Dynamical dark energy from extra dimensions

We consider multidimensional cosmological model with a higher-dimensional product manifold M = R x R^{d_0} x H^{d_1}/\Gamma where R^{d_0} is d_0-dimensional Ricci-flat external (our) space and H^{d_1}/\Gamma is d_1-dimensional compact hyperbolic internal space. M2-brane solution for this model has the stage of accelerating expansion of the external space. We apply this model to explain the late time acceleration of our Universe. Recent observational data (the Hubble parameter at the present time and the redshift when the deceleration parameter changes its sign) fix fully all free parameters of the model. As a result, we find that considered model has too big size of the internal space at the present time and variation of the effective four-dimensional fine structure constant strongly exceeds the observational limits.Comment: 5 pages, 3 figures, LaTex, a few remarks and reference adde

Multidimensional perfect fluid cosmology with stable compactified internal dimensions

Multidimensional cosmological models in the presence of a bare cosmological constant and a perfect fluid are investigated under dimensional reduction to 4-dimensional effective models. Stable compactification of the internal spaces is achieved for a special class of perfect fluids. The external space behaves in accordance with the standard Friedmann model. Necessary restrictions on the parameters of the models are found to ensure dynamical behavior of the external (our) universe in agreement with observations.Comment: 11 pages, Latex2e, uses IOP packages, submitted to Class.Quant.Gra

Integrable Multicomponent Perfect Fluid Multidimensional Cosmology II: Scalar Fields

We consider anisotropic cosmological models with an universe of dimension 4 or more, factorized into n>1 Ricci-flat spaces, containing an m-component perfect fluid of m non-interacting homogeneous minimally coupled scalar fields under special conditions. We describe the dynamics of the universe: It has a Kasner-like behaviour near the singularity and isotropizes during the expansion to infinity. Some of the considered models are integrable, and classical as well as quantum solutions are found. Some solutions produce inflation from "nothing". There exist classical asymptotically anti-de Sitter wormholes, and quantum wormholes with discrete spectrum.Comment: 28 pages, LaTeX, subm. to Gen. Rel. Gra

AdS and stabilized extra dimensions in multidimensional gravitational models with nonlinear scalar curvature terms 1/R and R^4

We study multidimensional gravitational models with scalar curvature nonlinearities of the type 1/R and R^4. It is assumed that the corresponding higher dimensional spacetime manifolds undergo a spontaneous compactification to manifolds with warped product structure. Special attention is paid to the stability of the extra-dimensional factor spaces. It is shown that for certain parameter regions the systems allow for a freezing stabilization of these spaces. In particular, we find for the 1/R model that configurations with stabilized extra dimensions do not provide a late-time acceleration (they are AdS), whereas the solution branch which allows for accelerated expansion (the dS branch) is incompatible with stabilized factor spaces. In the case of the R^4 model, we obtain that the stability region in parameter space depends on the total dimension D=dim(M) of the higher dimensional spacetime M. For D>8 the stability region consists of a single (absolutely stable) sector which is shielded from a conformal singularity (and an antigravity sector beyond it) by a potential barrier of infinite height and width. This sector is smoothly connected with the stability region of a curvature-linear model. For D<8 an additional (metastable) sector exists which is separated from the conformal singularity by a potential barrier of finite height and width so that systems in this sector are prone to collapse into the conformal singularity. This second sector is not smoothly connected with the first (absolutely stable) one. Several limiting cases and the possibility for inflation are discussed for the R^4 model.Comment: 28 pages, minor cosmetic improvements, Refs. added; to appear in Class. Quantum Gra

ОСУЧАСНЕННЯ ТА МОДЕРНІЗАЦІЯ СИСТЕМИ ЕЛЕКТРОННИХ ПЛАТЕЖІВ НАЦІОНАЛЬНОГО БАНКУ УКРАЇНИ ЗА ЄВРОПЕЙСЬКИМ ДОСВІДОМ У КОНТЕКСТІ ГЛОБАЛІЗАЦІЙНИХ ПРОЦЕСІВ

