On points avoiding measures Borodulin–Nadzieja, Piotr; Ranchynski, Artsiom
Topology and its applications,
09/2024, Volume:
354
Journal Article
Peer reviewed
Open access
We say that an element x of a topological space X avoids measures if for every Borel measure μ on X if μ({x})=0, then there is an open U∋x such that μ(U)=0. The negation of this property can viewed ...as a local version of the property of supporting a strictly positive measure. We study points avoiding measures in the general setting as well as in the context of ω⁎, the remainder of Stone-Čech compactification of ω.
The purpose of this note is to extend in a simple and unified way some results on orthogonal polynomials with respect to the weight function|Tm(x)|p1−x2,−1<x<1, where Tm is the Chebyshev polynomial ...of the first kind of degree m and p>−1. Namely, this note provides an explicit representation of the recurrence coefficients for polynomials orthogonal with respect to the above weight function and an explicit representation for these polynomials in terms of known functions.
In this paper, we characterize those positive Borel measurable symbols
μ
on
C
n
that induce the Toeplitz operators
T
μ
α
to be bounded or compact between different Fock–Sobolev–type spaces
F
α
p
and
...F
α
∞
with
0
<
p
≤
∞
.
This quantitative study queried perceptions of the gender corrective mechanism as part of a broader parliamentary gender balance reform programme in Southern European, EU island state Malta. A ...representative sample (n = 435) of the Maltese electorate showed support for increased representation of women (88.5%) and the integration of the gender corrective mechanism (66.5%); but manifested a preference for other measures, namely childcare facilities, full-time backbenchers and more females in the electoral commission. Consequently, should the preferred measures not be sufficiently addressed, the reform risks falling short of sustainable development. The study adds to literature about how the electorate engages with more representative parliaments when this is targeted using constitutional amendments. Recommendations include financial support for parties to attract candidates from under-represented genders, and an effective public information campaign that explains the gender corrective mechanism as a safety-valve that compensates for any gaps in representation that the other reform pillars fail to achieve.
In this paper, we first study the convergence in m-capacity. These results are used to obtain an extension of a Kolodziej's result and Ahag et al.'s result to the class
.
In the paper, we prove Steffensen type inequalities for positive finite measures by using functions which are convex in point. Further, we prove Steffensen type inequalities on Borel σ-algebra for ...the function of the form f/h which is convex in point. We conclude the paper by showing that these results also hold for convex functions.
We consider perturbations of dynamical semigroups on the algebra of all bounded operators in a Hilbert space generated by covariant completely positive measures on the semi-axis. The construction is ...based upon unbounded linear perturbations of generators of the preadjoint semigroups on the space of nuclear operators. As an application we construct a perturbation of the semigroup of non-unital *-endomorphisms on the algebra of canonical anticommutation relations resulting in the flow of shifts.
Numerous studies have shown that providing straw to pigs can reduce undesirable behaviours such as aggression, tail biting and stereotypy. The measurement of various neuromodulators can be helpful in ...assessing the development of positive behaviours and overall animal welfare. The oxytocin release is frequently linked to positive emotions and positive welfare. It has been suggested that oxytocin modulates the serotoninergic system. This study aims to investigate the potential effect of straw provision in pigs on peripheral levels of oxytocin and serotonin. In total, 18 mini-pigs were involved in an exploratory study conducted in two parallel groups, Enriched (n=10) and Control (n=8) groups. Pigs were divided by group and housed in pens of two individuals. Straw was provided continuously only in Enriched group and renewed each day for 2 weeks. Two blood samples were drawn from each animal 5 to 10 min before providing the straw, and 15 min after providing straw, during the 1st week, to analyse peripheral changes in oxytocin and serotonin before and after straw provision, and determine the existence of a putative short-term effect. The same procedure was carried out for Control group, without straw provision. Long-term effects of straw provision were also examined using blood samples drawn at the same hour from each animal in the 2nd and 3rd weeks. During this time, animals had the permanent possibility to explore the straw in Enriched group but not in Control group. At the end of each week, one animal-keeper completed two visual analogue scales for each mini-pig regarding the difficulty/ease to work with and handle it and its trust in humans. Results showed peripheral oxytocin increases in both groups after 2 weeks (P=0.02). Results did not demonstrate any effect of providing straw to allow exploratory behaviour on peripheral serotonin. Other results were not significant. This preliminary study explored the relationship between peripheral oxytocin and serotonin and the presence of straw that allow pigs to perform exploratory behaviour, suggesting that there was no relationship between them. Some future studies may include crossing oxytocin and serotonin with other parameters, such as behavioural measures, to obtain more information about the true state of the animal and any possible relationship with pig welfare.
The Lebesgue Measure on Rn Mărginean, Diana
Procedia technology,
2015, 2015-00-00, Volume:
19
Journal Article
Peer reviewed
Open access
Lebesgue measure on Rn is restriction of outer Lebesgue measure to the family of Lebesgue measurable sets. All properties of Lebesgue positive measure on R are transfered to Lebesgue measure on Rn.
...The Lebesgue measure on B is only meassure defined on σ-algebra of Borel sets of Rn, which is invariance to translation and ▪.
We consider two positive, normalized measures dA(x) and dB(x) related by the relationship dA(x)=Cx+DdB(x) or by dA(x)=Cx2+EdB(x) and dB(x) is symmetric. We show that then the polynomial sequences ...an(x),bn(x) orthogonal with respect to these measures are related by the relationship an(x)=bn(x)+κnbn-1(x) or by an(x)=bn(x)+λnbn-2(x) for some sequences κn and λn. We present several examples illustrating this fact and also present some attempts for extensions and generalizations. We also give some universal identities involving polynomials bn(x) and the sequence κn that have a form of the Fourier series expansion of the Radon–Nikodym derivative of one measure with respect to the other.
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