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In the theory of ordinary differential equations, there is a strange relationship between uniqueness of solutions and convergence of the successive approxi mations. There are examples of differential equations with unique solutions for which the successive approximations do not converge (8) and of differential equations with non-unique solutions for which the successive approximations do converge (2). However, in spite of the known logical independence of these two properties, almost all conditions which assure uniqueness also imply the convergence of the successive approximations. For example, the hypotheses of Kamke's general uniqueness theorem (5), have been shown by Coddington and Levinson to suffice for the convergence of successive approximations, after the addition of one simple monotonicity condition (4). There is one counterexample to this “principle,” a generalization of Kamke's result, to which another condition in addition to a monotonicity assumption must be added before convergence of the successive approximations can be proved (2).
Let L and M be linear ordinary differential operators defined on an interval I, not necessarily bounded, of the real line. We wish to consider the expansion of arbitrary functions in eigenfunctions of the differential equation Lu = λMu on I. The case where M is the identity operator and L has a self-adjoint realization as an operator in the Hilbert space L2(I) has been treated in various ways by several authors; an extensive bibliography may be found in (4) or (8).
Lyapunov's second method is a well-known and powerful tool for studying the behaviour of solutions of a system of differential equations. One approach to the theory is the comparison method developed by Corduneanu (4). This approach has the advantage that it also leads to other results on asymptotic behaviour which originally appeared to be unrelated to Lyapunov's method. Some of these results have been obtained by the author in (2). The purpose of this paper is to make use of the comparison method to obtain some refinements of Lyapunov's theory.
There are several ways to approach the eigenfunction expansion problem for ordinary differential operators via the spectral theorem for self-ad joint linear operators in Hilbert space. One can examine the resolvent, which requires a detailed study of the Green's function (4, 5, 7), or one can use the spectral theorem for unbounded operators (2, 3, 9). Since the eigenf unction expansion theorem also requires some multiplicity theory, unless one is prepared to use a rather powerful form of the spectral theorem for unbounded operators, as in (2, 9), the proof requires a good deal of work in addition to the spectral theorem.
Although much technical and philosophical attention has been given to relevance logics, the notion of relevance itself is generally left at an intuitive level. It is difficult to find in the literature an explicit account of relevance in formal reasoning. In this article I offer a formal explication of the notion of relevance in deductive logic and argue that this notion has an interesting place in the study of classical logic. The main idea is that a premise is relevant to an argument when it contributes to the validity of that argument. I then argue that the sequents which best embody this ideal of relevance are the so-called perfect sequents—that is, sequents which are valid but have no proper subsequents that are valid. Church’s theorem entails that there is no recursively axiomatizable proof-system that proves all and only the perfect sequents, so the project that emerges from studying perfection in classical logic is not one of finding a perfect subsystem of classical logic, but is rather a comparative study of classifying subsystems of classical logic according to how well they approximate the ideal of perfection.
Under which conditions are we epistemically justified to believe that what other people tell us is true? Traditionally, the answer has either been reductionist or anti-reductionist: Either our justification reduces to non-testimonial reasons, or we have a presumptive, though defeasible, right to believe what we are told. However, different cases pull in different directions. Intuitively, someone asking for the time is subject to different epistemic standards than a surgeon consulting a colleague before a dangerous operation. Following this line of thought, this paper develops an account of testimonial justification that captures our reductionist as well as our anti-reductionist intuitions. It is argued that the speaker's commitment to an epistemic norm, as well as the hearer's understanding of that norm, gives the hearer a presumptive right to believe what she is told. However, this justification doesn't apply to situations with high practical risks. Here, the hearer needs reductive reasons to believe that her interlocutor is especially qualified to give her the desired information.
