We define the Ihara zeta function ζ(u,X) and Artin–Ihara L-function of quotient graph groups X=Y//G, where G is a group acting on finite Y with trivial edge stabilizers. determine relationship between primes X show that projection map Y→X can be naturally viewed as an unramified Galois covering graphs groups. evaluated at regular representation equal to ζ(u,Y), divides ζ(u,Y). derive two-term t...

A deterministic automaton accepting a regular language L is a state-partition automaton with respect to a projection P if the state set of the deterministic automaton accepting the projected language P (L), obtained by the standard subset construction, forms a partition of the state set of the automaton. In this paper, we study fundamental properties of state-partition automata. We provide a co...

We present a simple and efficient fluid/solid coupling algorithm in two-spatial dimensions. In particular, we consider the numerical approximation of the Navier-Stokes equations on irregular domains and propose a novel approach for solving the projection step with Neumann boundary conditions on arbitrary shaped objects. This method is straightforward to implement and leads to a symmetric positi...

This paper addresses the recovery of structure and motion from two uncalibrated images of a scene under ful l perspective or under affine projection. Epipolar geometry, projective reconstruction, and affine reconstruction are elaborated in a way such that everyone having knowledge of linear algebra can understand the discussion without difficulty. A general expression of the fundamental matr ix...

Study of the afferents of the rat globus pallidus (GP) with Fluoro-gold, a retrograde tracer, revealed retrogradely labeled neurons in the ipsilateral parafascicular nucleus of the thalamus (PF), a previously undescribed afferent of the rat GP. We used the anterograde tracer, Phaseolus vulgaris-leucoagglutinin (PHA-L), to confirm and extend our findings. After injections of PHA-L in the PF, lab...

The Mojette transform is an entirely discrete form of the Radon transform developed in 1995. It is exactly invertible with both the forward and inverse transforms requiring only the addition operation. Over the last 10 years it has found many applications including image watermarking and encryption, tomographic reconstruction, robust data transmission and distributed data storage. This paper pr...

Nonsmooth operator equations in function spaces are considered, which depend on perturbation parameters. The nonsmoothness arises from a projection onto an admissible interval. Lipschitz stability in L∞ and Bouligand differentiability in L of the parameter-to-solution map are derived. An adjoint problem is introduced for which Lipschitz stability and Bouligand differentiability in L∞ are obtain...

We formalize an algorithm for solving the L(1)-norm best-fit hyperplane problem derived using first principles and geometric insights about L(1) projection and L(1) regression. The procedure follows from a new proof of global optimality and relies on the solution of a small number of linear programs. The procedure is implemented for validation and testing. This analysis of the L(1)-norm best-fi...

For the weight function (1− ||x||) on the unit ball, a closed formula of the reproducing kernel is modified to include the case −1/2 < m < 0. The new formula is used to study the orthogonal projection of the weighted L space onto the space of polynomials of degree at most n, and it is proved that the uniform norm of the projection operator has the growth rate of n (d−1)/2 for m < 0, which is th...