Coboundary Lie bialgebras and commutative subalgebras of universal enveloping algebras

We solve a functional version of the problem of twist quantization of a coboundary Lie bialgebra (g,r,Z). We derive from this the following results: (a) the formal Poisson manifolds g^* and G^* are isomorphic; (b) we construct a subalgebra of U(g^*), isomorphic to S(g^*)^g. When g can be quantized, we construct a deformation of the morphism S(g^*)^g subset U(g^*). When g is quasitriangular and nondegenerate, we compare our construction with Semenov-Tian-Shansky's construction of a commutative subalgebra of U(g^*). We also show that the canonical derivation of the function ring of G^* is Hamiltonian

Poisson algebras associated to quasi-Hopf algebras

We define admissible quasi-Hopf quantized universal enveloping (QHQUE) algebras by h-adic valuation conditions. We show that any QHQUE algebra is twist-equivalent to an admissible one. We prove a related statement: any associator is twist-equivalent to a Lie associator. We attach a quantized formal series algebra to each admissible QHQUE algebra and study the resulting Poisson algebras.Comment: We construct a lift for any Lie quasi-bialgebra with zero cobracke

Electron Beam Testing of Integrated Circuits Using a Picosecond Photoelectron Scanning Electron Microscope

A scanning electron microscope which uses an ultrashort pulsed laser / photocathode combination as an electron source produces electron pulses of about 1 ps in duration at a 100 MHz repetition rate. By using this instrument in the stroboscopic voltage contrast mode we have performed waveform measurements at the internal nodes of high speed silicon integrated circuits at room and at liquid nitrogen temperature, and studied the propagation of ultrafast electrical transients on various interconnection structures

New rr-Matrices for Lie Bialgebra Structures over Polynomials

For a finite dimensional simple complex Lie algebra $\mathfrak{g}$, Lie bialgebra structures on $\mathfrak{g}[[u]]$ and $\mathfrak{g}[u]$ were classified by Montaner, Stolin and Zelmanov. In our paper, we provide an explicit algorithm to produce $r$-matrices which correspond to Lie bialgebra structures over polynomials

On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization

We study classical twists of Lie bialgebra structures on the polynomial current algebra $\mathfrak{g}[u]$, where $\mathfrak{g}$ is a simple complex finite-dimensional Lie algebra. We focus on the structures induced by the so-called quasi-trigonometric solutions of the classical Yang-Baxter equation. It turns out that quasi-trigonometric $r$-matrices fall into classes labelled by the vertices of the extended Dynkin diagram of $\mathfrak{g}$. We give complete classification of quasi-trigonometric $r$-matrices belonging to multiplicity free simple roots (which have coefficient 1 in the decomposition of the maximal root). We quantize solutions corresponding to the first root of $\mathfrak{sl}(n)$.Comment: 41 pages, LATE

IQ driving QI: The Asia pacific consortium on osteoporosis (APCO): An innovative and collaborative initiative to improve osteoporosis care in the Asia pacific

Asia Pacific Consortium on Osteoporosis (APCO) comprises of clinical experts from across the Asia Pacific region, uniting to develop solutions to problems facing osteoporosis management and care. The vision of APCO is to reduce the burden of osteoporosis and fragility fractures in the Asia Pacific region.Introduction: The Asia Pacific (AP) region comprises 71 countries with vastly different healthcare systems. It is predicted that by 2050, more than half the world\u27s hip fractures will occur in this region. The Asia Pacific Consortium on Osteoporosis (APCO) was set up in May 2019 with the vision of reducing the burden of osteoporosis and fragility fractures in the AP region.Methods: APCO has so far brought together 39 clinical experts from countries and regions across the AP to develop solutions to challenges facing osteoporosis management and fracture prevention in this highly populous region of the world. APCO aims to achieve its vision by engaging with relevant stakeholders including healthcare providers, policy makers and the public. The initial APCO project is to develop and implement a Framework of pan-AP minimum clinical standards for the screening, diagnosis and management of osteoporosis.Results and conclusions: The Framework will serve as a platform upon which new national clinical guidelines can be developed or existing guidelines be revised, in a standardised fashion. The Framework will also facilitate benchmarking for provision of quality of care. It is hoped that the principles underlying the formation and functioning of APCO can be adopted by other regions and that every health care facility and progressively every country in the world can follow our aspirational path and progress towards best practice