Representations of integers by certain positive definite binary quadratic forms

We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n=x^2+Ny^2 for a squarefree integer N.Comment: 8 pages, submitte

Energy composition of the Universe: time-independent internal symmetry

The energy composition of the Universe, as emerged from the Type Ia supernova observations and the WMAP data, looks preposterously complex, -- but only at the first glance. In fact, its structure proves to be simple and regular. An analysis in terms of the Friedmann integral enables to recognize a remarkably simple time-independent covariant robust recipe of the cosmic mix: the numerical values of the Friedmann integral for vacuum, dark matter, baryons and radiation are approximately identical. The identity may be treated as a symmetry relation that unifies cosmic energies into a regular set, a quartet, with the Friedmann integral as its common genuine time-independent physical parameter. Such cosmic internal (non-geometrical) symmetry exists whenever cosmic energies themselves exist in nature. It is most natural for a finite Universe suggested by the WMAP data. A link to fundamental theory may be found under the assumption about a special significance of the electroweak energy scale in both particle physics and cosmology. A freeze-out model developed on this basis demonstrates that the physical nature of new symmetry might be due to the interplay between electroweak physics and gravity at the cosmic age of a few picoseconds. The big `hierarchy number' of particle physics represents the interplay in the model. This number quantifies the Friedmann integral and gives also a measure to some other basic cosmological figures and phenomena associated with new symmetry. In this way, cosmic internal symmetry provides a common ground for better understanding of old and recent problems that otherwise seem unrelated; the coincidence of the observed cosmic densities, the flatness of the co-moving space, the initial perturbations and their amplitude, the cosmic entropy are among them.Comment: 32 page

An intensive multimodal group programme for patients with psychotic disorders at risk of rehospitalization: A controlled intervention study

Background: On the basis of earlier experiences in Germany and England, we developed an intensive multimodal group programme (FACT Plus) for psychotic-spectrum patients. By combining it with regular Flexible Assertive Community Treatment (FACT) (care as usual), we intended to reduce psychiatric rehospitalizations and mental healthcare costs. Methods: We included adult patients (>18 years) with a psychotic spectrum disorder who had had at least one psychiatric admission in the 2 years before inclusion. FACT Plus was delivered weekly for 9 months. The intervention group was recruited in northern Rotterdam (the Netherlands), and the control group was recruited in southern Rotterdam. The primary outcome measure was length of stay (LOS) and the secondary outcome measures were mental healthcare costs and compulsory admissions. Results: We included 52 patients in the intervention group and 61 patients in the control group. During the 12-month observation period, the mean LOS per patient was 15.2 (intervention group) and 34.6 (control group). This represents a difference of 19.4 days (56.1%). This result was statistically significant (B = -.859, SE =.497, p =.042) in a regression model correcting for baseline differences between the groups. Mean total mental healthcare costs per patient were €21,098 in the intervention group) versus €25,054 in the control group, a difference of about €4000 per patient (16%). In addition, there were zero compulsory admissions in the intervention group and nine in the control group. Conclusions: After the addition of FACT Plus to regular FACT, psychiatric LOS was substantial

Application of direct bioautography and SPME-GC-MS for the study of antibacterial chamomile ingredients

The isolation and characterization of antibacterial chamomile components were performed by the use of direct bioautography and solid phase microextraction (SPME)-GC-MS. Four ingredients, active against Vibrio fischeri, were identified as the polyacetylene geometric isomers cis- and trans-spiroethers, the coumarin related herniarin, and the sesquiterpene alcohol (-)-alpha-bisabolol

How dangerousness evolves after court-ordered compulsory psychiatric admission: explorative prospec

Background Compulsory admission is commonly regarded as necessary and justified for patients whose psychiatric condition represents a severe danger to themselves and others. However, while studies on compulsory admissions have reported on various clinical and social outcomes, little research has focused specifically on dangerousness, which in many countries is the core reason for compulsory admission. Aims To study changes in dangerousness over time in adult psychiatric patients admitted by compulsory court order, and to relate these changes to these patients' demographic and clinical characteristics. Method In this explorative prospective observational cohort study of adult psychiatric patients admitted by compulsory court order, demographic and clinical data were collected at baseline. At baseline and at 6 and 12 month follow-up, dangerousness was assessed using the Dangerousness Inventory, an instrument based on the eight types of dangerousness towards self or others specified in Dutch legislation on compulsory admissions. We used descriptive statistics and logistic regression to analyse the data. Results We included 174 participants with a court-ordered compulsory admission. At baseline, the most common dangerousness criterion was inability to cope in society. Any type of severe or very severe dangerousness decreased from 86.2% at baseline to 36.2% at 6 months and to 28.7% at 12 months. Being homeless at baseline was the only variable which was significantly associated with persistently high levels of dangerousness. Conclusions Dangerousness decreased in about two-thirds of the patients after court-ordered compulsory admission. It persisted, however, in a substantial minority (approximately one-third). Declaration of interest None

Crucial factors preceding compulsory psychiatric admission

BACKGROUND: Compulsory admissions have a strong effect on psychiatric patients and represent a deprivation of personal liberty. Although the rate of such admissions is tending to rise in several Western countries, there is little qualitative research on the mental health-care process preceding compulsory admission. The objective of the study was to identify crucial factors in the mental health-care process preceding compulsory admission of adult psychiatric patients. METHODS: This retrospective, qualitative multiple-case study was based on the patient records of patients with severe mental illness, mainly schizophrenia and other psychotic disorders. Twenty two patient records were analyzed. Patients' demographic and clinical characteristics were heterogeneous. All were treated by Flexible Assertive Community Treatment teams (FACT teams) at two mental health institutions in the greater Rotterdam area in the Netherlands and had a compulsory admission in a predefined inclusion period. The data were analyzed according to the Prevention and Recovery System for Monitoring and Analysis (PRISMA) method, assessing acts, events, conditions, and circumstances, failing protective barriers and protective recovery factors. RESULTS: The most important patient factors in the process preceding compulsory admission were psychosis, aggression, lack of insight, care avoidance, and unauthorized reduction or cessation of medication. Neither were health-care professionals as assertive as they could be in managing early signs of relapse and care avoidance of these particular patients. CONCLUSION: The health-care process preceding compulsory admission is complex, being influenced by acts, events, conditions and circumstances, failing barriers, and protective factors. The most crucial factors are patients' lack of insight and cessation of medication, and health-care professionals' lack of assertiveness

Demonstration of the temporal matter-wave Talbot effect for trapped matter waves

We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially non-interacting matter waves and observe matter-wave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with sub-recoil resolution, allowing us to observe fractional Talbot fringes up to 10th order.Comment: 17 pages, 7 figure

Azimuthal anisotropy at RHIC: the first and fourth harmonics

We report the first observations of the first harmonic (directed flow, v_1), and the fourth harmonic (v_4), in the azimuthal distribution of particles with respect to the reaction plane in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC). Both measurements were done taking advantage of the large elliptic flow (v_2) generated at RHIC. From the correlation of v_2 with v_1 it is determined that v_2 is positive, or {\it in-plane}. The integrated v_4 is about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8) harmonics upper limits on the magnitudes are reported.Comment: 6 pages with 3 figures, as accepted for Phys. Rev. Letters The data tables are at http://www.star.bnl.gov/central/publications/pubDetail.php?id=3