On the Hopf–Schur group of a field

Let k be any field. We consider the Hopf–Schur group of k, defined as the subgroup of the Brauer group of k consisting of classes that may be represented by homomorphic images of finite-dimensional Hopf algebras over k. We show here that twisted group algebras and abelian extensions of k are quotients of cocommutative and commutative finite-dimensional Hopf algebras over k, respectively. As a consequence we prove that any tensor product of cyclic algebras over k is a quotient of a finite-dimensional Hopf algebra over k, revealing so that the Hopf–Schur group can be much larger than the Schur group of k.     

Sonochemical Coatings of ZnO and CuO Nanoparticles Inhibit Streptococcus mutans Biofilm Formation on Teeth Model

Antibiotic resistance has prompted the search for new agents that can inhibit bacterial growth. We recently reported on the antibiofilm activities of nanosized ZnO and CuO nanoparticles (NPs) synthesized by using sonochemical irradiation. In this study, we examined the antibacterial activity of ZnO and CuO NPs in a powder form and also examined the antibiofilm behavior of teeth surfaces that were coated with ZnO and CuO NPs using sonochemistry. Free ZnO and CuO NPs inhibited biofilm formation of Streptococcus mutans . Furthermore, by using the sonochemical procedure, we were able to coat teeth surfaces that inhibited bacterial colonization.     

Between arrow and Gibbard-Satterthwaite; A representation theoretic approach

A central theme in social choice theory is that of impossibility theorems, such as Arrow’s theorem [Arr63] and the Gibbard-Satterthwaite theorem [Gib73, Sat75], which state that under certain natural constraints, social choice mechanisms are impossible to construct. In recent years, beginning in Kalai [Kal01], much work has been done in finding robust versions of these theorems, showing “approximate” impossibility remains even when most, but not all, of the constraints are satisfied. We study a spectrum of settings between the case where society chooses a single outcome (à-la-Gibbard-Satterthwaite) and the choice of a complete order (as in Arrow’s theorem). We use algebraic techniques, specifically representation theory of the symmetric group, and also prove robust versions of the theorems that we state. Our relaxations of the constraints involve relaxing of a version of “independence of irrelevant alternatives”, rather than relaxing the demand of a transitive outcome, as is done in most other robustness results.     

Targeting Bone Metastases with a Bispecific Anticancer and Antiangiogenic Polymer–Alendronate–Taxane Conjugate

A polymer therapeutic designed for combination anticancer and antiangiogenic therapy inhibited the proliferation of prostate carcinoma cells and the proliferation, migration, and tube‐formation of endothelial cells. The nanoconjugate was formed from an N‐(2‐hydroxypropyl)methacrylamide (HPMA) copolymer, the bisphosphonate alendronate (for bone targeting), and the chemotherapy agent paclitaxel (PTX), which is cleaved by cathepsin B (see scheme).

     

Projective Resolutions for Modules over Infinite Groups

We define a notion of complexity for modules over group rings of infinite groups. This generalizes the notion of complexity for modules over group algebras of finite groups. We show that if M is a module over the group ring kG, where k is any ring and G is any group, and M has f-complexity (where f is some complexity function) over some set of finite index subgroups of G, then M has f-complexity over G (up to a direct summand). This generalizes the Alperin-Evens Theorem, which states that if the group G is finite then the complexity of M over G is the maximal complexity of M over an elementary abelian subgroup of G. We also show how we can use this generalization in order to construct projective resolutions for the integral special linear groups, SL(n, ℤ), where n ≥ 2.     

Wigner-Ville distribution for pulse propagation in random media: pulsed plane wave

The time-frequency Wigner-Ville distribution for a pulsed plane-wave signal propagating in a continuous random medium is found, based on the previously derived modal series expression for the two-frequency coherence function. The theory can address propagation in any homogeneous isotropic random medium, but closed-form expressions are specifically derived for a general power-law medium. Two alternative formulations are presented: a modal-wavefront approach wherein each mode is asymptotically transformed to the time domain and a collective approach wherein the mode series is summed collectively and then transformed to the time domain using pole contributions. The physical interpretation of these two different representations in the time-frequency domain as either a superposition of localized wavefronts or collective excitations is established, and their applications to the calculation of local moments are considered.