Boundary States, Extended Symmetry Algebra and Module Structure for certain Rational Torus Models

The massless bosonic field compactified on the circle of rational $R^2$ is reexamined in the presense of boundaries. A particular class of models corresponding to $R^2=\frac{1}{2k}$ is distinguished by demanding the existence of a consistent set of Newmann boundary states. The boundary states are constructed explicitly for these models and the fusion rules are derived from them. These are the ones prescribed by the Verlinde formula from the S-matrix of the theory. In addition, the extended symmetry algebra of these theories is constructed which is responsible for the rationality of these theories. Finally, the chiral space of these models is shown to split into a direct sum of irreducible modules of the extended symmetry algebra.Comment: 12 page

Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras

We prove the existence and associativity of the nonmeromorphic operator product expansion for an infinite family of vertex operator algebras, the triplet W-algebras, using results from P(z)-tensor product theory. While doing this, we also show that all these vertex operator algebras are C_2-cofinite.Comment: 21 pages, to appear in J. Phys. A: Math. Gen.; the exposition is improved and one reference is adde

Applying Brain Research to Classroom Strategies

Research in the field of neuroscience has exploded in the past decade. The word brain appears in the title of nearly 40,000 books and CDs indicating intense interest in this area of study. What can music educators learn from recent investigations—often termed brain research—to guide music teaching and learning? The following ideas are intended to have broad applications and may inspire you to investigate this fascinating area of literature more thoroughly. While some findings are new, other studies affirm what music educators have previously found to be effective

Applying Brain Research to Classroom Strategies

Research in the field of neuroscience has exploded in the past decade. The word brain appears in the title of nearly 40,000 books and CDs indicating intense interest in this area of study. What can music educators learn from recent investigations—often termed brain research—to guide music teaching and learning? The following ideas are intended to have broad applications and may inspire you to investigate this fascinating area of literature more thoroughly. While some findings are new, other studies affirm what music educators have previously found to be effective

Influence of Online and Classroom Multi-modal Instruction on Academic Achievement

The purpose of the study was to investigate the extent to which online and multi-modal classroom instruction influences academic achievement of undergraduate students. Instruction was enhanced with online multimodal materials used in the face-to-face classroom presentations and for online assignments. The current study investigates not only longitudinal effectiveness in aural and visual skills learning but also possible connections among increased aural and visual skills and academic achievement measured by overall GPA.https://scholarworks.waldenu.edu/archivedposters/1094/thumbnail.jp

Wind on the boundary for the Abelian sandpile model

We continue our investigation of the two-dimensional Abelian sandpile model in terms of a logarithmic conformal field theory with central charge c=-2, by introducing two new boundary conditions. These have two unusual features: they carry an intrinsic orientation, and, more strangely, they cannot be imposed uniformly on a whole boundary (like the edge of a cylinder). They lead to seven new boundary condition changing fields, some of them being in highest weight representations (weights -1/8, 0 and 3/8), some others belonging to indecomposable representations with rank 2 Jordan cells (lowest weights 0 and 1). Their fusion algebra appears to be in full agreement with the fusion rules conjectured by Gaberdiel and Kausch.Comment: 26 pages, 4 figure

Ghost Systems: A Vertex Algebra Point of View

Fermionic and bosonic ghost systems are defined each in terms of a single vertex algebra which admits a one-parameter family of conformal structures. The observation that these structures are related to each other provides a simple way to obtain character formulae for a general twisted module of a ghost system. The U(1) symmetry and its subgroups that underly the twisted modules also define an infinite set of invariant vertex subalgebras. Their structure is studied in detail from a W-algebra point of view with particular emphasis on Z_N-invariant subalgebras of the fermionic ghost system.Comment: 20 pages, plain Te