Effect of magnesium doping on the orbital and magnetic order in LiNiO2

In LiNiO2, the Ni3+ ions, with S=1/2 and twofold orbital degeneracy, are arranged on a trian- gular lattice. Using muon spin relaxation (MuSR) and electron spin resonance (ESR), we show that magnesium doping does not stabilize any magnetic or orbital order, despite the absence of interplane Ni2+. A disordered, slowly fluctuating state develops below 12 K. In addition, we find that magnons are excited on the time scale of the ESR experiment. At the same time, a g factor anisotropy is observed, in agreement with $| 3z^{2}-r^{2}>$ orbital occupancy

Syzygies in equivariant cohomology for non-abelian Lie groups

We extend the work of Allday-Franz-Puppe on syzygies in equivariant cohomology from tori to arbitrary compact connected Lie groups G. In particular, we show that for a compact orientable G-manifold X the analogue of the Chang-Skjelbred sequence is exact if and only if the equivariant cohomology of X is reflexive, if and only if the equivariant Poincare pairing for X is perfect. Along the way we establish that the equivariant cohomology modules arising from the orbit filtration of X are Cohen-Macaulay. We allow singular spaces and introduce a Cartan model for their equivariant cohomology. We also develop a criterion for the finiteness of the number of infinitesimal orbit types of a G-manifold.Comment: 28 pages; minor change

Mrk 421, Mrk 501, and 1ES 1426+428 at 100 GeV with the CELESTE Cherenkov Telescope

We have measured the gamma-ray fluxes of the blazars Mrk 421 and Mrk 501 in the energy range between 50 and 350 GeV (1.2 to 8.3 x 10^25 Hz). The detector, called CELESTE, used first 40, then 53 heliostats of the former solar facility "Themis" in the French Pyrenees to collect Cherenkov light generated in atmospheric particle cascades. The signal from Mrk 421 is often strong. We compare its flux with previously published multi-wavelength studies and infer that we are straddling the high energy peak of the spectral energy distribution. The signal from Mrk 501 in 2000 was weak (3.4 sigma). We obtain an upper limit on the flux from 1ES 1426+428 of less than half that of the Crab flux near 100 GeV. The data analysis and understanding of systematic biases have improved compared to previous work, increasing the detector's sensitivity.Comment: 15 pages, 14 figures, accepted to A&A (July 2006) August 19 -- corrected error in author lis

High magnetic field transport measurement of charge-ordered Pr0.5_{0.5}Ca0.5_{0.5}MnO3_3 strained thin films

We have investigated the magnetic-field-induced phase transition of charge-ordered (CO) Pr$_{0.5}$Ca$_{0.5}$MnO$_3$ thin films, deposited onto (100)-oriented LaAlO$_3$ and (100)-oriented SrTiO$_3$ substrates using the pulsed laser deposition technique, by measuring the transport properties with magnetic fields up to 22T. The transition to a metallic state is observed on both substrates by application of a critical magnetic field ($H_C>10T$ at 60K). The value of the field required to destroy the charge-ordered insulating state, lower than the bulk compound, depends on both the substrate and the thickness of the film. The difference of the critical magnetic field between the films and the bulk material is explained by the difference of in-plane parameters at low temperature (below the CO transition). Finally, these results confirm that the robustness of the CO state, depends mainly on the stress induced by the difference in the thermal dilatations between the film and the substrate.Comment: 10 pages, 6 figures. To be published in Phys. Rev.

Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary

Consider a finite dimensional (generally reducible) polynomial representation \rho of GL_n. A projective compactification of GL_n is the closure of \rho(GL_n) in the space of all operators defined up to a factor (this class of spaces can be characterized as equivariant projective normal compactifications of GL_n). We give an expicit description for all projective compactifications. We also construct explicitly (in elementary geometrical terms) a universal object for all projective compactifications of GL_n.Comment: 24 pages, corrected varian

Production properties of low-mass systems in pp collisions at 102 GeV/c

We examine in detail the properties of low-mass systems produced in the inclusive reaction p + p --> p + anything at 102 GeV/c. We find that the internal characteristics of these low-mass nucleon-multipion systems (the "anything"), at fixed values of mass (M), are similar to those found for produced hadrons in high-energy collisions at fixed incident hadron energies . The resemblance between the properties of the M2 system and the characteristics of [pi]p collisions at s = M2 is particularly striking.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22250/1/0000686.pd

Laboratory angular distributions for the production of charged secondaries in inelastic proton-proton collisions at 102 GeV/c

Lab angular distributions for the production of charged secondary particles in inelastic proton-proton collisions are presented. Data are separately displayed for protons and for positive and negative mesons (pions and kaons combined).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22255/1/0000691.pd

Generalizing Tanisaki's ideal via ideals of truncated symmetric functions

We define a family of ideals $I_h$ in the polynomial ring $\mathbb{Z}[x_1,...,x_n]$ that are parametrized by Hessenberg functions $h$ (equivalently Dyck paths or ample partitions). The ideals $I_h$ generalize algebraically a family of ideals called the Tanisaki ideal, which is used in a geometric construction of permutation representations called Springer theory. To define $I_h$, we use polynomials in a proper subset of the variables ${x_1,...,x_n}$ that are symmetric under the corresponding permutation subgroup. We call these polynomials {\em truncated symmetric functions} and show combinatorial identities relating different kinds of truncated symmetric polynomials. We then prove several key properties of $I_h$, including that if $h>h'$ in the natural partial order on Dyck paths then $I_{h} \subset I_{h'}$, and explicitly construct a Gr\"{o}bner basis for $I_h$. We use a second family of ideals $J_h$ for which some of the claims are easier to see, and prove that $I_h = J_h$. The ideals $J_h$ arise in work of Ding, Develin-Martin-Reiner, and Gasharov-Reiner on a family of Schubert varieties called partition varieties. Using earlier work of the first author, the current manuscript proves that the ideals $I_h = J_h$ generalize the Tanisaki ideals both algebraically and geometrically, from Springer varieties to a family of nilpotent Hessenberg varieties.Comment: v1 had 27 pages. v2 is 29 pages and adds Appendix B, where we include a recent proof by Federico Galetto of a conjecture given in the previous version. We also add some connections between our work and earlier results of Ding, Gasharov-Reiner, and Develin-Martin-Reiner. v3 corrects a typo in Valibouze's citation in the bibliography. To appear in Journal of Algebraic Combinatoric