‎this contribution mainly focuses on some aspects of lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with lipschitz multiplication and inversion map‎. ‎in the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be characterized as particular group objects in the category of metric spaces and lipschitz maps‎. ‎moreover‎, ‎up to an adjustment of the metric‎, ‎a...

a module is said to be $pi$-extending provided that every projection invariant submodule is essential in a direct summand of the module. in this paper, we focus on direct summands and indecomposable decompositions of $pi$-extending modules. to this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper ...

Interval analysis seeks static lower and upper bounds on the values of program variables. These bounds are useful, especially for inferring invariants to prove buffer overflow checks. In practice, however, intervals by themselves are often inadequate as invariants due to the lack of relational information among program variables. In this paper, we present a technique for deriving symbolic bound...

Many examples exist of one-dimensional systems that are topologically conjugate to the shift operator on Σ2 and are thus chaotic. Most of these examples which have invariant Cantor subsets, have Cantor subsets of measure zero. In this paper we outline the formulation of a C map on a closed interval that has an invariant Cantor subset of positive Lebesgue measure. We also survey techniques used ...

Consider a piecewise smooth expanding map of the interval possessing several invariant subintervals and the same number of ergodic absolutely continuous invariant probability measures (ACIMs). After this system is perturbed to make the subintervals lose their invariance in such a way that there is a unique ACIM, we show how to approximate the diffusion coefficient for an observable of bounded v...

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced maximal invariant measure study its properties. Further, how measures depend on parameters system. These results were illustrated by a simple example or risk management model where appear naturally.

A two interval forced choice constant stimuli method was used to determine: (i) the point of subjective equality (PSE); and (ii) the just-noticeable-difference (JND) in contrast for two luminance gratings, one held in short-term visual memory. Psychometric functions for delayed contrast discrimination were determined as a function of spatial frequency from 1 to 8 c/deg, reference contrast from ...