Representations of the quantum doubles of finite group algebras and solutions of the Yang--Baxter equation

Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter equation. Such solutions do not depend on a spectral parameter, and to date there has been little investigation into extending these solutions such that they do depend on a spectral parameter. Here we first explicitly construct the matrix elements of the generators for all irreducible representations of quantum doubles of the dihedral groups $D_n$. These results may be used to determine constant solutions of the Yang--Baxter equation. We then discuss Baxterisation ans\"atze to obtain solutions of the Yang--Baxter equation with spectral parameter and give several examples, including a new 21-vertex model. We also describe this approach in terms of minimal-dimensional representations of the quantum doubles of the alternating group $A_4$ and the symmetric group $S_4$.Comment: 19 pages, no figures, changed introduction, added reference

Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras

The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are viewed as descendants of the six-vertex model case, are then obtained using tensor product graph methods which were originally formulated for quantum algebras. Connections with the Fateev-Zamolodchikov model are discussed.Comment: 34 pages, 2 figure

The effect of a required Character Education and Class-Wide Peer Tutoring program on 5th-grade students\u27 reading and writing performance

The purpose of the study was to determine the effect of a required school year long Character Education and Class-Wide Peer Tutoring program (CE+CWPT) for students who scored at or below proficiency in one, two, or three of their reading fluency, reading comprehension, or writing assessments at the beginning of their 5th-grade school year. The study analyzed performance on criterion referenced tests, performance on norm-referenced tests, behavioral referrals, and attendance to determine what relationship, if any, exists between levels of achievement amongst students participating in a required CE+CWPT program. Following a year of program participation, 5th-grade students with one or two areas of measured non-proficiency (n = 14) demonstrated a significant pretest-posttest improvement on their reading fluency scores but did not significantly improve their reading comprehension and writing scores. 5th-grade students with three areas of measured non-proficiency ( n = 8) demonstrated a significant pretest-posttest improvement on reading fluency scores and writing scores but did not significantly improve their reading comprehension scores. On posttest-posttest comparisons, there were no significant differences between the groups on reading fluency, reading comprehension, and writing scores. Behavioral comparisons for both groups indicated that the percentage of zero office referrals improved from pretest to posttest with a corresponding decrease for one or more office referrals. Posttest-posttest behavioral comparisons support improvement primarily in the area of office referral frequencies and percents for both groups. The observed level of absence frequencies was consistent with reported elementary school behavioral issues. In light of the study results, program scale-up of the required CE+CWPT program should be considered

The Effect of a Required Character Education and Class-Wide Peer Tutoring Program on 5th-Grade Students’ Reading and Writing Performance

The purpose of the study was to determine the effect of a required school year long Character Education and Class-Wide Peer Tutoring program (CE+CWPT) for students who scored at or below proficiency in one, two, or three of their reading fluency, reading comprehension, or writing assessments at the beginning of their 5th-grade school year. The study analyzed performance on criterion referenced tests, performance on norm-referenced tests, behavioral referrals, and attendance to determine what relationship, if any, exists between levels of achievement amongst students participating in a required CE+CWPT program. Following a year of program participation, 5th-grade students with one or two areas of measured non-proficiency ( n = 14) demonstrated a significant pretest-posttest improvement on their reading fluency scores but did not significantly improve their reading comprehension and writing scores. 5th-grade students with three areas of measured non-proficiency ( n = 8) demonstrated a significant pretest-posttest improvement on reading fluency scores and writing scores but did not significantly improve their reading comprehension scores. On posttest-posttest comparisons, there were no significant differences between the groups on reading fluency, reading comprehension, and writing scores. Behavioral comparisons for both groups indicated that the percentage of zero office referrals improved from pretest to posttest with a corresponding decrease for one or more office referrals. Posttest-posttest behavioral comparisons support improvement primarily in the area of office referral frequencies and percents for both groups. The observed level of absence frequencies was consistent with reported elementary school behavioral issues. In light of the study results, program scale-up of the required CE+CWPT program should be considered

Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D_3) symmetry

The exact solution for the energy spectrum of a one-dimensional Hamiltonian with local two-site interactions and periodic boundary conditions is determined. The two-site Hamiltonians commute with the symmetry algebra given by the Drinfeld double D(D_3) of the dihedral group D_3. As such the model describes local interactions between non-Abelian anyons, with fusion rules given by the tensor product decompositions of the irreducible representations of D(D_3). The Bethe ansatz equations which characterise the exact solution are found through the use of functional relations satisfied by a set of mutually commuting transfer matrices.Comment: 19 page

SU(3) monopoles and their fields

Some aspects of the fields of charge two SU(3) monopoles with minimal symmetry breaking are discussed. A certain class of solutions look like SU(2) monopoles embedded in SU(3) with a transition region or ``cloud'' surrounding the monopoles. For large cloud size the relative moduli space metric splits as a direct product AH\times R^4 where AH is the Atiyah-Hitchin metric for SU(2) monopoles and R^4 has the flat metric. Thus the cloud is parametrised by R^4 which corresponds to its radius and SO(3) orientation. We solve for the long-range fields in this region, and examine the energy density and rotational moments of inertia. The moduli space metric for these monopoles, given by Dancer, is also expressed in a more explicit form.Comment: 17 pages, 3 figures, latex, version appearing in Phys. Rev.

Approaching zero : temporal effects of a restrictive antibiotic policy on hospital-acquired Clostridium difficile, extended-spectrum β-lactamase-producing coliforms and meticillin-resistant Staphylococcus aureus

A restrictive antibiotic policy banning routine use of ceftriaxone and ciprofloxacin was implemented in a 450-bed district general hospital following an educational campaign. Monthly consumption of nine antibiotics was monitored in defined daily doses (DDDs) per 1000 patient-occupied bed-days (1000 pt-bds) 9 months before until 16 months after policy introduction. Hospital-acquired Clostridium difficile, meticillin-resistant Staphylococcus aureus (MRSA) and extended-spectrum -lactamase (ESBL)- producing coliform cases per month/1000 pt-bds were identified and reviewed throughout the hospital. Between the first and final 6 months of the study, average monthly consumption of ceftriaxone reduced by 95% (from 46.213 to 2.129 DDDs/1000 pt-bds) and that for ciprofloxacin by 72.5% (109.804 to 30.205 DDDs/1000 pt-bds). Over the same periods, hospital-acquisition rates for C. difficile reduced by 77% (2.398 to 0.549 cases/1000 pt-bds), for MRSA by 25% (1.187 to 0.894 cases/1000 pt-bds) and for ESBL-producing coliforms by 17% (1.480 to 1.224 cases/1000 pt-bds). Time-lag modelling confirmed significant associations between ceftriaxone and C. difficile cases at 1 month (correlation 0.83; P < 0.005), and between ciprofloxacin and ESBL-producing coliform cases at 2 months (correlation 0.649; P = 0.002). An audit performed 3 years after the policy showed sustained reduction in C. difficile rates (0.259 cases/1000 pt-bds), with additional decreases for MRSA (0.409 cases/1000 pt-bds) and ESBL-producing coliforms (0.809 cases/1000 pt-bds). In conclusion, banning two antibiotics resulted in an immediate and profound reduction in hospital-acquired C. difficile, with possible longer-term effects on MRSA and ESBL-producing coliform rates. Antibiotic stewardship is fundamental in the control of major hospital pathogens