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...     

Flexible Liquid Crystal Polymer Technologies from Microwave to Terahertz Frequencies

With the emergence of fifth-generation (5G) cellular networks, millimeter-wave (mmW) and terahertz (THz) frequencies have attracted ever-growing interest for advanced wireless applications. The traditional printed circuit board materials have become uncompetitive at such high frequencies due to their high dielectric loss and large water absorption rates. As a promising high-frequency alternative, liquid crystal polymers (LCPs) have been widely investigated for use in circuit devices, chip integration, and module packaging over the last decade due to their low loss tangent up to 1.8 THz and good hermeticity. The previous review articles have summarized the chemical properties of LCP films, flexible LCP antennas, and LCP-based antenna-in-package and system-in-package technologies for 5G applications, although these articles did not discuss synthetic LCP technologies. In addition to wireless applications, the attractive mechanical, chemical, and thermal properties of LCP films enable interesting applications in micro-electro-mechanical systems (MEMS), biomedical electronics, and microfluidics, which have not been summarized to date. Here, a comprehensive review of flexible LCP technologies covering electric circuits, antennas, integration and packaging technologies, front-end modules, MEMS, biomedical devices, and microfluidics from microwave to THz frequencies is presented for the first time, which gives a broad introduction for those outside or just entering the field and provides perspective and breadth for those who are well established in the field.     

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.     

Biodegradable Oxamide‐Phenylene‐Based Mesoporous Organosilica Nanoparticles with Unprecedented Drug Payloads for Delivery in Cells

We describe biodegradable mesoporous hybrid nanoparticles (NPs) in the presence of proteins and their applications for drug delivery. We synthesized oxamide phenylene‐based mesoporous organosilica nanoparticles (MON) in the absence of a silica source which had remarkably high organic content and high surface areas. Oxamide functions provided biodegradability in the presence of trypsin model proteins. MON displayed exceptionally high payloads of hydrophilic and hydrophobic drugs (up to 84 wt %), and a unique zero premature leakage without the pore capping, unlike mesoporous silica. MON were biocompatible and internalized into cancer cells for drug delivery.     

On subsemigroups of βℕ and absolute coretracts

A semigroup S is called an absolute coretract if for any continuous homomorphism f from a compact Hausdorff right topological semigroup T onto a compact Hausdorff right topological semigroup containing S algebraically there exists a homomorphism g \colon S→ T such that f\circ g=id _S . The semigroup β\ben contains isomorphic copies of any countable absolute coretract. In this article we define a class C of semigroups of idempotents each of which is a decreasing chain of rectangular semigroups. It is proved that every semigroup from C is an absolute coretract and every finite semigroup of idempotents, which is an absolute coretract, belongs to C . July 25, 2000