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Comparison of uniformity decisions in DUS testing for full and reduced numbers of measurements

100%
Pilarczyk W., Kowalczyk B., Bakinowska E.
Biometrical Letters
|
2015
|
tom 52
|
nr 1
47-53
EN
It is investigated how a reduction in the number of measurements influences uniformity decisions in distinctness, uniformity and stability (DUS) testing. Using real data from DUS trials performed in Poland for several species, it is shown that when final decisions are taken after three years of testing, a reduction in the number of measurements by 50% of the numbers indicated in the Guidelines has very limited impact on decisions (rejection or approval of candidate variety). Decisions taken after one year (or two years) are more dependent on the numbers of measurements.
2
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On unitary Cauchy filters on topological monoids

100%
Averbukh B. G.
Topological Algebra and its Applications
|
2013
|
tom 1
46-59
EN
For Hausdorff topological monoids, the concept of a unitary Cauchy net is a generalization of the concept of a fundamental sequence of reals. We consider properties and applications of such nets and of corresponding filters and prove, in particular, that the underlying set of a given monoid, endowed with the family of such filters, forms a Cauchy space whose convergence structure defines a uniform topology. A commutative monoid endowed with the corresponding uniformity is uniform. A distant purpose of the paper is to transfer the classical concepts of a completeness and of a completion into the theory of topological monoids.
3
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Uniform Space

75%
Coghetto R.
Formalized Mathematics
|
2016
|
tom 24
|
nr 3
215-226
EN
In this article, we formalize in Mizar [1] the notion of uniform space introduced by André Weil using the concepts of entourages [2]. We present some results between uniform space and pseudo metric space. We introduce the concepts of left-uniformity and right-uniformity of a topological group. Next, we define the concept of the partition topology. Following the Vlach’s works [11, 10], we define the semi-uniform space induced by a tolerance and the uniform space induced by an equivalence relation. Finally, using mostly Gehrke, Grigorieff and Pin [4] works, a Pervin uniform space defined from the sets of the form ((X\A) × (X\A)) ∪ (A×A) is presented.
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