Instruction: what is the prompt that generates the input?

Input: We give a quantitative analysis of the previously published nuclear magneticresonance (NMR) experiments in the k-(ET)2X family of organic charge transfersalts by using the phenomenological spin fluctuation model of Moriya, andMillis, Monien and Pines (M-MMP). For temperatures above T_nmr ~ 50 K, themodel gives a good quantitative description of the data in the metallic phasesof several k-(ET)2X materials. These materials display antiferromagneticcorrelation lengths which increase with decreasing temperature and grow toseveral lattice constants by T_nmr. It is shown that the fact that thedimensionless Korringa ratio is much larger than unity is inconsistent with abroad class of theoretical models (such as dynamical mean-field theory) whichneglects spatial correlations and/or vertex corrections. For materials close tothe Mott insulating phase the nuclear spin relaxation rate, the Knight shiftand the Korringa ratio all decrease significantly with decreasing temperaturebelow T_nmr. This cannot be described by the M-MMP model and the most naturalexplanation is that a pseudogap, similar to that observed in the underdopedcuprate superconductors, opens up in the density of states below T_nmr. Such apseudogap has recently been predicted to occur in the dimerised organic chargetransfer salts materials by the resonating valence bond (RVB) theory. Wepropose specific new experiments on organic superconductors to elucidate theseissues. For example, measurements to see if high magnetic fields or highpressures can be used to close the pseudogap would be extremely valuable.


Instruction: what is the prompt that generates the input?

Input: The orbits of stars close to a massive black hole are nearly Keplerianellipses. Such orbits exert long term torques on each other, which lead to anenhanced angular momentum relaxation known as resonant relaxation. Undercertain conditions, this process can modify the angular momentum distributionand affect the interaction rates of the stars with the massive black hole moreefficiently than non-resonant relaxation. The torque on an orbit exerted by thecluster depends on the eccentricity of the orbit. In this paper, we calculatethis dependence and determine the resonant relaxation timescale as a functionof eccentricity. In particular, we show that the component of the torque thatchanges the magnitude of the angular momentum is linearly proportional toeccentricity, so resonant relaxation is much more efficient on eccentric orbitsthan on circular orbits.


Instruction: what is the prompt that generates the input?

Input: We study various topological invariants on a torsional geometry in thepresence of a totally anti-symmetric torsion H under the closed condition dH =0, which appears in string theory compactification scenarios. By using theidentification between the Clifford algebra on the geometry and the canonicalquantization condition of fermions in quantum mechanics, we construct N=1quantum mechanical sigma model in the Hamiltonian formalism. We extend thismodel to N=2 system, equipped with the totally anti-symmetric tensor associatedwith the torsion on the target space geometry. Next we construct transitionelements in the Lagrangian path integral formalism and apply them to theanalyses of the Witten indices in supersymmetric systems. We explicitly showthe formulation of the Dirac index on the torsional manifold which has alreadybeen studied. We also formulate the Euler characteristic and the Hirzebruchsignature on the torsional manifold.


Instruction: what is the prompt that generates the input?

Input: We report on the frequency performance of a low cost (~500$) radio-frequencysine wave generator, using direct digital synthesis (DDS) and afield-programmable gate array (FPGA). The output frequency of the device may bechanged dynamically to any arbitrary value ranging from DC to 10 MHz withoutany phase slip. Sampling effects are substantially reduced by a high samplerate, up to 1 MHz, and by a large memory length, more than 2.10^5 samples. Byusing a low noise external oscillator to clock the DDS, we demonstrate a phasenoise as low as that of the master clock, that is at the level of -113dB.rad^2/Hz at 1 Hz from the carrier for an output frequency of 3.75 MHz. Thedevice is successfully used to confine an ultracold atomic cloud of rubidium 87in a RF-based trap, and there is no extra heating from the RF source.


Instruction: what is the prompt that generates the input?

Input: In this study, using the analytical and recurrence relations suggested by theauthors in previous works, the new efficient and reliable program procedure forthe overlap integrals over Slater type orbitals (STOs) is presented. Theproposed procedure guarantees a highly accurate evaluation of the overlapintegrals with arbitrary values of quantum numbers, screening constants andinternuclear distances. It is demonstrated that the computational accuracy ofthe proposed procedure is not only dependent on the efficiency of formulas, ashas been discussed previously, but also on a number of other factors includingthe used program language package and solvent properties. The numerical resultsobtained using the algorithm described in the present work are in a completeagreement with those obtained using the alternative evaluation procedure. Wenotice that the program works without any restrictions and in all range ofintegral parameters.


Instruction: what is the prompt that generates the input?

Input: A consistent device model to describe current-voltage characteristics ofmetal/insulator/metal systems is developed. In this model the insulator and themetal electrodes are described within the same theoretical framework by usingdensity of states distributions. This approach leads to differential equationsfor the electric field which have to be solved in a self consistent manner byconsidering the continuity of the electric displacement and the electrochemicalpotential in the complete system. The model is capable of describing thecurrent-voltage characteristics of the metal/insulator/metal system in forwardand reverse bias for arbitrary values of the metal/ insulator injectionbarriers. In the case of high injection barriers, approximations are providedoffering a tool for comparison with experiments. Numerical calculations areperformed exemplary using a simplified model of an organic semiconductor.


Instruction: what is the prompt that generates the input?

