SUBSTANTIATION OF WEATHER CONDITIONS AND ASSESSMENT OF SIMILARITY OF INTRAEGETATIONAL PERIODS DURING SPRINKLING OF HAY-GRAZING HERBAL MIXTURE

В данной работе была выполнена оценка теплообеспеченности и увлажненности территории северо-восточной зоны Республики Беларусь при орошении дождеванием сенокосно-пастбищной травосмеси за теплый период (апрель-сентябрь) в 2016-2018 гг., а также установление взаимосвязи внутривегетационного распределения метеоусловий посредством сравнения конкретных лет с годами различной обеспеченности. В качестве методов исследования для оценки теплообеспеченности и увлажненности вегетационных периодов при орошении дождеванием сенокосно-пастбищной травосмеси в 2016-2018 гг. в данной работе была применена математическая обработка метеорологических величин, а также с целью установления вариации распределения метеорологических элементов при сравнении данных конкретного года со среднемноголетними условиями был применен метод дескриптивных множеств. На основании математической обработки метеорологических величин установлено, что 2016 год является оптимальным по влагообеспеченности и теплым; 2017 год ‒ средневлажным и оптимальным по теплообеспеченности; 2018 год ‒ близким к засушливому и теплым. По методу дескриптивных множеств при сравнении со среднемноголетними значениями суммарная мера сходства осадков с учетом месячных величин составила 82,4; 77,9 и 75,4 %, а с учетом декадных ‒ 79,9; 62,9 и 59,4 % соответственно за теплый период (апрель-сентябрь) в 2016-2018 гг. При сравнении со среднемноголетними значениями суммарная мера сходства среднесуточных температур воздуха с учетом месячных величин составила 95,7; 96,5 и 93,7 %, с учетом декадных ‒ 92,5; 91,2 и 91,6 % соответственно за теплый период (апрель-сентябрь) в 2016-2018 гг. In this work, the heat supply and moisturization of the territory of the north-eastern zone of the Republic of Belarus was assessed during sprinkling of hay-grazing trauma during the warm period (April-September) 2016... 2018, as well as the establishment of a relationship between the intravenous distribution of meteorological conditions by comparing specific years with years of different availability. As methods of research to assess heat availability and humidification of growing periods during sprinkling of hay-grazing trauma in 2016... 2018, mathematical processing of meteorological values was used in this work, as well as to establish variation of distribution of meteorological elements when comparing data of a particular year with average summer conditions, the method of descriptive sets was used. Based on the mathematical processing of meteorological values, it has been established that 2016 is optimal in moisture availability and warm; 2017 ‒ srednevlazhny and optimum on heatsecurity; 2018 ‒ close to droughty and warm on temperature. According to the method of descriptor sets when comparing with the average summer values, the total measure of similarity of precipitation taking into account monthly values was 82,4; 77,9 and 75,4 %, and taking into account decade ‒ 79,9; 62,9 and 59,4% respectively for the warm period (April-September) in 2016... 2018. When comparing with the average monthly values, the total measure of similarity of the average daily air temperatures for the warm period (April-September) 2016... 2018, taking into account monthly values, was 95,7; 96,5 and 93,7 %, taking into account decade ‒ 92,5; 91,2 and 91,6 %, respectively.

MAXIMUM OF ENTROPY FOR CREDAL SETS

In belief functions, there is a total measure of uncertainty that quantify the lack of knowledge and verifies a set of important properties. It is based on two measures: maximum of entropy and non-specificity. In this paper, we prove that the maximum of entropy verifies the same set of properties in a more general theory as credal sets and we present an algorithm that finds the probability distribution of maximum entropy for another interesting type of credal sets as probability intervals.

Linear combinations of harmonic measures and quadrature domains of signed measures with small supports

In this paper we discuss the shape of the quadrature domain of a signed measure for harmonic functions. It is known that the quadrature domain of a positive measure with small support is like a ball if the total measure is large enough. We show that, on the contrary, if the measure is not positive then the quadrature domain can be close to an arbitrary domain. This follows from a lemma concerning linear combinations of harmonic measures.

Corrections to ‘Invariant measures for higher-rank hyperbolic abelian actions’

The proofs of Theorems 5.1 and 7.1 of [2] contain a gap. We will show below how to close it under some suitable additional assumptions in these theorems and their corollaries. We will assume the notation of [2] throughout. In particular, $\mu$ is a measure invariant and ergodic under an $R^k$-action $\alpha$. Let us first explain the gap. Both theorems are proved by establishing a dichotomy for the conditional measures of $\mu$ along the intersection of suitable stable manifolds. They were either atomic or invariant under suitable translation or unipotent subgroups $U$. Atomicity eventually led to zero entropy. Invariance of the conditional measures showed invariance of $\mu$ under $U$. We then claimed that $\mu$ was algebraic using, respectively, unique ergodicity of the translation subgroup on a rational subtorus or Ratner's theorem (cf. [2, Lemma 5.7]). This conclusion, however, only holds for the $U$-ergodic components of $\mu$ which may not equal $\mu$. In fact, in the toral case, the $R^k$-action may have a zero-entropy factor such that the conditional measures along the fibers are Haar measures along a foliation by rational subtori. Since invariant measures with zero entropy have not been classified, we cannot conclude algebraicity of the total measure $\mu$ at this time. In the toral case, the existence of zero entropy factors turns out to be precisely the obstruction to our methods. The case of Weyl chamber flows is somewhat different as the ‘Haar’ direction of the measure may not be integrable. In this case, we need to use additional information coming from the semisimplicity of the ambient Lie group to arrive at the versions of Theorem 7.1 presented below.

The Topological Support of Gauss Measure on Hilbert Space

Let X be a Hilbert space. The topological support of a Radon probability measure P on X is the least closed subset M of X that carries the total measure 1.