Today for the System of Electronic Payments of the National Bank of Ukraine is actual modernization and updating according to the real needs of payment system participants in the current economic situation in Ukraine. For improvement forms of interbank payments important is a restructuring of the national payment system in accordance with international and EU standards. The article analyzes the functioning of the payment system TARGET2, discloses its advantages and principles of organization. The authors conducted a comparative analysis of payment systems TARGET2 and The System of Electronic Payments of the National Bank of Ukraine, as well as provided recommendations for improving the domestic payment system based on the experience of the European Union The NBU’s Electronic Payment System is quite modern and efficient, but the existence of a certain time in the payment process, insufficient level of regulatory and information support of the electronic payment system participants and its control lead to the possibility of opaque financial transactions in the system itself. The lack of organizational and financial mechanisms today is also a serious drawback in his work. In Ukraine, the technological level of the NBU system of calculations does not quite allow to use qualitatively most of the means of supporting intraday liquidity. This is a significant disadvantage of EPS compared to its foreign counterpart TARGET2. An analysis of the functioning of TARGET2 and SEP enabled us to examine in more detail the positives and negatives of both payment systems. A significant advantage of TARGET2 is its liquidity management system, which, under certain conditions, is an effective tool in the planning of settlement operations. This allows system members to prevent problems during the calculations and to solve them effectively. Optimization of liquidity management in the SEP is negligible. The National Bank of Ukraine, unlike the European Central Bank, does not provide full information on EPS, which indicates the closedness of the payment system and the NBU’s unwillingness to provide the most transparent settlement mechanism. Today, the TARGET2 settlement system is more modern and open compared to the NBU’s Electronic Payment System.На сьогодні для Системи електронних платежів Національного банку України актуальною є модернізація та осучаснення відповідно до реальних потреб учасників платіжної системи в умовах сучасної економічної ситуації в Україні. Для вдосконалення форм міжбанківських розрахунків важливою є перебудова національної платіжної системи відповідно до міжнародних стандартів і стандартів ЄС. Проведено аналіз функціонування платіжної системи ТАРГЕТ2, розкрито її переваги і принципи організації. Проведено порівняльний аналіз платіжних систем ТАРГЕТ2 та системи електронних платежів Національного банку, а також надано рекомендації щодо вдосконалення вітчизняної платіжної системи на основі досвіду Європейського Союзу. Система електронних платежів НБУ є досить сучасною та ефективною, але існування певного часу у проходженні платежу, недостатньо високий рівень нормативного та інформаційного забезпечення учасників системи електронних платежів та її контролю призводять до можливості непрозорих фінансових операцій у самій системі. В Україні технологічний рівень розрахункової системи НБУ не зовсім дозволяє якісно використовувати більшість із засобів підтримки внутрішньоденної ліквідності, що є значним недоліком СЕП у порівнянні з її зарубіжним аналогом — ТАРГЕТ2. Аналіз функціонування ТАРГЕТ2 та СЕП надав змогу більш детально розглянути позитивні і негативні моменти обох платіжних систем. Значною перевагою ТАРГЕТ2 є система управління ліквідністю, що за певних умов є дієвим інструментом при плануванні розрахункових операцій. Це дозволяє учасникам системи попереджувати виникнення проблем під час розрахунків та ефективно розв’язувати їх. Оптимізація управління ліквідністю у СЕП є незначною. Національний банк України, на відміну від Європейського центрального банку, надає інформацію стосовно СЕП не в повному обсязі, що свідчить про закритість платіжної системи та неготовність НБУ забезпечувати максимально прозорий механізм розрахунків. На сьогодні система розрахунків ТАРГЕТ2 є більш сучасною та відкритою у порівнянні із Cистемою електронних платежів НБУ

СПЕКТРОФОТОМЕТРИЧНЕ ВИЗНАЧЕННЯ 1-[7-(2-ГІДРОКСІЕТИЛ-1)-3-МЕТИЛКСАНТИН-8-ІЛ]ПІПЕРАЗИНІЙ ХЛОРИДУ

The aim of the work. To develop and validate the UV spectrophotometric procedure for the quantitative determination of 1-[7-(2-hydroxyethyl-1)-3-methylxanthine-8-yl]piperazine chloride.Materials and Methods. The study object was the substance of 1-[7-(2-hydroxyethyl-1)-3-methylxanthine-8-yl]piperazine chloride. Distilled water used as the solvent.Analytical equipment: spectrophotometer Specord 200, electronic balance AVT-120-5DM, measuring glassware of class A.Results and Discussion. The absorption band that observed at 260–320 nm with an absorption maximum at 289 nm was chosen to develop the quantitative determination method. According to SPU, the developed method was validated by the standard method for such validation characteristics as linearity, range of application, precision, accuracy and robustness. The calculated numerical values of linear dependence indicate that the method is linear throughout the selected concentration range (73–126 %). Precision was determined at the level of repeatability. It was found that the one-sided interval of a single value does not exceed the maximum permissible uncertainty of the analysis, so this method is accurate. It was proved that the absorption of the analyzed solutions remains stable for at least 1 hour. The predicted total uncertainty of the results for the quantitative determination method, which does not exceed its critical value, was also calculated. Thus, the method will give correct results in other laboratories.Conclusion. The UV spectrophotometric procedure for the quantitative determination of 1-[7-(2-hydroxyethyl-1)-3-methylxanthine-8-yl]piperazine chloride was developed and validated.Мета роботи. Розробити та валідувати УФ-спектрофотометричну методику кількісного визначення 1-[7-(2-гідроксіетил-1)-3-метилксантин-8-іл]піперазиній хлориду.Матеріали і методи.  Об’єктом дослідження була субстанція 1-[7-(2-гідроксіетил-1)-3-метилксантин-8-іл]піперазиній хлориду. В якості розчинника застосовували воду дистильовану.Аналітичне обладнання: спектрофотометр Specord 200, ваги електронні АВТ-120-5DM, мірний посуд класу А.Результати й обговорення. Для розробки методики кількісного визначення обрано смугу, що спостерігається при 260–320 нм із максимумом поглинання при 289 нм. Згідно з ДФУ розроблену методику валідовано методом стандарту за такими валідаційними характеристиками, як лінійність, діапазон застосування, прецизійність, правильність та робасність. Розраховані числові показники лінійної залежності свідчать, що методика лінійна в усьому обраному діапазоні концентрацій (73–126 %). Прецизійність визначали на рівні збіжності. Встановлено, що однобічний інтервал окремого значення не перевищує максимально припустиму невизначеність аналізу, тому дана методика є точною. Встановлено, що абсорбція аналізованих розчинів залишається стабільною протягом щонайменше однієї години. Також розраховано прогнозовану повну невизначеність результатів для методики кількісного визначення, яка не перевищує критичного значення. Отже, методика буде давати коректні результати і в інших лабораторіях.Висновок. Розроблено та валідовано УФ-спектрофотометричну методику кількісного визначення 1-[7-(2-гідроксіетил-1)-3-метилксантин-8-іл]піперазиній хлориду

