We prove that there exists a left-c.e. Polish space not homeomorphic to any right-c.e. space. Combined with some other recent works (to be cited), this finishes the task of comparing all classical notions of effective presentability of Polish spaces that frequently occur in the literature up to homeomorphism.

We employ our techniques to provide a new, relatively straightforward construction of a computable Polish space K not homeomorphic to any computably compact space. We also show that the Banach space $C(K;\mathbb {R})$ has a computable Banach copy; this gives a negative answer to a question raised by McNicholl.

We also give an example of a space that has both a left-c.e. and a right-c.e. presentation, yet it is not homeomorphic to any computable Polish space. In addition, we provide an example of a $\Delta ^0_2$ Polish space that lacks both a left-c.e. and a right-c.e. copy, up to homeomorphism.

A comparative analysis of sub-THz emission of stellar flares from red dwarfs has been carried out. ALMA observations indicate that the sub-THz emission flux from stellar flares with a duration of 10 s is an order of magnitude greater than for solar flares. The sub-THz emission is linearly polarized and decreases with frequency. The degree of polarization can reach tens of percent. We show that these types of spectrum slopes and linear polarization can be caused by the synchrotron emission of ultrarelativistic electrons. The origin of the observed relationships between sub-THz, low frequency radio, and X-ray emissions of stellar flares are discussed.

We investigate what it means for a (Hausdorff, second-countable) topological group to be computable. We compare several potential definitions based on classical notions in the literature. We relate these notions with the well-established definitions of effective presentability for discrete and profinite groups, and compare our results with similar results in computable topology.

We give a systematic technical exposition of the foundations of the theory of computably compact metric spaces. We discover several new characterizations of computable compactness and apply these characterizations to prove new results in computable analysis and effective topology. We also apply the technique of computable compactness to give new and less combinatorially involved proofs of known results from the literature. Some of these results do not have computable compactness or compact spaces in their statements, and thus these applications are not necessarily direct or expected.

When two waves interact within a rock sample, the interaction strength depends strongly on the sample’s microstructural properties, including the orientation of the sample layering. The study that established this dependence on layering speculated that the differences were caused by cracks aligned with the layers in the sample. To test this, we applied a uniaxial load to similar samples of Crab Orchard Sandstone and measured the nonlinear interaction as a function of the applied load and layer orientation. We show that the dependence of the nonlinear signal changes on applied load is exponential, with a characteristic load of 11.4–12.5 MPa that is independent of sample orientation and probe wavetype (P or S); this value agrees with results from the literature, but does not support the cracks hypothesis.

The main aim of this paper is to develop an optimal partial hedging strategy that minimises an investor’s shortfall subject to an initial wealth constraint. The risk criterion we employ is a robust tail risk measure called Range Value-at-Risk (RVaR) which belongs to a wider class of distortion risk measures and contains the well-known measures VaR and CVaR as important limiting cases. Explicit forms of such RVaR-based optimal hedging strategies are derived. In addition, we provide a numerical example to demonstrate how to apply this more comprehensive methodology of partial hedging in the area of mixed finance/insurance contracts in the market with long-range dependence.

We present and briefly discuss results of several studies of the source J2102+6015 with tentatively defined redshift z = 4.575 which demonstrates unusual properties in imaging and astrometric VLBI observations. Its properties might be considered as indications on the supermassive black hole binary which can be considered as a so far rare example of a high-redshift source of known electromagnetic and, possibly, predictable gravitational wave emissions.

Local fluctuations of electrostatic potential, poloidal electric field, magnetic potential and electron density are simultaneously measured in the T-10 tokamak by a heavy ion beam probe (HIBP) having a five-slit energy analyser, which allows an estimate of the turbulent particle flux and $\boldsymbol {E}\times \boldsymbol {B}$ rotation velocity in the off-minor-axis gradient zone of the toroidal plasma column. The high spatial and temporal resolution of the modern multichannel HIBP makes it an effective tool to study plasma oscillations. Motivated by previous work that has documented time-resolved interactions between measured plasma parameters using correlation analysis (coherence of $E_{\textrm {pol}}$ and density $n_e$, and cross-phase), a new result from bicorrelation analysis (bicoherence of magnetic potential $A_\zeta$ and density $n_e$, and biphase) is reported for documenting the evidence of wave–wave coupling and energy transfer associated with the interaction between geodesic acoustic modes (GAM) and broadband, quasi-coherent modes.

