We show that there is only one Hilbert space of entire functions that is invariant under the action of naturally defined weighted translations.

Human object recognition is generally considered to tolerate changes of the stimulus position in the visual eld. A number of recent studies, however, have cast doubt on the completeness of translation invariance. In a new series of experiments we tried to investigate whether positional speciicity of short-term memory is a general property of visual perception. We tested same-diierent discrimina...

All wavelets can be associated to a multiresolution like structure, i.e. an increasing sequence of subspaces of L(R). We consider the interaction of a wavelet and the translation operator in terms of which of the subspaces in this multiresolution like structure are invariant under the translation operator. This action defines the notion of the translation invariance property of order n. In this...

We give some sufficient conditions such that a crisp, interval, triangular, trapezoidal, parametric approximation of a fuzzy number, with or without additional requirements, to have the properties of invariance to translations or scale invariance.

ABSI'RACI' This paper concerns machine recognition of objects from their images, where the recognition is invariant to scale, translation, and rotation. A neural network used for recognizing input objects is four layer backpropagation network and a cluster of interconnected units spanning four layers of each network forms a functional block called a column. The 90" rotation invariance has been ...

We present a characterization of the Nash Bargaining Solution on a domain which is not closed under Scale Invariance. The characterization on this restricted domain relies on Symmetry, Efficiency, Translation Invariance, the Independence of Irrelevant Alternatives and Continuity, but does not require Scale Invariance. Surprisingly, without continuity there exist a wide variety of bargaining sol...