996 resultados para Condition Dependence
Condition number estimates for combined potential boundary integral operators in acoustic scattering
Resumo:
We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators.
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New experiments underpin the interpretation of the basic division in crystallization behaviour of polyethylene in terms of whether or not there is time for the fold surface to order before the next molecular layer is added at the growth front. For typical growth rates, in Regime 11, polyethylene lamellae form with disordered {001} fold surfaces then transform, with lamellar thickening and twisting, towards the more-ordered condition found for slower crystallization in Regime 1, in which lamellae form with and retain {201} fold surfaces. Several linear and linear-low-density polyethylenes have been used to show that, for the same polymer crystallized alone or in a blend, the growth rate at which the change in initial lamellar condition occurs is reasonably constant thereby supporting the concept of a specific time for surfaces to attain the ordered {201}) state. This specific time, in the range from milliseconds to seconds, increases with molecular length, and in linear-low-density polymer, for higher branch contents. (c) 2006 Elsevier Ltd. All rights reserved.
Resumo:
We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.
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An eddy-resolving numerical model of a zonal flow, meant to resemble the Antarctic Circumpolar Current, is described and analyzed using the framework of J. Marshall and T. Radko. In addition to wind and buoyancy forcing at the surface, the model contains a sponge layer at the northern boundary that permits a residual meridional overturning circulation (MOC) to exist at depth. The strength of the residual MOC is diagnosed for different strengths of surface wind stress. It is found that the eddy circulation largely compensates for the changes in Ekman circulation. The extent of the compensation and thus the sensitivity of the MOC to the winds depend on the surface boundary condition. A fixed-heat-flux surface boundary severely limits the ability of the MOC to change. An interactive heat flux leads to greater sensitivity. To explain the MOC sensitivity to the wind strength under the interactive heat flux, transformed Eulerian-mean theory is applied, in which the eddy diffusivity plays a central role in determining the eddy response. A scaling theory for the eddy diffusivity, based on the mechanical energy balance, is developed and tested; the average magnitude of the diffusivity is found to be proportional to the square root of the wind stress. The MOC sensitivity to the winds based on this scaling is compared with the true sensitivity diagnosed from the experiments.
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In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions.
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The frame dependence of the pair-term contribution to the electromagnetic form factor of the pion is studied within the Light Front approach. A symmetric ansatz for the pion Bethe-Salpeter amplitude with a pseudo scalar coupling of the constituent to the pion field is used. In this model, the pair term vanishes for the Drell-Yan condition, while it is dominant for momentum transfer along the light-front direction.
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In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification by Minchenko and Stakhovski that was called RCRCQ. We show that RCPLD is enough to ensure the convergence of an augmented Lagrangian algorithm and that it asserts the validity of an error bound. We also provide proofs and counter-examples that show the relations of RCRCQ and RCPLD with other known constraint qualifications. In particular, RCPLD is strictly weaker than CPLD and RCRCQ, while still stronger than Abadie's constraint qualification. We also verify that the second order necessary optimality condition holds under RCRCQ.
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The objective of this work was to assess the degree of multicollinearity and to identify the variables involved in linear dependence relations in additive-dominant models. Data of birth weight (n=141,567), yearling weight (n=58,124), and scrotal circumference (n=20,371) of Montana Tropical composite cattle were used. Diagnosis of multicollinearity was based on the variance inflation factor (VIF) and on the evaluation of the condition indexes and eigenvalues from the correlation matrix among explanatory variables. The first model studied (RM) included the fixed effect of dam age class at calving and the covariates associated to the direct and maternal additive and non-additive effects. The second model (R) included all the effects of the RM model except the maternal additive effects. Multicollinearity was detected in both models for all traits considered, with VIF values of 1.03 - 70.20 for RM and 1.03 - 60.70 for R. Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and it was classified as weak, with condition index values between 10.00 and 26.77. In general, the variables associated with additive and non-additive effects were involved in multicollinearity, partially due to the natural connection between these covariables as fractions of the biological types in breed composition.
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The aim of this thesis is to apply multilevel regression model in context of household surveys. Hierarchical structure in this type of data is characterized by many small groups. In last years comparative and multilevel analysis in the field of perceived health have grown in size. The purpose of this thesis is to develop a multilevel analysis with three level of hierarchy for Physical Component Summary outcome to: evaluate magnitude of within and between variance at each level (individual, household and municipality); explore which covariates affect on perceived physical health at each level; compare model-based and design-based approach in order to establish informativeness of sampling design; estimate a quantile regression for hierarchical data. The target population are the Italian residents aged 18 years and older. Our study shows a high degree of homogeneity within level 1 units belonging from the same group, with an intraclass correlation of 27% in a level-2 null model. Almost all variance is explained by level 1 covariates. In fact, in our model the explanatory variables having more impact on the outcome are disability, unable to work, age and chronic diseases (18 pathologies). An additional analysis are performed by using novel procedure of analysis :"Linear Quantile Mixed Model", named "Multilevel Linear Quantile Regression", estimate. This give us the possibility to describe more generally the conditional distribution of the response through the estimation of its quantiles, while accounting for the dependence among the observations. This has represented a great advantage of our models with respect to classic multilevel regression. The median regression with random effects reveals to be more efficient than the mean regression in representation of the outcome central tendency. A more detailed analysis of the conditional distribution of the response on other quantiles highlighted a differential effect of some covariate along the distribution.
