We introduce the process of symplectic reduction along a submanifold as uniform approach to taking quotients in geometry. This construction holds categories smooth manifolds, complex analytic spaces, and algebraic varieties, has an interpretation terms derived stacks shifted It also encompasses Marsden–Weinstein–Meyer reduction, Mikami–Weinstein pre-images Poisson transversals under moment maps...

Using the submanifold quantum mechanical scheme, the restricted Dirac operator in a submanifold is defined. Then it is shown that the zero mode of the Dirac operator expresses the local properties of the submanifold, such as the Frenet-Serret and generalized Weierstrass relations. In other words this article gives a representation of a further generalized Weierstrass relations for a general k-s...

An optimal linear system for integrating visual cues to 3D surface geometry weights cues in inverse proportion to their uncertainty. The problem of integrating texture and stereo information for judgments of planar surface slant provides a strong test of optimality in human perception. Since the accuracy of slant from texture judgments changes by an order of magnitude from low to high slants, o...

Research on the steel structures with confining of axial expansion in fixed beams has been quite intensive in the past decade. It is well established that the thermal behaviour has a key influence on steel structural behaviours. This paper describes mechanical behaviour of beams with bolted slant end-plate connection with nonsymmetric gravity load, subjected to temperature increase. Furthermore...

Judgments of relative slant were elicited by a paired-comparison method from 24 S"s in each of three experiments. The stimuli were computergenerated slides representing regular dot patterns (Exp. I), regular line patterns (Exp. II), or random dot patterns (Exp. Ill) rotated about a horizontal axis. The ratio of horizontal to vertical separations (form ratio) and perspective were independently v...

Texture can be an effective source of information for perception of slant and curvature. A computational assumption required for some texture cues is that texture must be flat along a surface. There are many textures which violate this assumption, and have some sort of texture relief: variations perpendicular to the surface. Some examples include grass, which has vertical elements, or scattered...

Three studies, involving a total of 145 observers examined quantitative theories of the overestimation of perceived optical slant. The first two studies investigated the depth/width anisotropies on positive and negative slant in both pitch and yaw at 2 and 8 m using calibrated immersive virtual environments. Observers made judgments of the relative lengths of extents that were frontal with thos...

The perception of depth and slant in three-dimensional scenes specified by texture was investigated in five experiments. Subjects were presented with computer-generated scenes of a ground and ceiling plane receding in depth. Compression, convergence, and grid textures were examined. The effect of the presence or absence of a gap in the center of the display was also assessed. Under some conditi...

This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a punctured sphere with fixed local monodromy. The submanifold is defined via products of involutions through Lagrangian subspaces. We show that the moduli space of Lagrangian representations is a Lagrangian submanifold of the moduli of unitary representations.

We consider the heat equation with Dirichlet boundary conditions on the tubular neighborhood of a closed Riemannian submanifold of a Riemannian manifold. We show that, as the tube radius decreases, the semigroup of a suitably rescaled and renormalized generator can be effectively described by a Hamiltonian on the submanifold with a potential that depends on the geometry of the submanifold and o...