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X-ray pulsars experiencing extreme mass accretion rates can produce neutrino emission in the MeV energy band. Neutrinos in these systems are emitted in close proximity to the stellar surface and subsequently undergo gravitational bending in the space curved by a neutron star. This process results in the formation of a distinct beam pattern of neutrino emission and gives rise to the phenomenon of neutrino pulsars. The energy flux of neutrinos, when averaged over the neutron star's pulsation period, can differ from the isotropic neutrino energy flux, which impacts the detectability of bright pulsars in neutrinos. We investigate the process of neutrino beam pattern formation, accounting for neutron star transparency to neutrinos and gravitational bending. Based on simulated neutrino beam patterns, we estimate the potential difference between the actual and apparent neutrino luminosity. We show that the apparent luminosity can greatly exceed the actual luminosity, albeit only in a small fraction of cases, depending on the specific equation of state and the mass of the star. For example, the amplification can exceed a factor of ten for $\approx0.05\%$ of typical neutron stars with mass of $1.4\,M_\odot$. Strong amplification is less probable for neutron stars of higher mass. In the case of strange stars, a fraction of high energy neutrinos can be absorbed and the beam pattern, as well as the amplification of apparent neutrino luminosity, depend on neutrino energy., Comment: submitted to MNRAS, 12 pages, 9 figures

Superbursts of neutron stars are rare but powerful events explained by the explosive burning of carbon in the deep layers of the outer envelope of the star. In this paper we perform a simulation of superbursts and propose a simple method for describing the neutrino stage of their cooling, as well as a method for describing the evolution of the burst energy on a scale of several months. We note a universal relation for the temperature distribution in the burnt layer at its neutrino cooling stage, as well as the unification of bolometric light curves and neutrino heat loss rates for deep and powerful bursts. We point out the possibility of long-term retention of the burst energy in the star's envelope. The results can be useful for interpretation of superburst observations., Comment: 8 pages, 6 figures, to be published in Astronomy Letters, 49, No.12 (2023)

A self-consistent radiation-hydrodynamics model of an accretion channel of subcritical X-ray pulsars is constructed. The influence of the presence of resonance in the scattering cross-section on the accretion process and radiation transfer is taken into account. It is shown that the efficiency of plasma deceleration by radiation depends on the magnitude of the magnetic field $B$. For $B=1.7\times 10^{12}$ G, the spectra and the degree of linear polarization of the radiation of the accretion channel are constructed. In the obtained spectra, the shape of the cyclotron line depends on the direction of the outgoing radiation. The calculated linear polarization degree of the outgoing radiation is $30 -40\%$ near the cyclotron resonance, whereas it can be small ($\lesssim 5 - 10\%$) at energies significantly lower than the resonant one., Comment: 8 pages, 7 figures, to be published in Astronomy Letters, Vol.49, No.10 (2023)

We carry out a statistical analysis of the spatial distribution of galaxies at cosmological redshifts $0.16 \leq z \leq 0.47$ based on the SDSS\ DR12\ LOWZ catalogue. Our aim is to search and study possible large-scale quasi-regular structures embedded in the {\it cosmic web}. We calculate projections of the Cartesian galaxy coordinates on different axes (directions) densely covering certain regions in the sky to look for special directions along which one-dimensional distributions of the projections contain significant quasi-periodic components. These components appear as peaks in the power spectra and lie in a narrow range of wave numbers $0.05 < k < 0.07$. Particular attention is paid to the evaluation of the significance of the peaks. It is found that the significance of the dominant peaks for some selected directions exceeds $(4 - 5)\sigma$. In order to reduce possible selection effects, we create a mock homogeneous catalogue of spatial distribution of galaxies by adding a random set of artificial objects (points) to the real galaxies under study. The power spectrum of this cumulative model data also demonstrates significant peak corresponding to approximately the same scale. As a result we assume the existence of an anisotropic cosmological quasi-periodic structure with characteristic scale $(116 \pm 10)~h^{-1}$~Mpc., Comment: 12 pages, 6 figures, accepted for publication by MNRAS

