Skymaps of observables of three-dimensional magnetohydrodynamic astrosphere models

Context. Three-dimensional models of astrospheres have recently become of interest. However, comparisons between these models and observations are non-trivial because of the two-dimensional nature of observations. Aims. By projecting selected physical values of three-dimensional models of astrospheres onto the surface of a sphere that is centred on a virtual all-sky observer, these models can be compared to observational data in different observables: the column density, bremsstrahlung flux, rotation measure, Hα flux, and synchrotron or cyclotron flux. Methods. Projections were calculated by rotating and moving the astrosphere model to the desired position and orientation and by then computing the value of a given patch on the sphere by a modified line-of-sight integration. Contributions to the selected observable made by all model cells that are connected to the patch by the line of sight in question were taken into account. Results. When the model produces a bow shock, a distinct parabolic structure produced by the outer astrosheath can be seen in every observable of the projection, the exact shape depending on the orientations of the line of sight and the stellar motion. Of all four examined astrosphere models, only that of λ Cephei shows fluxes that are higher than current observational thresholds. This is due to the strong stellar wind and interstellar inflow of the λ Cephei model.

Parabolic Structure of Essay/Short Parable Story “Za Hotar” by Olha Kobylianska

The paper deals with the story “Za hotar” (“Beyond the Boundary”) by Olha Kobylianska from the point of view of modernist sacral aesthetics, since, as it has been observed, its architectonic structure comprises the parable of the Good Samaritan. It is proven that the relationship between the parable and the story is displayed at different levels of the literary text. The plot of the story “Za hotar” has many obvious parallels with the Christ’s parable, down to the coincidences in the image of a merciless priest. The modernist sacral perspective of the literary work by Olha Kobylianska makes it possible not only to observe the presence of hidden signs of the New Testament parable, but also to interpret the possibility of a genre shift. This procedure allows denoting this literary work not as an essay, but as a short story, since the parable of the Good Samaritan has a characteristic feature of a short story (its main idea is represented in showing mercy by one of the Samaritans, who in biblical times were considered as people lacking any sympathy towards strangers). The work by Olha Kobylianska provides an extremely powerful and philosophically deep insight. The plot includes the death of a daughter. On the one hand, it is perceived as quite substantiated (the child ran outdoors undressed in winter), but in terms of the mystical perspective it becomes a symbol of Christian mercy, or even a Christian self-sacrifice. Thus, the literary work “Za hotar” by Olha Kobylianska is based on the architectonical ground of the parable about the Good Samaritan. From the realistic perspective it may be interpreted as an essay revealing the mental traditions, everyday life, ideological foundations of the Bukovynian village contemporary for the writer. Although it becomes a parable in the modernist sacral perspective, which hides the fundamental gospel basis behind a realistic plot.

Parabolic Higgs Bundles for Real Reductive Lie Groups

This chapter explains the correspondence between local systems on a punctured Riemann surface with the structure group being a real reductive Lie group G, and parabolic G-Higgs bundles. The chapter describes the objects involved in this correspondence, taking some time to motivate them by recalling the definitions of G-Higgs bundles without parabolic structure and of parabolic vector bundles. Finally, it explains the relevant polystability condition and the correspondence between local systems and Higgs bundles.

Parabolic dictionary learning for seismic wavefield reconstruction across the streamers

