Heisenberg Evolution WKB and Symplectic Area Phases

The Schrodinger and Heisenberg evolution operators are represented in quantum phase space by their Weyl symbols. Their semiclassical approximations are constructed in the short and long time regimes. For both evolution problems, the WKB representation is purely geometrical: the amplitudes are functions of a Poisson bracket and the phase is the symplectic area of a region in phase space bounded by trajectories and chords. A unified approach to the Schrodinger and Heisenberg semiclassical evolutions is developed by introducing an extended phase space. In this setting Maslov's pseudodifferential operator version of WKB analysis applies and represents these two problems via a common higher dimensional Schrodinger evolution, but with different extended Hamiltonians. The evolution of a Lagrangian manifold in the extended phase space, defined by initial data, controls the phase, amplitude and caustic behavior. The symplectic area phases arise as a solution of a boundary condition problem. Various applications and examples are considered.Comment: 32 pages, 7 figure

Development of Creative Abilities of Primary Schoolchildren in the Process of Primary School Education

В статье проведен анализ развития творческих способностей младших школьников посредством изобразительной деятельности. Анализированы мнения, подходы ученых по данной проблеме. Представленный материал можно использовать в качестве демонстрации реализации системы раскрытия творческого потенциала учащихся, а также в качестве источника цитирования.The article analyzes the development of the creative abilities of primary schoolchildren through visual activity. The opinions and approaches of scientists on this problem are analyzed. The presented material can be used as a demonstration of the implementation of the system for unlocking the creative potential of students, as well as as a source of citation

Development of Creative Abilities in Younger Students in Fine Arts Lessons

В статье рассматривается проблема развития творческих способностей у младших школьников посредством изобразительного искусства. Процесс формирования творческих способностей и организации творческой деятельности детей лежит в основе образовательного процесса. Авторами анализируются нормативно-правовые документы, программы «Изобразительное искусство и художественный труд» для I-IX классов по данной проблеме.The article deals with the problem of the development of creative abilities in junior schoolchildren through the visual arts. The process of forming creative abilities and organizing the creative activity of children lies at the heart of the educational process. The authors analyze regulatory documents, programs "Fine Arts and Artistic Work" for I-IX grades on this issue

On the generalised Ritt problem as a computational problem

The Ritt problem asks if there is an algorithm that tells whether one prime differential ideal is contained in another one if both are given by their characteristic sets. We give several equivalent formulations of this problem. In particular, we show that it is equivalent to testing if a differential polynomial is a zero divisor modulo a radical differential ideal. The technique used in the proof of equivalence yields algorithms for computing a canonical decomposition of a radical differential ideal into prime components and a canonical generating set of a radical differential ideal. Both proposed representations of a radical differential ideal are independent of the given set of generators and can be made independent of the ranking.Comment: 9 page

Investigation of eighth-grade students' understanding of the slope of the linear function

This study aimed to investigate eighth-grade students' difficulties and misconceptions and their performance of translation between the different representation modes related to the slope of linear functions. The participants were 115 Turkish eighth-grade students in a city in the eastern part of the Black Sea region of Turkey. Data was collected with an instrument consisting of seven written questions and a semi-structured interview protocol conducted with six students. Students' responses to questions were categorized and scored. Quantitative data was analyzed using the SPSS 17.0 statistical packet program with cross tables and one-way ANOVA. Qualitative data obtained from interviews was analyzed using descriptive analytical techniques. It was found that students' performance in articulating the slope of the linear function using its algebraic representation form was higher than their performance in using transformation between graphical and algebraic representation forms. It was also determined that some of them had difficulties and misunderstood linear function equations, graphs, and slopes and could not comprehend the connection between slope and the x- and y-intercepts

How “Humane” Is Your Endpoint?—Refining the Science-Driven Approach for Termination of Animal Studies of Chronic Infection

Public concern on issues such as animal welfare or the scientific validity and clinical value of animal research is growing, resulting in increasing regulatory demands for animal research. Abiding to the most stringent animal welfare standards, while having scientific objectives as the main priority, is often challenging. To do so, endpoints of studies involving severe, progressive diseases need to be established considering how early in the disease process the scientific objectives can be achieved. We present here experimental studies of tuberculosis (TB) in mice as a case study for an analysis of present practice and a discussion of how more refined science-based endpoints can be developed. A considerable proportion of studies in this field involve lethal stages, and the establishment of earlier, reliable indicators of disease severity will have a significant impact on animal welfare. While there is an increasing interest from scientists and industry in moving research in this direction, this is still far from being reflected in actual practice. We argue that a major limiting factor is the absence of data on biomarkers that can be used as indicators of disease severity. We discuss the possibility of complementing the widely used weight loss with other relevant biomarkers and the need for validation of these parameters as endpoints. Promotion of ethical guidelines needs to be coupled with systematic research in order to develop humane endpoints beyond the present euthanasia of moribund animals. Such research, as we propose here for chronic infection, can show the way for the development and promotion of welfare policies in other fields of research. Research on chronic infection relies heavily on the use of animals, as only the integral animal body can model the full aspect of an infection. That animals are generally made to develop a disease in infection studies exacerbates the tension between human benefit and animal well-being, which characterizes all biomedical research with animals. Scientists typically justify animal research with reference to potential human benefits, but if accepting the assumption that human benefits can offset animal suffering, it still needs to be argued that the same benefits could not be achieved with less negative effects on animal welfare. Reducing the animal welfare problems associated with research (“refinement” [1]) is therefore crucial in order to render animal-based research less of an ethical problem and to assure public trust in research. Studies that are designed to measure time of death or survival percentages present a particularly challenging situation in which at least some of the animals are made to die from the disease. These studies are frequent in experimental research on severe infections. The scientific community, industry, and regulatory authorities have responded to the ethical concerns over studies in which animals die from severe disease by developing new policies and guidelines for the implementation of humane endpoints as a key refinement measure (e.g., [2]–[4]). The most widely used definition considers a humane endpoint to be the earliest indicator in an animal experiment of severe pain, severe distress, suffering, or impending death [5], underlining that ideally such indicators should be identified before the onset of the most severe effects. Euthanizing animals, rather than awaiting their “spontaneous” death, is important to avoid unnecessary suffering in studies in which data on survival is thought to be required for scientific or legal reasons. However, several questions remain open regarding how humane endpoints are to be applied to address real animal welfare problems. We used TB experiments in mice as a case study to highlight the potential to establish biomarkers of disease progress that can replace survival time as a measure of disease severity.Fundação para a Ciência e Tecnologia (SFRH/BD/38337/2007)

The ATLAS Transition Radiation Tracker (TRT) proportional drift tube: design and performance

A straw proportional counter is the basic element of the ATLAS Transition Radiation Tracker (TRT). Its detailed properties as well as the main properties of a few TRT operating gas mixtures are described. Particular attention is paid to straw tube performance in high radiation conditions and to its operational stability