Nambu-Jona-Lasinio Model in Curved Spacetime with Magnetic Field

We discuss the phase structure of the NJL model in curved spacetime with magnetic field using $1/N$-expansion and linear curvature approximation. The effective potential for composite fields $\bar\psi \psi$ is calculated using the proper-time cut-off in the following cases: a) at non-zero curvature, b) at non-zero curvature and non-zero magnetic field, and c) at non-zero curvature and non-zero covariantly constant gauge field. Chiral symmetry breaking is studied numerically. We show that the gravitational field may compensate the effect of the magnetic field what leads to restoration of chiral symmetry.Comment: LaTex file, 11 pages, 5 figures (not included) avaliable by request from first or third autho

Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity

We investigate the future evolution of the dark energy universe in modified gravities including $F(R)$ gravity, string-inspired scalar-Gauss-Bonnet and modified Gauss-Bonnet ones, and ideal fluid with the inhomogeneous equation of state (EoS). Modified Friedmann-Robertson-Walker (FRW) dynamics for all these theories may be presented in universal form by using the effective ideal fluid with an inhomogeneous EoS without specifying its explicit form. We construct several examples of the modified gravity which produces accelerating cosmologies ending at the finite-time future singularity of all four known types by applying the reconstruction program. Some scenarios to resolve the finite-time future singularity are presented. Among these scenarios, the most natural one is related with additional modification of the gravitational action in the early universe. In addition, late-time cosmology in the non-minimal Maxwell-Einstein theory is considered. We investigate the forms of the non-minimal gravitational coupling which generates the finite-time future singularities and the general conditions for this coupling in order that the finite-time future singularities cannot emerge. Furthermore, it is shown that the non-minimal gravitational coupling can remove the finite-time future singularities or make the singularity stronger (or weaker) in modified gravity.Comment: 25 pages, no figure, title changed, accepted in JCA

Renormalization Group Flows for Brane Couplings

Field theories in the presence of branes encounter localized divergences that renormalize brane couplings. The sources of these brane-localized divergences are understood as arising either from broken translation invariance, or from short distance singularities as the brane thickness vanishes. While the former are generated only by quantum corrections, the latter can appear even at the classical level. Using as an example six-dimensional scalar field theory in the background of a 3-brane, we show how to interpret such classical divergences by the usual regularization and renormalization procedure of quantum field theory. In our example, the zero thickness divergences are logarithmic, and lead classically to non-trivial renormalization group flows for the brane couplings. We construct the tree level renormalization group equations for these couplings as well as the one-loop corrections to these flows from bulk-to-brane renormalization effects.Comment: 16 pages, LaTeX. References and an appendix adde

Dark energy problem: from phantom theory to modified Gauss-Bonnet gravity

The solution of dark energy problem in the models without scalars is presented. It is shown that late-time accelerating cosmology may be generated by the ideal fluid with some implicit equation of state. The universe evolution within modified Gauss-Bonnet gravity is considered. It is demonstrated that such gravitational approach may predict the (quintessential, cosmological constant or transient phantom) acceleration of the late-time universe with natural transiton from deceleration to acceleration (or from non-phantom to phantom era in the last case).Comment: LaTeX 8 pages, prepared for the Proceedings of QFEXT'05, minor correctons, references adde

Crossing the Phantom Divide Line in a DGP-Inspired F(R,ϕ)F(R,\phi)-Gravity

We study possible crossing of the phantom divide line in a DGP-inspired $F(R,\phi)$ braneworld scenario where scalar field and curvature quintessence are treated in a unified framework. With some specific form of $F(R,\phi)$ and by adopting a suitable ansatz, we show that there are appropriate regions of the parameters space which account for late-time acceleration and admit crossing of the phantom divide line.Comment: 23 Pages, 10 figs, Submitted to JCA

The horizon-entropy increase law for causal and quasi-local horizons and conformal field redefinitions

We explicitly prove the horizon-entropy increase law for both causal and quasi-locally defined horizons in scalar-tensor and $f(R)$ gravity theories. Contrary to causal event horizons, future outer trapping horizons are not conformally invariant and we provide a modification of trapping horizons to complete the proof, using the idea of generalised entropy. This modification means they are no longer foliated by marginally outer trapped surfaces but fixes the location of the horizon under a conformal transformation. We also discuss the behaviour of horizons in "veiled" general relativity and show, using this new definition, how to locate cosmological horizons in flat Minkowski space with varying units, which is physically identified with a spatially flat FLRW spacetime.Comment: 23 page

