Locales are Isabelle’s mechanism to deal with parametric theories. We present typical examples of locale specifications, along with interpretations between locales to change their hierarchic dependencies and interpretations to reuse locales in theory contexts and proofs. This tutorial is intended for locale novices; familiarity with Isabelle and Isar is presumed.

Let T(X) be the full transformation semigroup on a set X, and let L(V) under composition of all linear transformations vector space V over field. For subset Y X subspace W V, consider semigroups $${\overline{T}}(X, Y) = \{f\in T(X):Yf \subseteq Y\}$$ $${\overline{L}}(V, W) L(V):Wf W\}$$ composition. We describe unit-regular elements in Y)$$ W)$$ . Using these, we determine when are unit-regular...

r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

In this paper, the problem of non-regular static state feedback linearization of nonlinear switched systems is considered. Using semi-tensor product, some easily verifiable sufficient conditions for non-regular feedback linearization are obtained. Then an example is presented to illustrate the non-regular linearization process.

background : life style is the ordinal and daily activities of individuals in their own lives that they accepted so, these activities affect their health status. the aim of the current study was to determine  teachers' life style in gorgan city in 2009. methods : in a cross-sectional study 336 teachers of elementary, mid and high school were recruited through random stratified sampling method. ...

We consider a polymorphic type system (System F) with recursive types for the lambda calculus with constants. We use Leivant’s notion of rank to delimit the boundaries for decidable and undecidable type inference in our system. More precisely, we show that type inference in our system is undecidable at rank k ≥ 3. Similar results are known to hold for System F without recursive types. Our undec...

Many unsupervised learning algorithms make use of kernels that rely on the Euclidean distance between two samples. However, the Euclidean distance is optimal for Gaussian distributed data. In this paper, we relax the global Gaussian assumption made by the Euclidean distance, and propose a locale Gaussian modelling for the immediate neighbourhood of the samples, resulting in an augmented data sp...

We propose a unified and simple approach of capturing and recreating 3D sound fields by exploring the reciprocity principle that is satisfied between the two processes. Our approach makes the system easy to build, and practical. Using this approach, we can capture the 3D sound field by a spherical microphone array and recreate it using a spherical loudspeaker array, and ensure that the recreate...