M P = {A(x) ∈ M : det(A(x)− yIr) = P (x, y)}. The system (1) has an obvious symmetry group G = IPGLr(I C; J) which is the subgroup of the projective group IPGLr(I C) formed by matrices which commute with J . The group G acts on M by conjugation, the action is Poisson, and the reduced Hamiltonian system is completely integrable too. As the symmetry group G acts freely and properly on the general...

Understanding and simplified modeling of the Head Related Transfer Function (HRTF) holds the key to many applications in spatial audio. We develop an analytical solution to the problem of scattering of sound from a sphere in the vicinity of an infinite plane. Using this solution we study the influence of a nearby scattering rigid surface, on a spherical model for the HRTF.

This paper describes a new integrated scheme for metamorphosis between two closed manifold genus-0 polyhedral models. Spherical parameterizations of the source and target models are created first. To control the morphing, any number of feature vertex pairs is specified and a fold-over free warping method is used to align two spherical embeddings. Our method does not create a merged meta-mesh or...

Stone tools, often the sole remnant of prehistoric hunter-gatherer behavior, are frequently used as evidence of ancient human mobility, resource use, and environmental adaptation. In North America, studies of morphological variation in projectile points have provided important insights into migration and interactions of human groups as early as 12-13 kya. Using new approaches to 3D imaging and ...

We obtain the coefficients of a new fundamental plane for supermassive black holes at the centers of elliptical galaxies, involving measured central black hole mass and photometric parameters which define the light distribution. The galaxies are tightly distributed around this mass fundamental plane, with improvement in the rms residual over those obtained from the MBH − σ and MBH − L relations...

Using Barnes-Wall lattices and 1-cocycles on finite groups of monomial matrices, we give a procedure to construct tricosine spherical codes. This was inspired by a 14-dimensional code which Ballinger, Cohn, Giansiracusa and Morris discovered in studies of the universally optimal property. It has 64 vectors and cosines −37 ,− 1 7 , 1 7 . We construct the Optimism Code, a 4-cosine spherical code ...

The accuracy of the commonly used diffusion approximation as used in diffuse optical tomography is known to be limited in cases involving strong absorption and in these situations a higher ordered approximation is necessary. In this study, a light transport model has been developed based upon the three-dimensional frequency-domain simplified spherical harmonics (SP(N)) approximation for orders ...

MEG forward problem has been solved for about 2000 dipoles placed on the brain surface using a very ®ne 3-layer realistic model of the head and the boundary element method (BEM). For each dipole, spherical models, one-layer realistic BEM models and coarser 3-layer realistic BEM models, were used to reconstruct the dipole. It was found that the localization bias induced by using a spherical mode...

If p ∈ Rn, then we have the radial projection map from Rn\{p} onto a sphere. Sometimes one can construct similar mappings on metric spaces even when the space is nontrivially different from Euclidean space, so that the existence of such a mapping becomes a sign of approximately Euclidean geometry. The existence of such spherical mappings can be used to derive estimates for the values of a funct...

A realistic non-spherical model for bubble formation in a co-flowing liquid is presented. In the model, an interfacial element approach is applied to describe the dynamics of bubble formation. The effect of flowing liquid velocity is modeled by a combination of the bubble axis translation and liquid pressure analysis of each interfacial element. The bubble shapes during formation are predicted ...