Abstract We present a general notion of realizability encompass-ing both standard Kleene style realizability over partial combinatory algebras and Kleene style realizability overmore general structures, including all partial cartesian closed categories. We show how the general notion of re

We present a general notion of realizability encompassing both standard Kleene style realizability over partial combinatory algebras and Kleene style realizability over more general structures, including all partial cartesian closed categories. We show how the general notion of realizability can

In this paper we present the application of thermic effect on sonicity's theory. The sonic actions permit the best combination of facilities offered by the procesing of electrical signals (reduces energy) with sonical actions of great power and efficiency, which give the possibility of eliminating the bigest parts of a clasical hidraulical system (hidraulic reservoir, valve of regulating the debit), resulting on action which combine the opportunities offered by the processing the signals of low energy and the compact sonic actions, with high efficiency, with reduces volume, so very economic.

Summary. Orthoposets are defined. The approach is the standard one via order relation similar to common text books on algebra like [9].

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Statistical depth functions are being formulated ad hoc with increasing popularity in nonparametric inference for multivariate data. Here we introduce several general structures for depth functions, classify many existing examples as special cases, and establish results on the possession, or lack

-depth, is based on depth infima over a proper set Φ of Rd-valued linear functions. Several desirable properties are established for the Φ-depth and a generalized version of it. The general notions include known functional data depths, such as the band depth and graph depths of Lopez-Pintado and Romo, and many new

introduces two more general approaches to bounding mind changes. These are based on counting by going down in a linearly ordered set (Type 3) and on counting by going down in a partially ordered set (Type 4). In both cases the set must not contain infinite, descending, and computable sequences. These four

In this paper we introduce a general framework for defining the depth of a sequence with respect to a class of observers. We show that our general framework captures all depth notions introduced in complexity theory so far. We review most such notions, show how they are particular cases of our

In this article, we introduce the notion of a functor on coarse spaces being coarsely excisive- a coarse analogue of the notion of a functor on topological spaces being excisive. Further, taking cones, a coarsely excisive functor yields a topologically excisive functor, and for coarse topological