This paper presents a new algorithm for computing the hit point and normal of a ray and a general convex object. The algorithm is loosely based on the the Gilbert-Johnson-Keerthi algorithm for computing the distance between convex objects in the sense that it is applicable to the same family of convex objects and uses the same subalgorithm for computing the closest point of a simplex. Since thi...

We determine the cases of equality in the Riesz rearrangement inequality ZZ f (y)g(x ? y)h(x) dydx ZZ f (y)g (x ? y)h (x) dydx where f , g , and h are the spherically decreasing rearrangements of the functions f , g, and h on R n. We apply our results to the weak Young inequality. The Riesz rearrangement inequality states that the functional I(f; g; h) := Z f gh dx = ZZ f(y)g(x?y)h(x) dydx (1:1...

Asexual reproduction is one of the most important traits in the evolutionary history of corals. No real-time observations of asexual reproduction in azooxanthellate solitary scleractinian corals have been conducted to date. Here, we describe previously unknown aspects of asexual reproduction by using Truncatoflabellum spheniscus (Family Flabellidae) based on observations of transverse division ...

Data logics are logical formalisms that are used to specify properties on structures equipped with data (data words, data trees, runs from counter systems, timed words, etc.). In this survey talk, we shall see how satisfiability problems for such data logics are related to reachability problems for counter systems (including counter automata with errors, vector addition systems with states, etc...