A fast 5/2-approximation algorithm for hierarchical scheduling

International audienceWe present in this article a new approximation algorithm for scheduling a set of $n$ independent rigid (meaning requiring a fixed number of processors) jobs on hierarchical parallel computing platform. A hierarchical parallel platform is a collection of $k$ parallel machines of different sizes (number of processors). The jobs are submitted to a central queue and each job must be allocated to one of the $k$ parallel machines (and then scheduled on some processors of this machine), targeting the minimization of the maximum completion time (makespan). We assume that no job require more resources than available on the smallest machine. This problem is hard and it has been previously shown that there is no polynomial approximation algorithm with a ratio lower than $2$ unless $P=NP$. The proposed scheduling algorithm achieves a $\frac{5}{2}$ ratio and runs in $O(log(np_{max})knlog(n))$, where $p_{max}$ is the maximum processing time of the jobs. Our results also apply for the Multi Strip Packing problem where the jobs (rectangles) must be allocated on contiguous processors

Einstein and Brans-Dicke frames in multidimensional cosmology

Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold M= M_0 x M_1 ...x M_n are investigated under dimensional reduction to a D_0-dimensional effective non-minimally coupled sigma-model which generalizes the familiar Brans-Dicke model. It is argued that the Einstein frame should be considered as the physical one. The general prescription for the Einstein frame reformulation of known solutions in the Brans-Dicke frame is given. As an example, the reformulation is demonstrated explicitly for the generalized Kasner solutions where it is shown that in the Einstein frame there are no solutions with inflation of the external space.Comment: 27 pages, Revte

Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday

We discuss the modified gravity which includes negative and positive powers of the curvature and which provides the gravitational dark energy. It is shown that in GR plus the term containing negative power of the curvature the cosmic speed-up may be achieved, while the effective phantom phase (with $w$ less than -1) follows when such term contains the fractional positive power of the curvature. The minimal coupling with matter makes the situation more interesting: even 1/R theory coupled with the usual ideal fliud may describe the (effective phantom) dark energy. The account of $R^2$ term (consistent modified gravity) may help to escape of cosmic doomsday.Comment: LaTeX file, 9 pages, based on the talk given by S.D. Odintsov (Int. Conference Mathematical Methods in Physics, Rio de Janeiro, Augest, 2004), to appear in CQG, Letter

Multidimensional cosmological models: cosmological and astrophysical implications and constraints

We investigate four-dimensional effective theories which are obtained by dimensional reduction of multidimensional cosmological models with factorizable geometry and consider the interaction between conformal excitations of the internal space (geometrical moduli excitations) and Abelian gauge fields. It is assumed that the internal space background can be stabilized by minima of an effective potential. The conformal excitations over such a background have the form of massive scalar fields (gravitational excitons) propagating in the external spacetime. We discuss cosmological and astrophysical implications of the interaction between gravexcitons and four-dimensional photons as well as constraints arising on multidimensional models of the type considered in our paper. In particular, we show that due to the experimental bounds on the variation of the fine structure constant, gravexcitons should decay before nucleosynthesis starts. For a successful nucleosynthesis the masses of the decaying gravexcitons should be m>10^4 GeV. Furthermore, we discuss the possible contribution of gravexcitons to UHECR. It is shown that, at energies of about 10^{20}eV, the decay length of gravexcitons with masses m>10^4 GeV is very small, but that for m <10^2 GeV it becomes much larger than the Greisen-Zatsepin-Kuzmin cut-off distance. Finally, we investigate the possibility for gravexciton-photon oscillations in strong magnetic fields of astrophysical objects. The corresponding estimates indicate that even the high magnetic field strengths of magnetars are not sufficient for an efficient and copious production of gravexcitons.Comment: 16 pages, LaTeX2e, minor changes, improved references, to appear in PR