Representations of wreath products of algebras

Filtrations of modules over wreath products of algebras are studied and corresponding multiplicity formulas are given in terms of Littlewood–Richardson coefficients. An example relevant to Jantzen filtrations in Schur algebras is presented

A second-order class-D audio amplifier

Class-D audio amplifiers are particularly efficient, and this efficiency has led to their ubiquity in a wide range of modern electronic appliances. Their output takes the form of a high-frequency square wave whose duty cycle (ratio of on-time to off-time) is modulated at low frequency according to the audio signal. A mathematical model is developed here for a second-order class-D amplifier design (i.e., containing one second-order integrator) with negative feedback. We derive exact expressions for the dominant distortion terms, corresponding to a general audio input signal, and confirm these predictions with simulations. We also show how the observed phenomenon of “pulse skipping” arises from an instability of the analytical solution upon which the distortion calculations are based, and we provide predictions of the circumstances under which pulse skipping will take place, based on a stability analysis. These predictions are confirmed by simulations

A heterotic sigma model with novel target geometry

We construct a (1,2) heterotic sigma model whose target space geometry consists of a transitive Lie algebroid with complex structure on a Kaehler manifold. We show that, under certain geometrical and topological conditions, there are two distinguished topological half--twists of the heterotic sigma model leading to A and B type half--topological models. Each of these models is characterized by the usual topological BRST operator, stemming from the heterotic (0,2) supersymmetry, and a second BRST operator anticommuting with the former, originating from the (1,0) supersymmetry. These BRST operators combined in a certain way provide each half--topological model with two inequivalent BRST structures and, correspondingly, two distinct perturbative chiral algebras and chiral rings. The latter are studied in detail and characterized geometrically in terms of Lie algebroid cohomology in the quasiclassical limit.Comment: 83 pages, no figures, 2 references adde

An improved moving particle semi-implicit method for dam break simulation

Dam break is quite a common and hazard phenomenon in shipbuilding and ocean engineering. The objective of this study is to investigate dam break hydrodynamics with improved Moving Particle Semi-implicit method (MPS). Compared to traditional mesh methods, MPS is feasible to simulate surface flows with large deformation, however, during the simulation, the pressure oscillates violently, due to misjudgment of surface particles as well as particles gathering together. To modify these problems, a new arc method is applied to judge free surface particles, and a collision model is introduced to avoid particles from gathering together. Hydrostatic pressure is simulated by original and improved MPS. The results verify that improved MPS method is more effective. Based on these, dam break model is investigated with improved MPS

Kleshchev's decomposition numbers and branching coefficients in the Fock space

10.1090/S0002-9947-07-04202-XTransactions of the American Mathematical Society36031179-119

Dance and emotion in posterior parietal cortex: a low-frequency rTMS study

Background: The neural bases of emotion are most often studied using short non-natural stimuli and assessed using correlational methods. Here we use a brain perturbation approach to make causal inferences between brain activity and emotional reaction to a long segment of dance. <p>Objective/Hypothesis: We aimed to apply offline rTMS over the brain regions involved in subjective emotional ratings to explore whether this could change the appreciation of a dance performance.</p> <p>Methods: We first used functional magnetic resonance imaging (fMRI) to identify regions correlated with fluctuating emotional rating during a 4-minutes dance performance, looking at both positive and negative correlation. Identified regions were further characterized using meta-data interrogation. Low frequency repetitive TMS was applied over the most important node in a different group of participants prior to them rating the same dance performance as in the fMRI session.</p> <p>Results: FMRI revealed a negative correlation between subjective emotional judgment and activity in the right posterior parietal cortex. This region is commonly involved in cognitive tasks and not in emotional task. Parietal rTMS had no effect on the general affective response, but it significantly (p<0.05 using exact t-statistics) enhanced the rating of the moment eliciting the highest positive judgments.</p> <p>Conclusion: These results establish a direct link between posterior parietal cortex activity and emotional reaction to dance. They can be interpreted in the framework of competition between resources allocated to emotion and resources allocated to cognitive functions. They highlight potential use of brain stimulation in neuro-æsthetic investigations.</p&gt