It\^{o}'s theorem and monomial Brauer characters

Let $G$ be a finite solvable group, and let $p$ be a prime. In this note, we prove that $p$ does not divide $\varphi(1)$ for every irreducible monomial $p$-Brauer character $\varphi$ of $G$ if and only if $G$ has a normal Sylow $p$-subgroup.Comment: 3 pag

Inattentive Consumers and Product Quality

This paper studies a model in which some consumers shop on the basis of price alone, without attention to potential differences in product quality. A firm may offer a low-quality product to exploit these inattentive consumers. In the unique symmetric equilibrium of the model, firms choose prices with mixed strategies, similarly to Varian (1980) in which some consumers purchase from a random seller without attention to market prices. In our model, though, firms also choose quality stochastically, and there is both price and quality dispersion. Two stylized policy interventions are considered: competition policy, which acts to increase the number of sellers, and market transparency reforms which act to increase the fraction of attentive consumers. With fewer inattentive consumers, firms are less likely to "cheat" (i.e., cut quality) which therefore improves welfare, but profit and consumer surplus can either increase or decrease. When there is a large number of sellers, approximately half the sellers cheat (regardless of the fraction of inattentive consumers), and introducing more sellers boosts consumers surplus and reduces profit, while the impact on welfare is ambiguous.Oligopoly; Complex Products; Market transparency; Competition Policy

Design of Predictive Controllers by Dynamic Programming and Neural Networks

This paper proposes a method for the design of predictive controllers for nonlinear systems. The method consists of two phases, a solution phase and a learning phase. In the solution phase, dynamic programming is applied to obtain a closed-loop control law. In the learning phase, neural networks are used to simulate the control law. This phase overcomes the curse of dimensionality problem that has often hindered the implementation of control laws generated by dynamic programming. Experimental results demonstrate the effectiveness of the metho

Minimal constrained superfields and the Fayet-Iliopoulos model

We show how the necessary constraints to project out all the components of a chiral superfield except for some scalar degrees of freedom originate from simple operators in the microscopic theory. This is in particular useful in constructing the simplest models of a goldstone boson/inflaton; or extracting the Standard Model Higgs doublet from a supersymmetric electroweak sector. We use the Fayet-Iliopoulos model as an example of the origin for the supersymmetry breaking. We consider the regime where both gauge symmetry and supersymmetry are spontaneously broken, leaving (in the decoupling limit) the goldstino as the only light mode in this sector. We show in three different ways, both in components and in superspace language, how the nilpotent goldstino superfield emerges. We then use it to write different effective operators and extract some of the consequences for the low energy spectrum.Comment: 17 pages. References added. Published versio