368 research outputs found
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 there exist -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
() and three () 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 and the
dimension 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 and the reciprocal of the prescribed approximation accuracy . 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 âslangâ 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 âslangsâ of the English language. Therefore, there is still no single view on the concept of âslangâ. 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 peopleâs 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, childrenâs
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 â 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 âethnolinguistic and cultural areaâ, 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 factorsâ 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
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