E. B. Gliner started his scientific career in 1963 at the age of 40. In 1965, when the existence of the cosmological constant $\lambda$ seemed unnecessary to most cosmologists, he renewed interest in the problem by emphasizing a material interpretation of de Sitter space (i.e., the space curved in the presence of $\lambda$). According to that interpretation, the curvature is produced by a cosmological vacuum (now identified as dark energy of the universe). In 1970, Gliner proposed a description of exponential expansion (or contraction) of the universe at the early (or late) evolution stage dominated by cosmological vacuum. In 1975, Gliner (with I.G. Dyminikova) suggested a model of the early universe free of Big Bang singularity, and developed a scenario of nonsingular Friedmann cosmology. Many of these findings were used in the modern inflation scenarios of the universe, first proposed by A.A. Starobinsky (1979) and A. Guth (1981) and greatly multiplied later. However, these inflation scenarios differ from the scenario of Gliner and Dymnikova, and Gliner's contribution to cosmology is nearly forgotten. The history and the essence of this contribution are outlined, as well the difference from the inflation theories., Comment: 19 pages, 4 figures, types corrected

Compton scattering is a key process shaping spectra formation and accretion flow dynamics in accreting strongly magnetized neutron stars. A strong magnetic field affects the scattering cross section and makes it dependent on photon energy, momentum, and polarization state. Using Monte Carlo simulations, we investigate statistical features of Compton scattering of polarized X-ray radiation in a strong magnetic field. Our analysis is focused on photon gas behaviour well inside the scattering region. We take into account the resonant scattering at the fundamental cyclotron frequency, thermal distribution of electrons at the ground Landau level, and bulk velocity of the electron gas. We show that (i) the photons scattered around the cyclotron energy by the electron gas at rest tend to acquire the final energy close to the cyclotron one with a very small dispersion measure; (ii) the redistribution of photons within the Doppler core of cyclotron resonance differs significantly from the complete redistribution; (iii) the efficiency of momentum transfer from photons to the electron gas is affected by the temperature of electron gas both for photons at cyclotron energy and below it; (iv) the momentum transfer from photons to the electron gas of non-zero bulk velocity is more efficient in the case of magnetic scattering., Comment: 18 pages, 13 figures, accepted for publication in Phys.Rev.D

The aim of this study is to search for quasi-periodical structures at moderate cosmological redshifts $z \la 0.5 $. We mainly use the SDSS DR7 data on the luminous red galaxies (LRGs) with redshifts $0.16 \leq z \leq 0.47$. At first, we analyze features (peaks) in the power spectra of radial (shell-like) distributions using separate angular sectors in the sky and calculate the power spectra within each sector. As a result, we found some signs of a large-scale anisotropic quasi-periodic structure detectable through 6 sectors out of a total of 144 sectors. These sectors are distinguished by large amplitudes of dominant peaks in their radial power spectra at wavenumbers $k$ within a narrow interval of $0.05 < k < 0.07$~h~Mpc$^{-1}$. Then, passing from a spherical coordinate system to a Cartesian one, we found a special direction such that the total distribution of LRG projections on it contains a significant ($\ga$5$\sigma$) quasi-periodical component. We assume that we are dealing with a signature of a quasi-regular structure with a characteristic scale $116 \pm 10$~h$^{-1}$~Mpc. Our assumption is confirmed by a preliminary analysis of the SDSS DR12 data., Comment: 24 pages, 7 figures, 71 references