Dictionary learning (DL) methods are effective tools to automatically find a sparse representation of a data set. They train a set of basis vectors on the data to capture the morphology of the redundant signals. The basis vectors are called atoms, and the set is referred to as the dictionary. This dictionary can be used to represent the data in a sparse manner with a linear combination of a few of its atoms. In conventional DL, the atoms are unstructured and are only numerically defined over a grid that has the same sampling as the data. Consequently, the atoms are unknown away from this sampling grid, and a sparse representation of the data in the dictionary domain is not sufficient information to interpolate the data. To overcome this limitation, we have developed a DL method called parabolic DL, in which each learned atom is constrained to represent an elementary waveform that has a constant amplitude along a parabolic traveltime moveout. The parabolic structure is consistent with the physics inherent to the seismic wavefield and can be used to easily interpolate or extrapolate the atoms. Hence, we have developed a parabolic DL-based process to interpolate and regularize seismic data. Briefly, it consists of learning a parabolic dictionary from the data, finding a sparse representation of the data in the dictionary domain, interpolating the dictionary atoms over the desired grid, and, finally, taking the sparse representation of the data in the interpolated dictionary domain. We examine three characteristics of this method, i.e., the parabolic structure, the sparsity promotion, and the adaptation to the data, and we conclude that they strengthen robustness to noise and to aliasing and that they increase the accuracy of the interpolation. For both synthetic and field data sets, we have successful seismic wavefield reconstructions across the streamers for typical 3D acquisition geometries.

W cieniu mistrza. O etiudzie Stanisława Latałły Święta rodzina

The text contains an analysis of Stanisław Latałło’s short film The Holy Family, shot at the ŁódźFilm School in the autumn of 1969. The author reconstructs the parabolic structure of this work and reveals the historical context of its realization, tied to the events of March 1968.

Dynamics and Modal Analysis of Gyroelastic Body With Variable Speed Control Moment Gyroscopes

Gyroelastic body refers to a flexible structure with a distribution of stored angular momentum (called gyricity). In previous studies, it was assumed that each volume element of the structure possesses an infinitesimal spinning rotor so that the distribution of the gyricity is continuous. However, the momentum devices must be discretely distributed in engineering applications; therefore, this paper studies the gyroelastic body formed by directly mounting a set of variable speed control moment gyroscopes (CMGs) on the flexible structure. The detailed dynamics of the CMGs is incorporated to capture the interactions between the CMGs and the structure. The gyroelastic modes and pseudorigid modes are discussed based on the linearized mathematical model. The examples of a gyroelastic beam and a gyroelastic parabolic structure demonstrate several involved concepts and properties.

Local identification of spherical buildings and finite simple groups of Lie type

We give a short proof of the uniqueness of finite spherical buildings of rank at least 3 in terms of the structure of the rank 2 residues and use this result to prove a result making it possible to identify an arbitrary finite group of Lie type from knowledge of its “parabolic structure” alone. Our proof also involves a connection between loops, “Latin chamber systems” and buildings.

SOME INDEX FORMULAE ON THE MODULI SPACE OF STABLE PARABOLIC VECTOR BUNDLES

We study natural families of $\bar {\partial } $-operators on the moduli space of stable parabolic vector bundles. Applying a families index theorem for hyperbolic cusp operators from our previous work, we find formulae for the Chern characters of the associated index bundles. The contributions from the cusps are explicitly expressed in terms of the Chern characters of natural vector bundles related to the parabolic structure. We show that our result implies formulae for the Chern classes of the associated determinant bundles consistent with a result of Takhtajan and Zograf.

Configuration of a Thin Circular Membrane Subject to Solar Pressure

This paper addresses the preliminary design of a parabolic structure suitable for specific space applications, such as in solar power collector systems, which relies upon the sole use of an initially flat circular membrane rigidly constrained across its perimeter. In particular, the possibility for this concept to make use of solar pressure as a means of obtaining the intended parabolic curvature is explored. Assuming the membrane´s film as an ideally reflecting surface, parametric studies are conducted in order to determine several parameters of interest as functions of its radius and thickness. In order to do so, a set of numerical simulations are carried out using the finite element code ABAQUS®. It is shown that the shape of the deformed membrane is very close to parabolic, therefore being capable of concentrating sunlight power over a focal plane.

The Essential Dimension of Stacks of Parabolic Vector Bundles over Curves

We find upper bounds on the essential dimension of the moduli stack of parabolic vector bundles over a curve. When there is no parabolic structure, we improve the known upper bound on the essential dimension of the usual moduli stack. Our calculations also give lower bounds on the essential dimension of the semistable locus inside the moduli stack of vector bundles of rank r and degree d without parabolic structure.