Dilations and constrained algebras

It is well known that unital contractive representations of the disk algebra are completely contractive. Let A denote the subalgebra of the disk algebra consisting of those functions f whose first derivative vanishes at 0. We prove that there are unital contractive representations of A which are not completely contractive, and furthermore provide a Kaiser and Varopoulos inspired example for A and present a characterization of those contractive representations of A which are completely contractive. In the positive direction, for the algebra of rational functions with poles off the distinguished variety V in the bidisk determined by (z-w)(z+w)=0, unital contractive representations are completely contractive.Comment: New to version 2 is a proof of rational dilation for the distinguished variety in the bidisk determined by (z-w)(z+w)=

Coordinating on Reducing Advertising: Carbonated Soft Drinks Industry and Combating Obesity

Replaced with revised version of paper 06/08/11.television advertising, carbonated soft drink, oligopoly advertising, pulse advertising, Food Consumption/Nutrition/Food Safety, Health Economics and Policy, Industrial Organization, Marketing, I18, L13, M37,

Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems

We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. Firstly we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the R\"ossler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures -- thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length and network diameter are highly sensitive to the interior crisis captured in this particular data set

Phase Space Reconstruction and Nonlinear Equilibrium Dynamics in the United States Beef Market

This paper investigates dynamic interactions in the US beef market using phase space reconstruction, which has been developed to analyze nonlinear dynamical systems. This approach provides important and unique empirical insights into consumers behavior in the beef market. Our results from a phase space reconstruction analysis demonstrate distinct differences between intertemporal short run impacts from food safety outbreaks (e.g., E. Coli) and longer run health effects (e.g., cholesterol). Adjustments due to factors such as cholesterol are permanent changes and do not affect the manner by which people consume, while consumers react to food safety scares by adjusting consumption for a short period of time and then returning to their normal steady state cycle of consumption.nonlinear time series, phase space reconstruction, food safety, health effects, Livestock Production/Industries, Marketing,

California Off-Road Engines and Components Life Span Assessment

The useful life and warranty periods for off-road equipment in California for engines rated at 37 kilowatts (kW) and greater have not been updated since the Tier 1 rule phased in from 1996 to 2000; for engines rated below 37 kW, not since the Tier 2 and Tier 3 rules phased in from 2000 to 2008. The California Air Resources Board (CARB) staff is seeking information regarding useful life and warranty to evaluate whether amendments to those requirements are necessary after two decades of technology advancement. Cal Poly researchers called 55 service providers across the state of California to collect information regarding useful life of engines, repair of emission-related components, and warranty information associated with various off-road agricultural & construction equipment. The responses below reflect 40 completed interviews. The data was collected via telephone interview with the service manager of each company. The interviews took place during the post-harvest, pre-plant season of November 2022 through early May 2023. Most interviews took from 20 – 40 minutes to complete. Participants were asked about the types of equipment and most common range of horsepower (HP) engines they saw in their shop. The equipment each service provider dealt with mostly depended on the type of agriculture surrounding their area. Tree and vineyard crops typically use smaller HP tractors (less than 100), while large row crop operations in the southern San Joaquin Valley more commonly use 200 – 500 HP equipment. Construction equipment providers reported the largest horsepower, in the 400 – 600 HP range, though that varied depending on whether they were dealing with bulldozers, graders, or smaller equipment such as skid steers. Of the 40 service managers interviewed, 32 represented agricultural shops, six were exclusively construction and two shops worked on both agricultural and construction equipment, but tilted more heavily toward agriculture. The following data was collected for each participating service provider. Types of equipment and horsepower range Percentage of rebuild vs. replacement engine work Issues with replacement engines Customer decision factors for rebuilding vs. replacement Rebuild information for off-road engines Hourly Rate in Shop/Field Useful life & repair costs for various engine and emissions components: o Selective Catalytic Reduction Turbochargers Diesel Oxidation Catalysts (DOC) Exhaust Gas Recirculation (EGR) Valve and EGR Coolers Oxides of nitrogen (NOx) Sensors Diesel Particulate Filters (DPF) Fuel Injectors Diesel Exhaust Fluid (DEF) Doser/Header DEF Quality Sensors Engine Control Unit (ECU) Exhaust Manifold The power range of equipment most commonly serviced by each provider is noted in Table 1. Though most providers reported working on a wide variety of machinery, most had an engine size range that was more common, as noted below. The construction dealers were the most variable, while the agriculture equipment dealers typically had more common ranges of sizes based on the type of agriculture in the area