Input: The effect of Li substitution for Mg and of Li-C co-substitution on thesuperconducting properties and crystal structure of MgB2 single crystals hasbeen investigated. It has been found that hole doping with Li decreases thesuperconducting transition temperature Tc, but at a slower rate than electrondoping with C or Al. Tc of MgB2 crystals with simultaneously substituted Li forMg and C for B decreases more than in the case where C is substituted alone.This means that holes introduced by Li cannot counterbalance the effect ofdecrease of Tc caused by introduction of electrons coming from C. The possiblereason of it can be that holes coming from Li occupy the pi band whileelectrons coming from C fill the sigma band. The temperature dependences of theupper critical field Hc2 for Al and Li substituted crystals with the same Tcshow a similar dHc2/dT slope at Tc and a similar Hc2(T) behavior, despite ofmuch different substitution level. This indicates that the mechanismcontrolling Hc2 and Tc is similar in both hole and electron doped crystals.Electrical transport measurements show an increase of resistivity both in Lisubstituted crystals and in Li and C co-substituted crystals. This indicatesenhanced scattering due to defects introduced by substitutions includingdistortion of the lattice. The observed behavior can be explained as a resultof two effects, influencing both Tc and Hc2. The first one is doping related tothe changes in the carrier concentration, which may lead to the decrease or tothe increase of Tc. The second one is related to the introduction of newscattering centers leading to the modification of the interband and/orintraband scattering and therefore, to changes in the superconducting gaps andto the reduction of Tc.


Instruction: what is the prompt that generates the input?

Input: The threshold electrodisintegration of the deuteron at backward angles isstudied with a relativistic Hamiltonian, including a relativisticone-pion-exchange potential (OPEP) with off-shell terms as predicted bypseudovector coupling of pions to nucleons. The bound and scattering states areobtained in the center-of-mass frame, and then boosted from it to the Breitframe, where the evaluation of the relevant matrix elements of theelectromagnetic current operator is carried out. The latter includes, inaddition to one-body, also two-body terms due to pion exchange, as obtained,consistently with the OPEP, in pseudovector pion-nucleon coupling theory. Thefull Lorentz structure of these currents is retained. In order to estimate themagnitude of the relativistic effects we perform, for comparison, thecalculation with a non-relativistic phase-equivalent Hamiltonian and thestandard non-relativistic expressions for the one-body and two-bodypion-exchange currents. Our results for the electrodisintegration cross sectionshow that, in the calculations using one-body currents, relativisticcorrections become significant ({\it i.e.}, larger than 10%) only at highmomentum transfer $Q$ ($Q^2 \simeq 40$fm$^{-2}$ and beyond). However, theinclusion of two-body currents makes the relativistic predictions considerablysmaller than the corresponding non-relativistic results in the $Q^2$ region(18--40) fm$^{-2}$. The calculations based on the relativistic model alsoconfirm the inadequacy, already established in a non-relativistic context, ofthe present electromagnetic current model to reproduce accurately theexperimental data at intermediate values of momentum transfers.


Instruction: what is the prompt that generates the input?

Input: Building on the well-known Unruh-Davies effect, we examine the effects ofprojective measurements and quantum communications between accelerated andstationary observers. We find that the projective measurement by a uniformlyaccelerated observer can excite real particles from the vacuum in the inertialframe, even if no additional particles are created by the measurement processin the accelerating frame. Furthermore, we show that the particles created bythis accelerating measurement can be highly entangled in the inertial frame,and it is also possible to use this process to generate even maximallyentangled two-qubit states by a certain arrangement of measurements. As abyproduct of our analysis, we also show that a single qubit of information canbe perfectly transmitted from the accelerating observer to the inertial one. Inprinciple, such an effect could be exploited in designing an entangled stategenerator for quantum communication.


Instruction: what is the prompt that generates the input?

Input: In the work of Hoshino, Kato and Miyachi, the authors look at t-structuresinduced by a compact object, C, of a triangulated category, T, which is rigidin the sense of Iyama and Yoshino. Hoshino, Kato and Miyachi show that such anobject yields a non-degenerate t-structure on T whose heart es equivalent toMod(End(C)^op). Rigid objects in a triangulated category can be thought of asbehaving like chain differential graded algebras (DGAs).  Analogously, looking at objects which behave like cochain DGAs naturallygives the dual notion of a corigid object. Here, we see that a compact corigidobject, S, of a triangulated category, T, induces a structure similar to at-structure which we shall call a co-t-structure. We also show that the coheartof this non-degenerate co-t-structure is equivalent to Mod(End(S)^op), andhence an abelian subcategory of T.


Instruction: what is the prompt that generates the input?

Input: We argue that non-Abelian gauge fields can be treated as the pseudo-Goldstonevector bosons caused by spontaneous Lorentz invariance violation (SLIV). Tothis end, the SLIV which evolves in a general Yang-Mills type theory with thenonlinear vector field constraint $Tr(% \boldsymbol{A}_{\mu}\boldsymbol{A}^{\mu})=\pm M^{2}$ ($M$ is a proposed SLIV scale) imposed isconsidered in detail. With an internal symmetry group $G$ having $D$ generatorsnot only the pure Lorentz symmetry SO(1,3), but the larger accidental symmetry$SO(D,3D)$ of the SLIV constraint in itself appears to be spontaneously brokenas well. As a result, while the pure Lorentz violation still generates only onegenuine Goldstone vector boson, the accompanying pseudo-Goldstone vector bosonsrelated to the $SO(D,3D)$ breaking also come into play in the final arrangementof the entire Goldstone vector field multiplet. Remarkably, they remainstrictly massless, being protected by gauge invariance of the Yang-Mills theoryinvolved. We show that, although this theory contains a plethora of Lorentz and$CPT$ violating couplings, they do not lead to physical SLIV effects which turnout to be strictly cancelled in all the lowest order processes considered.However, the physical Lorentz violation could appear if the internal gaugeinvariance were slightly broken at very small distances influenced by gravity.For the SLIV scale comparable with the Planck one the Lorentz violation couldbecome directly observable at low energies.


