It is known that a typical n-dimensional convex body, in the Baire category sense, has the property that its set of umbilics of zero curvature has full measure in the boundary of the body. We show that a typical convex body has in addition the following properties. The spherical image of the set of umbilics of zero curvature has measure zero. The set of umbilics of infinite curvature is dense i...

‎‎The equivalence relation isoclinism partitions the class of all pairs of groups‎ ‎into families‎. ‎In this paper‎, ‎a complete classification of the set of all pairs $(G,G')$ is established‏‎,‎ whenever‎ $G$ is a $p$-group of order at most $p^5‎‏$‎ and ‎$p$ is a prime number greater than 3. Moreover‎, ‎the classification of pairs $(H,H')$ for extra special $p$-groups $H$ is also given.

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A 38-year-old male presented to our hospital with the chief complaint of chronic cough. Eight years previously he was diagnosed with cilioretinal malignant melanoma and underwent left ophthalmectomy. On chest CT, pleural effusion and diffuse thickening of left pleura were suspected (Picture 1). The differential diagnosis included mesothlioma and metastatic melanoma. In thoracoscopic findings mu...