Scattering theory for Klein-Gordon equations with non-positive energy

We study the scattering theory for charged Klein-Gordon equations: \{{array}{l} (\p_{t}- \i v(x))^{2}\phi(t,x) \epsilon^{2}(x, D_{x})\phi(t,x)=0,[2mm] \phi(0, x)= f_{0}, [2mm] \i^{-1} \p_{t}\phi(0, x)= f_{1}, {array}. where: \epsilon^{2}(x, D_{x})= \sum_{1\leq j, k\leq n}(\p_{x_{j}} \i b_{j}(x))A^{jk}(x)(\p_{x_{k}} \i b_{k}(x))+ m^{2}(x), describing a Klein-Gordon field minimally coupled to an external electromagnetic field described by the electric potential $v(x)$ and magnetic potential $\vec{b}(x)$. The flow of the Klein-Gordon equation preserves the energy: h[f, f]:= \int_{\rr^{n}}\bar{f}_{1}(x) f_{1}(x)+ \bar{f}_{0}(x)\epsilon^{2}(x, D_{x})f_{0}(x) - \bar{f}_{0}(x) v^{2}(x) f_{0}(x) \d x. We consider the situation when the energy is not positive. In this case the flow cannot be written as a unitary group on a Hilbert space, and the Klein-Gordon equation may have complex eigenfrequencies. Using the theory of definitizable operators on Krein spaces and time-dependent methods, we prove the existence and completeness of wave operators, both in the short- and long-range cases. The range of the wave operators are characterized in terms of the spectral theory of the generator, as in the usual Hilbert space case

Fulvenes as Isomers of Benzenoid Compounds

With regard to the nature of their bonding and reactivity, fulvenes occupy a position intermediate between their benzenoid isomers and the olefins. The chemical and physical behavior of the fulvenes is determined either by the diene character of the cross-conjugated system or by the cylic conjugation in the five-membered ring, depending on the type of substituent at the exocyclic carbon atom. In addtion to several new substitution reactions, a description is given of the syntheses and reactions of 6-amino- and 6-hydroxyfulvenes, isomeric with anilines and phenols, the derivatives of which can be used for the preparation of new types of nonbenzenoid cyclic conjugated systems such as carbocyclic and heterocyclic azulenes, pseudoazulenes, thiepines, dihydropyridazines, and s-indacene

Cluster-based density-functional approach to quantum transport through molecular and atomic contacts

We present a cluster-based density-functional approach to model charge transport through molecular and atomic contacts. The electronic structure of the contacts is determined in the framework of density functional theory, and the parameters needed to describe transport are extracted from finite clusters. A similar procedure, restricted to nearest-neighbor interactions in the electrodes, has been presented by Damle et al. [Chem. Phys. 281, 171 (2002)]. Here, we show how to systematically improve the description of the electrodes by extracting bulk parameters from sufficiently large metal clusters. In this way we avoid problems arising from the use of nonorthogonal basis functions. For demonstration we apply our method to electron transport through Au contacts with various atomic-chain configurations and to a single-atom contact of Al.Comment: 18 pages, 13 figure

Fulvene — Isomere benzoider Verbindungen

In ihrem Bindungszustand und ihrer Reaktivität nehmen die Fulvene eine Mittelstellung zwischen den ihnen isomeren benzoiden Verbindungen und den Olefinen ein. In Abhängigkeit von den Substituenten am exocyclischen C-Atom bestimmen der Diencharakter des gekreuzt konjugierten Systems oder die cyclische Konjugation im fünfgliedrigen Ring das chemische und physikalische Verhalten der Fulvene. Neben einigen neuen Substitutionsreaktionen werden besonders Synthesen und Reaktionen von den mit Anilinen und Phenolen isomeren 6-Amino- und 6-Hydroxy-fulvenen beschrieben. Derivate dieser Verbindungen ermöglichen die Darstellung neuartiger nichtbenzoider, cyclisch konjugierter Systeme wie carbo- und hetero-cyclischer Azulene, Pseudoazulene, Thiepine, Dihydropyridazine und des s-Indacens

What do individuals with schizophrenia need to increase their well-being

The aim of this qualitative study was to deepen the knowledge of how individuals with schizophrenia themselves describe what they need in order to increase their well-being in everyday life. Seven patients were interviewed. An open explorative approach was applied and grounded theory was used for the analysis resulting in five categories illustrating how patients with schizophrenia handle their struggle for a normal life. The patients stressed first the importance of receiving information about the disease: for themselves, for society, and for their families. Taking part in social contacts such as attending meeting places and receiving home visits were identified as important as well as having meaningful employment. They also pointed out the importance of taking part in secure professional relationships. Mainly they expressed the need for continuity in the relationships and the wish to be heard and seen by the professionals. Finally, interviewees addressed the need for support for sustaining independent living through practical housekeeping and financial help. To conclude, the participants in the present study described their need for help as mainly linked to activities in their overall life situation rather than just their psychosis

BRCA1 promoter methylation and clinical outcomes in ovarian cancer: an individual patient data meta-analysis