Instruction: what is the prompt that generates the input?

Input: Near-IR and X-ray flares have been detected from the supermassive black holeSgr A* at the center of our Galaxy with a (quasi)-period of ~17-20 minutes,suggesting an emission region only a few Schwarzschild radii above the eventhorizon. The latest X-ray flare, detected with XMM-Newton, is notable for itsdetailed lightcurve, yielding not only the highest quality period thus far, butalso important structure reflecting the geometry of the emitting region. RecentMHD simulations of Sgr A*'s disk have demonstrated the growth of a Rossby waveinstability, that enhances the accretion rate for several hours, possiblyaccounting for the observed flares. In this Letter, we carry out ray-tracingcalculations in a Schwarzschild metric to determine as accurately as possiblethe lightcurve produced by general relativistic effects during such adisruption. We find that the Rossby wave induced spiral pattern in the disk isan excellent fit to the data, implying a disk inclination angle of ~77 deg.Note, however, that if this association is correct, the observed period is notdue to the underlying Keplerian motion but, rather, to the pattern speed. Thefavorable comparison between the observed and simulated lightcurves providesimportant additional evidence that the flares are produced in Sgr A*'s innerdisk.


Instruction: what is the prompt that generates the input?

Input: In the classical one-dimensional solution of fluid dynamics equations allunknown functions depend only on time t and Cartesian coordinate x. Althoughfluid spreads in all directions (velocity vector has three components) thewhole picture of motion is relatively simple: trajectory of one fluid particlefrom plane x=const completely determines motion of the whole plane. Basing onthe symmetry analysis of differential equations we propose generalization ofthis solution allowing movements in different directions of fluid particlesbelonging to plane x=const. At that, all functions but an angle determining thedirection of particle's motion depend on t and x only, whereas the angledepends on all coordinates. In this solution the whole picture of motionsuperposes from identical trajectories placed under different angles in 3Dspace. Orientations of the trajectories are restricted by a finite relationpossessing functional arbitrariness. The solution describes three-dimensionalnonlinear processes and singularities in infinitely conducting plasma, gas orincompressible liquid.


Instruction: what is the prompt that generates the input?

Input: The function exp(iwt) describes an oscillating motion. Energy of theoscillator is proportional to the square of w. exp(iwt) is the solution of adifferential equation. We have replaced this differential equation by thecorresponding finite-time difference equation with d as the smallest span oftime. We have, then, symmetrized the equation so that it remains invariantunder the change d going to -d. This symmetric equation has solutions in pairs.The angular speed w is modified to w' or w". w' contains a part with aninteger. w" contains a part with a half-integer. This corresponds to quantummechanical oscillator energy levels. F= a.exp(iwt) describes oscillationbetween -a and +a. If we make w=0, F describes free oscillation between -a and+a. Reciprocal symmetric oscillator, thus, unifies quantum and classicalharmonic oscillators on one hand, and a harmonic oscillator and a free particlein a potential well on the other hand. No quantum mechanical postulates areinvolved.


Instruction: what is the prompt that generates the input?

Input: We present new observational results obtained for the Galactic non-thermalradio source G328.4+0.2 to determine both if this source is a pulsar windnebula or supernova remnant, and in either case, the physical properties ofthis source. Using X-ray data obtained by XMM, we confirm that the X-rayemission from this source is heavily absorbed and has a spectrum best fit by apower law model of photon index=2 with no evidence for a thermal component, theX-ray emission from G328.4+0.2 comes from a region significantly smaller thanthe radio emission, and that the X-ray and radio emission are significantlyoffset from each other. We also present the results of a new high resolution (7arcseconds) 1.4 GHz image of G328.4+0.2 obtained using the Australia TelescopeCompact Array, and a deep search for radio pulsations using the Parkes RadioTelescope. We find that the radio emission has a flat spectrum, though someareas along the eastern edge of G328.4+0.2 have a steeper radio spectral indexof ~-0.3. Additionally, we obtain a luminosity limit of the central pulsar ofL_{1400} < 30 mJy kpc^2, assuming a distance of 17 kpc. In light of theseobservational results, we test if G328.4+0.2 is a pulsar wind nebula (PWN) or alarge PWN inside a supernova remnant (SNR) using a simple hydrodynamic modelfor the evolution of a PWN inside a SNR. As a result of this analysis, weconclude that G328.4+0.2 is a young (< 10000 years old) pulsar wind nebulaformed by a low magnetic field (<10^12 G) neutron star born spinning rapidly(<10 ms) expanding into an undetected SNR formed by an energetic (>10^51 ergs),low ejecta mass (M < 5 Solar Masses) supernova explosion which occurred in alow density (n~0.03 cm^{-3}) environment.


