Remarks on Finite W Algebras

The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G=so(4,2), unitary representations of the conformal and Poincare algebras are recognized in this approach, which can be compared to the usual induced representation technique. When G=sp(2,R) or sp(4,R), the anyonic parameter can be seen as the eigenvalue of a W generator in such W representations of G. The generalization of such properties to the affine case is also discussed in the conclusion, where an alternative of the Wakimoto construction for sl(2) level k is briefly presented. This mini review is based on invited talks presented by P. Sorba at the ``Vth International Colloquium on Quantum Groups and Integrable Systems'', Prague (Czech Republic), June 1996; ``Extended and Quantum Algebras and their Applications to Physics'', Tianjin (China), August 1996; ``Selected Topics of Theoretical and Modern Mathematical Physics'', Tbilisi (Georgia), September 1996; to be published in the Proceedings.Comment: LaTeX, 16 pages, references adde

Yangians, finite W-algebras and the Non Linear Schrodinger hierarchy

We show an algebra morphism between Yangians and some finite W-algebras. This correspondence is nicely illustrated in the framework of the Non Linear Schrodinger hierarchy. For such a purpose, we give an explicit realization of the Yangian generators in terms of deformed oscillators.Comment: LaTeX2e, 10 pages, Talk presented by E. Ragoucy at ACTP-Nankai Symposium on Yang-Baxter systems, non linear models and their applications, Seoul (Korea) October 20-23, 199

W-algebras from symplectomorphisms

It is shown how $W$-algebras emerge from very peculiar canonical transformations with respect to the canonical symplectic structure on a compact Riemann surface. The action of smooth diffeomorphisms of the cotangent bundle on suitable generating functions is written in the BRS framework while a $W$-symmetry is exhibited. Subsequently, the complex structure of the symmetry spaces is studied and the related BRS properties are discussed. The specific example of the so-called $W_3$-algebra is treated in relation to some other different approaches.Comment: LaTex, 25 pages, no figures, to appear in Journ. Math. Phy

Parents' Perspectives on the School Experiences of Children with Cancer

Interviews with 59 parents of school age children with cancer indicate problems children encountered in returning to school: missing significant amounts of school due to illness and treatments, teasing by classmates and peers, and strained relations with teachers. Most parents report that despite missing much school their child was caught up with schoolwork, suggesting that academic difficulties are not paramount. Most parents also report receiving substantial help from sympathetic and competent educators. However, parents also indicate that some teachers were insensitive to their child's condition, while others were overprotective, suggesting the need for a delicate balance in defining appropriate teacher behavior. A responsive yet normalizing school environment can be facilitated by vigorous and proactive partnerships among the medical staff, family, and school system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68682/2/10.1177_027112148600500405.pd

Kinetic Approach to Fractional Exclusion Statistics

We show that the kinetic approach to statistical mechanics permits an elegant and efficient treatment of fractional exclusion statistics. By using the exclusion-inclusion principle recently proposed [Phys. Rev. E49, 5103 (1994)] as a generalization of the Pauli exclusion principle, which is based on a proper definition of the transition probability between two states, we derive a variety of different statistical distributions interpolating between bosons and fermions. The Haldane exclusion principle and the Haldane-Wu fractional exclusion statistics are obtained in a natural way as particular cases. The thermodynamic properties of the statistical systems obeying the generalized exclusion-inclusion principle are discussed.Comment: 6 pages, REVTE