We study heat diffusion after an energy release in a deep spherical layer of the outer neutron star crust (10^7 < \rho < 4 x 10^{11} g/cm^3). We demonstrate that this layer possesses specific heat-accumulating properties, absorbing heat and directing it mostly inside the star. It can absorb up to about 10^{43}-10^{44} erg due to its high heat capacity, until its temperature exceeds T ~ 3 x 10^9 K and triggers a rapid neutrino cooling. A warm layer with T ~ 10^8 - 3 x 10^9 K can serve as a good heat reservoir, which is thermally decoupled from the inner crust and the stellar core for a few months. We present a toy model to explore the heat diffusion within the heat-accumulating layer, and we test this model using numerical simulations. We formulate some generic features of the heat propagation which can be useful, for instance, for the interpretation of superbursts in accreting neutron stars. We present a self-similar analysis of late afterglow after such superbursts, which can be helpful to estimate properties of bursting stars., Comment: 17 pages, 9 figures, MNRAS, accepted, a few typos and bib references corrected

On the base of the simplest model of a modulation of 3D Gaussian field in $k$-space we produce a set of simulations to bring out the effects of a modulating function $f_{\rm mod} (k)=f_1 (k) + f_2 (k)$ on power spectra of radial (shell-like) distributions of cosmological objects, where a model function $f_1 (k)$ reproduces the smoothed power spectrum of underlying 3D density fluctuations, while $f_2 (k)$ is a wiggling function imitating the baryon acoustic oscillations (BAO). It is shown that some excess of realizations of simulated radial distributions actually displays quasi-periodical components with periods about a characteristic scale $2\pi/k \sim 100~h^{-1}$~Mpc detected as power-spectrum peaks in vicinity of the first maximum of the modulation function $f_2 (k)$. We revised our previous estimations of the significance of such peaks and found that they were largely overestimated. Thereby quasi-periodical components appearing in some radial distributions of matter are likely to be stochastic (rather than determinative), while the amplitudes of the respective spectral peaks can be quite noticeable. They are partly enhanced by smooth part of the modulating function $f_1(k)$ and, to a far lesser extent, by effects of the BAO (i.e. $f_2(k)$). The results of the simulations match quite well with statistical properties of the radial distributions of the brightest cluster galaxies (BCGs)., Comment: 13 pages, 5 figures, accepted for publication in Astrophysics and Space Science

We discuss the Berezin transform, a Markov operator associated to positive operator valued measures (POVMs), in a number of contexts including the Berezin-Toeplitz quantization, Donaldson's dynamical system on the space of Hermitian products on a complex vector space, representations of finite groups, and quantum noise. In particular, we calculate the spectral gap for quantization in terms of the fundamental tone of the phase space. Our results confirm a prediction of Donaldson for the spectrum of the Q-operator on Kahler manifolds with constant scalar curvature. Furthermore, viewing POVMs as data clouds, we study their spectral features via geometry of measure metric spaces and the diffusion distance., Comment: Final version, 47 pages. Section on Donaldson's iterations revised

We study thermal relaxation in a neutron star after internal heating events (outbursts) in the crust. We consider thin and thick spherically symmetric heaters, superfluid and non-superfluid crusts, stars with open and forbidden direct Urca processes in their cores. In particular, we analyze long-term thermal relaxation after deep crustal heating produced by nuclear transformations in fully or partly accreted crusts of transiently accreting neutron stars. This long-term relaxation has a typical relaxation time and an overall finite duration time for the crust to thermally equilibrate with the core. Neutron superfluidity in the inner crust greatly affects the relaxation if the heater is located in the inner crust. It shortens and unifies the time of emergence of thermal wave from the heater to the surface. This is important for the interpretation of observed outbursts of magnetars and transiently accreting neutron stars in quasi-persistent low-mass X-ray binaries., Comment: 15 pages, 10 figures, Astrophysics and Space Science, published

The ion temperature of the magnetosphere of Jupiter derived from Galileo PLS data was observed to increase by about an order of magnitude from 10 to 40 Jupiter radii. This suggests the presence of heating sources that counteract the adiabatic cooling effect of expanding plasma. There have been different attempts of explaining this phenomena, including a magnetohydrodynamic (MHD) turbulent heating model which is based on flux tube diffusion [Saur, Astrophys. J. Lett., 602, L137, 2004]. We explore an alternate turbulent heating model based on advection, similar to models commonly used in solar wind heating. Based on spectral analysis of Galileo magnetometer (MAG) data, we find that observed MHD turbulence could potentially provide the required heating to explain some of the increase in plasma temperature. This indicates that advection is a more appropriate way to describe radial transport of plasma in the jovian magnetosphere beyond 10 Jupiter radii., Comment: Submitted to Journal of Geophysical Research (Space Physics) on February 14, 2018

