Association schemes from the action of PGL(2,q)PGL(2,q) fixing a nonsingular conic in PG(2,q)

The group $PGL(2,q)$ has an embedding into $PGL(3,q)$ such that it acts as the group fixing a nonsingular conic in $PG(2,q)$. This action affords a coherent configuration $R(q)$ on the set $L(q)$ of non-tangent lines of the conic. We show that the relations can be described by using the cross-ratio. Our results imply that the restrictions $R_{+}(q)$ and $R_{-}(q)$ to the sets $L_{+}(q)$ of secant lines and to the set $L_{-}(q)$ of exterior lines, respectively, are both association schemes; moreover, we show that the elliptic scheme $R_{-}(q)$ is pseudocyclic. We further show that the coherent configuration $R(q^2)$ with $q$ even allow certain fusions. These provide a 4-class fusion of the hyperbolic scheme $R_{+}(q^2)$, and 3-class fusions and 2-class fusions (strongly regular graphs) of both schemes $R_{+}(q^2)$ and $R_{-}(q^2). The fusion results for the hyperbolic case are known, but our approach here as well as our results in the elliptic case are new.Comment: 33 page

Field-Induced Ferromagnetic Order and Colossal Magnetoresistance in La_{1.2}Sr_{1.8}Mn_2O_7: a ^{139}La NMR study

In order to gain insights into the origin of colossal magneto-resistance (CMR) in manganese oxides, we performed a ^{139}La NMR study in the double-layered compound La_{1.2}Sr_{1.8}Mn_2O_7. We find that above the Curie temperature T_C=126 K, applying a magnetic field induces a long-range ferromagnetic order that persists up to T=330 K. The critical field at which the induced magnetic moment is saturated coincides with the field at which the CMR effect reaches to a maximum. Our results therefore indicate that the CMR observed above T_C in this compound is due to the field-induced ferromagnetism that produces a metallic state via the double exchange interaction

What Fraction of the Young Clusters in the Antennae Galaxies are "Missing"?

A reexamination of the correspondence between 6 cm radio continuum sources and young star clusters in the Antennae galaxies indicates that 85 % of the strong thermal sources have optical counterparts, once the optical image is shifted 1.2 arcsec to the southwest. A sample of 37 radio-optical matches are studied in detail showing correlations between radio properties and a variety of optical characteristics. There is a strong correlation between the radio flux and the intrinsic optical brightness. In particular, the brightest radio source is also the intrinsically brightest optical cluster (WS80). It is also the most extincted cluster in the sample, the strongest CO source and the strongest 15 micron source . Furthermore, the brightest ten radio sources are all amongst the youngest clusters with ages in the range 0 - 4 Myr and extinctions from A_V = 0.5 to 7.6 mag (with a median value of 2.6 mag). Only a few of the very red clusters originally discovered by Whitmore & Schweizer are radio sources, contrary to earlier suggestions. Finally, a new hybrid method of determining cluster ages has been developed using both UBVI colors and H_alpha equivalent widths to break the age-reddening degeneracy.Comment: 51 pages, 13 postscript figures, LaTex. To appear in the Astronomical Journal, 124, 2002, Septembe

Phase transition in site-diluted Josephson junction arrays: A numerical study

We numerically investigate the intriguing effects produced by random percolative disorder in two-dimensional Josephson-junction arrays. By dynamic scaling analysis, we evaluate critical temperatures and critical exponents with high accuracy. It is observed that, with the introduction of site-diluted disorder, the Kosterlitz-Thouless phase transition is eliminated and evolves into a continuous transition with power-law divergent correlation length. Moreover, genuine depinning transition and creep motion are studied, evidence for distinct creep motion types is provided. Our results not only are in good agreement with the recent experimental findings, but also shed some light on the relevant phase transitions.Comment: 7 pages, 8 figures, Phys. Rev. B (in press

Interpretations and Implications of the Top Quark Rapidity Asymmetries AFBtA_{FB}^t and AFBℓA_{FB}^{\ell}

Forward-backward asymmetries $A_{FB}^t$ and $A_{FB}^\ell$ are observed in the top quark $t$ rapidity distribution and in the rapidity distribution of charged leptons $\ell$ from top quark decay at the Tevatron proton-antiproton collider, and a charge asymmetry $A_C$ is seen in proton-proton collisions at the Large Hadron Collider (LHC). In this paper, we update our previous studies of the Tevatron asymmetries using the most recent data. We provide expectations for $A_C$ at the LHC based first on model independent extrapolations from the Tevatron, and second based on new physics models that can explain the Tevatron asymmetries. We examine the relationship of the two asymmetries $A_{FB}^t$ and $A_{FB}^\ell$. We show their connection through the $(V-A)$ spin correlation between the charged lepton and the top quark with different polarization states. We show that the ratio of the two asymmetries provides independent insight into new physics models that are invoked to fit the top quark asymmetry. We emphasize the value of the measurement of both asymmetries, and we conclude that a model which produces more right-handed than left-handed top quarks is favored by the present Tevatron data.Comment: Some figures changed. A typo in appendix fixed. Published in Physical Review

Top Quark Polarization As A Probe of Models with Extra Gauge Bosons

New heavy gauge bosons exist in many models of new physics beyond the standard model of particle physics. Discovery of these W^\prime and Z^\prime resonances and the establishment of their spins, couplings, and other quantum numbers would shed light on the gauge structure of the new physics. The measurement of the polarization of the SM fermions from the gauge boson decays would decipher the handedness of the coupling of the new states, an important relic of the primordial new physics symmetry. Since the top quark decays promptly, its decay preserves spin information. We show how decays of new gauge bosons into third generation fermions (W^\prime \to tb, Z^\prime\to t\bar{t}) can be used to determine the handedness of the couplings of the new states and to discriminate among various new physics models

Proofs of two conjectures on ternary weakly regular bent functions

We study ternary monomial functions of the form f(x)=\Tr_n(ax^d), where x\in \Ff_{3^n} and \Tr_n: \Ff_{3^n}\to \Ff_3 is the absolute trace function. Using a lemma of Hou \cite{hou}, Stickelberger's theorem on Gauss sums, and certain ternary weight inequalities, we show that certain ternary monomial functions arising from \cite{hk1} are weakly regular bent, settling a conjecture of Helleseth and Kholosha \cite{hk1}. We also prove that the Coulter-Matthews bent functions are weakly regular.Comment: 20 page