On extremally disconnected topological groups

We introduce the notion of a partially selective ultrafilter and prove that (a) if G is an extremally disconnected topological group and p is a converging nonprincipal ultrafilter on G containing a countable discrete subset, then p is partially selective, and (b) the existence of a nonprincipal partially selective ultrafilter on a countable set implies the existence of a P-point in ω^∗. Thus it is consistent with ZFC that there is no extremally disconnected topological group containing a countable discrete nonclosed subset.     

Almost maximal spaces

A topological space X is called almost maximal if it is without isolated points and for every x∈X, there are only finitely many ultrafilters on X converging to x. We associate with every countable regular homogeneous almost maximal space X a finite semigroup Ult(X) so that if X and Y are homeomorphic, Ult(X) and Ult(Y) are isomorphic. Semigroups Ult(X) are projectives in the category F of finite semigroups. These are bands decomposing into a certain chain of rectangular components. Under MA, for each projective S in F, there is a countable almost maximal topological group G with Ult(G) isomorphic to S. The existence of a countable almost maximal topological group cannot be established in ZFC. However, there are in ZFC countable regular homogeneous almost maximal spaces X with Ult(X) being a chain of idempotents.     

Larger locally compact monothetic semigroups

Semigroup Forum - We show that for every $$k\in {\mathbb {N}}$$, there is a locally compact noncompact monothetic semigroup S with identity such that S is homeomorphic to a closed nowhere dense...     

Complemented Topologies on Abelian Groups

A topology on a group G is complemented if there exists an indiscrete topology ' on G such that UV={0} for suitable neighborhoods of zero U and V in the topologies and . The authors give a complementation test for an arbitrary topology. Locally compact groups with complemented topologies have been described. A group all of whose continuous homomorphic images are complete is proved to be compact. A family of 2 topologies that are pairwise complementary to one another is defined for an arbitrary group.     

Aggregation of Malmquist productivity indexes allowing for reallocation of resources

In this paper we consider aggregate Malmquist productivity index measures which allow inputs to be reallocated within the group (when in output orientation). This merges the single period aggregation results allowing input reallocation of Nesterenko and Zelenyuk (2007) with the aggregate Malmquist productivity index results of Zelenyuk (2006) to determine aggregate Malmquist productivity indexes that are justified by economic theory, consistent with previous aggregation results, and which maintain analogous decompositions to the original measures. Such measures are of direct relevance to firms or countries who have merged (making input reallocation possible), allowing them to measure potential productivity gains and how these have been realised (or not) over time.     

Completeness of maximal topological groups

Under the assumption of Booth's lemma a negative solution is obtained for Arnautov' s problem: is it true that each nondiscrete topology on a group can be strengthened to a discrete complete one?     

Partitions and sums with inverses in Abelian groups

Let G be an Abelian group and let be infinite. We construct a partition of A such that whenever (xn)_n<ω is a one-to-one sequence in A, g∈G and m<ω, one has

(g+FSI((xn)_n<ω))∩Am≠∅,     

High sensitivity and versatility of the DEER experiment on nitroxide radical pairs at Q-band frequencies

Measurement of distances with the Double Electron-Electron Resonance (DEER) experiment at X-band frequencies using a pair of nitroxides as spin labels is a popular biophysical tool for studying function-related conformational dynamics of proteins. The technique is intrinsically highly precise and can potentially access the range from 1.5 to 6-10 nm. However, DEER performance drops strongly when relaxation rates of the nitroxide spin labels are high and available material quantities are low, which is usually the case for membrane proteins reconstituted into liposomes. This leads to elevated noise levels, very long measurement times, reduced precision, and a decrease of the longest accessible distances. Here we quantify the performance improvement that can be achieved at Q-band frequencies (34.5 GHz) using a high-power spectrometer. More than an order of magnitude gain in sensitivity is obtained with a homebuilt setup equipped with a 150 W TWT amplifier by using oversized samples. The broadband excitation enabled by the high power ensures that orientation selection can be suppressed in most cases, which facilitates extraction of distance distributions. By varying pulse lengths, Q-band DEER can be switched between orientationally non-selective and selective regimes. Because of suppression of nuclear modulations from matrix protons and deuterons, analysis of the Q-band data is greatly simplified, particularly in cases of very small DEER modulation depth due to low binding affinity between proteins forming a complex or low labelling efficiency. Finally, we demonstrate that a commercial Q-band spectrometer can be readily adjusted to the high-power operation.     

On the Ultrafilter Semigroup of an Abelian Topological Group

The ultrafilter semigroup of a topological group G, denoted Ult(G), consists of all nonprincipal ultrafilters on G converging to the identity and is a closed subsemigroup in the Stone-Cech compactification β G_d of G as a discrete semigroup. We show that for every countable nondiscrete Abelian topological group G not containing an open Boolean subgroup, the structural group of the smallest ideal of Ult(G) has cardinality 2^c.     

Topologically free subsets of universal algebras

We prove that every infinite Abelian algebra and every countable field contain infinite topologically free subsets. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 651–661, May, 1997.