Higher Spin BRS Cohomology of Supersymmetric Chiral Matter in D=4

We examine the BRS cohomology of chiral matter in $N=1$, $D=4$ supersymmetry to determine a general form of composite superfield operators which can suffer from supersymmetry anomalies. Composite superfield operators \Y_{(a,b)} are products of the elementary chiral superfields $S$ and \ov S and the derivative operators D_\a, \ov D_{\dot \b} and \pa_{\a \dot \b}. Such superfields \Y_{(a,b)} can be chosen to have `$a$' symmetrized undotted indices \a_i and `$b$' symmetrized dotted indices \dot \b_j. The result derived here is that each composite superfield \Y_{(a,b)} is subject to potential supersymmetry anomalies if $a-b$ is an odd number, which means that \Y_{(a,b)} is a fermionic superfield.Comment: 15 pages, CPT-TAMU-20/9

Dominant partition method

By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails

The Theory Behind TheoryMine

Abstract. We describe the technology behind the TheoryMine novelty gift company, which sells the rights to name novel mathematical theorems. A tower of four computer systems is used to generate recursive theories, then to speculate conjectures in those theories and then to prove these conjectures. All stages of the process are entirely automatic. The process guarantees large numbers of sound, novel theorems of some intrinsic merit.

Color-dressed recursive relations for multi-parton amplitudes

Remarkable progress inspired by twistors has lead to very simple analytic expressions and to new recursive relations for multi-parton color-ordered amplitudes. We show how such relations can be extended to include color and present the corresponding color-dressed formulation for the Berends-Giele, BCF and a new kind of CSW recursive relations. A detailed comparison of the numerical efficiency of the different approaches to the calculation of multi-parton cross sections is performed.Comment: 31 pages, 4 figures, 6 table

Autonomous Integrated Receive System (AIRS) requirements definition. Volume 2: Design and development

Functional requirements and specifications are defined for an autonomous integrated receive system (AIRS) to be used as an improvement in the current tracking and data relay satellite system (TDRSS), and as a receiving system in the future tracking and data acquisition system (TDAS). The AIRS provides improved acquisition, tracking, bit error rate (BER), RFI mitigation techniques, and data operations performance compared to the current TDRSS ground segment receive system. A computer model of the AIRS is used to provide simulation results predicting the performance of AIRS. Cost and technology assessments are included

Testing Gravity in the Outer Solar System: Results from Trans-Neptunian Objects

The inverse square law of gravity is poorly probed by experimental tests at distances of ~ 10 AUs. Recent analysis of the trajectory of the Pioneer 10 and 11 spacecraft have shown an unmodeled acceleration directed toward the Sun which was not explained by any obvious spacecraft systematics, and occurred when at distances greater than 20 AUs from the Sun. If this acceleration represents a departure from Newtonian gravity or is indicative of an additional mass distribution in the outer solar system, it should be detectable in the orbits of Trans-Neptunian Objects (TNOs). To place limits on deviations from Newtonian gravity, we have selected a well observed sample of TNOs found orbiting between 20 and 100 AU from the Sun. By examining their orbits with modified orbital fitting software, we place tight limits on the perturbations of gravity that could exist in this region of the solar system.Comment: 20 pages, 4 figures, 2 tables, uses AASTex v5.x macro

The association between hysterectomy and ovarian cancer risk: A population-based record-linkage study

