Oles Honchar Dnipro National University

We study characteristic (quasinormal) modes of a D-dimensional Schwarzschild black hole. It is shown that the real parts of the complex quasinormal modes, representing the real oscillation frequencies, are proportional to the product of the number of dimensions and inverse horizon radius $\ensuremath{\sim}{\mathrm{Dr}}_{0}^{\ensuremath{-}1}.$ The asymptotic formula for large multipole number l and arbitrary D is derived. In addition, the WKB formula for computing QN modes, developed to the third order beyond the eikonal approximation, is extended to the sixth order here. This gives us an accurate and economic way to compute quasinormal frequencies.

Abstract Many universities offer Distance Education (DE) courses and programs to address the diverse educational needs of students and to stay current with advancing technology. Some Institutions of Higher Education (IHE) that do not offer DE find it difficult to navigate through the steps that are needed to provide such courses and programs. Investigating learners’ perceptions, attitudes and willingness to try DE can provide guidance and recommendations for IHEs that are considering expanding use of DE formats. A survey was distributed to undergraduate students in Portugal, UAE and Ukraine. The results of this pilot study showed that in all three countries, students’ major concerns about such programs were time management, motivation, and English language skills. Although students were somewhat apprehensive many indicated they were interested in taking DE courses. Six recommendations informed by interpretation of students’ responses and the literature, are offered to assist institutions who want to offer DE as part of their educational strategy.

We present a thorough analysis of the quasinormal (QN) behavior associated with the decay of scalar, electromagnetic, and gravitational perturbations of Schwarzschild black holes in anti--de Sitter (AdS) spacetimes. As is known, the AdS QN spectrum crucially depends on the relative size of the black hole to the AdS radius. There are three different types of behavior depending on whether the black hole is large, intermediate, or small. The results of previous works, concerning lower overtones for large black holes, are completed here by obtaining higher overtones for all three black hole regimes. There are two major conclusions that one can draw from this work: First, asymptotically for high overtones, all the modes are evenly spaced, and this holds for all three types of regime, large, intermediate, and small black holes, independently of l, where l is the quantum number characterizing the angular distribution; second, the spacing between modes is apparently universal in that it does not depend on the field; i.e., scalar, electromagnetic, and gravitational QN modes all have the same spacing for high overtones. We are also able to prove why scalar and gravitational perturbations are isospectral, asymptotically for high overtones, by introducing appropriate superpartner potentials.

The low-laying frequencies of characteristic quasi-normal modes (QNM) of Schwarzschild-de Sitter (SdS) black holes have been calculated for fields of different spin using the 6th-order WKB approximation and the approximation by the P"{o}shl-Teller potential. The well-known asymptotic formula for large $l$ is generalized here on a case of the Schwarzchild-de Sitter black hole. In the limit of the near extreme $L$ term the results given by both methods are in a very good agreement, and in this limit fields of different spin decay with the same rate. In addition, the fact that the spectrum of massless Dirac quasi-normal frequencies is the same for opposite chyrality has been numerically proved for SdS background.

We compute the quasinormal modes associated with the decay of the massless scalar field around a small Schwarzschild--anti-de Sitter black hole. The computations show that when the horizon radius is much less than the anti--de Sitter radius, the imaginary part of the frequency goes to zero as ${r}_{+}^{d\ensuremath{-}2}$ while the real part of $\ensuremath{\omega}$ decreases to its minimum and then goes to $d\ensuremath{-}1.$ Thus the quasinormal modes approach the usual AdS modes in the limit ${r}_{+}\ensuremath{\rightarrow}0.$ This agrees with suggestions of Horowitz and Hubeny [Phys. Rev. D 62, 024027 (2000)].

Signal integration in the brain is determined by the size and kinetics of rapid synaptic responses. The latter, in turn, depends on the concentration profile of neurotransmitter in the synaptic cleft. According to a traditional view, narrower clefts should correspond to higher intracleft concentrations of neurotransmitter, and therefore to the enhanced activation of synaptic receptors. Here, we argue that narrowing the cleft also increases electrical resistance of the intracleft medium and therefore reduces local receptor currents. We employ detailed theoretical analyses and Monte Carlo simulations to propose that these two contrasting phenomena result in a relatively narrow range of cleft heights at which the synaptic receptor current reaches its maximum. Over a physiological range of synaptic parameters, the "optimum" height falls between approximately 12 and 20 nm. This range is consistent with the structure of central synapses reported by electron microscopy. Therefore, our results suggest that a simple fundamental principle may underlie the synaptic cleft architecture: to maximize synaptic strength.

