6 plus SNP. This potentiating effect was further increased by sildenafil, not altered by atropine, however was completely blocked by the N-type Ca2+ channels. High concentrated levels of radiolabeled PnTx2-6 was specifically found in the cavernosum tissue, suggesting PnTx2-6 is an important toxin responsible for P. nigriventer spider accident-induced priapism. Conclusion. We show that PnTx2-6 slows Na+ channels inactivation in nitrergic neurons, allowing Ca2+ influx to facilitate NO/cGMP signalling, which promotes increased NO production. In addition, this relaxation effect is independent of phosphodiesterase enzyme type 5 inhibition. Our data displays PnTx2-6 as possible pharmacological tool to study alternative treatments for erectile dysfunction. Nunes KP, Cordeiro MN, Richardson M, Borges MN, Diniz SOF, Cardoso VN, Tostes R, De Lima ME, Webb RC, and Leite R. Nitric oxide-induced vasorelaxation in response to PnTx2-6 toxin from Phoneutria nigriventer spider in rat cavernosal tissue. J Sex Med 2010;7:3879-3888.

Three-dimensional solitons in cross-combined linear and nonlinear optical lattices

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