Some random versions of deterministic fixed point theorems for condensing and nonexpansive operators are obtained.

abstract introductiion. there are a lot of edentulous patients who need complete dentures in any society. one of the most important problems of edentulous patients is remaining dental lesions. atrophy of maxillary or mandibular bone, infections abcesses, tumors and so on are among some other problems. in this study we tried to evaluate the panoramic radiography in order to detect these problems...

Under a wide variety of conditions, the addition of condensing agents to dilute solutions of random-coil DNA gives rise to highly compact particles that are toroidal in shape. The size of these condensates is remarkably constant and is largely independent of DNA molecular weight and basepair sequence, and of the nature of condensing agent (e.g., multivalent cation, polymers, or added cosolvent)...

The authors used the computational tool Coh-Metrix to examine expert writers’ paraphrases and in particular, how experts paraphrase text passages using condensing strategies. The overarching goal of this study was to develop machine learning algorithms to aid in the automatic detection of paraphrases and paraphrase types. To this end, three experts were instructed to paraphrase by condensing a ...