We construct Bernstein-type operators on a triangle with one curved side. We study univariate operators, their product and Boolean sum, as well as their interpolation properties, the order of accuracy (degree of exactness, precision set) and the remainder of the corresponding approximation formulas. We also give some illustrative examples. Mathematics Subject Classification (2010). Primary 41A3...

This paper deals with left invertibility problem of implicit hyperbolic systems with delays in infinite dimensional Hilbert spaces. From a decomposition procedure, invertibility for this class of systems is shown to be equivalent to the left invertibility of a subsystem without delays.

Let n = 2 be the length of the broadcast cycle of the RBO broadcast scheduling protocol (see [1], [2]). Let lb and ub be the variables of the RBO receiver as defined in [2]. We show that the number of changes of lb (the left-side energy) is not greater than k+1. We also show that the number of changes of rb (the right-side energy) is not greater than k + 2. Thus the extra energy (defined in [2]...

Deep Neural Networks (DNNs) often struggle with one-shot learning where we have only one or a few labeled training examples per category. In this paper, we argue that by using side information, we may compensate the missing information across classes. We introduce two statistical approaches for fusing side information into data representation learning to improve one-shot learning. First, we pro...