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

Rosenberg: The Pretrial Conference and Effective Justice--A Controlled Test in Personal Injury Litigation

A Review of The Pretrial Conference and Effective Justice--A Controlled Test in Personal Injury Litigation by Maurice Rosenber

Flight directors for STOl aircraft

Flight director logic for flight path and airspeed control of a powered-lift STOL aircraft in the approach, transition, and landing configurations are developed. The methods for flight director design are investigated. The first method is based on the Optimal Control Model (OCM) of the pilot. The second method, proposed here, uses a fixed dynamic model of the pilot in a state space formulation similar to that of the OCM, and includes a pilot work-load metric. Several design examples are presented with various aircraft, sensor, and control configurations. These examples show the strong impact of throttle effectiveness on the performance and pilot work-load associated with manual control of powered-lift aircraft during approach. Improved performed and reduced pilot work-load can be achieved by using direct-lift-control to increase throttle effectiveness

Sumoylation silences the plasma membrane leak K+ channel K2P1.

Reversible, covalent modification with small ubiquitin-related modifier proteins (SUMOs) is known to mediate nuclear import/export and activity of transcription factors. Here, the SUMO pathway is shown to operate at the plasma membrane to control ion channel function. SUMO-conjugating enzyme is seen to be resident in plasma membrane, to assemble with K2P1, and to modify K2P1 lysine 274. K2P1 had not previously shown function despite mRNA expression in heart, brain, and kidney and sequence features like other two-P loop K+ leak (K2P) pores that control activity of excitable cells. Removal of the peptide adduct by SUMO protease reveals K2P1 to be a K+-selective, pH-sensitive, openly rectifying channel regulated by reversible peptide linkage

A Canonical Approach to the Quantization of the Damped Harmonic Oscillator

We provide a new canonical approach for studying the quantum mechanical damped harmonic oscillator based on the doubling of degrees of freedom approach. Explicit expressions for Lagrangians of the elementary modes of the problem, characterising both forward and backward time propagations are given. A Hamiltonian analysis, showing the equivalence with the Lagrangian approach, is also done. Based on this Hamiltonian analysis, the quantization of the model is discussed.Comment: Revtex, 6 pages, considerably expanded with modified title and refs.; To appear in J.Phys.

How unprovable is Rabin's decidability theorem?

We study the strength of set-theoretic axioms needed to prove Rabin's theorem on the decidability of the MSO theory of the infinite binary tree. We first show that the complementation theorem for tree automata, which forms the technical core of typical proofs of Rabin's theorem, is equivalent over the moderately strong second-order arithmetic theory $\mathsf{ACA}_0$ to a determinacy principle implied by the positional determinacy of all parity games and implying the determinacy of all Gale-Stewart games given by boolean combinations of ${\bf \Sigma^0_2}$ sets. It follows that complementation for tree automata is provable from $\Pi^1_3$- but not $\Delta^1_3$-comprehension. We then use results due to MedSalem-Tanaka, M\"ollerfeld and Heinatsch-M\"ollerfeld to prove that over $\Pi^1_2$-comprehension, the complementation theorem for tree automata, decidability of the MSO theory of the infinite binary tree, positional determinacy of parity games and determinacy of $\mathrm{Bool}({\bf \Sigma^0_2})$ Gale-Stewart games are all equivalent. Moreover, these statements are equivalent to the $\Pi^1_3$-reflection principle for $\Pi^1_2$-comprehension. It follows in particular that Rabin's decidability theorem is not provable in $\Delta^1_3$-comprehension.Comment: 21 page