Hawking's singularity theorem for C1,1C^{1,1}-metrics

We provide a detailed proof of Hawking's singularity theorem in the regularity class $C^{1,1}$, i.e., for spacetime metrics possessing locally Lipschitz continuous first derivatives. The proof uses recent results in $C^{1,1}$-causality theory and is based on regularisation techniques adapted to the causal structure.Comment: 19 pages, LaTeX; v2: corrected Lemma 4.2; v3: typos corrected, final versio

Web Application for Learning Mathematics

Web application which assists in the process of learning mathematics is presented in the paper. The application and its functionalities will be explained in detail. Also, there will be presented parts from the web application using diagrams such as the E-R diagrams and the UML diagram

Increasing efficiency of on-line shopping by optimizing the staff schedule

Problem proposed by: COOP Drive (online food shopping service provided by COOP Liguria), http://www.e-COOP.it/virtualShop/. The customers are making an online purchase and choose a time range for pick up. Making optimal staff scheduling such that each employee has ‘constant’ working hours, satisfying customers and employees in the same time. Constraints: Each employee can work at most 6 days a week. Each employee can work maximum 8 hours a day. Each employee needs to work continuous hours

Apigenin-7-O-glucoside versus apigenin

Bioactive potential of apigenin derivative apigenin-7-O-glucoside related to its antifungal activity on Candida spp. and cytotoxic effect on colon cancer cells was studied and compared with bioactive potential of apigenin. Antifungal activity was tested on 14 different isolates of Candida spp. using membrane permeability assay, measuring inhibition of reactive oxidative species and inhibition of CYP51 C. albicans enzyme. Cytotoxic potential of apigenin-7-O-glucoside was tested on colon cancer HCT116 cells by measuring cell viability, apoptosis rate and apoptosis- and colon cancer-related gene expression. Obtained results indicated considerable antifungal activity of apigenin-7-O-glucoside towards all Candida isolates. Breakdown of C. albicans plasma membrane was achieved upon treatment with apigenin-7-O-glucoside for shorter period of time then with apigenin. Reduction of intra- and extracellular reactive oxidative species was achieved with minimum inhibitory concentrations of both compounds, suggesting that reactive oxidative species inhibition could be a mechanism of antifungal action. None of the compounds exhibited binding affinity to C. albicans CYP51 protein. Besides, apigenin-7-O-glucoside was more effective compared to apigenin in reduction of cell’s viability and induction of cell death of HCT116 cells. Treatment with both compounds resulted in chromatin condensation, apoptotic bodies formation and apoptotic genes expression in HCT116 cells, but the apigenin-7-O-glucoside required a lower concentration to achieve the same effect. Compounds apigenin-7-O-glucoside and apigenin displayed prominent antifungal potential and cytotoxic effect on HCT116 cells. However, our results showed that apigenin-7-O-glucoside has more potent activity compared to apigenin in all assays that we used

Importance and Characteristics of Lobbying in the European Union

This paper presents the process and characteristics of modern lobbying as bargaining in order to reach the desired decision. Lobbying is as old as the human desire for power. In modern conditions of life lobby is free to be said, has become industry. Lobbying is now a legitimate part of any democratic society. Due to guided, and methods of the process, lobbying, often resulting in relation to corruption. For this reason, many of the modern state are lobbying placed under the legal system of their institutions

Atopic Dermatitis in Children Under 5: Prevalence Trends in Central, Eastern, and Western Europe

Background: Atopic dermatitis is a major public health issue worldwide, but data on trends in prevalence in children in European countries are sparse. The aim of this study was to assess the trends in the prevalence of atopic dermatitis in children under 5 in the Central, Eastern, and Western European sub-regions from 1990 to 2019. Methods: In this study, a descriptive, observational epidemiological method was applied. In addition, an ecological study design was used. Joinpoint regression analysis was used to assess trends. Results: A total of 118 million (54 million males and 64 million females) prevalent cases of atopic dermatitis in children under 5 were reported in European countries in 1990–2019. More than half of all cases of atopic dermatitis in children under 5 in Europe were recorded in the Western European sub-region. The highest prevalence rates of atopic dermatitis in children under 5 were observed in the Eastern European sub-region, with the highest rates in both males and females recorded in Estonia (equally at about 15,000 per 100,000), followed by the Russian Federation (equally at about 12,000 per 100,000). Moreover, the lowest prevalence rates were reported in the Eastern European sub-region (equally at about 5000 per 100,000 in Romania and Latvia). A sex disparity in the prevalence and trends of atopic dermatitis in children under 5 was observed. A significantly increased trend in atopic dermatitis prevalence in children under 5 was recorded in the Eastern European sub-region from 1990 to 2019 (by +0.3% per year in males and by +0.1% per year in females). Conversely, in the Western and Central European sub-regions, trends in the prevalence of atopic dermatitis in children under 5 slightly decreased (about −0.1% per year). The Pearson coefficient showed a significant negative correlation between the prevalence of atopic dermatitis in children under 5 and the Human Development Index in most countries in the Eastern European sub-region, while a significant positive correlation was reported between the prevalence and HDI in high-income countries in the Western European sub-region. Conclusions: High prevalence rates and mostly stable trends during the last three decades make atopic dermatitis still a major health issue in children under 5 in European countries

Testing the adaptive plasticity of gypsy moth digestive enzymes in response to tannic acid using phenotypic selection analysis

The adaptive significance of plasticity of digestive enzyme responses to allelochemical stress was tested on 32 full-sib gypsy moth families from an oak forest (the Quercus population) and 26 families from a locust-tree forest (the Robinia population), reared on control or tannic acid-supplemented diets. By using the relative growth rate as a fitness measure in phenotypic selection analyses, we revealed that higher specific activity of leucine aminopeptidase in Quercus larvae and lower specific activity of trypsin in Robinia larvae were adaptive in the control environment. In Quercus larvae, elevated specific activities of leucine aminopeptidase and lipase were adaptive in the stressful environment. There were no plasticity costs for the enzyme activities in either experimental group. The obtained results suggest that adaptive plasticity of digestive enzyme activity in gypsy moth larvae contributes to optimal growth rate under various environmental conditions.Serbian Ministry of Education, Science and Technological Development {[}173027