Polynomial super-gl(n) algebras

We introduce a class of finite dimensional nonlinear superalgebras $L = L_{\bar{0}} + L_{\bar{1}}$ providing gradings of $L_{\bar{0}} = gl(n) \simeq sl(n) + gl(1)$. Odd generators close by anticommutation on polynomials (of degree $>1$) in the $gl(n)$ generators. Specifically, we investigate `type I' super-$gl(n)$ algebras, having odd generators transforming in a single irreducible representation of $gl(n)$ together with its contragredient. Admissible structure constants are discussed in terms of available $gl(n)$ couplings, and various special cases and candidate superalgebras are identified and exemplified via concrete oscillator constructions. For the case of the $n$-dimensional defining representation, with odd generators $Q_{a}, \bar{Q}{}^{b}$, and even generators ${E^{a}}_{b}$, $a,b = 1,...,n$, a three parameter family of quadratic super-$gl(n)$ algebras (deformations of $sl(n/1)$) is defined. In general, additional covariant Serre-type conditions are imposed, in order that the Jacobi identities be fulfilled. For these quadratic super-$gl(n)$ algebras, the construction of Kac modules, and conditions for atypicality, are briefly considered. Applications in quantum field theory, including Hamiltonian lattice QCD and space-time supersymmetry, are discussed.Comment: 31 pages, LaTeX, including minor corrections to equation (3) and reference [60

Curriculum in early childhood education: critical questions about content, coherence, and control

A continuing struggle over curriculum in early childhood education is evident in contemporary research and debate at national and international levels. This reflects the dominant influence of developmental psychology in international discourses, and in policy frameworks that determine approaches to curriculum, pedagogy, and assessment. Focusing on early childhood education, we argue that this struggle generates critical questions about three significant themes within curriculum theory: content, coherence, and control. We outline two positions from which these themes can be understood: Developmental and Educational Psychology and contemporary policy frameworks. We argue that within and between these positions, curriculum content, coherence, and control are viewed in different and sometimes oppositional ways. Following this analysis, we propose that a focus on ‘working theories’ as a third position offers possibilities for addressing some of these continuing struggles, by exploring different implications for how content, coherence, and control might be understood. We conclude that asking critical questions of curriculum in early childhood education is a necessary endeavour to develop alternative theoretical frameworks for understanding the ways in which curriculum can be considered alongside pedagogy, assessment, play, and learning

HPLC determination of methylphenidate and its metabolite, ritalinic acid, by high-performance liquid chromatography with peroxyoxalate chemiluminescence detection.

An HPLC-peroxyoxalate chemiluminescence (PO-CL) method for simultaneous determination of methylphenidate (MPH) and ritalinic acid (RA) was developed. The method was used to monitor MPH and RA after administration of MPH to rats. Deproteinized plasma spiked with 1-(3-trifluoromethylphenyl)piperazine (IS) was dried and labeled with 4-(N,N-dimethylaminosulfonyl)-7-fluoro-2,1,3-benzoxadiazole (DBD-F). The labeled sample was cleaned with two kinds of solid-phase extraction cartridge, and the DBD-labels were separated on an ODS column with gradient elution using a mixture of CH(3)CN and imidazole-HNO(3) buffer. Separation of MPH and RA can be achieved within 33 min. The LODs of MPH and RA at a signal-to-noise ratio of 3 were 2.2 and 0.4 ng mL(-1), respectively. Moreover, monitoring of MPH and RA after MPH administration (10 mg kg(-1)) to rat could be performed. The concentration of RA 480 min after administration was eight times higher than that of MPH. The proposed HPLC-PO-CL method was useful for determination of MPH and RA in rat plasma and was successfully used to monitor these substances after MPH administration

Structures Related to the Emplacement of Shallow-Level Intrusions

A systematic view of the vast nomenclature used to describe the structures of shallow-level intrusions is presented here. Structures are organised in four main groups, according to logical breaks in the timing of magma emplacement, independent of the scales of features: (1) Intrusion-related structures, formed as the magma is making space and then develops into its intrusion shape; (2) Magmatic flow-related structures, developed as magma moves with suspended crystals that are free to rotate; (3) Solid-state, flow-related structures that formed in portions of the intrusions affected by continuing flow of nearby magma, therefore considered to have a syn-magmatic, non-tectonic origin; (4) Thermal and fragmental structures, related to creation of space and impact on host materials. This scheme appears as a rational organisation, helpful in describing and interpreting the large variety of structures observed in shallow-level intrusions