Quantum geometrodynamics of the Bianchi IX model in extended phase space

A way of constructing mathematically correct quantum geometrodynamics of a closed universe is presented. The resulting theory appears to be gauge-noninvariant and thus consistent with the observation conditions of a closed universe, by that being considerably distinguished from the conventional Wheeler - DeWitt one. For the Bianchi-IX cosmological model it is shown that a normalizable wave function of the Universe depends on time, allows the standard probability interpretation and satisfies a gauge-noninvariant dynamical Schrodinger equation. The Wheeler - DeWitt quantum geometrodynamics is represented by a singular, BRST-invariant solution to the Schrodinger equation having no property of normalizability.Comment: LaTeX, 18 pages, to be published in Int. J. Mod. Phys.

A view on the problems of Quantum Gravity

The existing approaches to quantization of gravity aim at giving quantum description of 3-geometry following to the ideas of the Wheeler -- DeWitt geometrodynamics. In this description the role of gauge gravitational degrees of freedom is missed. A probable alternative is to consider gravitational dynamics in extended phase space, taking into account the distinctions between General Relativity and other field theories. The formulation in extended phase space leads to some consequences at classical and quantum levels. At the classical level, it ensures that Hamiltonian dynamics is fully equivalent to Lagrangian dynamics, and the algebra of Poisson brackets is invariant under reparametrizations in a wide enough class including reparametrizations of gauge variables, meantime in the canonical Dirac approach the constraints' algebra is not invariant that creates problems with quantization. At the quantum level, the approach come to the description in which the observer can see various but complementary quantum gravitational phenomena in different reference frames that answers the spirit of General Relativity and Quantum Theory. Though until now the approach was applied to General Relativity in its original formulations, its implementation in different trends, including Quantum Loop Gravity or some other representations of gravitational variables, would also be of interest.Comment: 6 pages, talk presented at the International Conference on Quantum Gravity "Loops 11", Madrid, May 201

Time boundary terms and Dirac constraints

Time boundary terms usually added to action principles are systematically handled in the framework of Dirac's canonical analysis. The procedure begins with the introduction of the boundary term into the integral Hamiltonian action and then the resulting action is interpreted as a Lagrangian one to which Dirac's method is applied. Once the general theory is developed, the current procedure is implemented and illustrated in various examples which are originally endowed with different types of constraints.Comment: 12 page

Use Competency-Oriented Tasks in Teaching Mathematics

Переход на новые образовательные стандарты повысил интерес к использованию компетентностно-ориентированных заданий. К компетентностно-ориентированным относятся задания, в которых требуется дополнить условие, применить знания для решения практической задачи, исключить из текста лишние данные. В статье представлен анализ литературы по рассматриваемому вопросу. Анализ школьных учебников математики показал, что учителю необходимо самому составлять такие задания. В статье приведены варианты изменения стандартных заданий из учебника, в результате которых они становятся компетентностно-ориентированными. Рассмотрены примеры преобразования заданий для уровней: воспроизведения, установления связей и рассуждения. К составлению компетентностно-ориентированных заданий можно привлекать учеников. Для этого на дополнительных занятиях им объясняется суть работы. Использование КОЗ помогает повысить мотивацию, активности и самостоятельности обучающихся, усилить предметные и межпредметные связи. В ходе проведения исследования использовались методы: анализ литературы, моделирование содержания работы с компетентностно-ориентированными заданиями, элементы опытной работы.Transition to new educational standards increased interest in the use of competence-oriented tasks. To the competence-oriented are jobs in which required to Complement a condition to apply knowledge to solve practical problems, to remove excess data. The article presents the analysis of the literature on the subject. Analysis of school textbooks of mathematics showed that the teacher needs to make such assignments. The article provides options for modify the default given from the textbook, in which they become competence-oriented. Examples of conversion jobs for game play, communication and reasoning. To compile a competence-oriented tasks to attract students. On additional classes, they explained the essence of the work. The use of the GOAT helps to increase motivation, activity and independence of students, to strengthen the substantive and interdisciplinary connections. In the course of research methods were used: literature analysis, the modeling of the content of the work with the competence-oriented tasks, the elements of the practical work

Composition, properties and application of calendulas in medicine

veterinary medicine, drug plants, calendula, composition, properties, английский язык, лекарственные растения, календула, состав, свойств

Powerflow calculations in powersystems considering traction load

Nowadays, the negative impact of traction load on power system operation poses a serious problem that may lead to false tripping or even failures of relay protection devices and reduce the quality of electrical energy. This situation is typical for the Zabaikal power system, in which in some areas the share of electricity consumption by railway reaches 70% of total consumption. A computing tool, that would allow simultaneous analysis of the modes, both in the utility's grid and in the traction network, do not exist. The inability to carry out such analysis often leads to inconsistency in the actions of control centers and railway transport authorities, especially when maintenance planning. Mathematic modeling in such software systems as "Mustang", "RastrWin3", "MathCAD", “Matlab/Simulink”, “PSCAD”, “Kortes”. The developed model represents Zabaikal power system and contain detailed railway between substation Razmahnino and substation Shilka. Negative-sequence voltage unbalance factors were calculated for the case of train movement between substation Razmahnino and substation Shilka. Also, the necessity of back-up relays tripping values correction is stated. It was shown that for the powerflow calculations taking into account the traction load, it is rational to use a complex mathematical model, which uses compatible software systems with the ability of quick and easy data exchange