For a class of positive operator valued measures, we introduce the spectral gap, an invariant which shows up in a number of contexts: the quantum noise operator responsible for the unsharpness of quantum measurements, the Markov chain describing the state reduction for repeated quantum measurements, and the Berezin transform on compact Kahler manifolds. The spectral gap admits a transparent description in terms of geometry of certain metric measure spaces, is related to the diffusion distance, and exhibits a robust behaviour under perturbations in the Wasserstein metric., Comment: This paper has been withdrawn by the authors. Extended, significantly rewritten and incorporated into arXiv:1811.03155

Classical Spanier-Whitehead duality was introduced for the stable homotopy category of finite CW complexes. Here we provide a comprehensive treatment of a noncommutative version, termed Spanier-Whitehead $K$-duality, which is defined on the category of $C^*$-algebras whose $K$-theory is finitely generated and that satisfy the UCT with morphisms the $KK$-groups. We explore what happens when these assumptions are relaxed in various ways. In particular, we consider the relationship between Paschke duality and Spanier-Whitehead $K$-duality., Comment: 28 pages, Typos corrected and referees comments incorporated. To appear in Journal of Topology and Analysis

Investigations of thermal evolution of neutron stars with hyperon cores require neutrino emissivities for many neutrino reactions involving strongly degenerate particles (nucleons, hyperons, electrons, muons). We calculate the angular integrals $I_n$ (over orientations of momenta of $n$ degenerate particles) for major neutrino reactions with $n$ =3, 4, 5 at all possible combinations of particle Fermi momenta. The integrals $I_n$ are necessary ingredients for constructing a uniform database of neutrino emissivities in dense nucleon-hyperon matter. The results can also be used in many problems of physical kinetics of strongly degenerate systems., Comment: 11 pages, 4 figures, Astrophysics and Space Science, accepted

Given a symplectic surface $(\Sigma, \omega)$ of genus $g \ge 4$, we show that the free group with two generators embeds into every asymptotic cone of $(\mathrm{Ham}(\Sigma, \omega), d_\mathrm{H})$, where $d_\mathrm{H}$ is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds., Comment: 32 pages, 5 figures

The central compact object in the supernova remnant HESS J1731-347 appears to be the hottest observed isolated cooling neutron star. The cooling theory of neutron stars enables one to explain observations of this star by assuming the presence of strong proton superfluidity in the stellar core and the existence of the surface heat blanketing envelope which almost fully consists of carbon. The cooling model of this star is elaborated to take proper account of the neutrino emission due to neutron-neutron collisions which is not suppressed by proton superfluidity. Using the results of spectral fits of observed thermal spectra for the distance of 3.2 kpc and the cooling theory for the neutron star of age 27 kyr, new constraints on the stellar mass and radius are obtained which are more stringent than those derived from the spectral fits alone., Comment: 9 pages, 5 figures, MNRAS, accepted

We consider the effect of a partial coverage of quasar broad-line regions (QSO BLRs) by intervening H$_2$-bearing clouds when a part of quasar (QSO) radiation passes by a cloud not taking part in formation of an absorption-line system in the QSO spectrum. That leads to modification of observable absorption line profiles and consequently to a bias in physical parameters derived from standard absorption line analysis. In application to the H$_2$ {absorption} systems the effect has been revealed in the analysis of H$_2$ absorption system in the spectrum of Q~1232+082 (Ivanchik et al. 2010, Balashev et al. 2011). We estimate a probability of the effect to be detected in QSO spectra. To do this we derive distribution of BLR sizes of high-z QSOs from Sloan Digital Sky Survey (SDSS) Data Release 9 (DR9) catalogue and assume different distributions of cloud sizes. We conclude that the low limit of the probability is about $11\%$. The latest researches shows that about a fifth of observed H$_2$ absorption systems can be partially covered. Accounting of the effect may allow to revise significantly physical parameters of interstellar clouds obtained by the spectral analysis., Comment: 12 pages, 8 figures