Instruction: what is the prompt that generates the input?

Input: The effect of possible in-medium modifications of nucleon-nucleon ($NN$)cross sections on particle production is investigated in heavy ion collisions($HIC$) at intermediate energies. In particular, using a fully covariantrelativistic transport approach, we see that the density dependence of the {\itinelastic} cross sections appreciably affects the pion and kaon yields andtheir rapidity distributions. However, the $(\pi^{-}/\pi^{+})$- and$(K^{0}/K^{+})$-ratios depend only moderately on the in-medium behavior of theinelastic cross sections. This is particularly true for kaon yield ratios,since kaons are more uniformly produced in high density regions. Kaonpotentials are also suitably evaluated in two schemes, a chiral perturbativeapproach and an effective meson-quark coupling method, with consistent resultsshowing a similar repulsive contribution for $K^{+}$ and $K^{0}$. As aconsequence we expect rather reduced effects on the yield ratios. We concludethat particle ratios appear to be robust observables for probing the nuclearequation of state ($EoS$) at high baryon density and, particularly, itsisovector sector.


Instruction: what is the prompt that generates the input?

Input: The early-R stars are carbon-rich K-type giants. They are enhanced in C12,C13 and N14, have approximately solar oxygen, magnesium isotopes, s-process andiron abundances, have the luminosity of core-helium burning stars, are notrapid rotators, are members of the Galactic thick disk and, most peculiarly ofall, are all single stars. Conventional single-star stellar evolutionary modelscannot explain such stars, but mergers in binary systems have been proposed toexplain their origin.  We have synthesized binary star populations to calculate the number of mergedstars with helium cores which could be early-R stars. We find many possibleevolutionary channels. The most common of which is the merger of a helium whitedwarf with a hydrogen-burning red giant branch star during a common envelopephase followed by a helium flash in a rotating core which mixes carbon to thesurface. All the channels together give ten times more early-R stars than werequire to match recent Hipparcos observations - we discuss which channels arelikely to be the true early-R stars and which are not. For the first time wehave constructed a viable model of the early-R stars with which we can testsome of our ideas regarding common envelope evolution in giants, stellarmergers, rotation, the helium flash and the origin of the early-R stars.


Instruction: what is the prompt that generates the input?

Input: After the nontrivial quantum parameters $\Omega_{n}$ and quantum potentials$V_{n}$ obtained in our previous research, the circumstance of a real scalarwave in the bulk is studied with the similar method of Brevik (2001). Theequation of a massless scalar field is solved numerically under the boundaryconditions near the inner horizon $r_{e}$ and the outer horizon $r_{c}$. Unlikethe usual wave function $\Psi_{\omega l}$ in 4D, quantum number $n$ introducesa new functions $\Psi_{\omega l n}$, whose potentials are higher and wider withbigger n. Using the tangent approximation, a full boundary value problem aboutthe Schr$\ddot{o}$dinger-like equation is solved. With a convenient replacementof the 5D continuous potential by square barrier, the reflection andtransmission coefficients are obtained. If extra dimension does exist and isvisible at the neighborhood of black holes, the unique wave function$\Psi_{\omega l n}$ may say something to it.


Instruction: what is the prompt that generates the input?

Input: CO observations have been so far the best way to trace molecular gas inexternal galaxies, but at low metallicity the gas mass deduced could be largelyunderestimated. At present, the kinematic information of CO data cubes are usedto estimate virial masses and trace the total mass of the molecular clouds.Millimeter dust emission can also be used as a dense gas tracer and couldunveil H2 envelopes lacking CO. These different tracers must be compared indifferent environments. This study compares virial masses to masses deducedfrom millimeter emission, in two GMC samples: the local molecular clouds in ourGalaxy and their equivalents in the Small Magellanic Cloud (SMC), one of thenearest low metallicity dwarf galaxy. In our Galaxy, mass estimates deducedfrom millimeter emission are consistent with masses deduced from gamma rayanalysis and trace the total mass of the clouds. Virial masses aresystematically larger (twice on average) than mass estimates from millimeterdust emission. This difference decreases toward high masses and has alreadybeen reported in previous studies. In the SMC however, molecular cloud massesdeduced from SIMBA millimeter observations are systematically higher (twice onaverage for conservative values of the dust to gas ratio and dust emissivity)than the virial masses from SEST CO observations. The observed excess can notbe accounted for by any plausible change of dust properties. Taking a generalform for the virial theorem, we show that a magnetic field strength of ~15micro Gauss in SMC clouds could provide additional support to the clouds andexplain the difference observed. Masses of SMC molecular clouds have thereforebeen underestimated so far. Magnetic pressure may contribute significantly totheir support.


Instruction: what is the prompt that generates the input?

Input: The Gauss map of non-degenerate surfaces in the three-dimensional Minkowskispace are viewed as dynamical fields of the two-dimensional O(2,1) NonlinearSigma Model. In this setting, the moduli space of solutions with rotationalsymmetry is completely determined. Essentially, the solutions are warpedproducts of orbits of the 1-dimensional groups of isometries and elastic curvesin either a de Sitter plane, a hyperbolic plane or an anti de Sitter plane. Themain tools are the equivalence of the two-dimensional O(2,1) Nonlinear SigmaModel and the Willmore problem, and the description of the surfaces withrotational symmetry. A complete classification of such surfaces is obtained inthis paper. Indeed, a huge new family of Lorentzian rotational surfaces with aspace-like axis is presented. The description of this new class of surfaces isbased on a technique of surgery and a gluing process, which is illustrated byan algorithm.


