Uniqueness of Rankin-Selberg periods

Let $k$ be a local field of characteristic zero. Rankin-Selberg's local zeta integrals produce linear functionals on generic irreducible admissible smooth representations of $GL_n(k)\times GL_r(k)$, with certain invariance properties. We show that up to scalar multiplication, these linear functionals are determined by the invariance properties

Twisted vertex operators and unitary Lie algebras

A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral Z_2-lattice. The irreducible decomposition of the representation is explicitly computed and described. As a by-product, some fundamental representations of affine Kac-Moody Lie algebra of type $A_n^{(2)}$ are recovered by the new method.Comment: 26 page

Experience-weighted attraction learning in network coordination games

This paper studies the action dynamics of network coordination games with bounded-rational agents. I apply the experience-weighted attraction (EWA) model to the analysis as the EWA model has several free parameters that can capture different aspects of agents' behavioural features. I show that the set of possible long-term action patterns can be largely different when the behavioural parameters vary, ranging from a unique possibility in which all agents favour the risk-dominant option to some set of outcomes richer than the collection of Nash equilibria. Monotonicity and non-monotonicity in the relationship between the number of possible long-term action profiles and the behavioural parameters are explored. I also study the question of influential agents in terms of whose initial predispositions are important to the actions of the whole network. The importance of agents can be represented by a left eigenvector of a Jacobian matrix provided that agents' initial attractions are close to some neutral level. Numerical calculations examine the predictive power of the eigenvector for the long-run action profile and how agents' influences are impacted by their behavioural features and network positions

Estimation of soil water content and resident and effluent solute concentrations using time domain reflectometry

Monitoring solute concentrations within an undisturbed soil core during saturated and unsaturated flow can provide first-hand information for better understanding solute transport processes as well as data required for numerical simulation of solute transport. Time domain reflectometry (TDR) has recently been used to monitor solute concentration in both laboratory and field soils. Although TDR has been shown to measure resident solute concentrations, C r, it has not been fully developed to measure solute transport. The objectives of this study are to evaluate TDR\u27s abilities to accurately estimate Cr and to predict transport of the flux average concentration also termed effluent solute concentration, Ce;Relationships of TDR-measured apparent soil dielectric constant (K a) to water content (thetav), Ka to theta v and bulk soil electrical conductivity (sigmaa), and sigma a to thetav and Cr were developed using data obtained from incremental addition of solutions with different solute concentrations to four packed soil cores. The Cr breakthrough curves (BTC) were estimated using the sigmaa-thetav-Cr relationship and TDR-measured sigmaa and -estimated theta v for packed and undisturbed cores under steady flow conditions with various flow velocities. Effluent BTC was predicted from the Cr BTC either using solute transport models or by mass balance;Effects of sigmaa on Ka or thetav were site-specific and were not explained by TDR theory. A Ka to sigma a and thetav relationship developed from packed core data did not adequately describe the effects of sigmaa on TDR-measured Ka for an undisturbed soil core, the effect of sigmaa was only removed by individual calibrations. The sigmaa-theta v-Cr relationship developed in this study fitted packed soil core data with higher r2 and gave more accurate Cr estimation than three published models. An increase in flow velocity increased variation of TDR-measured sigmaa, and thus variation of TDR-estimated Cr for measurements on undisturbed soil cores over a range of pore water velocity (nu, 0.5--86.1 cm hr--1). The effluent breakthrough curve (BTC) predicted with solute transport models using solute transport parameters obtained by fitting the same models to TDR-estimated Cr BTC usually deviated from the measured effluent BTC; whereas, a simple mass balance method demonstrated the capability of accurately predicting effluent BTC