We propose that observations of "hidden" magnetars in central compact objects can be used to probe crustal activity of neutron stars with large internal magnetic fields. Estimates based on calculations by Perna \& Pons (2011), Pons \& Rea (2012) and Kaminker et al. (2014) suggest that central compact objects, which are proposed to be "hidden" magnetars, must demonstrate flux variations on the time scale of months-years. However, the most prominent candidate for the "hidden" magnetars --- CXO J1852.6+0040 in Kes 79, -- shows constant (within error bars) flux. This can be interpreted by lower variable crustal activity than in typical magnetars. Alternatively, CXO J1852.6+0040 can be in a high state of variable activity during the whole period of observations. Then we consider the source 1E161348-5055 in RCW103 as another candidate. Employing a simple 2D-modeling we argue that properties of the source can be explained by the crustal activity of the magnetar type. Thus, this object may be supplemented for the three known candidates for the "hidden" magnetars among central compact objects discussed in literature., Comment: 8 pages, accepted to PASA

Based on the formalism by Kaminker et al. (Astron. Astrophys. 343 (1999) 1009) we derive an analytic approximation for neutrino-pair bremsstrahlung emissivity due to scattering of electrons by atomic nuclei in the neutron star crust of any realistic composition. The emissivity is expressed through generalized Coulomb logarithm which we fit by introducing an effective potential of electron-nucleus scattering. In addition, we study the conditions at which the neutrino bremsstrahlung in the crust is affected by strong magnetic fields. The results can be applied for modelling of many phenomena in neutron stars, such as thermal relaxation in young isolated neutron stars and in accreting neutron stars with overheated crust in soft X-ray transients., Comment: 6 pages, 3 figures, EPL, accepted

Using 1D and 2D cooling codes we study thermal emission from neutron stars with steady state internal heaters of various intensities and geometries (blobs or spherical layers) located at different depths in the crust. The generated heat tends to propagate radially, from the heater down to the stellar core and up to the surface; it is also emitted by neutrinos. In local regions near the heater the results are well described with the 1D code. The heater's region projects onto the stellar surface forming a hot spot. There are two heat propagation regimes. In the first, conduction outflow regime (realized at heat rates $H_0 \lesssim 10^{20}$ erg cm$^{-3}$ s$^{-1}$ or temperatures $T_\mathrm{h} \lesssim 10^9$ K in the heater) the thermal surface emission of the star depends on the heater's power and neutrino emission in the stellar core. In the second, neutrino outflow regime ($H_0 \gtrsim 10^{20}$ erg cm$^{-3}$ s$^{-1}$ or $T_\mathrm{h} \gtrsim 10^9$ K) the surface thermal emission becomes independent of heater's power and the physics of the core. The largest (a few per cent) fraction of heat power is carried to the surface if the heater is in the outer crust and the heat regime is intermediate. The results can be used for modeling young cooling neutron stars (prior to the end of internal thermal relaxation), neutron stars in X-ray transients, magnetars and high-$B$ pulsars, as well as merging neutron stars., Comment: 13 pages, 7 figures, 4 tables, accepted for publication in MNRAS

