The normal cycle TK associated with a convex body K ⊂ Rn is a current which in principle contains complete information about K. It is known that if a sequence of convex bodies Ki, i ∈ N, converges to a convex body K in the Hausdorff metric, then the associated normal cycles TKi converge to TK in the dual flat seminorm. We give a quantitative improvement of this convergence result by providing a...

The local Minkowski tensors are valuations on the space of convex bodies in Euclidean space with values in a space of tensor measures. They generalize at the same time the intrinsic volumes, the curvature measures and the isometry covariant Minkowski tensors that were introduced by McMullen and characterized by Alesker. In analogy to the characterization theorems of Hadwiger and Alesker, we giv...

It is well known that predators can induce morphological changes in some fish: individuals exposed to predation cues increase body depth and the length of spines. We hypothesize that these structures may evolve synergistically, as together, these traits will further enlarge the body dimensions of the fish that gape-limited predators must overcome. We therefore expect that the orientation of the...

this study focused on the effect of teaching collocations on the awareness of two affective dimensions, evaluation and potency dimensions, of deep vocabulary knowledge as well as the general vocabulary knowledge of efl students. sixty intermediate efl female adult learners participated in this study; they were chosen among 90 students through the pet and a general vocabulary knowledge test. the...

The ball hull mapping β associates with each closed bounded convex setK in a Banach space its ball hull β(K), defined as the intersection of all closed balls containing K. We are concerned in this paper with continuity and Lipschitz continuity (with respect to the Hausdorff metric) of the ball hull mapping. It is proved that β is a Lipschitz map in finite dimensional polyhedral spaces. Both pro...

in current societies because of development of technology and information also ever increasing of variety of services and goods and… makes a vast difference in current and last generation's experience and decrease of reproduction of social values in new society. the aim of this study is to consider the difference of life style dimentions in mothers and daughters in yazd and then consider i...

determination of the total body absorbed dose consists of two parts: beta radiation absorbed dose and gamma radiation absorbed dose. the first part is generally determined by clinical data, while the second part has a parameter called absorbed ratio and is determined by computational methods. the monte-carlo computational methods have been shown to be the most suitable in determination of the a...

Let $G$ be a simple connected graph. In this paper, Szeged dimension and PI$_v$ dimension of graph $G$ are introduced. It is proved that if $G$ is a graph of Szeged dimension $1$ then line graph of $G$ is 2-connected. The dimensions of five composite graphs: sum, corona, composition, disjunction and symmetric difference with strongly regular components is computed. Also explicit formulas of Sze...