Existence, uniqueness, and numerical approximations for stochastic Burgers equations

In this paper we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existent fully explicit space-time discrete approximation scheme and, in particular, the fact that it satisfies suitable a priori estimates. As a byproduct we obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the paper to the stochastic Burgers equations with space-time white noise.Comment: 23 page

On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions

In the recent article [Jentzen, A., M\"uller-Gronbach, T., and Yaroslavtseva, L., Commun. Math. Sci., 14(6), 1477--1500, 2016] it has been established that for every arbitrarily slow convergence speed and every natural number $d \in \{4,5,\ldots\}$ there exist $d$-dimensional stochastic differential equations (SDEs) with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of convergence. In this paper we strengthen the above result by proving that this slow convergence phenomena also arises in two ($d=2$) and three ($d=3$) space dimensions.Comment: 25 page

A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients

In recent years deep artificial neural networks (DNNs) have been successfully employed in numerical simulations for a multitude of computational problems including, for example, object and face recognition, natural language processing, fraud detection, computational advertisement, and numerical approximations of partial differential equations (PDEs). These numerical simulations indicate that DNNs seem to possess the fundamental flexibility to overcome the curse of dimensionality in the sense that the number of real parameters used to describe the DNN grows at most polynomially in both the reciprocal of the prescribed approximation accuracy $\varepsilon > 0$ and the dimension $d \in \mathbb{N}$ of the function which the DNN aims to approximate in such computational problems. There is also a large number of rigorous mathematical approximation results for artificial neural networks in the scientific literature but there are only a few special situations where results in the literature can rigorously justify the success of DNNs in high-dimensional function approximation. The key contribution of this paper is to reveal that DNNs do overcome the curse of dimensionality in the numerical approximation of Kolmogorov PDEs with constant diffusion and nonlinear drift coefficients. We prove that the number of parameters used to describe the employed DNN grows at most polynomially in both the PDE dimension $d \in \mathbb{N}$ and the reciprocal of the prescribed approximation accuracy $\varepsilon > 0$. A crucial ingredient in our proof is the fact that the artificial neural network used to approximate the solution of the PDE is indeed a deep artificial neural network with a large number of hidden layers.Comment: 48 page

British and American English and the Position of Slang in These Languages

The meaning of the term “slang” in English is different from other languages. The main reason for this is the migration of the English-speaking population to other continents (North America, Australia, Asia) from the beginning of the 17th century, the fact that their languages became the dominant language by suppressing local languages, and due to the use of English by representatives of other nations who migrated to these places. Therefore, English is spoken in the Australian, Indian, South African and American varieties. These varieties are also called “slangs” of the English language. Therefore, there is still no single view on the concept of “slang”. In English lexicology, slangs include the most diverse words and word combinations, from jargons to neologisms. In American English, slangs are pronounced more obvious. Especially after American Revolutionary War, English became important in the United States, and now there are those who consider it an independent language. The American English was enriched by a variety of sources and adapted to the use of people who migrated to these areas. The article compares the British and American English at different levels and determines their different points

Multidisciplinary approach to suicide prevention of adolescents in Slovakia and Kyrgyzstan

The prevalence of suicides among young people continues to be a top health challenge worldwide. It affects individuals, families, and communities. The causes encompass both mental health issues and psychosocial stressors, which are exacerbated by a number of determinants such as financial constraints, poor family relationships, peer bullying and victimization, and any forms of abuse. Suicide prevention calls for strategies at every level of society. This approach should include a range of preventive strategies and activities to identify and intervene early, build young people’s life skills and provide access to appropriate services and support. As a holistic strategy, a multidisciplinary team is known for taking a thorough approach to prevent many youth issues, including suicide, bringing together different stakeholders, and is based on their current contexts and resources. The teams include specialists such as educators, primary health professionals, social workers, police, children’s organizations, and other stakeholders which work best in ensuring that individuals at risk of suicide receive the holistic care and support they need. However, there is a lack of long-term policy, practical tools, and evidence-based research that can guide social service providers working together in assessing adolescent suicidal ideation, putting general prevention into place, and reducing potential risks. This study aimed to analyze the system of work of the multidisciplinary teams in the prevention of adolescent suicide in educational settings in Slovakia and Kyrgyzstan. The study utilized a qualitative research method – a semi-structured interview of 10 various specialists from Slovakia and Kyrgyzstan. Despite different levels of development and practical implementation of multidisciplinary team concepts in both countries, the results revealed a generally positive image of the collaborative effort of various professionals in the prevention area. The teams in schools aim to create a protective environment with family and community support for young people contributing substantially in mitigating many issues of adolescents during their fragile period of upbringing. It is concluded in the study that prevention efforts require coordination among multiple social institutions with good governance and unified strategy. However, it has been noted that there is still potential for development, particularly in terms of better cooperation among specialists, recognition of the problem of youth suicide on the national level, and institutionalizing procedures to increase the status and education level of multidisciplinary teams. This research is innovative in its originality and adds a valuable and up-to-date point in suggesting a more comprehensive system for work of the multidisciplinary teams in both countries which potentially may contribute to suicide reduction among adolescents

INFECTION IN ACUTE PANCREATITIS: UNRAVELING THE RELATIONSHIP THROUGH A LITERATURE REVIEW

This article provides a comprehensive overview of the relationship between acute pancreatitis and infection, focusing on the prevalence, impact, management, and prevention of infections in acute pancreatitis cases. Acute pancreatitis, characterized by inflammation of the pancreas, is a significant cause of hospital admissions and morbidity globally. Infections, such as infected necrosis and fluid collections, frequently complicate acute pancreatitis and contribute to disease severity and adverse outcomes

Personal Names in the Families of Russian Germans: Challenges of Self-Identification of the Ethnic Group

The research deals with the topical issue of changing the ‘ethnolinguistic and cultural area’, a shift in the system of ethnolinguistic and cultural orientations and values of the people. The problem is discussed from the perspective of anthroponymic material in the families of ethnic Germans born in Russia, whose ancestors settled on Russian lands since the reign of Catherine II. The primary purpose of the study is to carry out a comprehensive analysis of some (often controversial) aspects of (self)identification of the linguistic personality of Russian Germans from the perspective of the corpus of personal names. Using the methods of functional historical analysis, continuous sampling, interview, systemisation, and interpretation, the authors of this study, based on the analysis of a relatively large corpus of collected personal names, as well as based on answers of 200 respondents, who are descendants of Russian Germans, attempted to determine which names are chosen for children and what language Russian Germans speak today. The problem is considered from a synergistic perspective: sociolinguistics, linguoculturology and ethnolinguistics, as well as anthroponymics. The authors conclude that the choice of names in the families of Russian Germans of German/non-German origin depends on several factors— traditions of the family; place of residence; the level of education; profession/specialisation. In the anthroponymicon of Russian Germans, under the influence of personal names of the surrounding ethnic groups, socio-cultural and historical changes result in internal changes in language units