Floodplain ecosystems are biodiversity hotspots and supply multiple ecosystem services. At the same time they are often prone to human pressures that increasingly impact their intactness. Multifunctional floodplain management can be defined as a management approach aimed at a balanced supply of multiple ecosystem services that serve the needs of the local residents, but also those of off-site populations that are directly or indirectly impacted by floodplain management and policies. Multifunctional floodplain management has been recently proposed as a key concept to reconcile biodiversity and ecosystem services with the various human pressures and their driving forces. In this paper we present biophysics and management history of floodplains and review recent multifunctional management approaches and evidence for their biodiversity effects for the six European countries Ireland, the Netherlands, Germany, Slovakia, Hungary and the Ukraine. Multifunctional use of floodplains is an increasingly important strategy in some countries, for instance in the Netherlands and Hungary, and management of floodplains goes hand in hand with sustainable economic activities resulting in flood safety and biodiversity conservation. As a result, biodiversity is increasing in some of the areas where multifunctional floodplain management approaches are implemented. We conclude that for efficient use of management resources and ecosystem services, consensual solutions need to be realized and biodiversity needs to be mainstreamed into management activities to maximize ecosystem service provision and potential human benefits. Multifunctionality is more successful where a broad range of stakeholders with diverse expertise and interests are involved in all stages of planning and implementation.

We find the gravitational resonance [quasinormal (QN)] modes of the higher-dimensional Schwarzschild and Reissner-Nordstr\"om black holes. The effect on the quasinormal behavior due to the presence of the $\ensuremath{\lambda}$ term is investigated. The QN spectrum is totally different for different signs of $\ensuremath{\lambda}.$ In more than four dimensions three types of gravitational modes were excited: scalar, vector, and tensor. They produce three different quasinormal spectra; thus, the isospectrality between scalar and vector perturbations, which takes place for $D=4$ Schwarzschild and Schwarzschild--de Sitter black holes, is broken in higher dimensions, that is, the scalar-type gravitational perturbations, connected with fluctuations of the black hole horizon, which damp most slowly and therefore dominate during late time of the black hole ringing.

Altered function of Na+ channels is responsible for increased hyperexcitability of primary afferent neurons that may underlie pathological pain states. Recent evidence suggests that the Nav1.9 subunit is implicated in inflammatory but not acute pain. However, the contribution of Nav1.9 channels to the cellular events underlying nociceptor hyperexcitability is still unknown, and there remains much uncertainty as to the biophysical properties of Nav1.9 current and its modulation by inflammatory mediators. Here, we use gene targeting strategy and computer modeling to identify Nav1.9 channel current signature and its impact on nociceptors' firing patterns. Recordings using internal fluoride in small DRG neurons from wild-type and Nav1.9-null mutant mice demonstrated that Nav1.9 subunits carry the TTX-resistant "persistent" Na+ current called NaN. Nav1.9(-/-) nociceptors showed no significant change in the properties of the slowly inactivating TTX-resistant SNS/Nav1.8 current. The loss in Nav1.9-mediated Na+ currents was associated with the inability of small DRG neurons to generate a large variety of electrophysiological behaviors, including subthreshold regenerative depolarizations, plateau potentials, active hyperpolarizing responses, oscillatory bursting discharges, and bistable membrane behaviors. We further investigated, using CsCl- and KCl-based pipette solutions, whether G-protein signaling pathways and inflammatory mediators upregulate the NaN/Nav1.9 current. Bradykinin, ATP, histamine, prostaglandin-E2, and norepinephrine, applied separately at maximal concentrations, all failed to modulate the Nav1.9 current. However, when applied conjointly as a soup of inflammatory mediators they rapidly potentiated Nav1.9 channel activity, generating subthreshold amplification and increased excitability. We conclude that Nav1.9 channel, the molecular correlate of the NaN current, is potentiated by the concerted action of inflammatory mediators that may contribute to nociceptors' hyperexcitability during peripheral inflammation.

We introduce the concept of soliton clusters--multisoliton bound states in a homogeneous bulk optical medium--and reveal a key physical mechanism for their stabilization associated with a staircaselike phase distribution that induces a net angular momentum and leads to cluster rotation. The ringlike soliton clusters provide a nontrivial generalization of the concepts of two-soliton spiraling, optical vortex solitons, and necklace-type optical beams.

