We discuss the total collision singularities of gravitational N-body problem on shape space. Shape space is relational configuration system obtained by quotienting ordinary with respect to similarity group translations, rotations, and scalings. For zero-energy gravitating system, dynamics can be constructed explicitly points collision, which are central zero momenta, analyzed in detail. It turn...

Car body lightening and crashworthiness are two important objectives of car design. Due to their excellent performance, composite materials are extensively used in the car industries. In addition, reducing the weight of vehicle is effective in decreasing the fuel consumption. Hat shape energy absorber is used in car’s doors for side impact protection. The aim of these numerical models and expe...

Ontogenetic changes in body shape and its associated allometry were studied in the Blacktail Shiner, Cyprinella venusta, using geometric morphometric methods. We used a single, large sample (n 5 397; 182 males, 215 females), collected in Catahoula Creek, Jourdan River drainage, Hancock County, Mississippi. Ten body landmarks were digitized from each specimen, which yielded partial warp scores t...

Recent developments in the study of shape-invariant Hamiltonians are briefly summarized. Relations between certain exactly solvable problems in many-body physics and shape-invariance are explored. Connection between Gaudin algebras and supersymmet-ric quantum mechanics is pointed out.

Detailed statistical models of body size and shape are valuable for wide range of statistical analyses. Most body shape models represent a single posture, usually standing. Previous efforts to model both posture and body shape have parameterized posture using joint angles. This paper presents a statistical model of body shape in supported seated postures using a posture measured derived from su...