The objective of the paper was to illustrate using and usefulness of a joint AMMI and cluster analyses to assess the grain yield adaptive response of Polish and foreign 31 winter wheat cultivars in a range of 20 environments (locations) and across 3 years (2005-2007) under integrated crop management, using data obtained in the post-registration variety testing trials (called PDO trials), to ide...

§1. I will start with a quick definition of descriptive set theory: It is the study of the structure of definable sets and functions in separable completely metrizable spaces. Such spaces are usually called Polish spaces. Typical examples are Rn, Cn, (separable) Hilbert space and more generally all separable Banach spaces, the Cantor space 2N, the Baire space NN, the infinite symmetric group S∞...

Given a topological group G let C(G) denote the Banach space of bounded, continous real valued function on G. Eberlein [1] defined a function f ∈ C(G) to be weakly almost periodic if the weak closure of all of its translates is compact in the weak topology on C(G) — in other words, if fx(y) is defined to be f(yx−1) then the weak closure of {fx | x ∈ G} is weakly compact. The set of weakly almos...

Let X be a separable complete metric space. We characterize completely the innnitesimal generators of semigroups of linear transformations in C b (X), the bounded real-valued continuous functions on X, that are induced by strongly continuous semigroups of continuous transformations in X. In order to do this, C b (X) is equipped with a locally convex topology known as the strict topology. Introd...

PROCESSES AND SPACE WEATHERING. A. Przepiórka 1 , S. Crites 2 , S. Quintana 3 , C. Santiago 4 , T. Trabucchi 5 , D. A. Kring 6 ; 1 Space Research Centre of the Polish Academy of Sciences, Warsaw, Poland, [email protected]; 2 University of Hawai’i, Honolulu, HI; 3 Brown University, Providence, RI; 4 University of Texas at El Paso, El Paso, TX; 5 University of New Brunswick, New Brunswick, C...

The singularity space consists of all germs (X, x), with X a Noetherian scheme and x a point, where we identify two such germs if they become the same after an analytic extension of scalars. This is a Polish space for the metric given by the order to which infinitesimal neighborhoods agree after base change. In other words, the classification of singularities up to analytic extensions of scalar...

The singularity space consists of all germs (X, x), with X a Noetherian scheme and x a point, where we identify two such germs if they become the same after an analytic extension of scalars. This is a Polish space for the metric given by the order to which infinitesimal neighborhoods agree after base change. In other words, the classification of singularities up to analytic extensions of scalar...

Correspondences, which are also called multifunctions, set valued maps, and random sets, have been studied extensively and acquired great importance in recent years. The study of measurable correspondences and their selections has applications to a variety of areas. These include optimization, control theory, pattern analysis, stochastic analysis, and mathematical economics. See [5], [11], [18]...