The triaxial deformation in 10 Be is investigated using a microscopic α+α+n+n model. The states of two valence neutrons are classified based on the molecular-orbit (MO) model, and the π-orbit is introduced about the axis connecting the two α-clusters for the description of the rotational bands. There appear two rotational bands comprised mainly of K π = 0 + and K π = 2 + , respectively, at low ...

The method of reduction of a non-Abelian gauge theory to the corresponding unconstrained system is exemplified for SU(2) Yang-Mills field theory. The reduced Hamiltonian which describes the dynamics of the gauge invariant variables is presented in the form of a strong coupling expansion. The physical variables are separated into fields, which are scalars under spatial rotations, and rotational ...

A generalized energy principle for finite-pressure, toroidal magnetohydrodynamic MHD equilibria in general three-dimensional configurations is proposed. The full set of ideal-MHD constraints is applied only on a discrete set of toroidal magnetic surfaces invariant tori , which act as barriers against leakage of magnetic flux, helicity, and pressure through chaotic field-line transport. It is ar...

Image matching is a key part of many remote sensing image processing and image analysis. The traditional gray correlation matching algorithm based on corner point because they do not have the rotational invariance requires manual intervention to roughly match can not be automated. SIFT (Scale invariant feature transform) algorithm to solve the image rotation, scaling and other issues, but for t...

Synthesizing controllers for rotational movements in feature space is an open research problem and is particularly challenging because of the need to precisely regulate the character’s global orientation, angular momentum and inertia. This paper presents feature-based controllers for a wide variety of rotational movements, including cartwheels, dives and flips. We show that the controllers can ...

Statistical tests are introduced for checking whether an image function f(x, y) defined on the unit disc D = {(x, y) : x + y ≤ 1} is invariant under certain symmetry transformations of D, given that discrete and noisy data are observed. We consider invariance under reflections or under rotations by rational angles, as well as rotational invariance of f(x, y). These symmetry relations can be nat...

Given a bowtie decomposition of the complete graph Kv admitting an automorphism group G acting transitively on the vertices of the graph, we give necessary conditions involving the rank of the group and the cycle types of the permutations in G. These conditions yield non–existence results for instance when G is the dihedral group of order 2v, with v ≡ 1, 9 (mod 12), or a group acting transitive...

This study investigates preschoolers’ ability to perceive the heaviness of objects by dynamic touch, a perceptual system that relies on the use of the muscle as a sensory organ. In total, 18 preschoolers were asked to hold objects by a handle without being able to see them. The 9 objects differed in mass and volume, allowing us to test the size–weight illusion by dynamic touch. Children were as...

For a two-dimensional surface M in the four-dimensional Euclidean space E we introduce an invariant linear map of Weingarten type in the tangent space of the surface, which generates two invariants k and κ. The condition k = κ = 0 characterizes the surfaces consisting of flat points. The minimal surfaces are characterized by the equality κ − k = 0. The class of the surfaces with flat normal con...

The stochastic equations of motion for a system of interacting rigid bodies in a solvent are formulated and studied. Three-dimensional bodies of arbitrary shape, with arbitrary couplings between translational and rotational degrees of freedom, as arise in coarse-grained models of polymers, are considered. Beginning from an Euler–Langevin form of the equations, two different, properly invariant,...