We examine conditions under which the spectral properties of lights and surfaces may be recovered by a trichromatic visual system that uses bilinear models. We derive criteria for perfect recovery, formulated in terms of invariant properties of model matrices, for situations in which either two or three lights are shown sequentially on a set of surfaces.

We classify the measures on SL(k,R)/SL(k,Z) which are invariant and ergodic under the action of the group A of positive diagonal matrices with positive entropy. We apply this to prove that the set of exceptions to Littlewood’s conjecture has Hausdorff dimension zero.

Self-similarity matrices have become an important tool for visualizing the repetitive structure of a music recording. Transforming an audio data stream into a feature sequence, one obtains a self-similarity matrix by pairwise comparing all features of the sequence with respect to a local cost measure. The basic idea is that similar audio segments are revealed as paths of low cost along diagonal...

Abstract: This paper gives some sufficient conditions for a given polyhedral set which is represented as a set of linear inequalities to be positive D-invariant for uncertain linear discrete-time systems in the case such that the systems matrices depend linearly on uncertain parameters whose ranges are given intervals. Further, the results will be applied to uncertain linear continuous systems ...

1. Introduction. We consider the resolution of large-scale nonlinear problems arising from the finite-element discretization of geometrically non-linear structural analysis problems. We use a classical Newton Raphson algorithm to handle the non-linearity which leads to the resolution of a sequence of linear systems with non-invariant matrices and right hand sides. The linear systems are solved ...

We analyze the asymptotic convergence of all infinite products of matrices taken in a given finite set by looking only at finite or periodic products. It is known that when the matrices of the set have a common nonincreasing polyhedral norm, all infinite products converge to zero if and only if all infinite periodic products with periods smaller than a certain value converge to zero. Moreover, ...

We study the four-weight spin models (W1, W2, W3, W4) introduced by Eiichi and Etsuko Bannai (Pacific J. of Math, to appear). We start with the observation, based on the concept of special link diagram, that two such spin models yield the same link invariant whenever they have the same pair (W1, W3), or the same pair (W2, W4). As a consequence, we show that the link invariant associated with a ...

The Garsia–Haiman module is a bigraded Sn-module whose Frobenius image Macdonald polynomial. method of orbit harmonics promotes an Sn-set X to graded polynomial ring. can be applied prove cyclic sieving phenomena which notion that encapsulates the fixed-point structure finite group action on set. By applying this idea module, we provide results regarding enumeration matrices are invariant under...

in this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. in fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. some examples are provided to verify the effectiveness and applicability of our results.