We show that the representation theory for the toroidal extended affine Lie algebra is controlled by a VOA which is a tensor product of four VOAs: a sub-VOA V + Hyp of a hyperbolic lattice VOA, affine ˙ g and sl N VOAs and a Virasoro VOA. A tensor product of irre-ducible modules for these VOAs admits the structure of an irreducible module for the toroidal extended affine Lie algebra. We also sh...

The goals of the present paper are to initiate a program to systematically study and rigorously establish what a physicist might refer to as the “operator content of orbifold models.” To explain what this might mean, and to clarify the title of the paper, we will assume that the reader is familiar with the algebraic formulation of 2-dimensional CFT in the guise of vertex operator algebras (VOA)...

This paper offers a brief introduction to silicon photonics including the basic optical waveguide, passive optical circuit performance, the addition of doped pand njunctions adjacent to the intrinsic silicon waveguide to inject a current across the waveguide, free-carrier dispersion, performance of the variable optical attenuator (VOA), and a monolithic, dual-function splitter-VOA array circuit.

Analysis of dissolved light hydrocarbon gas concentrations (primarily methane and ethane) in water supply wells is commonly used to establish conditions before and after drilling in areas of shale gas and oil extraction. Several methods are currently used to collect samples for dissolved gas analysis from water supply wells; however, the reliability of results obtained from these methods has no...

This paper is a continuation of [33] at which several coset subalgebras of the lattice VOA V2E8 were constructed and the relationship between such algebras with the famous McKay observation on the extended E8 diagram and the Monster simple group were discussed. In this article, we shall provide the technical details. We completely determine the structure of the coset subalgebras constructed and...

We demonstrate a variable optical attenuator (VOA) at lambda=1.55 microm using a sheared polymer network liquid crystal (SPNLC). The SPNLC exhibits a fast response time and weak wavelength dependency. Comparing with other polymer-stabilized liquid crystals, the SPNLC has lower driving voltage and negligible light scattering loss when the wavelength exceeds 700 nm. A reflection type VOA with ~0....

In this article we study VOAs with two Miyamoto involutions generating S3. In [M3], Miyamoto showed that a VOA generated by two conformal vectors whose Miyamoto involutions generate an automorphism group isomorphic to S3 is isomorphic to one of the four candidates he listed. We construct one of them and prove that our VOA is actually the same as VA(e, f) studied by Miyamoto.

Purpose – The primary purpose of this study is to illustrate an analytical method to identify tangible and intangible customer values and to translate those values into brand identity differentiators and product specifications. Design/methodology/approach – The authors adapt a product development analysis tool, the Value Opportunity Analysis (VOA), to the design of a brand identity, illustratin...

In this article we study VOAs with two Miyamoto involutions generating S3. In [M3], Miyamoto showed that a VOA generated by two conformal vectors whose Miyamoto involutions generate an automorphism group isomorphic to S3 is isomorphic to one of the four candidates he listed. We construct one of them and prove that our VOA is actually the same as VA(e, f) studied by Miyamoto.

In an attempt to clarify regional signal intensity changes, which may accompany the performance of the Stroop Color-Word task, healthy subjects were imaged using the fMRI BOLD technique while performing a modified version of the task. Both the AAA and VOA subdivisions of the anterior cingulate cortex were significantly activated during the interference condition; however, only the signal intens...