In this paper we investigate the approximation of a class of parabolic partial differential equations on the unit spheres S n ⊂ R n+1 using spherical basis functions. Error estimates in the Sobolev norm are derived.

Traditionally, optimality and uniqueness of an (n, N, t) spherical code is proved using linear programming bounds. However, this approach does not apply to the parameter (4, 10, 1/6). We use semidefinite programming bounds instead to show that the Petersen code (which are the vertices of the 4dimensional second hypersimplex or the midpoints of the edges of the regular simplex in dimension 4) is...

We developed an open source software for crustal strain analysis using the least-squares collocation method based on the spherical model of the earth. The software is able to simultaneously determine the signal and noise of the velocities at the observation points with the best possible removal of the observational errors, or at any other position with no velocity observation. Furthermore, the ...

The intra-voxel incoherent motion (IVIM) model assumes that blood flowing in isotropically distributed capillary segments induces a phase dispersion of the MR signal, which increases the signal attenuation in diffusion-weighted images. However, in most tissue types the capillary network has an anisotropic micro-architecture. In this study, we investigated the possibility to indirectly infer the...

Abstract The studies that compare the metastatic potential of tumor cell clusters in microcirculation to single cells show contribute significantly metastasizing. is conditioned by presence cancer near vessel walls. Detailed understanding dynamical behavior walls can thus elucidate process adhesion. We have developed a biomechanical model capable simulating both strong and weak adhesion among c...

background and objective: cerebral arteriovenous malformation (cavm) hemodynamic is disease condition, results changes in the flow and pressure level in cerebral blood vessels. measuring flow and pressure without catheter intervention along the vessel is big challenge due to vessel bifurcations/complex bifurcations in arteriovenous malformation patients. the vessel geometry in cavm patients are...

New spherical codes called laminated spherical codes are constructed in dimensions 2–49 using a technique similar to the construction of laminated lattices. Each spherical code is recursively constructed from existing spherical codes in one lower dimension. Laminated spherical codes outperform the best known spherical codes in the minimum distance sense for many code sizes. The density of a lam...

We prove that the D4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in S, based on numerical computations suggesting that every 5-design consisting of 24 points in S is in a 3-parameter family (which we describe explicitly, based on a constr...

in this paper we will determine the multiple point manifolds of certain self-transverse immersions in euclidean spaces. following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to dold manifold $v^5$ or a boundary. we will show there is an immersion of $s^7times p^2$ in $mathbb{r}^{13...

background and objective: the circle of willis (cow) supports adequate blood supply to the brain. the cardiovascular system, in the current study, is modeled using an equivalent electronic system focusing on the cow. method: in our previous study we used 42 compartments to model whole car- diovascular system. in the current study, nevertheless, we extended our model by using 63 compartments to ...