BACKGROUND BRCA1 methylation has been associated with homologous recombination deficiency, a biomarker of platinum sensitivity. Studies evaluating BRCA1-methylated tubal/ovarian cancer (OC) do not consistently support improved survival following platinum chemotherapy. We examine the characteristics of BRCA1-methylated OC in a meta-analysis of individual participant data. METHODS 2636 participants' data across 15 studies were analyzed. BRCA1-methylated tumors were defined according to their original study. Associations between BRCA1 methylation and clinico-pathological characteristics were evaluated. The effects of methylation on overall survival (OS) and progression-free survival (PFS) were examined using mixed-effects models. All statistical tests were two-sided. RESULTS 430 (16.3%) tumors were BRCA1-methylated. BRCA1 methylation was associated with younger age and advanced-stage high-grade serous OC. There were no survival differences between BRCA1-methylated and non-BRCA1-methylated OC (median PFS = 20.0 vs 18.5 months, HR = 1.01, 95% CI = 0.87-1.16, P=0.98; median OS = 46.6 vs 48.0 months, HR = 1.02, 95% CI = 0.87-1.18, P=0.96). Where BRCA1/2 mutations were evaluated (n = 1248), BRCA1 methylation displayed no survival advantage over BRCA1/2 intact (BRCA1/2 wild type non-BRCA1-methylated) OC. Studies used different methods to define BRCA1 methylation. Where BRCA1 methylation was determined using methylation-specific PCR and gel electrophoresis (n = 834), it was associated with improved survival (PFS: HR = 0.80, 95% CI = 0.66-0.97, P=0.02; OS: HR = 0.80, 95% CI = 0.63-1.00, P=0.05) on mixed-effects modelling. CONCLUSION BRCA1-methylated OC displays similar clinico-pathological features to BRCA1-mutated OC, but is not associated with survival. Heterogeneity within BRCA1 methylation assays influences associations. Refining these assays may better identify cases with silenced BRCA1 function and improved patient outcomes

Khat use as risk factor for psychotic disorders: A cross-sectional and case-control study in Somalia

BACKGROUND: Little is known about the prevalence of khat-induced psychotic disorders in East African countries, where the chewing of khat leaves is common. Its main psycho-active component cathinone produces effects similar to those of amphetamine. We aimed to explore the prevalence of psychotic disorders among the general population and the association between khat use and psychotic symptoms. METHODS: In an epidemiological household assessment in the city of Hargeisa, North-West Somalia, trained local interviewers screened 4,854 randomly selected persons from among the general population for disability due to severe mental problems. The identified cases were interviewed based on a structured interview and compared to healthy matched controls. Psychotic symptoms were assessed using the items of the WHO Composite International Diagnostic Interview and quantified with the Positive and Negative Symptoms Scale. Statistical testing included Student's t-test and ANOVA. RESULTS: Local interviewers found that rates of severe disability due to mental disorders were 8.4% among males (above the age of 12) and differed according to war experiences (no war experience: 3.2%; civilian war survivors: 8.0%; ex-combatants: 15.9%). The clinical interview verified that in 83% of positive screening cases psychotic symptoms were the most prominent manifestations of psychiatric illness. On average, cases with psychotic symptoms had started to use khat earlier in life than matched controls and had been using khat 8.6 years before positive symptoms emerged. In most cases with psychotic symptoms, a pattern of binge use (> two 'bundles' per day) preceded the onset of psychotic symptoms, in contrast to controls of the same age. We found significant correlations between variables of khat consumption and clinical scales (0.35 to 0.50; p < 0.05), and between the age of onset of khat chewing and symptom onset (0.70; p <0.001). CONCLUSION: Evidence indicates a relationship between the consumption of khat and the onset of psychotic symptoms among the male population, whereby not the khat intake per se but rather early onset and excessive khat chewing seemed to be related to psychotic symptoms. The khat problem must be addressed by means other than prohibition, given the widespread use and its role in Somali culture

Fast-timing measurements in ⁹⁶Pd:improved accuracy for the lifetime of the 4⁺₁ state

Direct lifetime measurements via γ–γ coincidences using the FATIMA fast-timing LaBr3(Ce) array were performed for the excited states below previously reported isomers. In the N = 50 semi-magic 96Pd nucleus, lifetimes below the I π = 8+ seniority isomer were addressed as a benchmark for further analysis. The results for the I π = 2+ and 4 + states confirm the published values. Increased accuracy for the lifetime value was achieved for the 4 + state.peerReviewe

Geodesy and metrology with a transportable optical clock

partially_open24openGrotti, Jacopo; Koller, Silvio; Vogt, Stefan; Häfner, Sebastian; Sterr, Uwe; Lisdat, Christian; Denker, Heiner; Voigt, Christian; Timmen, Ludger; Rolland, Antoine; Baynes, Fred N.; Margolis, Helen S.; Zampaolo, Michel; Thoumany, Pierre; Pizzocaro, Marco; Rauf, Benjamin; Bregolin, Filippo; Tampellini, Anna; Barbieri, Piero; Zucco, Massimo; Costanzo, Giovanni A.; Clivati, Cecilia; Levi, Filippo; Calonico, DavideGrotti, Jacopo; Koller, Silvio; Vogt, Stefan; Häfner, Sebastian; Sterr, Uwe; Lisdat, Christian; Denker, Heiner; Voigt, Christian; Timmen, Ludger; Rolland, Antoine; Baynes, Fred N.; Margolis, Helen S.; Zampaolo, Michel; Thoumany, Pierre; Pizzocaro, Marco; Rauf, Benjamin; Bregolin, Filippo; Tampellini, Anna; Barbieri, Piero; Zucco, Massimo; Costanzo, Giovanni A.; Clivati, Cecilia; Levi, Filippo; Calonico, David