On a P\'olya functional for rhombi, isosceles triangles, and thinning convex sets

Let $\Omega$ be an open convex set in ${\mathbb R}^m$ with finite width, and let $v_{\Omega}$ be the torsion function for $\Omega$, i.e. the solution of $-\Delta v=1, v\in H_0^1(\Omega)$. An upper bound is obtained for the product of $\Vert v_{\Omega}\Vert_{L^{\infty}(\Omega)}\lambda(\Omega)$, where $\lambda(\Omega)$ is the bottom of the spectrum of the Dirichlet Laplacian acting in $L^2(\Omega)$. The upper bound is sharp in the limit of a thinning sequence of convex sets. For planar rhombi and isosceles triangles with area $1$, it is shown that $\Vert v_{\Omega}\Vert_{L^{1}(\Omega)}\lambda(\Omega)\ge \frac{\pi^2}{24}$, and that this bound is sharp.Comment: 12 pages, 4 figure

De waterhuishouding van het Grevelingenbekken en de watervoorziening van de landbouw in Zuid - Nederland

De voorzieningen ter afsluiting van de zeegaten in Zuidwest-Nederland hadden in het kader van de Deltawet o.m. twee belangrijke doelstellingen. De eerste was de bescherming van het gebied tegen toekomstig overstromingsgevaar, de tweede was de schepping van een zoetwaterbekken, dat verschillende functies zou kunnen vervullen. De gedachte-ontwikkeling over milieu-aspecten heeft inmiddels geleid tot het besluit om de Oosterschelde weliswaar af te dammen, maar het water zo zout mogelijk te houden. Nu het Grevelingenbekken is afgesloten en ook daar van sommige zijden belangstelling bestaat voor een zoutwaterbekken, rijst de vraag welke belangen van andere zijde gediend zouden zijn met een zoetwaterbekken

The Contribution of Acupuncture and Moxibustion to Healthcare: an Evidence-based Approach

Patients deserve the “best of both worlds” when it comes to their healthcare. Ideally healthcare blends the best of both worlds by combining healthcare options from the perspective of both Western and complementary medicine. The synergy between modern medicine and complementary health care, and the value of blending these disciplines, has been the focus of this thesis. The aim was to identify the strengths and limitations of acupuncture and moxibustion, as described in Traditional Chinese Medicine, and evaluate how these therapies can be implemented in modern medicine, taking the perspective of patients, physicians, complementary therapists, health insurers, and healthcare policymakers. The thesis consists of three parts. Part one, the general approach, introduces the use of acupuncture in a general practice. The observational study presents the health-related quality of life in patients with musculoskeletal complaints in a general acupuncture practice. The aim of this pragmatic study was to gain insight into whether the HRQoL of patients undergoing routine acupuncture treatment for musculoskeletal complaints differs with that in a Dutch population sample; and to investigate changes in HRQoL during the course of acupuncture treatment. In the second part we discuss also using TCM in the diagnosing of patients with complex regional pain syndrome type 1. The pilot study reports a different TCM-approach to diagnose the patient with CRPS1, by questioning the menstrual cycle conform TCM, which might eventually lead to a new treatment approach. The topic of the third part of the thesis is breech presentation. Described is the development and tracking of nonvertex position (mainly breech position) throughout pregnancy and the prognostic value of ultrasound in predicting nonvertex presentation at delivery in the Generation R study. The aim was to get better information about the natural history of the position of the fetus that leads to breech at delivery. In addition, systematic review and meta-analysis of the existing literature about (randomized) controlled trials on the acupuncture-type interventions on Zhiyin (BL 67) was performed, to elicit a version of a fetus in breech position, including a letter about the same topic. Finally, the results of the modeling approach of a decision analysis and cost analysis of breech version by acumoxa offered to women with a breech fetus at 33 weeks of gestation are reported. In this modeling approach, with sensitivity analysis, also the selective use of a) Moxa, b) the manipulation using external cephalic version, and c) home-births was considered