Instruction: what is the prompt that generates the input?

Input: We report on measurements of the adiabatic temperature change in the inversemagnetocaloric Ni$_{50}$Mn$_{34}$In$_{16}$ alloy. It is shown that this alloyheats up with the application of a magnetic field around the Curie point due tothe conventional magnetocaloric effect. In contrast, the inverse magnetocaloriceffect associated with the martensitic transition results in the unusualdecrease of temperature by adiabatic magnetization. We also providemagnetization and specific heat data which enable to compare the measuredtemperature changes to the values indirectly computed from thermodynamicrelationships. Good agreement is obtained for the conventional effect at thesecond-order paramagnetic-ferromagnetic phase transition. However, at the firstorder structural transition the measured values at high fields are lower thanthe computed ones. Irreversible thermodynamics arguments are given to show thatsuch a discrepancy is due to the irreversibility of the first-order martensitictransition.


Instruction: what is the prompt that generates the input?

Input: In the absence of direct kinematic measurements, the mass of an accretingblack hole is sometimes inferred from the X-ray spectral parameters of itsaccretion disk; specifically, from the temperature and normalization of adisk-blackbody model fit. Suitable corrections have to be introduced when theaccretion rate approaches or exceeds the Eddington limit. We summarizephenomenological models that can explain the very high state, with apparentlyhigher disk temperatures and lower inner-disk radii. Conversely, ultraluminousX-ray sources often contain cooler disks with large characteristic radii. Weintroduce another phenomenological model for this accretion state. We arguethat a standard disk dominates the radiative output for radii larger than acharacteristic transition radius R_c ~ mdot x R_{ISCO}, where mdot is theaccretion rate in Eddington units and R_{ISCO} is the innermost stable orbit.For R_{ISCO} < R < R_c, most of the accretion power is released via non-thermalprocesses. We predict the location of such sources in a luminosity-temperatureplot. We conclude that black holes with masses ~ 50-100 Msun accreting at mdot~ 10-20 may explain the X-ray properties of many ULXs.


Instruction: what is the prompt that generates the input?

Input: We study phonon-mediated transitions between translational levels of an atomin a surface-induced potential. We present a general master equation governingthe dynamics of the translational states of the atom. In the framework of theDebye model, we derive compact expressions for the rates for both upward anddownward transitions. Numerical calculations for the transition rates areperformed for a deep silica-induced potential allowing for a large number ofbound levels as well as free states of a cesium atom. The total absorption rateis shown to be determined mainly by the bound-to-bound transitions for deepbound levels and by bound-to-free transitions for shallow bound levels.Moreover, the phonon emission and absorption processes can be orders ofmagnitude larger for deep bound levels as compared to the shallow bound ones.We also study various types of transitions from free states. We show that, forthermal atomic cesium with temperature in the range from 100 $\mu$K to 400$\mu$K in the vicinity of a silica surface with temperature of 300 K, theadsorption (free-to-bound decay) rate is about two times larger than theheating (free-to-free upward decay) rate, while the cooling (free-to-freedownward decay) rate is negligible.


Instruction: what is the prompt that generates the input?

Input: We consider a cognitive network consisting of n random pairs of cognitivetransmitters and receivers communicating simultaneously in the presence ofmultiple primary users. Of interest is how the maximum throughput achieved bythe cognitive users scales with n. Furthermore, how far these users must befrom a primary user to guarantee a given primary outage. Two scenarios areconsidered for the network scaling law: (i) when each cognitive transmitteruses constant power to communicate with a cognitive receiver at a boundeddistance away, and (ii) when each cognitive transmitter scales its poweraccording to the distance to a considered primary user, allowing the cognitivetransmitter-receiver distances to grow. Using single-hop transmission, suitablefor cognitive devices of opportunistic nature, we show that, in both scenarios,with path loss larger than 2, the cognitive network throughput scales linearlywith the number of cognitive users. We then explore the radius of a primaryexclusive region void of cognitive transmitters. We obtain bounds on thisradius for a given primary outage constraint. These bounds can help in thedesign of a primary network with exclusive regions, outside of which cognitiveusers may transmit freely. Our results show that opportunistic secondaryspectrum access using single-hop transmission is promising.


Instruction: what is the prompt that generates the input?

Input: We consider the simplest generalizations of the valence bond physics of SU(2)singlets to SU(N) singlets that comprise objects with N sites -- these areSU(N) singlet plaquettes with N=3 and N=4 in three spatial dimensions.Specifically, we search for a quantum mechanical liquid of such objects -- aresonating singlet valence plaquette phase that generalizes the celebratedresonating valence bond phase for SU(2) spins. We extend the Rokhsar-Kivelsonconstruction of the quantum dimer model to the simplest SU(4) model for valenceplaquette dynamics on a cubic lattice. The phase diagram of the resultingquantum plaquette model is analyzed both analytically and numerically. We findthat the ground state is solid everywhere, including at the Rokhsar-Kivelsonpoint where the ground state is an equal amplitude sum. By contrast, the equalamplitude sum of SU(3) singlet triangular plaquettes on the face centered cubiclattice is liquid and thus a candidate for describing a resonating singlevalence plaquette phase, given a suitably defined local Hamiltonian.