Background: Recent studies have called into question the long-held belief that hysterectomy without oophorectomy protects against ovarian cancer. This population-based longitudinal record-linkage study aimed to explore this relationship, overall and by age at hysterectomy, time period, surgery type, and indication for hysterectomy. Methods: We followed the female adult Western Australian population (837 942 women) across a 27-year period using linked electoral, hospital, births, deaths, and cancer records. Surgery dates were determined from hospital records, and ovarian cancer diagnoses (n¼1640) were ascertained from cancer registry records.We used Cox regression to estimate hazard ratios (HRs) and 95% confidence intervals (CIs) for the association between hysterectomy and ovarian cancer incidence. Results: Hysterectomy without oophorectomy (n¼78 594) was not associated with risk of invasive ovarian cancer overall (HR ¼ 0.98, 95% CI ¼ 0.85 to 1.11) or with the most common serous subtype (HR ¼ 1.05, 95% CI ¼ 0.89 to 1.23). Estimates did not vary statistically significantly by age at procedure, time period, or surgical approach. However, among women with endometriosis (5.8%) or with fibroids (5.7%), hysterectomy was associated with substantially decreased ovarian cancer risk overall (HR ¼ 0.17, 95% CI ¼ 0.12 to 0.24, and HR ¼ 0.27, 95% CI ¼ 0.20 to 0.36, respectively) and across all subtypes. Conclusions: Our results suggest that for most women, having a hysterectomy with ovarian conservation is not likely to substantially alter their risk of developing ovarian cancer. However, our results, if confirmed, suggest that ovarian cancer risk reduction could be considered as a possible benefit of hysterectomy when making decisions about surgical management of endometriosis or fibroids

Spinning test particles and clock effect in Schwarzschild spacetime

We study the behaviour of spinning test particles in the Schwarzschild spacetime. Using Mathisson-Papapetrou equations of motion we confine our attention to spatially circular orbits and search for observable effects which could eventually discriminate among the standard supplementary conditions namely the Corinaldesi-Papapetrou, Pirani and Tulczyjew. We find that if the world line chosen for the multipole reduction and whose unit tangent we denote as $U$ is a circular orbit then also the generalized momentum $P$ of the spinning test particle is tangent to a circular orbit even though $P$ and $U$ are not parallel four-vectors. These orbits are shown to exist because the spin induced tidal forces provide the required acceleration no matter what supplementary condition we select. Of course, in the limit of a small spin the particle's orbit is close of being a circular geodesic and the (small) deviation of the angular velocities from the geodesic values can be of an arbitrary sign, corresponding to the possible spin-up and spin-down alignment to the z-axis. When two spinning particles orbit around a gravitating source in opposite directions, they make one loop with respect to a given static observer with different arrival times. This difference is termed clock effect. We find that a nonzero gravitomagnetic clock effect appears for oppositely orbiting both spin-up or spin-down particles even in the Schwarzschild spacetime. This allows us to establish a formal analogy with the case of (spin-less) geodesics on the equatorial plane of the Kerr spacetime. This result can be verified experimentally.Comment: IOP macros, eps figures n. 2, to appear on Classical and Quantum gravity, 200

Note on graviton MHV amplitudes

Two new formulas which express n-graviton MHV tree amplitudes in terms of sums of squares of n-gluon amplitudes are discussed. The first formula is derived from recursion relations. The second formula, simpler because it involves fewer permutations, is obtained from the variant of the Berends, Giele, Kuijf formula given in Arxiv:0707.1035.Comment: 10 page

Characterizing Triviality of the Exponent Lattice of A Polynomial through Galois and Galois-Like Groups

The problem of computing \emph{the exponent lattice} which consists of all the multiplicative relations between the roots of a univariate polynomial has drawn much attention in the field of computer algebra. As is known, almost all irreducible polynomials with integer coefficients have only trivial exponent lattices. However, the algorithms in the literature have difficulty in proving such triviality for a generic polynomial. In this paper, the relations between the Galois group (respectively, \emph{the Galois-like groups}) and the triviality of the exponent lattice of a polynomial are investigated. The \bbbq\emph{-trivial} pairs, which are at the heart of the relations between the Galois group and the triviality of the exponent lattice of a polynomial, are characterized. An effective algorithm is developed to recognize these pairs. Based on this, a new algorithm is designed to prove the triviality of the exponent lattice of a generic irreducible polynomial, which considerably improves a state-of-the-art algorithm of the same type when the polynomial degree becomes larger. In addition, the concept of the Galois-like groups of a polynomial is introduced. Some properties of the Galois-like groups are proved and, more importantly, a sufficient and necessary condition is given for a polynomial (which is not necessarily irreducible) to have trivial exponent lattice.Comment: 19 pages,2 figure