Given a group-invariant quasi-free state on the algebra of canonical commutation relations (CCR), we show how group averaging techniques can be used to obtain a symmetry reduced CCR algebra and reduced quasi-free state. When the group is compact this method of symmetry reduction leads to standard results which can be obtained using other methods. When the group is non-compact the group averagin...

A family of sets in the plane is said to have a 3-transversal if there exists a set of 3 points such that each member of the family contains at least one of them. A conjecture of Grünbaum’s says that a planar family of translates of a convex compact set has a 3-transversal provided that any two of its members intersect. Recently the conjecture has been proved affirmatively (see [1]). We provide...

Let K ⊂ Rn be a compact definable set in an o-minimal structure over R, e.g., a semi-algebraic or a subanalytic set. A definable family {Sδ| 0 < δ ∈ R} of compact subsets of K, is called a monotone family if Sδ ⊂ Sη for all sufficiently small δ > η > 0. The main result of the paper is that when dimK ≤ 2 there exists a definable triangulation of K such that for each (open) simplex Λ of the trian...

Human calumenin (hCALU) is a six EF-hand protein belonging to the CREC family. As other members of the family, it is localized in the secretory pathway and regulates the activity of SERCA2a and of the ryanodine receptor in the endoplasmic reticulum (ER). We have studied the effects of Ca2+ binding to the protein and found it to attain a more compact structure upon ion binding. Circular Dichrois...

A Tychonoff space X is called RG if the embedding of C(X) → C(Xδ) is an epimorphism of rings. Compact RG spaces are known and easily described. We study the pseudocompact RG spaces. These must be scattered of finite Cantor Bendixon degree but need not be locally compact. However, under strong hypotheses, (countable compactness, or small cardinality) these spaces must, indeed, be compact. The ma...

A separated cell A of a topological space X is a family of pairwise disjoint open sets with the property that, for any partition A= A1 ∪ A2 of A, ⋃ A1 and ⋃ A2 are completely separated. The separated cellularity sc(X) of X is the supremum of all cardinals of separated cells. A space X has finite separation if it has no infinite separated cells. With X compact, every separated cell of X has size...

In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

We show that the quantum family of all maps from a finite space to a finite dimensional compact quantum semigroup has a canonical quantum semigroup structure. Let X be a finite space and Y be a compact space. Then the space F (X,Y ) of all maps from X to Y , is a compact space with compact-open topology. The notion of quantum family of all maps, defined by Woronowicz [8] and Soltan [5], is a no...