Norton's Trace Formulae for the Griess Algebra¶of a Vertex Operator Algebra with Larger Symmetry

Formulae expressing the trace of the composition of several (up to five) adjoint actions of elements of the Griess algebra of a vertex operator algebra are derived under certain assumptions on the action of the automorphism group. They coincide, when applied to the moonshine module V , with the trace formulae obtained in a different way by S. Norton, and the spectrum of some idempotents related to 2A, 2B, 3A and 4A elements of the Monster is determined by the representation theory of the Virasoro algebra at c= 1/2, the W ₃ algebra at c= 4/5 or the W ₄ algebra at c= 1. The generalization to the trace function on the whole space is also given for the composition of two adjoint actions, which can be used to compute the McKay-Thompson series for a 2A involution of the Monster. Received: 24 July 2000 / Accepted: 15 June 2001     

Flame dynamics under various backpressures in a model scramjet with and without a cavity flameholder

Flame dynamics under various backpressure conditions were experimentally investigated using direct flame visualization, high-speed CH* chemiluminescence imaging, and wall pressure measurements. The stagnation pressure and temperature used in the present study were 100 kPa and 2500 K, respectively, with a freestream Mach number of 4.5. Rectangular scramjet models with and without a cavity were used to explore the effects of the cavity on flame dynamics when operating in scramjet mode, ramjet mode, and unstart. The flow rate of the ethylene jet was varied to impose backpressures corresponding to each operation mode. For both models, reverse flame propagation was observed for ramjet mode and unstart. For ramjet mode, flame fluctuation occurred within the isolator due to the coupling of fluid dynamics and combustion. The presence of a cavity enhanced combustion and reduced flame fluctuation in both scram and ramjet mode. The cavity promoted unstart because of the greater heat release from combustion. Further research using spatially resolved diagnostic techniques is needed to identify the flame locations for ramjet mode and unstart.     

A system for measuring absolute frequencies of up to 4.25 THz using a Josephson point contact

A system for measuring the absolute frequency of a far-infrared (FIR) laser is described. Josephson point contacts have been utilized in the system as a frequency harmonic mixer connecting microwaves and optically pumped CH₃OH laser lines. The Josephson point contacts are capable of generating beat signals of 90 GHz microwaves and FIR waves of up to 4.25 THz. To measure the frequency of the beat signals from the Josephson junction with a frequency counter, tracking oscillators have been developed, which tracks the beat signals by phase locking and regenerate clean signals for frequency counting. It is shown that the absolute frequency can be measured to an accuracy of about 100 Hz by using the tracking oscillators.     

Semaphorins and their receptors: Novel features of neural guidance molecules

Semaphorins were originally identified as axon guidance cues involved in the development of the nervous system. In recent years, it is emerging that they also participate in various biological systems, including physiological and pathological processes. In this review, we primarily focus on our cumulative findings for the role of semaphorins and their receptors in the regulation of the immune system, while also summarizing recent progress in the context of cardiovascular system.     

Structure of dioctadecyl l-glutamide-derived lipid self-assembled monolayers on Au(1 1 1) surface

An l-glutamic acid-derived lipid with a terminal thiol has been synthesized and its corresponding self-assembled structure on Au(1 1 1) surfaces described. The surface morphology of the lipid self-assembled monolayer (SAM) exhibits nano-order patterning, where the height of the monolayer (approximately 1.5 nm) could be interpreted as due to the monolayer structure estimated from molecular models. The molecular orientation in the monolayer is almost perpendicular to the Au(1 1 1) surface depending on the three-point hydrogen-bonding sites in the molecule.