Cosmological Evolution in 1/R-Gravity Theory

Recently, corrections of the $L(R)$ type to Einstein-Hilbert action that become important at small curvature are proposed. Those type of models intend to explain the observed cosmic acceleration without dark energy. We derive the full Modified Friedmann equation in the Palatini formulation of those modified gravity model of the $L(R)$ type. Then, we discuss various cosmological predictions of the Modified Friedmann equation.Comment: 7 pages, 5 figures. Accepted for publication in Class.Quant.Gra

ПРОБЛЕМЫ СОЗДАНИЯ ИНФОРМАЦИОННЫХ СИСТЕМ УПРАВЛЕНИЯ ЭФФЕКТИВНОСТЬЮ БИЗНЕСА

The modern information technology makes it possible not only to run business but to optimize business performance management with Business Performance Management Systems (BPM-systems). The performance management is a new approach based on the evolution of the well-known principles and laws of business management. It requires to create the advanced means of information support. To build such systems it is necessary to synthesize the theory of targeted management and balanced scorecard. However, in practice, the creation of new systems faces several problems; the most important of them can be summarized as follows: search and calculation of the index which measures the manageable efficiency; transformation of network structures that reflect target causal relationships into hierarchical ones; providing soft replacement of resources in the process of performance management; the need to use multiple-argument functions in calculations designed to find the target requirements; the need to solve problems on limitations of dynamics and ways to achieve goals.The theory of back calculations providing transformation of strategic management requirements into the control requirements (target budget or target indicators) may be used as a platform to solve the above mentioned problems. The reasons of occurrence of these problems as well as their semantics and features are analyzed in terms of practical creation of BPM-systems. Particular attention is paid to processing of indicators measured in different scales and the transformation of network structures that reflect the causal relationships between the objectives of the enterprise into treelike ones.The paper discusses the following functions BPM-systems: modeling and development of the balanced scorecard and strategy map of company’s operation; forecasting strategic indicators of the company and key performance indicators; adjusting the company’s goals and calculation of the planned values; monitoring the activities of company and performing financial and economic analysis of the company’s operation. Современный уровень развития информационных технологий позволяет управлять не просто бизнесом, но и его эффективностью с помощью систем Business Performance Management (BPM-систем). Управление эффективностью — это новый взгляд, базирующийся на эволюции известных принципов и законов управления предприятиями, что, в свою очередь, потребовало создания под него новых средств информационной поддержки, аккумулирующих в себе новейшие достижения информатики.Однако их реальное создание сталкивается с проблемами синтеза теорий целевого управления и сбалансированной системы данных, важнейшими среди которых можно назвать следующие: поиск и расчет показателя, измеряющего управляемую эффективность; превращение сетевых структур, отображающих целевые причинно-следственные связи, в иерархические; обеспечение мягкого замещения одних ресурсов другими в процессе управления эффективностью; необходимость использования многоаргументных функций в  расчетах, предназначенных для поиска целевых предписаний, а  также необходимость решения задач поиска ограничений на динамику и пути достижения целей. В качестве платформы для их решения предлагается использовать теорию обратных вычислений, обеспечивающую трансформацию требований стратегического управления в управляющие предписания (целевые бюджетные или плановые показатели).Причины появления перечисленных проблем, их семантика и особенности анализируются здесь с точки зрения практического создания BPM-систем. Особое внимание при этом уделяется вопросам обработки показателей, измеряемых в различных шкалах, и превращения сетевых структур, отражающих причинно-следственные связи между целями предприятия, в древовидные.Обсуждаются следующие функции BPM-систем: моделирование и разработка системы сбалансированных показателей и стратегической карты функционирования предприятия; прогнозирование стратегических индикаторов деятельности предприятия и ключевых показателей эффективности, корректировка их целей и расчет плановых значений; мониторинг деятельности предприятия и финансово-экономический анализ состояния предприятия.

