Quasi-Quantum Planes and Quasi-Quantum Groups of Dimension p3p^3 and p4p^4

The aim of this paper is to contribute more examples and classification results of finite pointed quasi-quantum groups within the quiver framework initiated in \cite{qha1, qha2}. The focus is put on finite dimensional graded Majid algebras generated by group-like elements and two skew-primitive elements which are mutually skew-commutative. Such quasi-quantum groups are associated to quasi-quantum planes in the sense of nonassociative geomertry \cite{m1, m2}. As an application, we obtain an explicit classification of graded pointed Majid algebras with abelian coradical of dimension $p^3$ and $p^4$ for any prime number $p.$Comment: 12 pages; Minor revision according to the referee's suggestio

Relativistic Measurements from Timing the Binary Pulsar PSR B1913+16

We present relativistic analyses of 9257 measurements of times-of-arrival from the first binary pulsar, PSR B1913+16, acquired over the last thirty-five years. The determination of the 'Keplerian' orbital elements plus two relativistic terms completely characterizes the binary system, aside from an unknown rotation about the line of sight; leading to a determination of the masses of the pulsar and its companion: 1.438 $\pm$ 0.001 solar masses and 1.390 $\pm$ 0.001 solar masses, respectively. In addition, the complete system characterization allows the creation of tests of relativistic gravitation by comparing measured and predicted sizes of various relativistic phenomena. We find that the ratio of observed orbital period decrease due to gravitational wave damping (corrected by a kinematic term) to the general relativistic prediction, is 0.9983 pm 0.0016; thereby confirming the existence and strength of gravitational radiation as predicted by general relativity. For the first time in this system, we have also successfully measured the two parameters characterizing the Shapiro gravitational propagation delay, and find that their values are consistent with general relativistic predictions. We have also measured for the first time in any system the relativistic shape correction to the elliptical orbit, $\delta_{\theta}$,although its intrinsic value is obscured by currently unquantified pulsar emission beam aberration. We have also marginally measured the time derivative of the projected semimajor axis, which, when improved in combination with beam aberration modelling from geodetic precession observations, should ultimately constrain the pulsar's moment of inertia.Comment: Accepted by APJ 2016 June

Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories

By viewing Clifford algebras as algebras in some suitable symmetric Gr-categories, Albuquerque and Majid were able to give a new derivation of some well known results about Clifford algebras and to generalize them. Along the same line, Bulacu observed that Clifford algebras are weak Hopf algebras in the aforementioned categories and obtained other interesting properties. The aim of this paper is to study generalized Clifford algebras in a similar manner and extend the results of Albuquerque, Majid and Bulacu to the generalized setting. In particular, by taking full advantage of the gauge transformations in symmetric linear Gr-categories, we derive the decomposition theorem and provide categorical weak Hopf structures for generalized Clifford algebras in a conceptual and simpler manner

The Green rings of pointed tensor categories of finite type

In this paper, we compute the Clebsch-Gordan formulae and the Green rings of connected pointed tensor categories of finite type.Comment: 14 page

The mPEG-PCL Copolymer for Selective Fermentation of Staphylococcus lugdunensis Against Candida parapsilosis in the Human Microbiome.

Many human skin diseases, such as seborrheic dermatitis, potentially occur due to the over-growth of fungi. It remains a challenge to develop fungicides with a lower risk of generating resistant fungi and non-specifically killing commensal microbes. Our probiotic approaches using a selective fermentation initiator of skin commensal bacteria, fermentation metabolites or their derivatives provide novel therapeutics to rein in the over-growth of fungi. Staphylococcus lugdunensis (S. lugdunensis) bacteria and Candida parapsilosis (C. parapsilosis) fungi coexist in the scalp microbiome. S. lugdunensis interfered with the growth of C. parapsilosis via fermentation. A methoxy poly(ethylene glycol)-b-poly(ε-caprolactone) (mPEG-PCL) copolymer functioned as a selective fermentation initiator of S. lugdunensis, selectively triggering the S. lugdunensis fermentation to produce acetic and isovaleric acids. The acetic acid and its pro-drug diethyleneglycol diacetate (Ac-DEG-Ac) effectively suppressed the growth of C. parapsilosis in vitro and impeded the fungal expansion in the human dandruff. We demonstrate for the first time that S. lugdunensis is a skin probiotic bacterium that can exploit mPEG-PCL to yield fungicidal short-chain fatty acids (SCFAs). The concept of bacterial fermentation as a part of skin immunity to re-balance the dysbiotic microbiome warrants a novel avenue for studying the probiotic function of the skin microbiome in promoting health