673 research outputs found
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
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