Kinematic geometry of regular motions in homogeneous space

Assessing users' visual perception based on the regular and irregular geometry of space organizer

Perception is a cognitive process depends on various factors of the environment. The user's mentality can affect his perception, understanding, and behavior in the environment. Organizing the environment is one of the important factors in the formation of spatial communication of elements that can be an important factor in understanding the person from his or her surroundings. In this research,...

The Geometry of Whirls and Whirl-motions in Space

An Analysis of Kinematic Vertical Motions

Several techniques exist for computing vertical motions. In this paper, radiosonde wind observations are used to compute vertical motions by the kinematic method. The presence of cumulative bias errors necessitates adjustment techniques. Simple tests of two techniques indicate that, for the period of this study, a divergence adjustment that is a function of pressure yields the best adjusted ver...

The Kinematic Formula in Riemannian Homogeneous Spaces

Let G be a Lie group and K a compact subgroup of G. Then the homogeneous space G/K has an invariant Riemannian metric and an invariant volume form ΩG. Let M and N be compact submanifolds of G/K, and I(M ∩ gN) an “integral invariant” of the intersection M ∩ gN . Then the integral

Complexity of regular invertible p-adic motions.

We consider issues of computational complexity that arise in the study of quasi-periodic motions (Siegel discs) over the p-adic integers, where p is a prime number. These systems generate regular invertible dynamics over the integers modulo p(k), for all k, and the main questions concern the computation of periods and orbit structure. For a specific family of polynomial maps, we identify condit...