As virtual worlds demand ever more realistic 3D models, attention is being focussed on systems that can acquire graphical models from real objects. This paper describes a system which, given a sequence of images of an object rotating about a single axis, generates a textured 3D model fully automatically. In contrast to previous approaches, the technique described here requires no prior informat...

We consider two families of weighted zero-sum constant for finite abelian groups. For a finite abelian group (G,+), a set of weights W ⊂ Z, and an integral parameter m, the m-wise Davenport constant with weights W is the smallest integer n such that each sequence over G of length n has at least m disjoint zero-subsums with weights W . And, for an integral parameter d, the d-constrained Davenpor...

We define a quasi–projective reduction of a complex algebraic variety X to be a regular map from X to a quasi–projective variety that is universal with respect to regular maps from X to quasi–projective varieties. A toric quasi–projective reduction is the analogous notion in the category of toric varieties. For a given toric variety X we first construct a toric quasi–projective reduction. Then ...

For a finite subgroup G ⊂ SL(3,C), Bridgeland, King and Reid proved that the moduli space of G-clusters is a crepant resolution of the quotient C/G. This paper considers the moduli spaces Mθ, introduced by Kronheimer and further studied by Sardo Infirri, which coincide with G -Hilb for a particular choice of GIT parameter θ. For G Abelian, we prove that every projective crepant resolution of C/...

A problem of recurring interest involves the construction of a panoramic video mosaic from a video sequence generated from a camera and then obtain high resolution images of regions of interest in the mosaic. The camera motions are estimated by calculating the parameters of a projective model and then superresolution is attained by an algorithm for constructing a high resolution image from unde...

We characterize the geometrical and topological aspects of a dynamical system by associating a geometric phase with a phase space trajectory. Unlike Berry’s phase, the path underlying this “anholonomy” is not in parameter space, but in a projective space of the phase space, which directly characterizes the geometry of the trajectories. Using the example of a non-linear driven damped oscillator,...

By introducing a feedback control to a proposed Sprott E system, an extremely complex chaotic attractor with only one stable equilibrium is derived. The system evolves into periodic and chaotic behaviors by detailed numerical as well as theoretical analysis. Analysis results show that chaos also can be generated via a period-doubling bifurcation when the system has one and only one stable equil...

Diversity sum, which is calculated from the Frobenius norm of the difference of two distinct elements in a signal constellation, is the significant parameter to predict a unitary group constellation having a good performance in low SNR. In this paper, we propose a method to compute the diversity sum of a unitary group constellation using a character table. Some examples of using our method to d...

In this paper we continue the investigation of coherent systems of type (n, d, k) on the projective line which are stable with respect to some value of a parameter α. We consider the case k = 1 and study the variation of the moduli spaces with α. We determine inductively the first and last moduli spaces and the flip loci, and give an explicit description for ranks 2 and 3. We also determine the...

We show that the bounded proper forcing axiom BPFA implies that there is a well-ordering of P(ω1) which is ∆1 definable with parameter a subset of ω1. Our proof shows that if BPFA holds then any inner model of the universe of sets that correctly computes א2 and also satisfies BPFA must contain all subsets of ω1. We show as applications how to build minimal models of BPFA and that BPFA implies t...