Take an n-dimensional manifold M . Endow it with a distribution, by which I mean a smooth linear subbundle D ⊂ TM of its tangent bundle TM . So, for x ∈ M , we have a k-plane Dx ⊂ TxM , and by letting x vary we obtain a smoothly varying family of k-planes on M . Put a smoothly varying family g of inner products on each k-plane. The data (M,D, g) is, by definition, a sub-Riemannian geometry. Tak...

Visualization of 3-D volume data through maximum intensity projections (MIP) requires isotropic voxels for generation of undistorted projected images. Unfortunately, due to the inherent scanning geometry, X-ray computed tomographic (CT) images are mostly axial images with submillimeter pixel resolution, with the slice spacing on the order of half to one centimeter. These axial images must be in...

Take an n-dimensional manifold M . Endow it with a distribution, by which I mean a smooth linear subbundle D ⊂ TM of its tangent bundle TM . So, for x ∈ M , we have a k-plane Dx ⊂ TxM , and by letting x vary we obtain a smoothly varying family of k-planes on M . Put a smoothly varying family g of inner products on each k-plane. The data (M,D, g) is, by definition, a sub-Riemannian geometry. Tak...

This note presents a brief synopsis of analysis of magnetotelluric data for model dimensionality and strike and its application to the data used in the main paper. Magnetotelluric (MT) data begin as time series of horizontal magnetic (H) and electric (E) fields collected at Earth's surface. After cross-correlation of the field components in orthogonal measurement directions (x,y), the frequency...

Abstract. AMotzkin path of length n is a lattice path from (0, 0) to (n, 0) in the plane integer lattice Z × Z consisting of horizontal-steps (1, 0), up-steps (1, 1), and down-steps (1,−1), which never passes below the x-axis. A u-segment (resp. h-segment ) of a Motzkin path is a maximum sequence of consecutive up-steps (resp. horizontal-steps). The present paper studies two kinds of statistics...

Observers judged whether 2 successive computer-displayed rotations of a cube were the same or different. With respect to the observers, each rotation was about a vertical axis (Y), a horizontal (line-of-sight) axis (Z), an axis tilted just 10 degrees from vertical or horizontal, or a maximally oblique axis. Independently, with respect to the cube, each rotation was about a symmetry axis through...

X–Z inverted pendulum is a new kind of inverted pendulum and it can move with the combination of the vertical and horizontal forces. In this paper, the control problem of X-Z inverted pendulum with system uncertainties is addressed, and a pair of decoupled adaptive fuzzy sliding mode control method is proposed. The fuzzy logic system is employed to approximate the system uncertainties as well a...

Alternative chicane-type beam lines are proposed for exact emittance exchange between horizontal phase space (x, x′) and longitudinal phase space (z, δ). Methods to achieve exact phase space exchanges, i.e. mapping x to z, x′ to δ, z to x and δ to x′ are suggested. Methods to mitigate the thick-lens effect of the transverse cavity on emittance exchange are discussed. Some applications of the ph...

In this talk, we consider an oriented percolation model in a random environment, this model was proposed and studied by Kesten, Sidoravicius and Vares in [4]. Consider the following North-East oriented site percolation model on Z+. Given the parameters δ, p and ∆ ∈ [0, 1], for each line Hi := {(x, y) ∈ Z+;x+y = i}, ∀i ∈ Z+ we associate the 0-1 (‘good’ or ‘bad’) random variable, ξi, independentl...