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- Author or Editor: Gabriella Hajdu x
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Summary
We show that a well-known identity of Ramanujan admits only a bounded number of solutions over general finitely generated domains. The bound is explicit and uniform in the sense that it depends only on the dimensions of the domains involved. Our method is constructive, and opens up a possibility to determine the solutions in concrete instances. In some special cases all solutions are determined. Our results can also be considered as a continuation of some theorems of Z. Darczy and G. Hajdu, obtained over Z. We note that in case of Hossz's equation, similar results were obtained by several authors.
Abstract
In recent years, in order to increase the energy efficiency of older buildings in Hungary, several tenders have supported the modernization of the thermal insulation. Various thermal insulation materials have been installed on walls, on slab and on floor. Unfortunately there are cases where thermal insulation materials are not installed in accordance with the construction permit or the manufacturer’s instructions, which poses a serious danger in case of a fire. During the research the effects of heat on the behavior of Expanded PolyStyrene, a thermal insulation material often used in Hungary is examined. Laboratory tests and computer simulations were carried out, which are presented in detail in this paper. The aim of the research is to contribute to increase the fire safety of buildings.
Abstract
In Hungary a lot of people live in condominiums or in block of flats where fire often occurs despite of precise design and effective fire protection arrangements. This means a hazard for the people living there, for the building constructions and also for the environment. A deeper knowledge of the burning process and examining the negative effects of fire load on building constructions with scientific methods are actual questions nowadays. In order to get to know the phenomena more accurately, fire spread in a bedroom was modeled and numerical simulation was carried out, which is presented in this paper in detail. These experiences may help increasing the fire safety and preventing fires in apartments. The simulations were carried out considering the characteristics of the Hungarian architecture.
Despite the development in the identification of Nocardia spp., common challenges exist in the laboratory diagnosis and management of nocardiosis. We report two cases of disseminated nocardiosis in a patient with hematologic disorder and in a patient with systemic lupus erythematosus, where the cooperation between various specialists was essential to set up the adequate diagnosis of disseminated nocardiosis.