Instruction: what is the prompt that generates the input?

Input: From several points of view it is strongly suggested that the currentuniverse is unstable and will ultimately decay to one that is exactlysupersymmetric (susy). The possibility that atoms and molecules form in thisfuture universe requires that the degenerate electron/selectron mass isnon-zero and hence that electroweak symmetry breaking (EWSB) survives the phasetransition to exact susy. However, the minimal supersymmetric standard model(MSSM) and several of its extensions have no EWSB in the susy limit. Among theextended higgs models that have been discussed one stands out in this regard.The higgs sector that is revealed at the Large Hadron Collider (LHC) willtherefore have implications for the future universe. We also address thequestion as to whether the transition to the exact susy phase with EWSB isexothermic.


Instruction: what is the prompt that generates the input?

Input: We present observations of probable line-of-sight acceleration of a broadabsorption trough of C IV in the quasar SDSS J024221.87+004912.6. We alsodiscuss how the velocity overlap of two other outflowing systems in the sameobject constrains the properties of the outflows. The Si IV doublet in eachsystem has one unblended transition and one transition which overlaps withabsorption from the other system. The residual flux in the overlapping troughis well fit by the product of the residual fluxes in the unblended troughs. Forthese optically thick systems to yield such a result, at least one of them mustconsist of individual subunits rather than being a single structure withvelocity-dependent coverage of the source. If these subunits are identical,opaque, spherical clouds, we estimate the cloud radius to be r = 3.9 10^15 cm.If they are identical, opaque, linear filaments, we estimate their width to bew = 6.5 10^14 cm. These subunits are observed to cover the Mg II broad emissionline region of the quasar, at which distance from the black hole the abovefilament width is equal to the predicted scale height of the outer atmosphereof a thin accretion disk. Insofar as that scale height is a natural size scalefor structures originating in an accretion disk, these observations areevidence that the accretion disk can be a source of quasar absorption systems.Based on data from ESO program 075.B-0190(A).


Instruction: what is the prompt that generates the input?

Input: Atmospheric water vapor causes significant undesired phase fluctuations forthe Submillimeter Array (SMA) interferometer, particularly in its highestfrequency observing band of 690 GHz. One proposed solution to this atmosphericeffect is to observe simultaneously at two separate frequency bands of 230 and690 GHz. Although the phase fluctuations have a smaller magnitude at the lowerfrequency, they can be measured more accurately and on shorter timescales dueto the greater sensitivity of the array to celestial point source calibratorsat this frequency. In theory, we can measure the atmospheric phase fluctuationsin the 230 GHz band, scale them appropriately with frequency, and apply them tothe data in 690 band during the post-observation calibration process. Theultimate limit to this atmospheric phase calibration scheme will be set by theinstrumental phase stability of the IF and LO systems. We describe themethodology and initial results of the phase stability characterization of theIF and LO systems.


Instruction: what is the prompt that generates the input?

Input: Multiwavelength observations are reported here of the Be/X-ray binary pulsarsystem GRO J1008-57. Over ten years worth of data are gathered together to showthat the periodic X-ray outbursts are dependant on both the binary motion andthe size of the circumstellar disk. In the first instance an accurate orbitalsolution is determined from pulse periods, and in the second case the strengthand shape of the Halpha emission line is shown to be a valuable indicator ofdisk size and its behaviour. Furthermore, the shape of the emission linepermits a direct determination of the disk size which is in good agreement withtheoretical estimates. A detailed study of the pulse period variations duringoutbursts determined the binary period to be 247.8, in good agreement with theperiod determined from the recurrence of the outbursts.


Instruction: what is the prompt that generates the input?

Input: We investigate theoretically and experimentally the capillary-gravity wavescreated by a small object moving steadily at the water-air interface along acircular trajectory. It is well established that, for straight uniform motion,no steady waves appear at velocities below the minimum phase velocity $c_{min}= 23 \rm{cm \cdot s}^{-1}$. We show theoretically that no such velocitythreshold exists for a steady circular motion, for which, even at smallvelocities, a finite wave drag is experienced by the object. This wave dragoriginates from the emission of a spiral-like wave pattern. Our results are ingood agreement with direct experimental observations of the wave patterncreated by a circularly moving needle in contact with water. Our study leads tonew insights into the problem of animal locomotion at the water-air interface.


Instruction: what is the prompt that generates the input?

Input: We develop here a mechanism that, without making use of a cosmologicalconstant, reproduces an accelerating universe. This is done by taking intoaccount Casimir vacuum energy density, assuming that the underlying theoryallows a maximum momentum, that turns out to be the leading contribution termto Einstein equations in a large expanding FRW universe. As stated in numerousquantum gravity studies, we postulate that maximum momentum is related to theexistence of the Planck length as a fundamental length. This insight, togetherwith the assumption of a Planck scale correction to the energy/momentumdispersion-relation on a FRW background, is used here to calculate Casimirvacuum energy. We show that, under these hypothesis, an accelerated universeexpansion is obtained. As last step we analyze the compatibility of theresulting model with experimental data, writing down the equation of state forCasimir energy and pressure and observing that this equation of state belongsto a class of models that naturally fits cosmological observations. Weemphasize that our result relies, once a fundamental length is introduced inCasimir effect, just on general arguments thus it is independent on an explicitform of the energy-momentum dispersion relation.


Instruction: what is the prompt that generates the input?

