Solvability of subprincipal type operators

In this paper we consider the solvability of pseudodifferential operators in the case when the principal symbol vanishes of order $k \ge 2$ at a nonradial involutive manifold $\Sigma_2$. We shall assume that the operator is of subprincipal type, which means that the $k$:th inhomogeneous blowup at $\Sigma_2$ of the refined principal symbol is of principal type with Hamilton vector field parallel to the base $\Sigma_2$, but transversal to the symplectic leaves of $\Sigma_2$ at the characteristics. When $k = \infty$ this blowup reduces to the subprincipal symbol. We also assume that the blowup is essentially constant on the leaves of $\Sigma_2$, and does not satisfying the Nirenberg-Treves condition (${\Psi}$). We also have conditions on the vanishing of the normal gradient and the Hessian of the blowup at the characteristics. Under these conditions, we show that $P$ is not solvable.Comment: Changed the formulation of Theorem 2.15, added an assuption. Corrected errors and clarified the arguments. Added reference

Some size relationships in phytoflagellate motility

Data from the literature are used to assess some hypothesised adaptive advantages of the flagellate life form among phytoplankton. Possible advantages include increased nutrient uptake by movement through a homogeneous medium as opposed to exploitation of spatial hetrogeneity of the environment. Maximal migrational amplitudes and maximal swimming velocities of phytoflagellates were compared to body size. Both were found to increase with size. Relative amplitudes and relative velocities, however, were found to decrease with size. Hydrophysical considerations show that additional gain of nutrients by swimming through a homogeneous medium is only minimal for small flagellates at their attainable swimming velocities. It is suggested that exploitation of environmental heterogeneity in nutrient distribution may be one of the most important advantages for flagellates over coccoid algae

The electric wind of Venus: A global and persistent "polar wind"-like ambipolar electric field sufficient for the direct escape of heavy ionospheric ions

Understanding what processes govern atmospheric escape and the loss of planetary water is of paramount importance for understanding how life in the universe can exist. One mechanism thought to be important at all planets is an “ambipolar” electric field that helps ions overcome gravity. We report the discovery and first quantitative extraterrestrial measurements of such a field at the planet Venus. Unexpectedly, despite comparable gravity, we show the field to be five times stronger than in Earth's similar ionosphere. Contrary to our understanding, Venus would still lose heavy ions (including oxygen and all water-group species) to space, even if there were no stripping by the solar wind. We therefore find that it is possible for planets to lose heavy ions to space entirely through electric forces in their ionospheres and such an “electric wind” must be considered when studying the evolution and potential habitability of any planet in any star system

A pilot randomised controlled trial of personalised care for depressed patients with symptomatic coronary heart disease in South London general practices: the UPBEAT-UK RCT protocol and recruitment.

ABSTRACT: Background: Community studies reveal people with coronary heart disease (CHD) are twice as likely to be depressed as the general population and that this co-morbidity negatively affects the course and outcome of both conditions. There is evidence for the efficacy of collaborative care and case management for depression treatment, and whilst NICE guidelines recommend these approaches only where depression has not responded to psychological, pharmacological, or combined treatments, these care approaches may be particularly relevant to the needs of people with CHD and depression in the earlier stages of stepped care in primary care settings. Methods: This pilot randomised controlled trial will evaluate whether a simple intervention involving a personalised care plan, elements of case management and regular telephone review is a feasible and acceptable intervention that leads to better mental and physical health outcomes for these patients. The comparator group will be usual general practitioner (GP) care. 81 participants have been recruited from CHD registers of 15 South London general practices. Eligible participants have probable major depression identified by a score of ≥8 on the Hospital Anxiety and Depression Scale depression subscale (HADS-D) together with symptomatic CHD identified using the Modified Rose Angina Questionnaire. Consenting participants are randomly allocated to usual care or the personalised care intervention which involves a comprehensive assessment of each participant’s physical and mental health needs which are documented in a care plan, followed by regular telephone reviews by the case manager over a 6-month period. At each review, the intervention participant’s mood, function and identified problems are reviewed and the case manager uses evidence based behaviour change techniques to facilitate achievement of goals specified by the patient with the aim of increasing the patient’s self efficacy to solve their problems. Depressive symptoms measured by HADS score will be collected at baseline and 1, 6- and 12 months post randomisation. Other outcomes include CHD symptoms, quality of life, wellbeing and health service utilisation. Discussion: This practical and patient-focused intervention is potentially an effective and accessible approach to the health and social care needs of people with depression and CHD in primary care. Trial registration: ISRCTN21615909

Local recurrence and distant metastases 18 years after resection of the greater omentum hemangiopericytoma

