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Structural behaviour of masonry in monumental buildings
Published in George G. Penelis, Gregory G. Penelis, Structural Restoration of Masonry Monuments, 2020
George G. Penelis, Gregory G. Penelis
Finally, it is of some purpose to analyse the way of transmission of loads from the base of the ring to the base of the drum, in case, of course, a drum exists. In circular buildings (rotundas), which consist of the dome, the ring and the drum only, the last is foreseen with such a thickness, so that the thrust line always passes through the third of the cross section under the assumption of zero ring forces. A characteristic building of this type in Greece is the Rotunda of Thessaloniki, where it has been proven that the thrust line passes through the base of the drum almost through its centre line (Figure 4.26). This was accomplished by choosing for the drum a ratio of height to thickness equal to 2.8; that is, for a height of the drum of 18.0 m, its thickness was designed 6.25 m. In a cross-domed church, where the dome is usually very large, the drum is kept very low and coincides with the ring (Figure 4.27). Openings are provided all around the ring for lighting the building as the tensile forces at the ring are not necessary for the equilibrium of the system.
Telescopes
Published in Daniel Malacara-Hernández, Brian J. Thompson, Fundamentals and Basic Optical Instruments, 2017
Marija Strojnik, Maureen S. Kirk
In Figure 11.36c, we see a layout with a single central segment missing, the actual Keck configuration, while in Figure 11.36d, the first ring of mirrors is additionally missing. The six remaining mirrors are placed on the outside of the configuration shown in Figure 11.36c. There are three potential benefits realized with this modification. In both figures, we observe the first zero ring that defines the resolution of the telescope, corresponding to a hexagonal shape of the aperture. The diameter of the first zero ring, representing the telescope resolution in Figure 11.36d is smaller than that in Figure 11.36c due to its larger outer diameter and larger inner hole. Additionally, the placement of six segments on the outside increases the diameter of the telescope. Therefore, the cutoff frequency is larger along these directions. If the segmented configuration is parabolic or hyperbolic in cross-section, then the curvature of the segment decreases with the distance from the apex of the primary mirror.
New Hydroprocessing Catalysts Prepared from Molecular Complexes
Published in Michael C. Oballa, Stuart S. Shih, Catalytic Hydroprocessing of Petroleum and Distillates, 2020
Clay-gel separation (ASTM D2007) was used to separate the liquid product into polars, aromatics, and saturates. Following this, the saturate and aromatic fractions were characterized by mass spectrometry (ASTM D2786-71 for saturates, ASTMD3239-76 for aromatics) according to the ring numbers (Paraffins are classified as zero-ring naphthenes). These procedures provided concentrations of seven naphthenic ring-number fractions and 21 aromatic ring number fractions. The latter also included three thiopheno-aromatic fractions (benzothiophenes, dibenzothiophenes, and benzonaphthothiophenes).
Topological and threading effects in polydisperse ring polymer solutions
Published in Molecular Physics, 2021
Iurii Chubak, Christos N. Likos, Jan Smrek
Another novel point in this work is the quantification of the threading contributions to the effective potential. For the finite lengths we simulated, the states that are not threading despite zero ring separation constitute a small, but finite fraction of all possible states, as signified by the barrier of about in Figure 7. Whether this remains finite also in the limit remains a yet another interesting open question. Furthermore, it is interesting to estimate the impact of threading on the effective interaction in dilute systems of other topologically restricted polymer architectures, like tadpoles [33] or catenanes [45–47]. Finally, these results, in dilute conditions, are the first steps towards a better understanding of the threading constraints in dense systems. There, the understanding of the threading costs hinders the construction of an equilibrated melt of rings from first principles [27]. This would further enable the development of appropriate scaling theory that would take threading explicitly into account, allowing for a reliable predictions on the existence of an equilibrium topological glass.
General remainder theorem and factor theorem for polynomials over non-commutative coefficient rings
Published in International Journal of Mathematical Education in Science and Technology, 2020
A. Cuida, F. Laudano, E. Martinez-Moro
In abstract algebra, a division ring (cf. Lam & Leroy, 1988; Martínez-Penas, 2018), also called a skew field (cf. Smits, 1968), is a ring in which division is possible. Specifically, it is a non-zero ring in which every non-zero element a has a multiplicative inverse, i.e. an element x with ax = xa = 1. Stated differently, a ring is a division ring if and only if the group of units equals the set of all non-zero elements. A division ring is a type of non-commutative ring.