Generalization of Einstein-Lovelock theory to higher order dilaton gravity

A higher order theory of dilaton gravity is constructed as a generalization of the Einstein-Lovelock theory of pure gravity. Its Lagrangian contains terms with higher powers of the Riemann tensor and of the first two derivatives of the dilaton. Nevertheless, the resulting equations of motion are quasi-linear in the second derivatives of the metric and of the dilaton. This property is crucial for the existence of brane solutions in the thin wall limit. At each order in derivatives the contribution to the Lagrangian is unique up to an overall normalization. Relations between symmetries of this theory and the O(d,d) symmetry of the string-inspired models are discussed.Comment: 18 pages, references added, version to be publishe

Towards a Proof Theory of G\"odel Modal Logics

Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish completeness and complexity results for these fragments

Dark energy from modified F(R)-scalar-Gauss-Bonnet gravity

The modified F(R)-scalar-Gauss-Bonnet gravity is proposed as dark energy model. The reconstruction program for such theory is developed. It is explicitly demonstrated that the known classical universe expansion history (deceleration epoch, transition to acceleration and effective quintessence, phantom or cosmological constant era) may naturally occur in such unified theory for some (reconstructed) classes of scalar potentials. Gauss-Bonnet assisted dark energy is also proposed. The possibility of cosmic acceleration is studied there.Comment: LaTeX, 8 pages, no figure, refs. added, version to appear in Physics Letters

A map of dependencies among three-valued logics

International audienceThree-valued logics arise in several fields of computer science, both inspired by concrete problems (such as in the management of the null value in databases) and theoretical considerations. Several three-valued logics have been defined. They differ by their choice of basic connectives, hence also from a syntactic and proof-theoretic point of view. Different interpretations of the third truth value have also been suggested. They often carry an epistemic flavor. In this work, relationships between logical connectives on three-valued functions are explored. Existing theorems of functional completeness have laid bare some of these links, based on specific connectives. However we try to draw a map of such relationships between conjunctions, negations and implications that extend Boolean ones. It turns out that all reasonable connectives can be defined from a few of them and so all known three-valued logics appear as a fragment of only one logic. These results can be instrumental when choosing, for each application context, the appropriate fragment where the basic connectives make full sense, based on the appropriate meaning of the third truth-value

Casimir dark energy, stabilization of the extra dimensions and Gauss–Bonnet term

A Casimir dark energy model in a five-dimensional and a six-dimensional spacetime including non-relativistic matter and a Gauss–Bonnet term is investigated. The Casimir energy can play the role of dark energy to drive the late-time acceleration of the universe while the radius of the extra dimensions can be stabilized. The qualitative analysis in four-dimensional spacetime shows that the contribution from the Gauss–Bonnet term will effectively slow down the radion field at the matter-dominated or radiation-dominated epochs so that it does not pass the point at which the minimum of the potential will arise before the minimum has formed. The field then is trapped at the minimum of the potential after the formation leading to the stabilization of the extra dimensions

