the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...

Design issues for a 30-m highly segmented mirror are explored, with emphasis on parametric models of simple, inexpensive segments. A mirror with many small segments offers cost savings through quantity production and permits high-order active and adaptive wave-front corrections. For a 30-m f/1.5 paraboloidal mirror made of spherical, hexagonal glass segments, with simple warping harnesses and t...

Three-dimensional registration is the process of aligning scans of different incomplete views of an object such that their corresponding regions agree in space and time. It is used to build digital complete models from partial acquisitions of real-world objects which typically contain noise, outliers, and acquisition holes due to occlusions and hardware limitations. For non-rigid models, such a...

A vanishing cause can lead to a large response in quantum systems which undergo cyclic deformations that pinch a point of level crossing. We call such behavior homeopathic. We illustrate this behavior by studying charge circulation in quantum models of necklaces of atoms driven by a running wave of small amplitude.

The surface partition of large clusters is derived analytically for a simple statistical model by using the Laplace-Fourier transformation method. In the limit of small amplitude deformations, a suggested "hills and dales model" reproduces the leading term of the Fisher result for the surface entropy to within a few percent. The model also gives the degeneracy prefactor of large clusters. The s...