Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]

Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so contains a \textit{universal $R$-matrix} in the tensor product algebra which satisfies the Yang-Baxter equation. Applying the vector representation $\pi$, which acts on the vector module $V$, to one side of a universal $R$-matrix gives a Lax operator. In this paper a Lax operator is constructed for the $C$-type quantum superalgebras $U_q[osp(2|n)]$. This can in turn be used to find a solution to the Yang-Baxter equation acting on $V \otimes V \otimes W$ where $W$ is an arbitrary $U_q[osp(2|n)]$ module. The case $W=V$ is included here as an example.Comment: 15 page

Interventions to improve hand hygiene compliance in patient care

Background Health care‐associated infection is a major cause of morbidity and mortality. Hand hygiene is regarded as an effective preventive measure. This is an update of a previously published review. Objectives To assess the short‐ and long‐term success of strategies to improve compliance to recommendations for hand hygiene, and to determine whether an increase in hand hygiene compliance can reduce rates of health care‐associated infection. Search methods We conducted electronic searches of the Cochrane Register of Controlled Trials, PubMed, Embase, and CINAHL. We conducted the searches from November 2009 to October 2016. Selection criteria We included randomised trials, non‐randomised trials, controlled before‐after studies, and interrupted time series analyses (ITS) that evaluated any intervention to improve compliance with hand hygiene using soap and water or alcohol‐based hand rub (ABHR), or both. Data collection and analysis Two review authors independently screened citations for inclusion, extracted data, and assessed risks of bias for each included study. Meta‐analysis was not possible, as there was substantial heterogeneity across studies. We assessed the certainty of evidence using the GRADE approach and present the results narratively in a 'Summary of findings' table. Main results This review includes 26 studies: 14 randomised trials, two non‐randomised trials and 10 ITS studies. Most studies were conducted in hospitals or long‐term care facilities in different countries, and collected data from a variety of healthcare workers. Fourteen studies assessed the success of different combinations of strategies recommended by the World Health Organization (WHO) to improve hand hygiene compliance. Strategies consisted of the following: increasing the availability of ABHR, different types of education for staff, reminders (written and verbal), different types of performance feedback, administrative support, and staff involvement. Six studies assessed different types of performance feedback, two studies evaluated education, three studies evaluated cues such as signs or scent, and one study assessed placement of ABHR. Observed hand hygiene compliance was measured in all but three studies which reported product usage. Eight studies also reported either infection or colonisation rates. All studies had two or more sources of high or unclear risks of bias, most often associated with blinding or independence of the intervention. Multimodal interventions that include some but not all strategies recommended in the WHO guidelines may slightly improve hand hygiene compliance (five studies; 56 centres) and may slightly reduce infection rates (three studies; 34 centres), low certainty of evidence for both outcomes. Multimodal interventions that include all strategies recommended in the WHO guidelines may slightly reduce colonisation rates (one study; 167 centres; low certainty of evidence). It is unclear whether the intervention improves hand hygiene compliance (five studies; 184 centres) or reduces infection (two studies; 16 centres) because the certainty of this evidence is very low. Multimodal interventions that contain all strategies recommended in the WHO guidelines plus additional strategies may slightly improve hand hygiene compliance (six studies; 15 centres; low certainty of evidence). It is unclear whether this intervention reduces infection rates (one study; one centre; very low certainty of evidence). Performance feedback may improve hand hygiene compliance (six studies; 21 centres; low certainty of evidence). This intervention probably slightly reduces infection (one study; one centre) and colonisation rates (one study; one centre) based on moderate certainty of evidence. Education may improve hand hygiene compliance (two studies; two centres), low certainty of evidence. Cues such as signs or scent may slightly improve hand hygiene compliance (three studies; three centres), low certainty of evidence. Placement of ABHR close to point of use probably slightly improves hand hygiene compliance (one study; one centre), moderate certainty of evidence. Authors' conclusions With the identified variability in certainty of evidence, interventions, and methods, there remains an urgent need to undertake methodologically robust research to explore the effectiveness of multimodal versus simpler interventions to increase hand hygiene compliance, and to identify which components of multimodal interventions or combinations of strategies are most effective in a particular context

A class of quadratic deformations of Lie superalgebras

We study certain Z_2-graded, finite-dimensional polynomial algebras of degree 2 which are a special class of deformations of Lie superalgebras, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. We derive the equivalent of the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate in detail one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.Comment: 26pp, LaTeX. Original title: "Finite dimensional quadratic Lie superalgebras"; abstract re-worded; text clarified; 3 references added; rearrangement of minor appendices into text; new subsection 4.

Generalised Perk--Schultz models: solutions of the Yang-Baxter equation associated with quantised orthosymplectic superalgebras

The Perk--Schultz model may be expressed in terms of the solution of the Yang--Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra $U_q[sl(m|n)]$, with a multiparametric co-product action as given by Reshetikhin. Here we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras $U_q[osp(m|n)]$. In this manner we obtain generalisations of the Perk--Schultz model.Comment: 10 pages, 2 figure

Nonequilibrium phase transitions and tricriticality in a three-dimensional lattice system with random-field competing kinetics

We study a nonequilibrium Ising model that stochastically evolves under the simultaneous operation of several spin-flip mechanisms. In other words, the local magnetic fields change sign randomly with time due to competing kinetics. This dynamics models a fast and random diffusion of disorder that takes place in dilute metallic alloys when magnetic ions diffuse. We performe Monte Carlo simulations on cubic lattices up to L=60. The system exhibits ferromagnetic and paramagnetic steady states. Our results predict first-order transitions at low temperatures and large disorder strengths, which correspond to the existence of a nonequilibrium tricritical point at finite temperature. By means of standard finite-size scaling equations, we estimate the critical exponents in the low-field region, for which our simulations uphold continuous phase transitions.Comment: 14 pages, 7 figures, accepted for publication in Phys. Rev.

Static inverters which sum a plurality of waves Patent

Describing static inverter with single or multiple phase outpu