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Existence of positive periodic solutions of an SEIR model with periodic coefficients

Tailei Zhang, Junli Liu, Zhidong Teng (2012)

Applications of Mathematics

An SEIR model with periodic coefficients in epidemiology is considered. The global existence of periodic solutions with strictly positive components for this model is established by using the method of coincidence degree. Furthermore, a sufficient condition for the global stability of this model is obtained. An example based on the transmission of respiratory syncytial virus (RSV) is included.

Extension of point-finite partitions of unity

Haruto Ohta, Kaori Yamazaki (2006)

Fundamenta Mathematicae

A subspace A of a topological space X is said to be P γ -embedded ( P γ (point-finite)-embedded) in X if every (point-finite) partition of unity α on A with |α| ≤ γ extends to a (point-finite) partition of unity on X. The main results are: (Theorem A) A subspace A of X is P γ (point-finite)-embedded in X iff it is P γ -embedded and every countable intersection B of cozero-sets in X with B ∩ A = ∅ can be separated from A by a cozero-set in X. (Theorem B) The product A × [0,1] is P γ (point-finite)-embedded in X...

Extension operators on balls and on spaces of finite sets

Antonio Avilés, Witold Marciszewski (2015)

Studia Mathematica

We study extension operators between spaces of continuous functions on the spaces σ ( 2 X ) of subsets of X of cardinality at most n. As an application, we show that if B H is the unit ball of a nonseparable Hilbert space H equipped with the weak topology, then, for any 0 < λ < μ, there is no extension operator T : C ( λ B H ) C ( μ B H ) .

Extensions of Borel Measurable Maps and Ranges of Borel Bimeasurable Maps

Petr Holický (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We prove an abstract version of the Kuratowski extension theorem for Borel measurable maps of a given class. It enables us to deduce and improve its nonseparable version due to Hansell. We also study the ranges of not necessarily injective Borel bimeasurable maps f and show that some control on the relative classes of preimages and images of Borel sets under f enables one to get a bound on the absolute class of the range of f. This seems to be of some interest even within separable spaces.

Extensions of generic measure-preserving actions

Julien Melleray (2014)

Annales de l’institut Fourier

We show that, whenever Γ is a countable abelian group and Δ is a finitely-generated subgroup of Γ , a generic measure-preserving action of Δ on a standard atomless probability space ( X , μ ) extends to a free measure-preserving action of Γ on ( X , μ ) . This extends a result of Ageev, corresponding to the case when Δ is infinite cyclic.

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