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Quercus robur L. (pedunculate oak) and Quercus petraea (Matt.) Liebl. (sessile oak) are two European oak species of great economic and ecological importance. Even though both oaks have wide ecological amplitudes of suitable growing conditions, forests dominated by oaks often fail to regenerate naturally. The regeneration performance of both oak species is assumed to be subject to a variety of variables that interact with one another in complex ways. The novel approach of this research was to study the effect of many ecological variables on the regeneration performance of both oak species together and identify key variables and interactions for different development stages of the oak regeneration on a large scale in the field. For this purpose, overstory and regeneration inventories were conducted in oak dominated forests throughout southern Germany and paired with data on browsing, soil, and light availability. The study was able to verify the assumption that the occurrence of oak regeneration depends on a set of variables and their interactions. Specifically, combinations of site and stand specific variables such as light availability, soil pH and iron content on the one hand, and basal area and species composition of the overstory on the other hand. Also browsing pressure was related to oak abundance. The results also show that the importance of variables and their combinations differs among the development stages of the regeneration. Light availability becomes more important during later development stages, whereas the number of oaks in the overstory is important during early development stages. We conclude that successful natural oak regeneration is more likely to be achieved on sites with lower fertility and requires constantly controlling overstory density. Initially sufficient mature oaks in the overstory should be ensured. In later stages, overstory density should be reduced continuously to meet the increasing light demand of oak seedlings and saplings.
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Russian gas industry: The current condition of the gas industry is one of the most crucial factors influencing the Russian state·s functioning, internal situation and international position. Not only is gas the principal energy resource in Russia, it also subsidises other sectors of the economy. Status of the main European gas exporter strengthens also Russia's importance in the international arena. New regional in-security: Ten years have passed since the Central Asian states declared their independence, but their relationship with Russia still remains close, and the latter treats them as its exclusive zone of influence. A crucial reason for keeping Central Asia within the orbit of Moscow·s influence is the fact that Russia exercises control over the most important transport routes out of the region of raw materials for the power industry, on which the economic development of Asia depends on. But this is the only manifestation of Central Asia·s economic dependence on Russia. Moscow lacks solid economic instruments (i.e. investment input or power industry dependence) to shape the situation in the region. Caspian oil and gas: Caspian stocks of energy resources are not, and most probably will not be, of any great significance on the world scale. Nevertheless it is the Caspian region which will have the opportunity to become an oil exporter which will reduce the dependence of the European countries on Arabian oil, and which will guarantee Russia the quantities of gas which are indispensable both for meeting its internal demands and for maintaining its current level of export. For Azerbaijan, Kazakhstan and Turkmenistan, the confirmation of the existence of successive oil strata is not only an opportunity to increase income, but also an additional bargaining chip in the game for the future of the whole region. The stake in this game is the opportunity to limit the economic, and by extension the political influences of Russia in the region.
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Objective: Dysphoria and depression have been cited as side effects of the opioid antagonist naltrexone. We aimed to assess whether depressive symptoms are a clinically relevant side effect in a population receiving naltrexone as a treatment for opioid dependence. Methods: We carried out a randomized controlled, open-label trial comparing rapid opiate detoxification under anesthesia and naltrexone treatment with continued methadone maintenance at the Alcohol and Drug Service, Royal Brisbane and Women's Hospital, Brisbane, Australia. The study subjects were patients stabilized on methadone maintenance treatment for heroin dependence who wished to transfer to naltrexone treatment. The Beck Depression Inventory, State-Trait Anxiety Inventory and Opiate Treatment Index subscales for heroin use and social functioning were used at baseline and follow-up assessments at 1, 2, 3 and 6 months. Results: Forty-two participants were allocated to receive naltrexone treatment, whereas 38 continued methadone maintenance as the control condition. Participants who received naltrexone did not exhibit worsening of depressive symptoms. In participants attending all follow-up assessments, there was a trend for those receiving naltrexone to exhibit an improvement in depression over time compared with the control group. Participants who were adherent to naltrexone treatment exhibited fewer depressive symptoms than those who were nonadherent. Conclusions: These results suggest that depression need not be considered a common adverse effect of naltrexone treatment or a treatment contraindication and that engaging with or adhering to naltrexone treatment may be associated with fewer depressive symptoms.
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PURPOSE: Opioid dependence (OD) is a serious and growing clinical condition with increasing social costs that requires expanding treatment beyond opioid agonist substitution. The opioid antagonist naltrexone has displayed a remarkable association of theoretical effectiveness and poor clinical utility in treating OD due to noncompliant behavior and low acceptability among patients, only partly modified by psychosocial interventions. We reviewed pharmacological studies, including naltrexone depot formulations and combination treatments. METHOD: We searched PubMed for clinical studies on the use of naltrexone implants and slow-release injections in OD, and investigations using adjunct medications to improve naltrexone maintenance therapy of OD. We discussed the results in view of their application to the clinical practice. RESULTS: Significant reduction in opioid use and improved retention in treatment have been found in several studies using depot naltrexone formulations, some of which are controlled clinical trials. Pilot investigations have gathered initial positive results on the use of naltrexone in combination with serotonin reuptake inhibitors, α-2 adrenergic, opioid, and γ-aminobutyric acid agonist medications. CONCLUSION: Current evidence suggests that more research on effectiveness and safety is needed in support of depot naltrexone treatment for OD. Further research comparing slow-release with oral naltrexone and opioid agonist medications will help characterize the role of opioid antagonist-mediated treatment of OD. Preliminary investigations on naltrexone combination treatments suggest the opportunity to continue study of new mixed receptor activities for the treatment of OD and other drug addictions.