We show that it is consistent, relative to ω many supercompact cardinals, that the super tree property holds at אn for all 2 ≤ n < ω but there are weak square and a very good scale at אω .

a quantum chemical investigation was carried out to study the properties of intermolecular f•••f, br•••br and br•••o interactions in crystalline 1-bromo-2,3,5,6-tetrafluoro-nitrobenzene (bfnb). this system was selected to mimic the halogen-halogen as well as halogen bonding interactions found within crystal structures as well as within biological systems. we found that fluorine atoms have weak ...

We investigate some problems of the following type: For which sets H is it true that if f is in a given class F of periodic functions and the difference functions ∆hf(x) = f(x + h) − f(x) are in a given smaller class G for every h ∈ H then f itself must be in G? Denoting the class of counter-example sets by H(F ,G), that is, H(F ,G) = {H ⊂ R/Z : (∃f ∈ F \ G) (∀h ∈ H) ∆hf ∈ G}, we try to charact...

We study a number of conditions on the Hilbert function of a level artinian algebra which imply the Weak Lefschetz Property (WLP). Possibly the most important open case is whether a codimension 3 SI-sequence forces the WLP for level algebras. In other words, does every codimension 3 Gorenstein algebra have the WLP? We give some new partial answers to this old question: we prove an affirmative a...

By introducing the concepts of order almost Dunford-Pettis and almost weakly limited operators in Banach lattices, we give some properties of them related to some well known classes of operators, such as, order weakly compact, order Dunford-Pettis, weak and almost Dunford- Pettis and weakly limited operators. Then, we characterize Banach lat- tices E and F on which each operator from E into F t...

In this work, we show that if f is a uniformly continuous map defined over Polish metric space, then the set of f-invariant measures with zero entropy G δ $G_\delta$ (in weak topology). particular, generic f-periodic dense in measures. This settles conjecture posed by Sigmund (Trans. Amer. Math. Soc. 190 (1974), 285–299), which states an invariant measure topological dynamical system satisfies ...

We study the weak bounded approximation property (weak BAP) of pairs and show that each of the spaces c0 and `1 has a subspace having the approximation property but failing the weak BAP.