Identifying climates favoring extreme weather phenomena is a primary aim of paleoclimate and paleohydrological research. Here, we present a well-dated, late Holocene Dead Sea sediment record of debris flows covering 3.3 to 1.9 cal ka BP. Twenty-three graded layers deposited in shallow waters near the western Dead Sea shore were identified by microfacies analysis. These layers represent distal subaquatic deposits of debris flows triggered by torrential rainstorms over the adjacent western Dead Sea escarpment. Modern debris flows on this escarpment are induced by rare rainstorms with intensities exceeding >30 mm h−1 for at least one hour and originate primarily from the Active Red Sea Trough synoptic pattern. The observed late Holocene clustering of such debris flows during a regional drought indicates an increased influence of Active Red Sea Troughs resulting from a shift in synoptic atmospheric circulation patterns. This shift likely decreased the passages of eastern Mediterranean cyclones, leading to drier conditions, but favored rainstorms triggered by the Active Red Sea Trough. This is in accord with present-day meteorological data showing an increased frequency of torrential rainstorms in regions of drier climate. Hence, this study provides conclusive evidence for a shift in synoptic atmospheric circulation patterns during a late Holocene drought.
We developed a self-report tool to assess patients’ experiences with lifestyle services in team-based primary care and pilot tested the questionnaire as part of a lifestyle intervention study to reverse metabolic syndrome.
Older client satisfaction questionnaires have been generally inadequate for quality improvement purposes, as they have been focused mainly on interpersonal skills of providers and/or in the context of one disease. New approaches to assessing the patient experience of lifestyle programs in primary care are needed and could inform quality improvement efforts over time.
The first phase in developing the questionnaire involved a group-administered questionnaire distributed to 38 healthcare providers in five groups to prioritize variables to include in the survey. Concepts were taken from a previous review of available questionnaires assessing primary care services. The draft questionnaire was reviewed by 11 participants from a lifestyle program using think-aloud cognitive interviewing techniques. The modified self-administered questionnaire (paper and online versions) was then pilot tested with 164 recipients of a nutrition and physical activity intervention program.
Providers ranked the top variables to include in the questionnaire as: ‘trust,’ ‘general communication,’ ‘first-contact accessibility,’ ‘whole-person care,’ and ‘respectfulness.’ After cognitive interviewing and revisions, 21 multiple choice and two open-ended questions were used for pilot testing. Pilot testing identified additional minor wording changes that were needed for clarity, a decreased number of questions for redundant concepts, and decreased options for ceiling effects, resulting in 20 multiple choice and one open-ended question.
The modified self-administered patient experience questionnaire to assess lifestyle services in primary care has undergone rigorous development. Further validation is needed. The assessment of patient experience of lifestyle programs can be used to supplement other data to assess the overall effectiveness of such programs.
Violators of cooperation norms may be informally punished by their peers. How such norm enforcement is judged by others can be regarded as a meta-norm (i.e., a second-order norm). We examined whether meta-norms about peer punishment vary across cultures by having students in eight countries judge animations in which an agent who over-harvested a common resource was punished either by a single peer or by the entire peer group. Whether the punishment was retributive or restorative varied between two studies, and findings were largely consistent across these two types of punishment. Across all countries, punishment was judged as more appropriate when implemented by the entire peer group than by an individual. Differences between countries were revealed in judgments of punishers vs. non-punishers. Specifically, appraisals of punishers were relatively negative in three Western countries and Japan, and more neutral in Pakistan, UAE, Russia, and China, consistent with the influence of individualism, power distance, and/or indulgence. Our studies constitute a first step in mapping how meta-norms vary around the globe, demonstrating both cultural universals and cultural differences.
We describe a numerical model to simulate the non-linear elasto-plastic dynamics of compressible materials. The model is fully Eulerian and it is discretized on a fixed Cartesian mesh. The hyperelastic constitutive law considered is neohookean and the plasticity model is based on a multiplicative decomposition of the inverse deformation tensor. The model is thermodynamically consistent and it is shown to be stable in the sense that the norm of the deviatoric stress tensor beyond yield is non increasing. The multimaterial integration scheme is based on a simple numerical flux function that keeps the interfaces sharp. Numerical illustrations in one to three space dimensions of high-speed multimaterial impacts in air are presented.
This practical text offers a comprehensive guide to perioperative temperature management for anaesthetists, surgeons and nurses. The physiological basics of thermoregulation and heat exchange are covered, before the changes that occur during general and regional anaesthesia are outlined. The relevant adverse scenarios associated with perioperative hypothermia, including morbid cardiac events, impairment of coagulation, increased blood loss and surgical site infections are discussed, before the methods of measuring core temperature and the equipment and techniques to keep patients warm are described. Richly illustrated and clearly structured for quick reference, Perioperative Temperature Management is an essential daily resource to help ensure safe, effective practice.