<p>Abstract</p> <p>Background</p> <p>Hemangiopericytoma occurs with increasing frequency in 5^thdecade of life and has prediction for retroperitoneum and extremities. A case of a local recurrence and metastases of hemangiopericytoma is described.</p> <p>Case presentation</p> <p>Recurrence of hemangiopericytoma in the greater omentum and the jejunal mesentery as well as metastases in the retroperitoneal space were diagnosed in a 61-year-old patient who had a hemangiopericytoma of the greater omentum excised 18 years before.</p> <p>Conclusion</p> <p>Because of the rarity of this disease and its typical clinical course associated with late recurrence and metastases, the authors decided to present this case emphasizing the necessity of systematic oncological follow-up after the end of treatment.</p

A systematic review of the evidence for single stage and two stage revision of infected knee replacement

BACKGROUND: Periprosthetic infection about the knee is a devastating complication that may affect between 1% and 5% of knee replacement. With over 79 000 knee replacements being implanted each year in the UK, periprosthetic infection (PJI) is set to become an important burden of disease and cost to the healthcare economy. One of the important controversies in treatment of PJI is whether a single stage revision operation is superior to a two-stage procedure. This study sought to systematically evaluate the published evidence to determine which technique had lowest reinfection rates. METHODS: A systematic review of the literature was undertaken using the MEDLINE and EMBASE databases with the aim to identify existing studies that present the outcomes of each surgical technique. Reinfection rate was the primary outcome measure. Studies of specific subsets of patients such as resistant organisms were excluded. RESULTS: 63 studies were identified that met the inclusion criteria. The majority of which (58) were reports of two-stage revision. Reinfection rated varied between 0% and 41% in two-stage studies, and 0% and 11% in single stage studies. No clinical trials were identified and the majority of studies were observational studies. CONCLUSIONS: Evidence for both one-stage and two-stage revision is largely of low quality. The evidence basis for two-stage revision is significantly larger, and further work into direct comparison between the two techniques should be undertaken as a priority

Erythropoietin Attenuates Brain Injury, Subventricular Zone Expansion, and Sensorimotor Deficits in Hypoxic-Ischemic Neonatal Rats

The aim of this study was to investigate the effect of erythropoietin (EPO) on histological brain injury, subventricular zone (SVZ) expansion, and sensorimotor function deficits induced by hypoxia-ischemia (HI) in newborn rat pups. Seven-day-old male rat pups were divided into six groups: normoxia control, normoxia EPO, hypoxia control, hypoxia EPO, HI control, and HI EPO group. Sham surgery or HI was performed in all animals. HI was induced by ligation of the right common carotid artery followed by 90 min of hypoxia with 8% oxygen. Recombinant human EPO 3 U/g or saline was administered intraperitoneally, immediately, at 24- and 48-hr after insult. At two weeks after insult, animals were challenged with cylinder-rearing test for evaluating forelimb asymmetry to determine sensorimotor function. All animals were then sacrificed for volumetric analysis of the cerebral hemispheres and the SVZ. The saline-treated HI rats showed marked asymmetry by preferential use of the non-impaired, ipsilateral paw in the cylinder-rearing test. Volumetric analysis of brains revealed significantly decreased preserved ipsilateral hemispheric volume and increased ipsilateral SVZ volume compared with the sham-operated animals. Treatment of EPO significantly improved forelimb asymmetry and preserved ipsilateral hemispheric volume along with decreased expansion of ipsilateral SVZ following HI compared to the saline-treated HI rats. These results support the use of EPO as a candidate drug for treatment of neonatal hypoxic-ischemic brain damage

Persistence of back pain symptoms after pregnancy and bone mineral density changes as measured by quantitative ultrasound - a two year longitudinal follow up study

<p>Abstract</p> <p>Background</p> <p>Previous research has shown a loss of bone mineral density (BMD) during pregnancy. This loss has been correlated to the occurrence of back pain symptoms during pregnancy. The objective of this study was to evaluate whether persistence of back pain symptoms 2 years after pregnancy could be associated with BMD changes as measured by quantitative USG of the os calcis.</p> <p>Methods</p> <p>A cohort of patients who reported significant back pain symptoms during pregnancy were surveyed for persistent back pain symptoms 24 to 28 months after the index pregnancy. Os calcis BMD was measured by quantitative ultrasound and compared with the BMD values during pregnancy.</p> <p>Results</p> <p>A cohort of 60 women who had reported significant back pain symptoms in their index pregnancy completed a 24-28 months follow-up survey and BMD reassessment. Persistence of significant back pain symptoms was seen in 24 (40%) of this cohort. These women had higher BMD loss during pregnancy compared to those without further pain (0.047 Vs 0.030 g/cm²; p = 0.03). Those that remained pain free after pregnancy appeared to have completely recovered their BMD loss in pregnancy, while those with persistent pain had lower BMD values (ΔBMD - 0.007 Vs - 0.025 g/cm²; p = 0.023) compared to their early pregnancy values.</p> <p>Conclusion</p> <p>Persistence of back pain symptoms after pregnancy could be related to an inability to recover fully from BMD loss during the index pregnancy.</p