Input: Our group recently reproduced the water-assisted growth method, so-called"super growth", of millimeter-thick single-walled carbon nanotube (SWNT)forests by using C2H4/ H2/ H2O/ Ar reactant gas and Fe/ Al2O3 catalyst. In thiscurrent work, a parametric study was carried out on both reaction and catalystconditions. Results revealed that a thin Fe catalyst layer (about 0.5 nm)yielded rapid growth of SWNTs only when supported on Al2O3, and that Al2O3support enhanced the activity of Fe, Co, and Ni catalysts. The growth windowfor the rapid SWNT growth was narrow, however. Optimum amount of added H2Oincreased the SWNT growth rate but further addition of H2O degraded both theSWNT growth rate and quality. Addition of H2 was also essential for rapid SWNTgrowth, but again, further addition decreased both the SWNT growth rate andquality. Because Al2O3 catalyzes hydrocarbon reforming, Al2O3 support possiblyenhances the SWNT growth rate by supplying the carbon source to the catalystnanoparticles. The origin of the narrow window for rapid SWNT growth will alsobe discussed.


Instruction: what is the prompt that generates the input?

Input: This paper proposes the use of particle swarm optimization method (PSO) forfinite element (FE) model updating. The PSO method is compared to the existingmethods that use simulated annealing (SA) or genetic algorithms (GA) for FEmodel for model updating. The proposed method is tested on an unsymmetricalH-shaped structure. It is observed that the proposed method gives updatednatural frequencies the most accurate and followed by those given by an updatedmodel that was obtained using the GA and a full FE model. It is also observedthat the proposed method gives updated mode shapes that are best correlated tothe measured ones, followed by those given by an updated model that wasobtained using the SA and a full FE model. Furthermore, it is observed that thePSO achieves this accuracy at a computational speed that is faster than that bythe GA and a full FE model which is faster than the SA and a full FE model.


Instruction: what is the prompt that generates the input?

Input: We investigate whether the floating phase (where the correlation length isinfinite and the spin-spin correlation decays algebraically with distance)exists in the temperature($T$) - frustration parameter ($\kappa$) phase diagramof 2D ANNNI model. To identify this phase, we look for the region where (i)finite size effect is prominent and (ii) some relevant physical quantitychanges somewhat sharply and this change becomes sharper as the system sizeincreases. For $\kappa < 0.5 $, the low temperature phase is ferromagnetic andwe study energy and magnetization. For $\kappa > 0.5 $, the low temperaturephase is antiphase and we study energy, layer magnetization, length of domainwalls running along the direction of frustration, number of domain-interceptsthat are of length 2 along the direction of frustration, and the number ofdomain walls that do not touch the upper and/or lower boundary. In agreementwith some previous studies, our final conclusion is that, the floating phaseexists, if at all, only along a line.


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Input: We study the effects of lepton flavour violation (LFV) on the productionprocesses e+e- --> \chi+_i \chi-_j at a linear collider with longitudinal e+and e- beam polarizations. In the case of LFV the sneutrino mass eigenstateshave no definite flavour, therefore, in the t-channel more than one sneutrinomass eigenstate can contribute to the chargino production cross sections. Ourframework is the Minimal Supersymmetric Standard Model (MSSM) including LFVterms. We show that in spite of the restrictions on the LFV parameters due tothe current limits on rare lepton decays, the cross section \sigma(e+e- -->\chi+_1 \chi-_1) can change by a factor of 2 or more when varying the LFVmixing angles. We point out that even if the present bound on BR(tau- --> e-gamma) improves by a factor of thousand the influence of LFV on the charginoproduction cross section can be significant. These results could have animportant impact on the strategies for determining the underlying modelparameters at the linear collider.


Instruction: what is the prompt that generates the input?

Input: We employ X-ray stacking techniques to examine the contribution from X-rayundetected, mid-infrared-selected sources to the unresolved, hard (6-8 keV)cosmic X-ray background (CXB). We use the publicly available, 24 micron SpitzerSpace Telescope MIPS catalogs from the Great Observatories Origins Deep Survey(GOODS) - North and South fields, which are centered on the 2 Ms Chandra DeepField-North and the 1 Ms Chandra Deep Field-South, to identify bright (S_24 >80 microJy) mid-infrared sources that may be powered by heavily obscured AGNs.We measure a significant stacked X-ray signal in all of the X-ray bandsexamined, including, for the first time, a significant (3.2 sigma) 6-8 keVstacked X-ray signal from an X-ray undetected source population. We find thatthe X-ray-undetected MIPS sources make up about 2% (or less) of the total CXBbelow 6 keV, but about 6% in the 6-8 keV band. The 0.5-8 keV stacked X-rayspectrum is consistent with a hard power-law (Gamma = 1.44 +/- 0.07), with thespectrum hardening at higher X-ray energies. Our findings show that thesebright MIPS sources do contain obscured AGNs, but are not the primary source ofthe unresolved 50% of 6-8 keV CXB. Our study rules out obscured, luminous QSOsas a significant source of the remaining unresolved CXB and suggests that itmost likely arises from a large population of obscured, high-redshift (z > 1),Seyfert-luminosity AGNs.


Instruction: what is the prompt that generates the input?

