A Decision Algorithm for Linear Isomorphism of Types with Complexity Cn(log2(n))

It is known that ordinary isomorphisms (associativity and commutativityof "times", isomorphisms for "times" unit and currying)provide a complete axiomatisation for linear isomorphism of types.One of the reasons to consider linear isomorphism of types instead ofordinary isomorphism was that better complexity could be expected.Meanwhile, no upper bounds reasonably close to linear were obtained.We describe an algorithm deciding if two types are linearly isomorphicwith complexity Cn(log2(n))

Russian-Golden Horde Borderl and on the Oka-Don Plain

The paper presents an overview of the results of studies of written and archaeological sources related to a section of the border territory between the Ryazan Principality and the Golden Horde in the 13th–15th centuries. Based on the sources, it is concluded that there is a particular buffer zone territory in the southern part of the Oka-Don Plain, which was named “Chervlyony Yar”. It was identified as a rather vast (from the Khopyor to the Don) territory with an ethnically diverse population (Orthodox Russians, Tatars, Cumans, possibly Mordovians) living according to the customs of free feudal independent communities with elements of self-government in relative dependence on the Golden Horde. Its economic foundation was the mutually beneficial cooperation of semi-nomadic cattle farmers who roamed the steppe interfluves, and the population living in the riverine forest belts, whose economy made up for the underdeveloped sectors of the nomadic cattle farmers, in particular, haymaking and certain types of crafts. Over seventy archaeological sites of various types have presently been discovered in the area

Mineral Resources of the Ocean: a Pragmatical Reality of the Foreseeable Future or Geopolitical Phantom

Изложено состояние изученности твердых полезных ископаемых Мирового океана (ЖМК, КМК, ГПС), дана оценка возможного вклада в минерально-сырьевую базу страны. Отмечается, что проблема минеральных ресурсов океана уже в обозримом будущем может иметь не только геополитическое, но и реальное практическое значение.The study is dedicated to the state of knowledge of the oceanic minerals (FMN, CMC, DSPS) and estimation of their possible contribution to the raw materials base of the Country. The problem of oceanic mineral resources may have not only geopolitical, but also practical value in the foreseeable futur

Commensurate lock-in and incommensurate supersolid phases of hardcore bosons on anisotropic triangular lattices

We investigate the interplay between commensurate lock-in and incommensurate supersolid phases of the hardcore bosons at half-filling with anisotropic nearest-neighbor hopping and repulsive interactions on triangular lattice. We use numerical quantum and variational Monte Carlo as well as analytical Schwinger boson mean-field analysis to establish the ground states and phase diagram. It is shown that, for finite size systems, there exist a series of jumps between different supersolid phases as the anisotropy parameter is changed. The density ordering wavevectors are locked to commensurate values and jump between adjacent supersolids. In the thermodynamic limit, however, the magnitude of these jumps vanishes leading to a continuous set of novel incommensurate supersoild phases.Comment: 5 pages, 5 figures, added new results, changed title and conclusio

SDSS J080434.20+510349.2: Eclipsing WZ Sge-Type Dwarf Nova with Multiple Rebrightenings

We observed the 2006 superoutburst of SDSS J080434.20+510349.2 during its plateau phase, rebrightening phase, and post-superoutburst final decline. We found that this object is a grazing eclipsing system with a period of 0.0590048(2) d. Well-defined eclipses were only observed during the late stage of the superoutburst plateau and the depth decreased during the subsequent stages. We determined the superhump period during the superoutburst plateau to be 0.059539(11) d, giving a fractional superhump excess of 0.90(2)%. During the rebrightening and post-superoutburst phases, persisting superhumps with periods longer than those of superhumps during the plateau phase: 0.059632(6) during the rebrightening phase and 0.05969(4) d during the final fading. This phenomenon is very well in line with the previously known long-period "late superhumps" in GW Lib, V455 And and WZ Sge. The amplitudes of orbital humps between different states of rebrightenings suggest that these humps do not arise from the classical hot spot, but are more likely a result of projection effect in a high-inclination system. There was no clear evidence for the enhanced hot spot during the rebrightening phase. We also studied previously reported "mini-outbursts" in the quiescent state and found evidence that superhumps were transiently excited during these mini-outbursts. The presence of grazing eclipses and distinct multiple rebrightenings in SDSS J080434.20+510349.2 would provide a unique opportunity to understanding the mechanism of rebrightenings in WZ Sge-type dwarf novae.Comment: 14 pages, 12 figures, PASJ accepte

Integrable boundary interaction in 3D target space: the "pillow-brane" model

We propose a model of boundary interaction, with three-dimensional target space, and the boundary values of the field {\vec X}\in R^3 constrained to lay on a two-dimensional surface of the "pillow" shape. We argue that the model is integrable, and suggest that its exact solution is described in terms of certain linear ordinary differential equation.Comment: 28 pages, 4 figure

