In this paper, a new camera calibration algorithm is proposed, which is from the quasi-affine invariance of two parallel circles. Two parallel circles here mean two circles in one plane, or in two parallel planes. They are quite common in our life. Between two parallel circles and their images under a perspective projection, we set up a quasi-affine invariance. Especially, if their images under...

Final-syllable invariance is characteristic of diminutives (e.g., doggie), which are a pervasive feature of the child-directed speech registers of many languages. Invariance in word endings has been shown to facilitate word segmentation (Kempe, Brooks, & Gillis, 2005) in an incidental-learning paradigm in which synthesized Dutch pseudonouns were used. To broaden the cross-linguistic evidence fo...

We introduce a novel notion of invariance feedback entropy to quantify the state information that is required by any controller that enforces a given subset of the state space to be invariant. We establish a number of elementary properties, e.g. we provide conditions that ensure that the invariance feedback entropy is finite and show for the deterministic case that we recover the well-known not...

motivating the perturbations of frames in hilbert and banach spaces, in this paper we introduce the invariance of fr'echet frames under perturbation. also we show that for any fr'echet spaces, there is a fr'echet frame and any element in these spaces  has a series expansion.

Theory of classical basis including Schauder basis is sufficiently well developed, and quite a good number of monographs such as Day 1 , Singer 2, 3 , Young 4 , Bilalov, Veliyev 5 , Ch. Heil 6 , and so forth have been dedicated to it so far. There are different versions and generalizations of the concept of classical basis for more details see 2, 3 . One of such generalizations is proposed in 5...