Various definitions of directional derivatives in topological vector spaces are compared. Directional derivatives in the sense of G~teaux, Fr6chet, and Hadamard are singled out from the general framework of cr-directional differentiability. It is pointed out that, in the case of finite-dimensional spaces and locally Lipschitz mappings, all these concepts of directional differentiability are equ...

We refer to human-robot relationships as Lovotics. In this paper a design process for Lovotics is presented. In order to invoke these relationships, technological solutions can only take us so far. Design played an important role in order to engage users to explore the possibilities of bi-directional, human-robot love. We conducted a user-centric study in order to understand these factors and i...

Experiments were performed which demonstrate some of the length-measuring characteristics of a grid consisting of two sets of parallel lines crossing each other at right angles. If lines of various shapes are repeatedly superimposed at random on such a grid, the mean number of intersections each of these lines makes with the lines of the grid is directly proportional to the length of the line. ...

Steerable filters have been used to analyze local orientation patterns in imagery. Such filters are typically based on directional derivatives, whose symmetry produces orientation responses that are periodic with period pi, independent of image structure. We present a more general set of steerable filters that alleviate this problem.

This paper deals with the number of meaningful compositions of higher order of differential operations and the Gateaux directional derivative.

In this paper, we introduce a new differential-difference operator Tξ (ξ ∈ R ) by using projections associated to orthogonal subsystems in root systems. Similarly to Dunkl theory, we show that these operators commute and we construct an intertwining operator between Tξ and the directional derivative ∂ξ. In the case of one variable, we prove that the Kummer functions are eigenfunctions of this o...

In this paper we address the issue of recognizing Farsi handwritten words. Two types of gradient features are extracted from a sliding vertical stripe which sweeps across a word image. These are directional and intensity gradient features. The feature vector extracted from each stripe is then coded using the Self Organizing Map (SOM). In this method each word is modeled using the discrete Hidde...

In this paper, based on a partial order, we study the characterizations of directional derivatives and the subdifferential of fuzzy function. At the same time, we also discuss the relation between the directional derivative and the subdifferential.

This paper describes the use of a system of semantic rules to generate noun compounds, vague or polyse-mous words, and cases of metonymy. The rules are bi-directional and are used by the understanding system to interpret the same constructions.