The modern Very Long Baseline Interferometry (VLBI) relativistic delay model, as documented in the IERS Conventions, refers to the time epoch when the signal passes one of two stations of an interferometer baseline (selected arbitrarily from the pair of stations and called the ‘reference station’ or ‘station 1’). This model consists of the previous correlation procedure used before the year 2002. However, since 2002 a new correlation procedure that produces the VLBI group delays referring to the time epoch of signal passage at the geocenter has been used. A corresponding correction to the conventional VLBI model delay has to be introduced. However, this correction has not been thoroughly presented in peer reviewed journals, and different approaches are used at the correlators to calculate the final group delays officially published in the IVS database. This may cause an inconsistency up to 6 ps for ground-based VLBI experiments between the group delay obtained by the correlator and the geometrical model delay from the IERS Conventions used in data analysis software. Moreover, a miscalculation of the signal arrival moment to the ‘reference station’ could result in a larger modelling error (up to 50 ps). The paper presents the justification of the correction due to transition between two epochs elaborated from the Lorentz transformation and the approach to model the uncertainty of the calculation of the signal arrival moment. Both changes are particularly essential for upcoming broadband technology geodetic VLBI observations.

We study computable Polish spaces and Polish groups up to homeomorphism. We prove a natural effective analogy of Stone duality, and we also develop an effective definability technique which works up to homeomorphism. As an application, we show that there is a $\Delta ^0_2$ Polish space not homeomorphic to a computable one. We apply our techniques to build, for any computable ordinal $\alpha $, an effectively closed set not homeomorphic to any $0^{(\alpha )}$-computable Polish space; this answers a question of Nies. We also prove analogous results for compact Polish groups and locally path-connected spaces.

We describe punctual categoricity in several natural classes, including binary relational structures and mono-unary functional structures. We prove that every punctually categorical structure in a finite unary language is ${\text {PA}}(0')$-categorical, and we show that this upper bound is tight. We also construct an example of a punctually categorical structure whose degree of categoricity is $0''$. We also prove that, with a bit of work, the latter result can be pushed beyond $\Delta ^1_1$, thus showing that punctually categorical structures can possess arbitrarily complex automorphism orbits.

As a consequence, it follows that binary relational structures and unary structures are not universal with respect to primitive recursive interpretations; equivalently, in these classes every rich enough interpretation technique must necessarily involve unbounded existential quantification or infinite disjunction. In contrast, it is well-known that both classes are universal for Turing computability.

Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems.

Mingantu Spectral Radioheliograph (MUSER) is an aperture-synthesis imaging telescope, dedicated to observe the Sun, operating on multiple frequencies in dm to cm range. The ability of MUSER to get images and measure Stokes I and V parameters simultaneously at many frequencies in a wide band is of fundamental importance. It allows one to approach/solve such important problems as measuring the strength, geometry and dynamics of magnetic field at coronal heights. Here we consider some of the recently developed radio physics methods to be used for solving the problems. These methods allow us to obtain information that is unattainable in other areas of the electromagnetic spectrum.

A structure is automatic if its domain, functions, and relations are all regular languages. Using the fact that every automatic structure is decidable, in the literature many decision problems have been solved by giving an automatic presentation of a particular structure. Khoussainov and Nerode asked whether there is some way to tell whether a structure has, or does not have, an automatic presentation. We answer this question by showing that the set of Turing machines that represent automata-presentable structures is ${\rm{\Sigma }}_1^1 $-complete. We also use similar methods to show that there is no reasonable characterisation of the structures with a polynomial-time presentation in the sense of Nerode and Remmel.

The survey contains a detailed discussion of methods and results in the new emerging area of online “punctual” structure theory. We also state several open problems.

Spongolite from the State of Mato Grosso do Sul, Brazil, contains the remains of fossil sponges and hollow needles or microcapillaries with uniform surfaces. The central tunnels are ∼1/10 to 1/2 of the cylinder's diameter. The material is essentially X-ray amorphous though it contains small amounts of orthosilicic acids. The other main elements were Ti and Fe. Spongolite may have uses as a sorbent, as a bioavailable silicon source or, after blending with glass waste, it can be used in the fabrication of lightweight products having a closed-cell structure, potentially useful as an industrial insulator.

Using methods from computable analysis, we establish a new connection between two seemingly distant areas of logic: computable structure theory and invariant descriptive set theory. We extend several fundamental results of computable structure theory to the more general setting of topological group actions. As we will see, the usual action of ${S_\infty }$ on the space of structures in a given language is effective in a certain algorithmic sense that we need, and ${S_\infty }$ itself carries a natural computability structure (to be defined). Among other results, we give a sufficient condition for an orbit under effective ${\cal G}$-action of a computable Polish ${\cal G}$ to split into infinitely many disjoint effective orbits. Our results are not only more general than the respective results in computable structure theory, but they also tend to have proofs different from (and sometimes simpler than) the previously known proofs of the respective prototype results.