A statistical analysis of radial (line-of-sight) 1D-distributions of brightest cluster galaxies (BCGs) within the redshift interval $0.044 \leq z \leq 0.78$ and Mg II absorption-line systems ($0.37 \leq z \leq 2.28$) is carried out. Power spectra and two-point radial correlation functions are calculated. It is found that both radial distributions of spectroscopic redshifts of 52,683 BCGs and 32,840 Mg II absorption systems incorporate similar quasi-periodical components relatively to the comoving distance. Significance of the components exceeds $4\sigma$-level and admits an increase ($\geq 5\sigma$) for some broad subsamples. For the {\Lambda}CDM cosmological model the periodicities correspond to spatial comoving scales ($98 \pm 3$) and ($101 \pm 2$)h$^{-1}$ Mpc, respectively. These quasi-periods turn out to be close to the characteristic scale ($101 \pm 6$)h$^{-1}$Mpc of the quasi-periodical component obtained earlier for the radial distribution of luminous red galaxies (LRGs). On the other hand, the scales are close to the spatial scale corresponding to the baryon acoustic oscillations (BAOs) revealed by many authors at the last decade. Fourier transform phases obtained for the BCGs and LRGs are found to be close, while the phases calculated for the Mg II absorption systems and LRGs are opposite. Discussions of the results in a context of the BAO and large-scale structure characteristic scales are outlined., Comment: 8 pages, 4 figures, accepted by MNRAS

Let D be a set of n disks in the plane. We present a data structure of size O(n) that can compute, for any query point q, the largest disk in D that contains q, in O(log n) time. The structure can be constructed in O(n log^3 n) time. The optimal storage and query time of the structure improve several recent solutions by Augustine et al. and by Kaplan and Sharir., Comment: 15 pages, 9 figures

A statistical analysis of radial distributions of Luminous Red Galaxies (LRGs) from the Sloan Digital Sky Survey (SDSS DR7) catalogue within an interval $0.16 \leq z \leq 0.47$ is carried out. We found that the radial distribution of $\sim$ 106,000 LRGs incorporates a few quasi-periodical components relatively to a variable $\eta$, dimensionless line-of-sight comoving distance calculated for the $\Lambda$CDM cosmological model. The most significant peaks of the power spectra are obtained for two close periodicities corresponding to the spatial comoving scales $(135 \pm 12) h^{-1}$ Mpc and $(101 \pm 6)h^{-1}$ Mpc. The latter one is dominant and consistent with the characteristic scale of the baryon acoustic oscillations. We analyse also the radial distributions of two other selected LRG samples: $\sim$ 33,400 bright LRGs ($-23.2 < M \leq -21.8$) and $\sim$ 60,300 all LRGs within a rectangle region on the sky, and show differences of the quasi-periodical features characteristic for different samples. Being confirmed the results would allow to give preference of the spatial against temporal models which could explain the quasi-periodicities discussed here. As a caveat we show that estimations of the significance levels of the peaks strongly depend on a smoothed radial function (trend) as well as characteristics of random fluctuations., Comment: 12 pages, 8 figures. To be published in ApSS. Comments are welcome

Let {D_x} be a family of unbounded self-adjoint Fredholm operators representing an element of K^1(M). Consider the first two components of the Chern character of the family. It is known that these correspond to the spectral flow of the family and the index gerbe. In this paper we consider descriptions of these classes, both of which are in the spirit of holonomy. These are then studied for families parametrized by a closed 3-manifold. A connection between the multiplicity of the spectrum (and how it varies) and these classes is developed., Comment: References and misprints corrected

The K-theoretic analog of Spanier-Whitehead duality for noncommutative C*-algebras is shown to hold for the Ruelle algebras associated to irreducible Smale spaces. This had previously been proved only for shifts of finite type. Implications of this result as well as relations to the Baum-Connes conjecture and other topics are also considered., Comment: 36 pages

The spatial-temporal distribution of absorption-line systems (ALSs) observed in QSO spectra within the cosmological redshift interval z = 0.0--4.3 is investigated on the base of our updated catalog of absorption systems. We consider so called metallic systems including basically lines of heavy elements. The sample of the data displays regular variations (with amplitudes ~ 15 -- 20%) in the z-distribution of ALSs as well as in the eta-distribution, where eta is a dimensionless line-of-sight comoving distance, relatively to smoother dependences. The eta-distribution reveals the periodicity with period Delta eta = 0.036 +/- 0.002, which corresponds to a spatial characteristic scale (108 +/- 6) h(-1) Mpc or (alternatively) a temporal interval (350 +/- 20) h(-1) Myr for the LambdaCDM cosmological model. We discuss a possibility of a spatial interpretation of the results treating the pattern obtained as a trace of an order imprinted on the galaxy clustering in the early Universe., Comment: AASTeX, 13 pages, with 9 figures, Accepted for publication in Astrophysics & Space Science

