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Minkowski difference and Sallee elements in an ordered semigroup

100%

Borowska D. , Grzybowski J.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2007

tom Vol. 47, [Z] 1

77-83

In the manner of Pallaschke and Urbański ([5], chapter 3) we generalize the notions of the Minkowski difference and Sallee sets to a semigroup. Sallee set (see [7], definition of the family S on p. 2) is a compact convex subset A of a topological vector space X such that for all subsets B the Minkowski difference A-B of the sets A and B is a summand of A. The family of Sallee sets characterizes the Minkowski subtraction, which is important to the arithmetic of compact convex sets (see [5]). Sallee polytopes are related to monotypie poly topes (see [4]). We generalize properties of Minkowski difference and Sallee sets to semigroup and investigate the families of Sallee elements in several specific semigroups.

Strongly monotypic polytopes in R3

100%

Borowska D. , Grzybowski J.

2008

tom Vol. 41, nr 1

165-169

McMullen et al. [3] characterized all three-dimensional monotypic polytopes by presenting four types of such polytopes. They stated that three of these types are strongly monotypic polytopes. We examine which monotypic polytopes of the fourth type are strongly monotypic. This way we complete the description of all strongly monotypic polytopes in R3.

Metoda krążkowo-dyfuzyjna w weterynaryjnej diagnostyce bakteriologicznej - praktyczne dane

80%

Borowska D. , Jablonski A. , Pejsak Z.

2014

tom 89

nr 02

Application of quantitative PCR for detection of Mycoplasma suis in blood samples

51%

Jablonski A. , Borowska D. , Zebek S. , Kowalczyk A. , Dors A. , Zmudzki J. , Nowak A. , Pejsak Z.

tom 58

nr 4

The aim of the study was to develop and validate a real-time PCR method, using a TaqMan probe, for quantification of Mycoplasma suis in porcine blood. No PCR signals with closely related non-haemotrophic mycoplasmas were obtained. The detection limit of PCR for plasmid combined with blood DNA was determined to be 10³/reaction (5 µL of DNA) (1.2x10⁵ target copies in 1 mL of blood). The linearity of real-time PCR (near 1) indicates its use as a quantitative method. Real-time and quantitative PCR were sensitive and specific for the detection and quantification of M. suis in the blood of animals with acute and chronic form of eperythrozoonosis. Developed quantitative PCR cannot be used to detect carrier animals with a small amount of M. suis in their blood. The validity of real-time PCR used in the studies was confirmed by the low inter- and intra-assay coefficients of variation. This fact confirms the applicability of the assay in other laboratories.

Four years of African swine fever in Poland. New insights into epidemiology and prognosis of future disease spread

51%

Pejsak Z. , Niemczuk K. , Frant M. , Mazur M. , Pomorska-Mol M. , Zietek-Barszcz A. , Bocian L. , Lyjak M. , Borowska D. , Wozniakowski G.

Polish Journal of Veterinary Sciences

2018

tom 21

nr 4