Morse theory on spaces of braids and Lagrangian dynamics

In the first half of the paper we construct a Morse-type theory on certain spaces of braid diagrams. We define a topological invariant of closed positive braids which is correlated with the existence of invariant sets of parabolic flows defined on discretized braid spaces. Parabolic flows, a type of one-dimensional lattice dynamics, evolve singular braid diagrams in such a way as to decrease their topological complexity; algebraic lengths decrease monotonically. This topological invariant is derived from a Morse-Conley homotopy index and provides a gloablization of `lap number' techniques used in scalar parabolic PDEs. In the second half of the paper we apply this technology to second order Lagrangians via a discrete formulation of the variational problem. This culminates in a very general forcing theorem for the existence of infinitely many braid classes of closed orbits.Comment: Revised version: numerous changes in exposition. Slight modification of two proofs and one definition; 55 pages, 20 figure

Herbal weight-loss products: how informed are we?

Objective: Non-prescription, weight-loss products are advertised as quick-solution alternatives to long-term lifestyle changes.Design: Cross-sectional descriptive.Setting: Free State province.Subjects: Fifty-six dietitians registered to the Free State branch of the Association of Dietetics in South Africa, excluding lecturers and students, and 88 pharmacists working in the Bloemfontein area.Outcome measures: Structured telephonic interviews were conducted with 25 dietitians and 46 pharmacists to ascertain whether or not they had heard of the individual ingredients listed in non-prescription, weight-loss products and if they knew if each of these ingredients were scientifically proven to induce weight loss.Results: Most dietitians and pharmacists reported that they had heard of green tea extract (92% and 89%), chromium picolinate (76% and 59%), apple cider vinegar (100% and 96%), lemon juice (100% and 87%) and alcohol (100% and 91%), respectively, being ingredients in weight-loss products. More dietitians and pharmacists reported that, to their knowledge, green tea extract (52% vs. 26%), chromium picolinate (52% vs. 15%), apple cider vinegar (64% vs. 33%), lemon juice (80% vs. 64%) and alcohol (76% vs. 61%), were not scientifically proven to be effective in attaining weight loss. Both groups included a percentage who were not familiar with the ingredients, or who thought that these ingredients had been demonstrated to be effective, despite no conclusive evidence existing in the literature.Conclusion: Healthcare professionals need to actively educate themselves about non-prescription weight-loss products in order to guide the public and reduce consumer confusion

Large deviations for ideal quantum systems

We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a subdomain of the container are described by a large deviation function related to the pressure of the system. That is, untypical densities occur with a probability exponentially small in the volume of the subdomain, with the coefficient in the exponent given by the appropriate thermodynamic potential. Furthermore, small fluctuations satisfy the central limit theorem.Comment: 28 pages, LaTeX 2

A Massive Neutron Star in the Globular Cluster M5

We report the results of 19 years of Arecibo timing for two pulsars in the globular cluster NGC 5904 (M5), PSR B1516+02A (M5A) and PSR B1516+02B (M5B). This has resulted in the measurement of the proper motions of these pulsars and, by extension, that of the cluster itself. M5B is a 7.95-ms pulsar in a binary system with a > 0.13 solar mass companion and an orbital period of 6.86 days. In deep HST images, no optical counterpart is detected within ~2.5 sigma of the position of the pulsar, implying that the companion is either a white dwarf or a low-mass main-sequence star. The eccentricity of the orbit (e = 0.14) has allowed a measurement of the rate of advance of periastron: (0.0142 +/-0.0007) degrees per year. We argue that it is very likely that this periastron advance is due to the effects of general relativity, the total mass of the binary system then being 2.29 +/-0.17 solar masses. The small measured mass function implies, in a statistical sense, that a very large fraction of this total mass is contained in the pulsar: 2.08 +/- 0.19 solar masses (1 sigma); there is a 5% probability that the mass of this object is < 1.72 solar masses and a 0.77% probability that is is between 1.2 and 1.44 solar masses. Confirmation of the median mass for this neutron star would exclude most ``soft'' equations of state for dense neutron matter. Millisecond pulsars (MSPs) appear to have a much wider mass distribution than is found in double neutron star systems; about half of these objects are significantly more massive than 1.44 solar masses. A possible cause is the much longer episode of mass accretion necessary to recycle a MSP, which in some cases corresponds to a much larger mass transfer.Comment: 10 pages in ApJ emulate format, 2 tables, 6 figures. Added February 2008 data, slightly revised mass limits. Accepted for publication in Ap