Graded Contractions of Affine Kac-Moody Algebras

The method of graded contractions, based on the preservation of the automorphisms of finite order, is applied to the affine Kac-Moody algebras and their representations, to yield a new class of infinite dimensional Lie algebras and representations. After the introduction of the horizontal and vertical gradings, and the algorithm to find the horizontal toroidal gradings, I discuss some general properties of the graded contractions, and compare them with the In\"on\"u-Wigner contractions. The example of $\hat A_2$ is discussed in detail.Comment: 23 pages, Ams-Te

Graded contractions of bilinear invariant forms of Lie algebras

We introduce a new construction of bilinear invariant forms on Lie algebras, based on the method of graded contractions. The general method is described and the $\Bbb Z_2$-, $\Bbb Z_3$-, and $\Bbb Z_2\otimes\Bbb Z_2$-contractions are found. The results can be applied to all Lie algebras and superalgebras (finite or infinite dimensional) which admit the chosen gradings. We consider some examples: contractions of the Killing form, toroidal contractions of $su(3)$, and we briefly discuss the limit to new WZW actions.Comment: 15 page

Family centered nursing practices towards women and their families in the birthing context: A qualitative systematic review

Aim Synthesize qualitative evidence examining how nurses' attitudes, beliefs, and sense of efficacy and the context surrounding birth facilitate or hinder family-centered nursing practice. Design Thematic synthesis of qualitative studies. Methods A literature search was conducted in CINAHL, MEDLINE, PsycINFO, SCOPUS, SCIENCE DIRECT, REPÈRES, CAIRN, and ÉRUDIT from October 2020 to June 2021. The PRISMA guidelines were followed, and studies were critically appraised using the Critical Appraisal Skills Programme checklist. Data were extracted by two independent reviewers, and Thomas and Harden's qualitative thematic synthesis method was performed for data analysis. Results Thirteen studies were included. Three analytical themes were generated: (1) sharing power: opposing beliefs, (2) feeling a sense of efficacy in fulfilling one's role, and (3) managing a challenging work environment. Patient or Public Contribution Synthesizing nurses' experience is essential to promote implementation of favourable changes for care that is more focused on the needs of families

On the electrodynamics of moving bodies at low velocities

We discuss the seminal article in which Le Bellac and Levy-Leblond have identified two Galilean limits of electromagnetism, and its modern implications. We use their results to point out some confusion in the literature and in the teaching of special relativity and electromagnetism. For instance, it is not widely recognized that there exist two well defined non-relativistic limits, so that researchers and teachers are likely to utilize an incoherent mixture of both. Recent works have shed a new light on the choice of gauge conditions in classical electromagnetism. We retrieve Le Bellac-Levy-Leblond's results by examining orders of magnitudes, and then with a Lorentz-like manifestly covariant approach to Galilean covariance based on a 5-dimensional Minkowski manifold. We emphasize the Riemann-Lorenz approach based on the vector and scalar potentials as opposed to the Heaviside-Hertz formulation in terms of electromagnetic fields. We discuss various applications and experiments, such as in magnetohydrodynamics and electrohydrodynamics, quantum mechanics, superconductivity, continuous media, etc. Much of the current technology where waves are not taken into account, is actually based on Galilean electromagnetism

Production of Pairs of Sleptoquarks in Hadron Colliders

We calculate the cross section for the production of pairs of scalar leptoquarks (sleptoquarks) in a supersymmetric $E_6$ model, at hadron colliders. We estimate higher order corrections by including $\pi^2$ terms induced by soft-gluon corrections. Discovery bounds on the sleptoquark mass are estimated at collider energies of 1.8, 2, and 4 TeV (Tevatron), and 16 TeV (LHC).Comment: 8 pages, REVTEX, (1 fig. available on request), LAVAL-PHY-94-13/McGILL-94-26/SPhT-94-07

Cloning and expression of Geotrichum candidum lipase II gene in yeast. Probing of the enzyme active site by site-directed mutagenesis.

The three-dimensional structure of lipase II of Geotrichum candidum strain ATCC34614 (GCL II) has provided insights with respect to the nature of the catalytic machinery of lipases. To support these structural observations, we have carried out an analysis of GCL II by mutagenesis. The gene encoding lipase II of Geotrichum candidum strain ATCC34614 (GCL II) was amplified using the polymerase chain reaction, cloned, and sequenced. The intronless lipase gene was expressed and secreted from Saccharomyces cerevisiae at approximately 5 mg/liter of culture. Recombinant GCL II was purified by immunoaffinity chromatography and characterized using a combination of substrates and independent analytical methods. The recombinant enzyme and the enzyme isolated from its natural source have comparable specific activities against triolein of about 1000 mumol of oleic acid released/min/mg of protein. The putative catalytic triad Ser217-His463-Glu354 was probed by site-directed mutagenesis. The substitution of Ser217 by either Cys or Thr and of His463 by Ala led to a complete elimination of the activity against both triolein and tributyrin. Substitution of Glu354 by either Ser, Ala or Gln renders the enzyme inactive and also perturbs the enzyme stability. However, the enzyme with the conservative replacement Glu354 Asp is stable and displays only a small decrease of triolein activity but a 10-fold decrease in activity against tributyrin. There was no appreciable difference in esterase activity between the native, recombinant wild type, and Glu354 Asp mutant. These results confirm that the triad formed by Ser217-Glu354-His463 is essential for catalytic activity. They also show that the active site of GCL II is more tolerant to a conservative change of the carboxylic side chain within the triad than are other hydrolases with similar catalytic triads

Central extensions of the families of quasi-unitary Lie algebras

The most general possible central extensions of two whole families of Lie algebras, which can be obtained by contracting the special pseudo-unitary algebras su(p,q) of the Cartan series A_l and the pseudo-unitary algebras u(p,q), are completely determined and classified for arbitrary p,q. In addition to the su(p,q) and u({p,q}) algebras, whose second cohomology group is well known to be trivial, each family includes many non-semisimple algebras; their central extensions, which are explicitly given, can be classified into three types as far as their properties under contraction are involved. A closed expression for the dimension of the second cohomology group of any member of these families of algebras is given.Comment: 23 pages. Latex2e fil