To study arithmetic structures of natural numbers, we introduce a notion entropy functions, called anqie entropy. This possesses some crucial properties common to both Shannon's and Kolmogorov's entropies. We show that all functions with zero form C*-algebra. Its maximal ideal space defines our compactification which is totally disconnected but not extremely disconnected. also compute the $K$-g...

A single spin flip stochastic energy conserving dynamics for the XY model is considered. We study the ergodicity properties of the dynamics. It is shown that phase space trajectories densely fill the geometrically connected parts of the energy surface. We also show that while the dynamics is discrete and the phase point jumps around, it cannot make transitions between closed disconnected parts ...

We introduce the medial axis as a tool in the analysis of geometric structure of void space in porous media. The medial axis traces the fundamental geometry of the void pathways. We describe an algorithm for generating the medial axis of the void structure from digitized three dimensional images of porous media obtained from X ray CAT scans. The medial axis is constructed during an iterative er...

Selected configuration interaction (SCI) for atomic and molecular electronic structure calculations is reformulated in a general framework encompassing all CI methods. The linked cluster expansion is used as an intermediate device to approximate CI coefficients B(K) of disconnected configurations (those that can be expressed as products of combinations of singly and doubly excited ones) in term...

Only two examples of extremally Ricci pinched G2-structures can be found in the literature and they are both homogeneous. We study this paper existence structure such very special closed on Lie groups. Strong structural conditions algebra proved to hold. As an application, we obtain three new that all necessarily steady Laplacian solitons. The deformation rigidity structures also studied.