An SIS waveguide heterodyne receiver for 600 HGz-635 GHz

A waveguide SIS heterodyne receiver using a Nb/AlO_X/Nb junction has been built for astronomical observations of molecular transitions in the frequency range 600 GHz - 635 GHz, and has been successfully used at the Caltech Submillimeter Observatory (CSO). We report double sideband (DSB) receiver noise temperatures as low as 245 K at 600 GHz -610 GHz, and near 300 K over the rest of the bandwidth. These results confirm that SIS quasiparticle mixers work well at submillimeter-wave frequencies corresponding to photon energies of at least 90% of the superconductor energy gap. In addition, we have systematically investigated the effect on the receiver performance of the overlap between first-order and second-order photon steps of opposite sign at these frequencies. The receiver noise increases by as much as 40% in the region of overlap. We infer potential limitations for operating submillimeter-wave Nb/AlO_x/Nb mixers.     

MR imaging findings in recurrent primary osseous Ewing sarcoma

The objective of this study was to determine the value of magnetic resonance (MR) imaging in diagnosing local recurrence of Ewing sarcoma. We retrospectively reviewed radiographs, Tc^99m-methylene diphosphonate (MDP) skeletal scintigraphy, computed tomography scans, and MR studies of 11 patients who had local recurrences of osseous Ewing sarcoma following initial responses to chemotherapy and local radiation. The MR images were compared to those of a control group of nine patients who had no evidence of relapse. T₁- and T₂-weighted MR images identified 9 of the 11 recurrences. Computed tomography was diagnostic in 4 of 6 cases evaluated, Tc^99m-MDP bone scintigraphy in 4 of 11 cases, and plain radiographs in 2 of 10. MR findings at relapse included changes in signal intensity, increased extent of abnormal marrow signal on T₁- and T₂-weighted images, and identification of a new soft tissue mass. These findings suggest that MR imaging is valuable in the routine follow-up of parimary osseous Ewing sarcoma.     

Factorization in dedekind domains with finite class group

LetD be a Dedekind domain. It is well known thatD is then an atomic integral domain (that is to say, a domain in which each nonzero nonunit has a factorization as a product of irreducible elements). We study factorization properties of elements in Dedekind domains with finite class group. IfD has the property that any factorization of an elementα into irreducibles has the same length, thenD is called a half factorial domain (HFD, see [41]). IfD has the property that any factorization of an elementα into irreducibles has the same length modulor (for somer>1), thenD is called a congruence half factorial domain of orderr. In Section I we consider some general factorization properties of atomic integral domains as well as the interrelationship of the HFD and CHFD property in the Dedekind setting. In Section II we extend many of the results of [41], [42] and [36] concerning HFDs when the class group ofD is cyclic. Finally, in Section III we consider the CHFD property in detail and determine some basic properties of Dedekind CHFDs. IfG is any Abelian group andS any subset ofG−[0], then {G, S} is called a realizable pair if there exists a Dedekind domainD with class groupG such thatS is the set of nonprincipal classes ofG which contain prime ideals. We prove that for a finite abelian groupG there exists a realizable pair {G, S} such that any Dedekind domain associated to {G, S} is CHFD for somer>1 but not HFD if and only ifG is not isomorphic toZ ₂,Z ₂,Z ₂ ⊕Z ₂, orZ ₃ ⊕Z ₃. The first author received support under the John M. Bennett Fellowship at Trinity University and also gratefully acknowledges the support of The University of North Carolina at Chapel Hill.     

On Bayes and unbiased estimators of loss

We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In 3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988, On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly, that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss. Research supported by NSF Grant DMS-97-04524.     

Diffraction by a wedge at skew incidence: integral representations of Cauchy-Carleman for the electromagnetic fields

An electromagnetic diffraction problem in a wedge shaped region is reduced to a system of coupled functional difference equations by means of Sommerfeld integrals and Malyuzhinets theorem. By introducing an integral operator it is shown that the solutions of this system of functional equations can be defined in terms of integral representations whose kernels are solutions of a singular integral equation of Cauchy-Carleman type for which an explicit solution is given.     

Independence Sequences of Well-Covered Graphs: Non-Unimodality and the Roller-Coaster Conjecture

A graph G is well-covered provided each maximal independent set of vertices has the same cardinality. The term s_k of the independence sequence (s₀,s₁,,s) equals the number of independent k-sets of vertices of G. We investigate constraints on the linear orderings of the terms of the independence sequence of well-covered graphs. In particular, we provide a counterexample to the recent unimodality conjecture of Brown, Dilcher, and Nowakowski. We formulate the Roller-Coaster Conjecture to describe the possible linear orderings of terms of the independence sequence. We are grateful to Jason Brown for a helpful discussion in December of 1999 and to Richard Stanley for valuable feedback in August of 2000. The work of the second author was partially supported by the Naval Academy Research Council and ONR grant N0001400WR20041     

Spline collocation for strongly elliptic equations on the torus

Summary We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4].     

Ramsey partitions of integers and pair divisions

Ifk ₁ andk ₂ are positive integers, the partitionP = (₁,₂,..., _n ) ofk ₁+k ₂ is said to be a Ramsey partition for the pairk ₁,k ₂ if for any sublistL ofP, either there is a sublist ofL which sums tok ₁ or a sublist ofP –L which sums tok ₂. Properties of Ramsey partitions are discussed. In particular it is shown that there is a unique Ramsey partition fork ₁,k ₂ having the smallest numbern of terms, and in this casen is one more than the sum of the quotients in the Euclidean algorithm fork ₁ andk ₂.An application of Ramsey partitions to the following fair division problem is also discussed: Suppose two persons are to divide a cake fairly in the ratiok ₁k ₂. This can be done trivially usingk ₁+k ₂-1 cuts. However, every Ramsey partition ofk ₁+k ₂ also yields a fair division algorithm. This method yields fewer cuts except whenk ₁=1 andk ₂=1, 2 or 4.     

The decays of theρ′1 andω′1 mesons

New measurements of the reactione ⁺ e ^– confirm previous evidence for the decay₁ and provide a strong constraint on the mass of the₁. The results from a detailed analysis of these data are compared with those from a corresponding analysis of new data on the reactione ⁺ e ^–. It is shown that in accord with expectation. This identification of a strong₁ decay supports a previous claim that the₁ and theC(1480), observed in the channel, cannot be different manifestations of the same particle.