It is well known that the charged scalar perturbations of the Reissner-Nordstr\"om metric will decay slower at very late times than the neutral ones, thereby dominating in the late time signal. We show that, at the stage of quasinormal (QN) ringing, on the contrary, the neutral perturbations will decay slower for RN, RNAdS and dilaton black holes. The QN frequencies of the nearly extreme RN black hole have the same imaginary parts (damping times) for charged and neutral perturbations. An explanation of this fact is not clear but, possibly, is connected with the Choptuik scaling.

The physical assumptions underlying the static and dynamic Jiles-Atherton (JA) hysteresis models are critically analyzed. It is shown that the energy-balance method used in deriving these models is actually closer to a balance of coenergies, thereby depriving the resulting JA phenomenology of physical meaning. The non-physical basis of its dynamic extension is demonstrated by a sharp contrast between hysteresis loops predicted by the model and those measured for grain-oriented steel under conditions of controlled sinusoidal flux density at frequencies of 50, 100, and 200 Hz.

Albumin is one of the most abundant proteins in the body of mammals: about 40% of its pool is located in the intravascular space and the remainder is found in the interstitial space. The content of this multifunctional protein in blood is about 60-65% of total plasma proteins. A decrease in its synthesis or changes of functional activity can destabilize oncotic blood pressure, cause a violation of transporting hormones, fatty acids, metals, and drugs. Albumin properties change under ischemic attacks associated with oxidative stress, production of reactive oxygen species, and acidosis. Under these conditions, ischemia-modified albumin (IMA) is generated that has a reduced metal-binding capacity, especially for transition metals, such as copper, nickel, and cobalt. The method of determining the cobalt-binding capability of HSA was initially proposed to evaluate IMA level and then licensed as an ACB test for routine clinical analysis for myocardial ischemia. Subsequent studies have shown the viability of the ACB test in diagnosing other diseases associated with the development of oxidative stress. This review examines recent data on IMA generation mechanisms, describes principles, advantages, and limitations of methods for evaluation of IMA levels, and provides detailed analysis of its use in diagnostic and monitoring therapeutic efficacy in different diseases.

BACKGROUND: The mammalian brain expresses a wide range of state-dependent network oscillations which vary in frequency and spatial extension. Such rhythms can entrain multiple neurons into coherent patterns of activity, consistent with a role in behaviour, cognition and memory formation. Recent evidence suggests that locally generated fast network oscillations can be systematically aligned to long-range slow oscillations. It is likely that such cross-frequency coupling supports specific tasks including behavioural choice and working memory. PRINCIPAL FINDINGS: We analyzed temporal coupling between high-frequency oscillations and EEG theta activity (4-12 Hz) in recordings from mouse parietal neocortex. Theta was exclusively present during active wakefulness and REM-sleep. Fast oscillations occurred in two separate frequency bands: gamma (40-100 Hz) and fast gamma (120-160 Hz). Theta, gamma and fast gamma were more prominent during active wakefulness as compared to REM-sleep. Coupling between theta and the two types of fast oscillations, however, was more pronounced during REM-sleep. This state-dependent cross-frequency coupling was particularly strong for theta-fast gamma interaction which increased 9-fold during REM as compared to active wakefulness. Theta-gamma coupling increased only by 1.5-fold. SIGNIFICANCE: State-dependent cross-frequency-coupling provides a new functional characteristic of REM-sleep and establishes a unique property of neocortical fast gamma oscillations. Interactions between defined patterns of slow and fast network oscillations may serve selective functions in sleep-dependent information processing.

BACKGROUND: Breast cancer is a leading cause of morbidity and mortality worldwide. Although mammography screening is available, there is an ongoing interest in improved early detection and prognosis. Herein, we have analysed a combination of serological biomarkers in a case-control cohort of sera taken before diagnosis. METHODS: This nested case-control study within the UK Collaborative Trial of Ovarian Cancer Screening (UKCTOCS) used serum samples from 239 women who subsequently developed breast cancer and 239 matched cancer-free controls. Sera were screened by ELISA for 9 candidate markers. Univariate and multivariate analyses were performed to examine associations with clinico-pathological features and between case controls in different time groups before diagnosis. RESULTS: Significant associations with clinico-pathological features related to prognosis were found for several candidates (CA15-3, HSP90A and PAI-1). However, there were no consistent differences between cases and controls for any candidate in the lead up to diagnosis. Whilst combination models outperformed single markers, there was no increase in performance towards diagnosis. CONCLUSIONS: This study using unique pre-diagnosis samples shows that CA15-3, HSP90A and PAI-1 have potential as early prognostic markers and warrant further investigation. However, none of the candidates or combinations would be useful for screening.