We study the thermal structure and evolution of magnetars as cooling neutron stars with a phenomenological heat source in an internal layer. We focus on the effect of magnetized (B > 10^{14} G) non-accreted and accreted outermost envelopes composed of different elements, from iron to hydrogen or helium. We discuss a combined effect of thermal conduction and neutrino emission in the outer neutron star crust and calculate the cooling of magnetars with a dipole magnetic field for various locations of the heat layer, heat rates and magnetic field strengths. Combined effects of strong magnetic fields and light-element composition simplify the interpretation of magnetars in our model: these effects allow one to interpret observations assuming less extreme (therefore, more realistic) heating. Massive magnetars, with fast neutrino cooling in their cores, can have higher thermal surface luminosity., Comment: 13 pages, 10 figures, 5 tables, accepted for publication in MNRAS

In this paper we begin a study of the space of unbounded self-adjoint Fredholm operators as a classifying space for K^{1}(X), with the goal of incorporating the information in the eigenspaces and eigenvalues of the operators. In particular, the role that the multiplicity of eigenvalues plays is developed here., Comment: Typos fixed and application improved

We study a Hopf algebroid, $\calh$, naturally associated to the groupoid $U_n^\delta\ltimes U_n$. We show that classes in the Hopf cyclic cohomology of $\calh$ can be used to define secondary characteristic classes of trivialized flat $U_n$-bundles. For example, there is a cyclic class which corresponds to the universal transgressed Chern character and which gives rise to the continuous part of the $\rho$-invariant of Atiyah-Patodi-Singer. Moreover, these cyclic classes are shown to extend to the K-theory of the associated $C^{*}$-algebra. This point of view gives leads to homotopy invariance results for certain characteristic numbers. In particular, we define a subgroup of the cohomology of a group analogous to the Gelfand-Fuchs classes described by Connes, \cite{connes:transverse}, and show that the higher signatures associated to them are homotopy invariant., Comment: 24 pages

We review current state of neutron star cooling theory and discuss the prospects to constrain the equation of state, neutrino emission and superfluid properties of neutron star cores by comparing the cooling theory with observations of thermal radiation from isolated neutron stars., Comment: 9 pages, 4 figures, 3 tables, to appear in the proceedings of "40 Years of Pulsars" held in Montreal, Canada, August 12-17, 2007, eds. C. Bassa, Z. Wang, A. Cumming, V. Kaspi, AIP, in press (v.2 - minor bibliography corrections)

A statistical analysis of the space-time distribution of absorption-line systems (ALSs) observed in QSO spectra within the cosmological redshift interval $z$=0.0--3.7 is carried out on the base of our catalog of absorption systems (Ryabinkov et al. 2003). We confirm our previous conclusion that the $z$-distribution of absorbing matter contains non-uniform component displaying a pattern of statistically significant alternating maxima (peaks) and minima (dips). Using the wavelet transformation we determine the positions of the maxima and minima and estimate their statistical significance. The positions of the maxima and minima of the $z$-distributions obtained for different celestial hemispheres turn out to be weakly sensitive to orientations of the hemispheres. The data reveal a regularity (quasi-periodicity) of the sequence of the peaks and dips with respect to some rescaling functions of $z$. The same periodicity was found for the one-dimensional correlation function calculated for the sample of the ALSs under investigation. We assume the existence of a regular structure in the distribution of absorption matter, which is not only spatial but also temporal in nature with characteristic time varying within the interval 150--650 Myr for the cosmological model applied., Comment: 28 pages, 10 figures, accepted by MNRAS