Ultralight, Strong, Three-Dimensional SiC Structures

Dynamic Analysis of Three Dimensional Asymmetric Isolated Structures

Dynamic Analysis of Three Dimensional Asymmetric Isolated Structures

Three Dimensional DNA Structures in

We show that 3-dimensional graph structures can be used for solving computational problems with DNA molecules. Vertex building blocks consisting of k-armed (k = 3 or k = 4) branched junction molecules are used to form graphs. We present procedures for the 3-SAT and 3-vertex-colorability problems. Construction of one graph structure (in many copies) is suucient to determine the solution to the p...

Three-dimensional strong convexity and visibility

We define the notions of strong convexity and strong visibility. These notions generalize standard convexity and visibility, as well as several types of nontraditional convexity, such as iso-oriented rectangles and C-oriented polygons. We explore the properties of strong convexity and strong visibility in two and three dimensions. In particular, we establish analogs of the following properties ...

Strong approximations of three-dimensional Wiener sausages

In this paper we prove that the centered three-dimensional Wiener sausage can be strongly approximated by a one-dimensional Brownian motion running at a suitable time clock. The strong approximation gives all possible laws of iterated logarithm as well as the convergence in law in terms of process for the normalized Wiener sausage. The proof relies on Le Gall [10]’s fine L-norm estimates betwee...