ИТЕРАЦИОННЫЙ МЕТОД ОПТИМИЗАЦИИ УПРАВЛЕНИЯ ПРЕДПРИЯТИЯМИ СРЕДСТВАМИ ОБРАТНЫХ ВЫЧИСЛЕНИЙ

Optimization models based on linear models are referred to as «rigid» because in the majority of cases they do not provide needed results. Therefore, some authors suggest non-linear «soft» models as a substitute for linear ones since they are supposed to make an optimized system more robust. The rigidity of a model that is set as an optimization task is concerned not so much with linearity or non-linearity of its target function as with the lack of flexible substitution of resources in case of their shortage. Furthermore, the dependence of the management criterion (the target function) on the current resource constraints is reflected in a one-level, i.e. very simplified way. Hence a necessity arises to use integrated criteria of economic management efficiency, which requires a different look at the reflection of dependences between strategic and tactical purposes, on the one hand, and resources, on the other hand. This requirement encourages the search of new optimization methods. The proposed method is based on the expanded «resource» concept, which in turn has made it possible to introduce a concept of interchangeability of resources of various nature. The method is oriented at the use of inverse calculations when calculations are carried out from a known increment of function values towards unknown increments of performance indicators as arguments to reflect the level of reaching prioritized management goals. The paper formulates and substantiates the principles and provides a step-by-step description of an alternative approach to the optimization of management solutions. The first and foremost principle concerns reversing the direction of the search for the extreme value of the target function: the «constraints → target function» direction is changed for that of «target function → constraints». The second principle means replacement of static (rigid) constraints with «soft» ones making it possible to realize the idea of interchangeability of resources. In the situation of increasing shortage of resources, more attention is being paid to methods ensuring their maximum saving, therefore this problem is viewed in the paper as a possible sphere for application of the optimization method described herein.Оптимизационные модели, в основе которых лежат линейные модели, называют «жесткими», так как они в большинстве случаев не приводят к желаемым результатам. Поэтому ряд авторов предлагают перейти от линейных моделей к нелинейным, т.е. к «мягким», что и должно, по их мнению, обеспечить устойчивость оптимизируемой системы. Жесткость модели, заданной в форме оптимизационной задачи, заключается не только в линейности или нелинейности ее целевой функции или ограничений, но также и в отсутствии гибкой взаимозаменяемости ресурсов в случае их нехватки. Кроме того, имеет место одноуровневое, т.е. сильно упрощенное отражение зависимости критерия управления (целевой функции) от имеющихся ограничений на ресурсы. Отсюда появляется настоятельная потребность в использовании интегрированных критериев эффективности экономического управления, что требует изменения во взглядах на отражение зависимостей между стратегическими и оперативными целями, с одной стороны, и ресурсами - с другой. Такое требование стимулирует поиск новых методов оптимизации. Предлагаемый метод базируется на расширенном понятии «ресурс», позволившем, в свою очередь, ввести понятие взаимозаменяемости ресурсов различной природы. Метод ориентируется на применение обратных вычислений, заключающийся в том, что расчеты ведутся от известного прироста значений функции к неизвестным приростам аргументов-показателей, отражающих уровень в достижении целей управления с заданной приоритетностью. Сформулированы и обоснованы принципы, а также изложены этапы иного взгляда на оптимизацию управленческих решений. Первый и главный принцип заключается в изменении направления поиска экстремального значения целевой функции на противоположный: направление «ограничения → целевая функция» меняется на направление «целевая функция → ограничения». Второй принцип заключается в замене статических (жестких) ограничений на «мягкие», позволяющие реализовать идею взаимозаменяемости ресурсов. При возрастающей нехватке ресурсов все больше внимания уделяется методам, ориентированным на их максимальную экономию, поэтому в настоящей работе данная проблема рассматривается в качестве перспективной сферы приложения излагаемого метода оптимизации

Casimir energy and a cosmological bounce

We review different computation methods for the renormalised energy momentum tensor of a quantised scalar field in an Einstein Static Universe. For the extensively studied conformally coupled case we check their equivalence; for different couplings we discuss violation of different energy conditions. In particular, there is a family of masses and couplings which violate the weak and strong energy conditions but do not lead to spacelike propagation. Amongst these cases is that of a minimally coupled massless scalar field with no potential. We also point out a particular coupling for which a massless scalar field has vanishing renormalised energy momentum tensor. We discuss the backreaction problem and in particular the possibility that this Casimir energy could both source a short inflationary epoch and avoid the big bang singularity through a bounce.Comment: 13 pages, LaTeX, 8 figure