Partial inversion of the 2D attenuated $ X $-ray transform with data on an arc

<p style='text-indent:20px;'>In two dimensions, we consider the problem of inversion of the attenuated <inline-formula><tex-math id="M2">\begin{document}$ X $\end{document}</tex-math></inline-formula>-ray transform of a compactly supported function from data restricted to lines leaning on a given arc. We provide a method to reconstruct the function on the convex hull of this arc. The attenuation is assumed known. The method of proof uses the Hilbert transform associated with <inline-formula><tex-math id="M3">\begin{document}$ A $\end{document}</tex-math></inline-formula>-analytic functions in the sense of Bukhgeim.</p>

Partial inversion in English

A typical finite clause in English has a single constituent that serves as subject. This constituent precedes the finite verb in non-inverted clauses like simple declarative clauses, follows the finite verb in inverted clauses like polar questions, agrees in person and number with the finite verb and with a tag subject when a tag is present, undergoes subject raising, and so on (Postal 2004). Five constructions violate these generalizations and in the literature have called into question the identity of the subject constituent. In each of these five constructions the finite verb agrees with a following constituent in a declarative clause despite the fact, among others, that the constituent preceding the verb exhibits subject behaviors of the kind identified by Keenan (1976). To the authors’ knowledge, despite intensive analysis of several of these patterns, the group as a whole has not been subject to prior study. The constructions are: Presentational Inversion (e.g., On the porch stood marble pillars), Presentational there (e.g., The earth was now dry, and there grew a tree in the middle of the earth, Deictic Inversion (e.g., Here comes the bus), Existential there (e.g., There’s a big problem here) and Reversed Specificational be (e.g., The only thing we’ve taken back recently are plants). The approach of Sign-Based Construction Grammar (Sag 2012) enables us to establish precisely what all five patterns have in common and what is particular to each, revealing that a constructional, constraint-based approach can extract the correct grammatical generalizations, not only in ‘core’ areas of a grammar, but also in the hard cases, where concepts such as subject, which readily handle the more tractable facts, fail to fit the facts at hand. We see further that the five split-subject patterns, sometimes identified as clausal, yield to a strictly lexical analysis.

Cenozoic tectonic model of the Bohai Bay Basin in China

Modelling results and seismic interpretation illustrate that the Cenozoic evolution of the Bohai Bay Basin (BBB) can be divided into different stages. A transtensional phase during Paleocene – early Oligocene time created NE-trending strike-slip faults and E–W-trending normal faults which were driven roughly by N–S–extension, making an angle of 25° with the strike-slip faults. Seismic data interpretation yields evidence that inversion phases occurred within the NE Xialiaohe Depression of the greater Bohai Bay Basin. This inversion phase is attributed to rotation and partial inversion that occurred during late Oligocene time, leading to formation of inversion structures along the NE part of Tanlu Fault. This episode is attributed to an anticlockwise rotation of the eastern part of the BBB driven by the convergence between the Pacific and Eurasian plates. The tectonic scenario described was simulated in scaled analogue models, which were extended by pulling two basement plates away from each other. Partial inversion was simulated by rotation of one of the plates relative to the other. Model results show many of the features observed in the BBB. Our model results are used to argue that, unlike the two-episode extension and whole-basin inversion models previously proposed for the BBB, a single N–S-aligned extension followed by anticlockwise rotation accounts for the Cenozoic evolution of the BBB and produces some of the structural complexities observed in the basin.

Chronic uterine inversion secondary to submucous fibroid

Nonpuerperal uterine inversion is a rare condition. We describe a case report of chronic inversion secondary to submucous fibroid. A 37 years lady presented with acute retention of urine with submucous fibroid. Diagnosis of partial inversion was made intra operatively and she underwent abdominal hysterectomy. Health Renaissance; September-December 2012; Vol 10 (No.3);242-2431DOI: http://dx.doi.org/10.3126/hren.v10i3.7055