Related papers: The Star Height Hierarchy Vs. The Variable Hierarc…
We prove that there is a structure, indeed a linear ordering, whose degree spectrum is the set of all non-hyperarithmetic degrees. We also show that degree spectra can distinguish measure from category.
Visual photometry, the estimation of stellar brightness by eye, continues to provide valuable data even in this highly-instrumented era. However, the eye-brain system functions differently from electronic sensors and its products can be…
In type theories, universe hierarchies are commonly used to increase the expressive power of the theory while avoiding inconsistencies arising from size issues. There are numerous ways to specify universe hierarchies, and theories may…
Properties of galaxies like their absolute magnitude and their stellar mass content are correlated. These correlations are tighter for close pairs of galaxies, which is called galactic conformity. In hierarchical structure formation…
The spectrum of a first-order logic sentence is the set of natural numbers that are cardinalities of its finite models. In this paper we study the hierarchy of first-order spectra based on the number of variables. It has been conjectured…
The distribution of distances in the star graph $ST_n$, ($1<n\in\Z$), is established, and subsequently a threaded binary tree is obtained that realizes an orientation of $ST_n$ whose levels are given by the distances to the identity…
An explanation for the so-called constrained hierarhies is presented by linking them with the symmetries of the KP hierarchy. While the existence of ordinary symmetries (belonging to the hierarchy) allows one to reduce the KP hierarchy to…
In this paper, we consider the upper bound of the probabilistic star discrepancy based on Hilbert space filling curve sampling. This problem originates from the multivariate integral approximation, but the main result removes the strict…
This study introduces a new "Non-Dimensional" star identification algorithm to reliably identify the stars observed by a wide field-of-view star tracker when the focal length and optical axis offset values are known with poor accuracy. This…
We prove level-by-level upper and lower bounds on the strength of determinacy for finite differences of sets in the hyperarithmetical hierarchy in terms of subsystems of finite-and transfinite-order arithmetic, extending the…
The variational principle for stars with a phase transition has been investigated. The term outside the integral in the expression for the second variation of the total energy of a star is shown to be obtained by passage to the limit from…
A bar-like central feature is commonly observed in both nearby and distant spiral-type galaxies, including the Milky Way. While many methods exist to categorise this morphology, no one method has emerged as the field-wide standard. To…
Scalar-tensor~(ST) theories of gravity are natural phenomenological extensions to general relativity. Although these theories are severely constrained both by solar system experiments and by binary pulsar observations, a large set of ST…
There are different classes of pulsating stars in the H-R diagram. While many of those classes are undisputed, some remain a mystery such as the objects historically called "Maia variables". Whereas the presence of such a class was…
The hanging chain is a very instructive system for demonstrating more advanced methods and ideas for the analysis of normal modes of one-dimensional systems, beyond the standard ordinary (horizontal) string. Accordingly, the normal modes of…
When there are models with clear-cut judgment results for several data points, it is possible that most models exhibit a relationship where if they correctly judge one target, they also correctly judge another target. Conversely, if most…
We discuss the mechanism of cluster formation in hierarchically collapsing molecular clouds. Recent evidence, both observational and numerical, suggests that molecular clouds (MCs) may be undergoing global, hierarchical gravitational…
A new approach to the construction of general persistent polyhierarchical classifications is proposed. It is based on implicit description of category polyhierarchy by a generating polyhierarchy of classification criteria. Similarly to…
Young stellar groupings and clusters have hierarchical patterns ranging from flocculent spiral arms and star complexes on the largest scale to OB associations, OB subgroups, small loose groups, clusters and cluster subclumps on the smallest…
The structure of cloud complexes appears to be well described by a "tree structure" representation when the image is partitioned into "clouds". In this representation, the parent-child relationships are assigned according to containment.…