The low lying characteristic (quasinormal) modes of black holes can be evaluated with the help of the semi-analytic method based on a modified WKB approach. We extend the 3rd order WKB formula of Iyer and Will to the 6th order beyond the eikonal approximation and attain thereby an accurate formula for computing QN modes. With the help of the obtained formula we find quasinormal modes corresponding to decay of scalar, dirac, electromagnetic, gravitino, and graviton fields in the Schwarzschild background. For Schwarzschild BH the 6th order WKB lower overtone modes, corresponding to scalar, elctromagnetic and gravitational perturbations, coincide with numerical results already for l 1, while the 3rd order formula does the same at l 4.

Lead-free Na0.5Bi0.5TiO3 -BaTiO3 ceramics have been prepared in the whole range of concentrations and studied at room-temperature by means of X-ray, Raman scattering and infrared techniques. X-ray measurements revealed rhombohedral, rhombohedral-tetragonal boundaries and tetragonal modifacations depending on the contents of BaTiO3. The distinct changes of the Raman and infrared spectra with increasing of BaTiO3 content, which were correlated with X-ray results, were observed. The broad phonon spectra indicated the disorder in the A site of Na0.5Bi0.5TiO3 -BaTiO3 system.

The following methods for the determination of adenosine triphosphate reported in the past 25 years are considered: bioluminescence methods with the use of the firefly luciferase enzyme (with sensitivity to 10−14 M); chromatographic methods (ion-exchange, thin-layer, and high performance liquid chromatography) for the determination of adenine nucleotides in mixtures with other nucleotides, nucleosides, and nitrogen bases; and fluorescence, spectrophotometric, and electrochemical techniques (including those with the use of sensors), which are promising but not commonly used for the determination of adenine nucleotides. The advantages and disadvantages of these methods are demonstrated.

The review analyzes methods of synthesis of 1,4-oxazines (morpholines) starting from vicinal amino alcohols and their derivatives, oxiranes, and aziridines. Examples of using morpholines in medicinal and organic chemistry as catalysts, auxiliaries, biologically active substances, and building blocks for their preparation are considered. The data published until February 2013 have been covered.

Antibacterial activity of plants is a subject of interest in the search for new antibiotics and fungicidal preparations. This article analyzes the effectiveness of the action of extracts of plants on microorganisms: six species of bacteria (Salmonella typhimurium, Listeria monocytogenes, Escherichia coli, Klebsiella pneumoniae, Corynebacterium xerosis, Proteus vulgaris) and one fungus (Candida albicans). For the assay, we used herbal material of 50 species (seeds, grass, shoots, leaves, compound fruit, peel) obtained at different periods of the growing season. We studied Levisticum officinale, Petroselinum crispum, Nerium oleander, Vinca minor, Eleutherococcus senticosus, E. sieboldianus, Yucca filamentosa, Artemisia annua, Echinacea purpurea, Matricaria recutita, Tanacetum vulgare, Betula pendula, Corylus avellana, Buxus sempervirens, Humulus lupulus, Crassula ovata, Bryophyllum daigremontianum, Juniperus communis, Platycladus orientalis, Cycas revoluta, Calluna vulgaris, Rhododendron ferrugineum, Ceratonia siliqua, Trigonella foenum-graecum, Ribes nigrum, Phellinus tuberculosus, Lavandula angustifolia, Melissa officinalis, Monarda fistulosa, Origanum vulgare, Salvia sclarea, Laurus nobilis, Punica granatum, Hibiscus rosa-sinensis, Menispermum dauricum, Ficus benjamina, Morus alba, Paeonia suffruticosa, Picea abies, Adonis vernalis, Amelanchier ovalis, Prunus armeniaca, Crataegus monogyna, Citrus sinensis, Salix babylonica, Bergenia crassifolia, Schisandra chinensis, Taxus baccata and Xanthoria parietina. The alcohol tincture was filtered with sterile multi-layer gauze disc filters. Before the discs were put on the surface of agar with inoculation of the corresponding culture, they were dried in a sterile laminar box under ultraviolet rays. Antibacterial activity of various tinctures was determined by the disk diffusion method in agar with the measurement of the diameter of the growth suppression zone of the culture using a template ruler. Maximum inhibiting effect was achieved for Punica granatum on K. рneumonia, L. monocytogenes, S. typhimurium, P. vulgaris, C. хerosis and E. сoli, Lavandula angustifolia – on P. vulgaris, K. рneumonia and S. typhimurium, Echinacea purpurea – on C. аlbicans, E. сoli, P. vulgaris, K. рneumonia, Bergenia crassifolia – on P. vulgaris, K. pneumonia and S. typhimurium.