The structure of quantum Lie algebras for the classical series B_l, C_l and D_l

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at $q=1$. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint x adjoint ---> adjoint. We present a practical method for the determination of these quantum Clebsch-Gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum Lie algebras associated to the classical Lie algebras B_l, C_l and D_l. In the quantum case also the structure constants of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invariant Killing form on the quantum Lie algebras and find that it takes values which are simple q-deformations of the classical ones.Comment: 25 pages, amslatex, eepic. Final version for publication in J. Phys. A. Minor misprints in eqs. 5.11 and 5.12 correcte

Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters

We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form. We exploit the fact that quantum non-compact algebras such as $U_q(su(1,1))$ and type-I quantum superalgebras such as $U_q(gl(1|1))$ and $U_q(gl(2|1))$ are known to admit non-trivial one-parameter families of infinite-dimensional and finite dimensional irreps, respectively, even for generic $q$. We develop a technique for constructing the corresponding spectral-dependent R-matrices. As examples we work out the the $R$-matrices for the three quantum algebras mentioned above in certain representations.Comment: 13 page

On Quantum Lie Algebras and Quantum Root Systems

As a natural generalization of ordinary Lie algebras we introduce the concept of quantum Lie algebras ${\cal L}_q(g)$. We define these in terms of certain adjoint submodules of quantized enveloping algebras $U_q(g)$ endowed with a quantum Lie bracket given by the quantum adjoint action. The structure constants of these algebras depend on the quantum deformation parameter $q$ and they go over into the usual Lie algebras when $q=1$. The notions of q-conjugation and q-linearity are introduced. q-linear analogues of the classical antipode and Cartan involution are defined and a generalised Killing form, q-linear in the first entry and linear in the second, is obtained. These structures allow the derivation of symmetries between the structure constants of quantum Lie algebras. The explicitly worked out examples of $g=sl_3$ and $so_5$ illustrate the results.Comment: 22 pages, latex, version to appear in J. Phys. A. see http://www.mth.kcl.ac.uk/~delius/q-lie.html for calculations and further informatio

Boundary breathers in the sinh-Gordon model

We present an investigation of the boundary breather states of the sinh-Gordon model restricted to a half-line. The classical boundary breathers are presented for a two parameter family of integrable boundary conditions. Restricting to the case of boundary conditions which preserve the \phi --> -\phi symmetry of the bulk theory, the energy spectrum of the boundary states is computed in two ways: firstly, by using the bootstrap technique and subsequently, by using a WKB approximation. Requiring that the two descriptions of the spectrum agree with each other allows a determination of the relationship between the boundary parameter, the bulk coupling constant, and the parameter appearing in the reflection factor derived by Ghoshal to describe the scattering of the sinh-Gordon particle from the boundary.Comment: 16 pages amslate

Analytical Bethe Ansatz for open spin chains with soliton non preserving boundary conditions

We present an ``algebraic treatment'' of the analytical Bethe ansatz for open spin chains with soliton non preserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe ansatz. It allows us to deal with a generic gl(N) open SNP spin chain possessing on each site an arbitrary representation. As a result, we obtain the Bethe equations in their full generality. The classification of finite dimensional irreducible representations for the twisted Yangians are directly linked to the calculation of the transfer matrix eigenvalues.Comment: 1

Predictors of Left Ventricular Remodeling after Aortic Valve Replacement in Pediatric Patients with Isolated Aortic Regurgitation

Objective. To identify the risk factors that could predict postoperative outcome after aortic valve replacement in pediatric patients with isolated aortic regurgitation ( AR ). Background. There is controversy regarding the appropriate timing of surgery in asymptomatic or minimally symptomatic patients with isolated AR . In the pediatric age group, there are limited studies in this regard and most of them are on combined aortic valve stenosis and regurgitation. Methods. All patients with biventricular physiology and morphologic left ventricle ( LV ) who underwent aortic valve surgery for AR from J anuary 1988 to J uly 2010 were included in the study. Demographic, clinical, and echocardiographic data were collected at presurgical visit, early postoperative, 1 year, and most recent follow‐up. Results. Among 53 patients (36 males), 18 had LV end‐diastolic diameter ( LVEDD ) z ‐score >4 standard deviation ( SD ) (group I ) and 35 had LVEDD 4 SD predicted persistent LV dilation (>2 SD ) at early post‐op ( P  4 SD ) are significant predictors of incomplete LV remodeling or persistent LV dysfunction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97538/1/chd703.pd

Risk Factors for Extubation Failure following Neonatal Cardiac Surgery

Objective: Extubation failure after neonatal cardiac surgery has been associated with considerable postoperative morbidity, although data identifying risk factors for its occurrence are sparse. We aimed to determine risk factors for extubation failure in our neonatal cardiac surgical population. Design: Retrospective chart review. Setting: Urban tertiary care free-standing children’s hospital. Patients: Neonates (0–30 d) who underwent cardiac surgery at our institution between January 2009 and December 2012 was performed. Interventions: Extubation failure was defined as reintubation within 72 hours after extubation from mechanical ventilation. Multivariate logistic regression analysis was performed to determine independent risk factors for extubation failure. Measurements and Main Results: We included 120 neonates, of whom 21 (17.5%) experienced extubation failure. On univariate analysis, patients who failed extubation were more likely to have genetic abnormalities (24% vs 6%; p = 0.023), hypoplastic left heart (43% vs 17%; p = 0.009), delayed sternal closure (38% vs 12%; p = 0.004), postoperative infection prior to extubation (38% vs 11%; p = 0.002), and longer duration of mechanical ventilation (median, 142 vs 58 hr; p = 0.009]. On multivariate analysis, genetic abnormalities, hypoplastic left heart, and postoperative infection remained independently associated with extubation failure. Furthermore, patients with infection who failed extubation tended to receive fewer days of antibiotics prior to their first extubation attempt when compared with patients with infection who did not fail extubation (4.9 ± 2.6 vs 7.3 ± 3; p = 0.073). Conclusions: Neonates with underlying genetic abnormalities, hypoplastic left heart, or postoperative infection were at increased risk for extubation failure. A more conservative approach in these patients, including longer pre-extubation duration of antibiotic therapy for postoperative infections, may be warranted

Prevalence and Risk Factors for Upper Airway Obstruction after Pediatric Cardiac Surgery

Objective To determine the prevalence of and risk factors for extrathoracic upper-airway obstruction after pediatric cardiac surgery. Study design A retrospective chart review was performed on 213 patients younger than 18 years of age who recovered from cardiac surgery in our multidisciplinary intensive care unit in 2012. Clinically significant upper-airway obstruction was defined as postextubation stridor with at least one of the following: receiving more than 2 corticosteroid doses, receiving helium-oxygen therapy, or reintubation. Multivariate logistic regression analysis was performed to determine independent risk factors for this complication. Results Thirty-five patients (16%) with extrathoracic upper-airway obstruction were identified. On bivariate analysis, patients with upper-airway obstruction had greater surgical complexity, greater vasoactive medication requirements, and longer postoperative durations of endotracheal intubation. They also were more difficult to calm while on mechanical ventilation, as indicated by greater infusion doses of narcotics and greater likelihood to receive dexmedetomidine or vecuronium. On multivariable analysis, adjunctive use of dexmedetomedine or vecuronium (OR 3.4, 95% CI 1.4-8) remained independently associated with upper-airway obstruction. Conclusion Extrathoracic upper-airway obstruction is relatively common after pediatric cardiac surgery, especially in children who are difficult to calm during endotracheal intubation. Postoperative upper-airway obstruction could be an important outcome measure in future studies of sedation practices in this patient population