The dissipation of sound at an edge

A general formula is established for the rate at which acoustic energy is dissipated at the sharp edges of a rigid boundary by the generation of vorticity in the presence of a low, subsonic mean flow of uniform mean density. Experimental results relating to the radiation of sound from a jet pipe are used to show how the formula can be used to make quantitative predictions in the absence of a detailed knowledge of the unsteady flow field.     

Optimal interception with time constraint

This paper considers the problem of minimum-fuel interception with time constraint. The maneuver consists of using impulsive thrust to bring the interceptor from its initial orbit into a collision course with a target which is moving on a well-defined trajectory. The intercept time is either prescribed or is restricted to be less than an upper limit.The necessary conditions and the transversality conditions for optimality are discussed. The method of solution amounts to first solving a set of equations to obtain the primer vector for an initial one-impulse solution. Then, based on the information provided by the primer vector, rules are established to search for the optimal solution if the initial one-impulse trajectory is not optimal. The method is general, in the sense that it allows for solving the problem of three-dimensional interception with arbitrary motion for the target.Several numerical examples are presented, including orbital interceptions and interception at hyperbolic speeds of a ballistic missile.This research was supported by US Army Strategic Defense Command, Contract No. DASG60-88-C-0037.     

Second moments of ESR signals from poly(p-phenylene) and the deuterated analog

The second moments of the ESR signals obtained from poly(p-phenylene) (PPP) and deuterated PPP were measured at 9.5 and 35 GHz. The theoretical and experimental contributions to the second moments were considered. It is shown that for deuterated PPP, deuteron hyperfine splitting makes a negligible contribution to the observed second moment. The proton hyperfine contributions to the second moments of the radical species in PPP and p-sexiphenyl were estimated and it was concluded that the unpaired electron was delocalized over only 2-4 phenylene units. A rationale is offered in terms of polarons present as defects in the PPP chains.     

Directional correlation measurements in69Ga

Gamma-gamma directional correlation measurements have been made on the 553.35-318.63, 234.79–871.98 and 1,052.02-871.98 keV cascades in⁶⁹Ga from the decay of⁶⁹Ge using a NaI(Tl)-Ge(Li) coincidence set up. On the basis of these measurements the spin parity of 1/2^?, 3/2^?, 3/2^? and 5/2^? have been assigned respectively to the 318.63, 871.98, 1,106.77 and 1,924.00 keV states in⁶⁹Ga. The results have been discussed and compared with the previous works.     

Impossibility of perturbative restoration of F type spontaneously broken supersymmetry

We prove that higher order corrections cannot restore supersymmetry if it is spontaneously broken at the tree level by an F type mechanism even if not all terms consistent with the symmetries have been included.     

NEGOTIATING OVER EXTERNALITIES

We present a simple model in which two perfectly informed, risk neutral agents will not negotiate an efficient agreement to lessen the effects of an externality and for which the outcome of negotiation depends on the legal assignment of property rights. The model permits agents to pre-commit themselves to refuse to negotiate particular agenda issues. The result is obtained because we prove that one player is always made strictly worse off from the addition of side-payments to a bargaining game. Along the way, we devise a supporting hyperplane for the n-person Nash bargaining game solution. We also display a simple game which establishes that our main result holds true—for at least some games—for an array of alternative bargaining game solutions such as that of Raiffa, Kalai, and Smorodinski.     

The Capelli identity,the double commutant theorem,and multiplicity-free actions

Partially supported by NSF grant #DMS-8807336     

Quantum mechanics and partial differential equations

This paper develops the basic theory of pseudo-differential operators on Rⁿ, through the Calderón-Vaillancourt (0, 0) L²-estimate, as a natural part of the harmonic analysis on the Heisenberg group, the group-theoretic embodiment of Heisenberg's Canonical Commutation Relations. The symbol mapping is given a group-theoretic interpretation consistent with the Kirillov method of orbits. By comparing different well-known realizations of the unique irreducible representation of the Heisenberg group, the Toeplitz operators on the complex n-ball are shown essentially to be pseudo-differential operators. The proof of the Calderón-Vaillancourt estimate is almost purely group-theoretic. Criteria for positivity, and for compactness are also given.     

(GLn,GLm)-duality and symmetric plethysm

In [7] the author has given an exposition of the theory of invariants of binary forms in terms of a particular version of Classical Invariant Theory. Reflection shows that many aspects of the development apply also ton-ary forms. The purpose of this paper is to make explicit this more general application. The plethysms S’(S^p(ℂⁿ)) are computed quite explicitly forl = 2, 3 and 4. Partially supported by NSF Grant No. DMS 8506130.     

Preparation and stereochemistry of 3-phenacylidenephthalimidines

Yields of 3-phenacylidenephthalimidines are maximized and yields of phthalimide byproducts are minimized by use of acetic acid as the solvent in reactions of amines with 3-phenacylidenephthalides. The 3-phenacylidenephthalimidines are formed as E, Z mixtures, in which the E isomers predominate. A homonuclear NOE nmr experiment was employed to determined product stereochemistry.