This paper investigates the Vitali Covering Theorem from various constructive angles. A Vitali Cover of a metric space is a cover such that for every point there exists an arbitrarily small element of the cover containing this point. The Vitali Covering Theorem now states, that for any Vitali Cover one can find a finite family of pairwise disjoint sets in the Vitali Cover that cover the entire ...

We prove a local variational principle of pressure for any given open cover. More precisely, for a given dynamical system (X,T ), an open cover U of X, and a continuous, realvalued function f on X, we show that the corresponding local pressure P (T, f ;U) satisfies P (T, f ;U) = sup{hμ(T,U) + ∫ X f(x)dμ(x) : μ is a T -invariant measure}, and moreover, the supremum can be attained by a T -invari...

the study of the exclosure effects on the vegetation changes undergrazing and non-grazing conditions in the rangeland areas has particularimportance in the rangeland improvement and revivification projects. theresearch was accomplished in semi-steppe khoybilehvar area, from 1999 to2005. vegetation cover was annually measured within fixed plots during transact.the results showed that during nine...

Let K be the function field of a connected regular scheme S of dimension 1, and let f : X → Y be a finite cover of projective smooth and geometrically connected curves over K with g(X) ≥ 2. Suppose that f can be extended to a finite cover X → Y of semi-stable models over S (it is known that this is always possible up to finite separable extension of K). Then there exists a unique minimal such c...

metric (mapping evapotranspiration at high resolution with internalized calibration) is known as an appropriate surface energy balance model for the estimation of the spatial distribution of evapotranspiration (et) in semi-arid regions. based on lysimeter measurements, metric has shown et estimates of 10% on a sub-field scale on a daily basis. there is a need to identify how the model is sensit...

plant biomass is an important factor for determining arid and semi-aridrangelands capacity. due to the lack of proper and annual sampling of rangelands, there areno suitable data to determine biomass, range condition and proper range managementoperations. plant biomass is one of the measurable attributes that can be assessed inrangeland studies. since the clip and weight method is destructive a...

Semi-supervised learning techniques are gaining popularity due to their capability of building models that effective, even when scarce amounts labeled data available. In this paper, we present a framework and specific tasks for self-supervised pretraining \textit{multichannel} models, such as the fusion multispectral synthetic aperture radar images. We show proposed approach is highly effective...