Local anisotropy and giant enhancement of local electromagnetic fields in fractal aggregates of metal nanoparticles

We have shown within the quasistatic approximation that the giant fluctuations of local electromagnetic field in random fractal aggregates of silver nanospheres are strongly correlated with a local anisotropy factor S which is defined in this paper. The latter is a purely geometrical parameter which characterizes the deviation of local environment of a given nanosphere in an aggregate from spherical symmetry. Therefore, it is possible to predict the sites with anomalously large local fields in an aggregate without explicitly solving the electromagnetic problem. We have also demonstrated that the average (over nanospheres) value of S does not depend noticeably on the fractal dimension D, except when D approaches the trivial limit D=3. In this case, as one can expect, the average local environment becomes spherically symmetrical and S approaches zero. This corresponds to the well-known fact that in trivial aggregates fluctuations of local electromagnetic fields are much weaker than in fractal aggregates. Thus, we find that, within the quasistatics, the large-scale geometry does not have a significant impact on local electromagnetic responses in nanoaggregates in a wide range of fractal dimensions. However, this prediction is expected to be not correct in aggregates which are sufficiently large for the intermediate- and radiation-zone interaction of individual nanospheres to become important.Comment: 9 pages 9 figures. No revisions from previous version; only figure layout is change

Application of resonance functions in estimating the parameters of interwell zones

It is shown that the use of force resonance leads to the effect of “shaking” the formation, followed by breaking up the film oil and involving it in the further filtration process. For the first time in oilfield geophysics, the concept of passive noise-metering method is justified for monitoring oil and gas deposit development by measuring the quality factor of the contours in the point areas of formation development channels in interwell zones. It is established that determining the depth of modulation for the reactive substitution parameter of the linear FDC chain is crucial not only for determining the parametric excitation in FDC attenuation systems, but also without attenuation in the metrological support for the analysis of petrophysical properties of rock samples from the wells. It is shown that based on the method of complex amplitudes (for formation pressure current, differential flow rates, impedance), different families of resonance curves can be plotted: displacement amplitudes (for differential flow rates on the piezocapacity of the studied formation section), velocities (amplitudes of formation pressure current) and accelerations (amplitudes of differential flow rates on the linear piezoinductivity of the FDC section). The use of predicted permeability and porosity properties of the reservoir with its continuous regulation leads to increased accuracy of isolation in each subsequent sub-cycle of new segment formation in the FDC trajectories, which contributes to a more complete development of productive hydrocarbon deposits and increases the reliability of prediction for development indicators

Potential of sub-THz-wave generation in Li2B4O7 nonlinear crystal at room and cryogenic temperatures

Due to their high optical damage threshold, borate crystals can be used for the efficient nonlinear down-conversion of terawatt laser radiation into the terahertz (THz) frequency range of the electromagnetic spectrum. In this work, we carried out a thorough study of the terahertz optical properties of the lithium tetraborate crystal (Li2B4O7; LB4) at 295 and 77 K. Approximating the terahertz refractive index in the form of Sellmeier’s equations, we assessed the possibility of converting the radiation of widespread high-power laser sources with wavelengths of 1064 and 800 nm, as well as their second and third harmonics, into the THz range. It was found that four out of eight types of three-wave mixing processes are possible. The conditions for collinear phase matching were fulfilled only for the o - e -o type of interaction, while cooling the crystal to 77 K did not practically affect the phase-matching curves. However, a noticeable increase of birefringence in the THz range with cooling (from 0.12 to 0.16) led to an increase in the coherence length for o-o-e and e-e-e types of interaction, which are potentially attractive for the down-conversion of ultrashort laser pulses

Security challenges of small cell as a service in virtualized mobile edge computing environments

Research on next-generation 5G wireless networks is currently attracting a lot of attention in both academia and industry. While 5G development and standardization activities are still at their early stage, it is widely acknowledged that 5G systems are going to extensively rely on dense small cell deployments, which would exploit infrastructure and network functions virtualization (NFV), and push the network intelligence towards network edges by embracing the concept of mobile edge computing (MEC). As security will be a fundamental enabling factor of small cell as a service (SCaaS) in 5G networks, we present the most prominent threats and vulnerabilities against a broad range of targets. As far as the related work is concerned, to the best of our knowledge, this paper is the first to investigate security challenges at the intersection of SCaaS, NFV, and MEC. It is also the first paper that proposes a set of criteria to facilitate a clear and effective taxonomy of security challenges of main elements of 5G networks. Our analysis can serve as a staring point towards the development of appropriate 5G security solutions. These will have crucial effect on legal and regulatory frameworks as well as on decisions of businesses, governments, and end-users