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.

The Certification Qualifications of Junior High School Teachers in Selected Illinois Counties

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