Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

Tour into the picture (TIP) proposed by Horry et al.[1] is a method for generating a sequence of walk-through images from a single reference picture (or image). By navigating a 3D scene model constructed from the picture, TIP produced convincing 3D effects. Assuming that the picture has one vanishing point, they proposed the scene modeling scheme called spidery mesh. However, this scheme has to...

In this paper, we study a class of Finsler metrics with orthogonal invariance. We find an equation that characterizes these Finsler metrics of almost vanishing H-curvature. As a consequence, we show that all orthogonally invariant Finsler metrics of almost vanishing H-curvature are of almost vanishing Ξ-curvature and corresponding one forms are exact, generalizing a result previously only known...

From a single view that contains a three dimensional scene is possible to obtain substantial information about the object and even its partial reconstruction. This analysis can provide, in the case of Photogrammetry, measures of the original object, and in the case of Computer Vision, useful information to 3D reconstruction. Nevertheless, to carry out this analysis, a critical part of the proce...

This paper uses generating function approach with spectral decomposition to analyze discrete queues with arrival and service processes characterized by Markov chain (MC). Both generating function and distribution function of the queue are constructed from vanishing and non-vanishing roots. The vanishing roots are used to obtain linear solutions for the boundary probabilities; each non-vanishing...

An example of homogeneous space which has no metric but has a connection with non–vanishing curvature suggests that " spacetime " should be not defined as a pair (M, g), a manifold plus a metric, but as a pair (M, Γ) — a differentiable manifold plus a connection. The general theory of homogeneous spaces ensures the existence of a certain well–defined connection independently of the existence of...

Construction of wavelet frames with matrix dilation is studied. We found a necessary condition and a sufficient condition under which a given pair of refinable functions generates dual wavelet systems with a given number of vanishing moments. For image compression and some other applications, it is very desirable to have wavelets with vanishing moment property. In particular, vanishing moments ...

It has been conjectured that sparse paving matroids will eventually predominate in any asymptotic enumeration of matroids, i.e. that limn→∞ sn/mn = 1, where mn denotes the number of matroids on n elements, and sn the number of sparse paving matroids. In this paper, we show that lim n→∞ log sn logmn = 1. We prove this by arguing that each matroid on n elements has a faithful description consisti...

If A• is a bounded, constructible complex of sheaves on a complex analytic space X, and f : X → C and g : X → C are complex analytic functions, then the iterated vanishing cycles φg[−1](φf [−1]A •) are important for a number of reasons. We give a formula for the stalk cohomology H∗(φg[−1]φf [−1]A •)x in terms of relative polar curves, algebra, and the normal Morse data and micro-support of A•.

The subject of this paper is a first-order system least-squares formulation for the Stokes equation which remains uniformly valid in the limit of vanishing viscosity. For this so-called Darcy-Stokes flow problem we establish continuity and coercivity of the corresponding least-squares functional in appropriate norms. Two types of finite element spaces for the approximation of the velocity field...