Wpływ składników diety na objawy ADHD u dzieci

U większości dzieci przyczyna występowania ADHD nie jest do końca znana, a jego etiologia jest wieloaspektowa. Konwencjonalne leczenie tego schorzenia oparte jest na połączeniu terapii behawioralnej, psychologicznej oraz farmakoterapii. Farmakoterapia wykazuje wysoką skuteczność w leczeniu ADHD, jednak często wiąże się ona z występowaniem niepożądanych efektów ubocznych, takich jak: brak apetytu, utrata masy ciała, zahamowanie wzrostu, bóle brzucha, bóle głowy, problemy z zasypianiem, wzrost ciśnienia krwi. W ostatnich latach można zauważyć wzrastające zainteresowanie zastosowaniem dietoterapii w leczeniu ADHD, zwłaszcza kiedy standardowa farmakoterapia nie przynosi poprawy stanu zdrowia. Zarówno dieta kobiety ciężarnej, karmiącej, jak i dziecka może mieć wpływ na rozwój i pogłębienie objawów zespołu hiperkinetycznego. Istnieje wiele dowodów, które wskazują, że ADHD jest związany z czynnikami żywieniowymi. Przewlekłe niedobory niektórych składników mineralnych, takich jak: cynk, żelazo, magnez, jod mogą mieć znaczący wpływ na rozwój i pogłębienie objawów ADHD u dzieci. Szczególną rolę w diecie kobiety w ciąży, karmiącej oraz dziecka odgrywają także kwasy tłuszczowe omega-3, a głównie DHA, które są niezbędne do prawidłowego rozwoju i czynności mózgu u dziecka. Ich przewlekły niedobór może przyczyniać się do zwiększonego ryzyka występowania ADHD u dzieci. Autorzy kilku badań wykazali korzystny wpływ eliminacji produktów spożywczych zawierających syntetyczne dodatki do żywności, m.in. barwniki i konserwanty na zachowanie u dzieci z ADHD. Pozytywne efekty przyniosła także eliminacja z diety produktów będących bogatym źródłem salicylanów. Zaobserwowano ponadto, że spożycie produktów z niskim indeksem glikemicznym przyczynia się do zmniejszenia objawów choroby u niektórych osób nadaktywnych. Dostarczenie odpowiedniej podaży składników odżywczych i mineralnych oraz ewentualne wyeliminowanie niektórych produktów spożywczych z diety jest szczególnie istotne w okresie rozwoju i intensywnego wzrostu dziecka. Omówiono zagadnienia dotyczące roli diety w leczeniu dzieci, u których rozpoznano ADHD oraz znaczenia niedoborów niektórych składników mineralnych i długołańcuchowych wielonienasyconych kwasów tłuszczowych w przebiegu ciąży i rozwoju dziecka. Istnieje potrzeba dalszych badań w tym zakresie, w celu oceny potencjalnej skuteczności diety w leczeniu objawów ADHD.In most children with ADHD the cause of the disease is not exactly known, and its etiology is multifactorial. The conventional treatment is based on the combination of behavioral and psychological therapy and the pharmacotherapy. The pharmacotherapy has a high effectiveness in ADHD treatment, but it is often associated with undesirable side effects, such as: loss of appetite and weight, growth inhibition, abdominal pain, headaches, sleeping problems and increased blood pressure. In the recent years, much attention was devoted to the issue of an appropriate diet in this disease, especially when the standard pharmacotherapy is not effective. The diet of pregnant and lactating woman, and child may have an impact on the development and deepening of the hyperkinetic syndrome. There is much evidence to indicate that it is linked to nutritional factors. Chronic deficiencies of certain minerals such as zinc, iron, magnesium and iodine and insufficient dietary intake of long-chain polyunsaturated fatty acids may have a significant impact on the development and deepening of the symptoms of ADHD in children. A crucial role in the diet of pregnant and lactating women, and child plays also polyunsaturated omega-3 fatty acids, mainly DHA, which are necessary for proper development and function of brain. Their chronic deficiency may contribute to increase risk of ADHD in children. The authors of several studies also demonstrated the positive impact of the elimination food products containing synthetic food additives, like artificial food dyes and preservatives on the behavior of children with ADHD. The beneficial effects brought also the elimination of food products, that are rich in salicylates. It was found that the intake of food products with a low glycemic index helps to reduce symptoms in some hyperactive children. Providing an appropriate supply of nutrients and minerals and elimination of certain food products from diet is especially important during intensive growth and development of the child. In this article the issues concerning the role of the diet in treatment of the children with diagnosed ADHD and the importance of deficiency of certain minerals and long-chain polyunsaturated fatty acids in pregnancy and child growth was discussed. There is a need for further studies in this area to evaluate the potential effectiveness of the diet in treating the symptoms of ADHD