Linear differential operators on contact manifolds

We consider differential operators between sections of arbitrary powers of the determinant line bundle over a contact manifold. We extend the standard notions of the Heisenberg calculus: noncommutative symbolic calculus, the principal symbol, and the contact order to such differential operators. Our first main result is an intrinsically defined "subsymbol" of a differential operator, which is a differential invariant of degree one lower than that of the principal symbol. In particular, this subsymbol associates a contact vector field to an arbitrary second order linear differential operator. Our second main result is the construction of a filtration that strengthens the well-known contact order filtration of the Heisenberg calculus

Conformal symbols and the action of contact vector fields over the superline

Let K be the Lie superalgebra of contact vector fields on the supersymmetric line. We compute the action of K on the modules of differential and pseudodifferential operators between spaces of tensor densities, in terms of their conformal symbols. As applications we deduce the geometric subsymbols, 1-cohomology, and various uniserial subquotients of these modules. We also outline the computation of the K-equivalences and symmetries of their subquotients.Comment: 48 page

Centers and characters of Jacobi group-invariant differential operator algebras

We study the algebras of differential operators invariant with respect to the scalar slash actions of real Jacobi groups of arbitrary rank. These algebras are non-commutative and are generated by their elements of orders 2 and 3. We prove that their centers are polynomial in one variable and are generated by the Casimir operator. For slash actions with invertible indices we also compute the characters of the IDO algebras: in rank exceeding 1 there are two, and in rank 1 there are in general five. In rank 1 we compute in addition all irreducible admissible representations of the IDO algebras.Comment: 16 page

Demographic and psychological variables affecting test subject evaluations of ride quality

Ride-quality experiments similar in objectives, design, and procedure were conducted, one using the U.S. Air Force Total In-Flight Simulator and the other using the Langley Passenger Ride Quality Apparatus to provide the motion environments. Large samples (80 or more per experiment) of test subjects were recruited from the Tidewater Virginia area and asked to rate the comfort (on a 7-point scale) of random aircraft motion typical of that encountered during STOL flights. Test subject characteristics of age, sex, and previous flying history (number of previous airplane flights) were studied in a two by three by three factorial design. Correlations were computed between one dependent measure, the subject's mean comfort rating, and various demographic characteristics, attitudinal variables, and the scores on Spielberger's State-Trait Anxiety Inventory. An effect of sex was found in one of the studies. Males made higher (more uncomfortable) ratings of the ride than females. Age and number of previous flights were not significantly related to comfort ratings. No significant interactions between the variables of age, sex, or previous number of flights were observed

Evolution & Voting: How Nature Makes us Public Spirited

If one assumes that voters are rational, the most plausible explanation for high voter turnouts seems to be that agents receive benefits from the act of voting itself. We show that public-spirited agents have an evolutionary advantage over those who are not as public-spirited for a range of situations. We also explore conditions under which this kind of altruistic behavior is disadvantageous to agents. The details depend on the costs of voting, the degree to which different types of agents have different preferences over public policies and the relative proportions of various preference types in the population. We conclude that evolution may often be a force that causes agents to internalize the benefits their actions confer on others.

A psychological perspective on the decision process of successful farm managers : an empirical test of a satisficing model

The study was designed to develop and test a realistic model of farm management decision making. A general model of decision making comprised decision model that related net farm income, the indicator used for managerial success, as a function of economic resource endowment, the decision criterion and information; a perception of risk model that stated the perceived probability of success to be a function of economic factors affecting that perception; a dynamic learning model that related the results of a previous choice to the perception of alternatives in the next decision. The theory of achievement motivation was incorporated in the decision model and the learning model to explain choice under conditions of uncertainty and persistence of behavior at a particular choice, respectively. The data were obtained from a survey questionnaire and 1974 farm records kept by 108 farmers participating in the Resource Management Program. Measurement of the need for achievement, the fear of failure and information were obtained from the questionnaire. Values for economic resource endowment and net income were found in the farm reco-rds. Regression analysis was used to estimate the effect of the resource endowment, the decision criterion and information on net income and to determine the effect of economic factors affecting the perception of risk. The resource endowment explained the largest amount of variation in net income of any group of variables. Livestock, labor, buildings and credit capital proved significant while land and machinery did not. All but land, machinery and credit capital had the hypothesized positive signs. The decision criterion, while insignifi-cant, was found to have the largest effect, 2638.53, of any variable on net income. The coefficients of the information variables of educa-tion, training and information seeking were not significant. Altogether, the independent variables explained 38.4 percent of the variation in net farm income. The estimation of the perception of risk model was disappointing. Two measures of perceived probability of success were used as the dependent variable in separate estimations. The estimated equations accounted for only 2.5 percent and 3.8 percent of the variation in perceived probability. None of the independent variables were signi-ficant. A Chi-square analysis was used to evaluate the learning model. A contingency table of prior and posterior probabilities of selection of farm plans was devised for those 53 farmers who had altered their original plan. A Bayesian theorem was used to determine the posterior probabilities. The Chi-square analysis showed a significant difference between the probability of selecting a farm plan prior to its imple-mentation and after its alteration. An increase in farm prices took place over the same years as the study. This increase could be the cause of the change in perception of farm plan success. Both learning and increased prices are consistent with the statistical results