Input: Formal actions of Lie algebras over vector spaces are introduced in a purelyalgebraic way, as a mimic of infinitesimal operations of Banach Lie algebrasover Banach analytic manifolds. In analogy with the case of abstract groups,complete wreath products and triangular actions are then defined for Liealgebras acting "en cascade" over vector spaces. Finally, a Kaloujnine-Krasnertype theorem for Lie algebra extensions is proved.  -----  En mimant les lois d'op\'erations infinit\'esimales des alg\`ebres de Lie surles vari\'et\'e s analytiques banachiques, on introduit de mani\`ere purementalg\`ebrique la notion d'action formelle d'une alg\`ebre de Lie sur un espacevectoriel. Ensuite, par analogie avec le cas des groupes abstraits, et enfaisant op\'erer les alg\`ebres de Lie "en cascade", on d\'efinit produitd'entrelacement ("wreath product") et action triangulaire pour les alg\`ebresde Lie. On d\'emontre enfin un th\'eor\`eme du type Kaloujnine-Krasner pour lesextensions d'alg\`ebres de Lie.


Instruction: what is the prompt that generates the input?

Input: A theory of chiral lipid membranes is proposed on the basis of a concise freeenergy density which includes the contributions of the bending and the surfacetension of membranes, as well as the chirality and orientational variation oftilting molecules. This theory is consistent with the previous experiments[J.M. Schnur \textit{et al.}, Science \textbf{264}, 945 (1994); M.S. Spector\textit{et al.}, Langmuir \textbf{14}, 3493 (1998); Y. Zhao, \textit{et al.},Proc. Natl. Acad. Sci. USA \textbf{102}, 7438 (2005)] on self-assembled chirallipid membranes of DC$_{8,9}$PC. A torus with the ratio between its twogenerated radii larger than $\sqrt{2}$ is predicted from the Euler-Lagrangeequations. It is found that tubules with helically modulated tilting state arenot admitted by the Euler-Lagrange equations, and that they are lessenergetically favorable than helical ripples in tubules. The pitch angles ofhelical ripples are theoretically estimated to be about 0$^\circ$ and35$^\circ$, which are close to the most frequent values 5$^\circ$ and28$^\circ$ observed in the experiment [N. Mahajan \textit{et al.}, Langmuir\textbf{22}, 1973 (2006)]. Additionally, the present theory can explain twistedribbons of achiral cationic amphiphiles interacting with chiral tartratecounterions. The ratio between the width and pitch of twisted ribbons ispredicted to be proportional to the relative concentration difference of left-and right-handed enantiomers in the low relative concentration differenceregion, which is in good agreement with the experiment [R. Oda \textit{et al.},Nature (London) \textbf{399}, 566 (1999)].


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Input: We use high-resolution hydrodynamic re-simulations to investigate theproperties of the thermal Sunyaev-Zel'dovich (SZ) effect from galaxy clusters.We compare results obtained using different physical models for theintracluster medium (ICM), and show how they modify the SZ emission in terms ofcluster profiles and scaling relations. We also produce realistic mockobservations to verify whether the results from hydrodynamic simulations can beconfirmed. We find that SZ profiles depend marginally on the modelled physicalprocesses, while they exhibit a strong dependence on cluster mass. The centraland total SZ emission strongly correlate with the cluster X-ray luminosity andtemperature. The logarithmic slopes of these scaling relations differ from theself-similar predictions by less than 0.2; the normalization of the relationsis lower for simulations including radiative cooling. The observational testsuggests that SZ cluster profiles are unlikely to be able to probe the ICMphysics. The total SZ decrement appears to be an observable much more robustthan the central intensity, and we suggest using the former to investigatescaling relations.


Instruction: what is the prompt that generates the input?

Input: Given a finite irreducible Coxeter group $W$, a positive integer $d$, andtypes $T_1,T_2,...,T_d$ (in the sense of the classification of finite Coxetergroups), we compute the number of decompositions $c=\si_1\si_2 cdots\si_d$ of aCoxeter element $c$ of $W$, such that $\si_i$ is a Coxeter element in asubgroup of type $T_i$ in $W$, $i=1,2,...,d$, and such that the factorisationis "minimal" in the sense that the sum of the ranks of the $T_i$'s,$i=1,2,...,d$, equals the rank of $W$. For the exceptional types, thesedecomposition numbers have been computed by the first author. The type $A_n$decomposition numbers have been computed by Goulden and Jackson, albeit using asomewhat different language. We explain how to extract the type $B_n$decomposition numbers from results of B\'ona, Bousquet, Labelle and Leroux onmap enumeration. Our formula for the type $D_n$ decomposition numbers is new.These results are then used to determine, for a fixed positive integer $l$ andfixed integers $r_1\le r_2\le ...\le r_l$, the number of multi-chains $\pi_1\le\pi_2\le ...\le \pi_l$ in Armstrong's generalised non-crossing partitionsposet, where the poset rank of $\pi_i$ equals $r_i$, and where the "blockstructure" of $\pi_1$ is prescribed. We demonstrate that this result impliesall known enumerative results on ordinary and generalised non-crossingpartitions via appropriate summations. Surprisingly, this result on multi-chainenumeration is new even for the original non-crossing partitions of Kreweras.Moreover, the result allows one to solve the problem of rank-selected chainenumeration in the type $D_n$ generalised non-crossing partitions poset, which,in turn, leads to a proof of Armstrong's $F=M$ Conjecture in type $D_n$.


Instruction: what is the prompt that generates the input?

Input: In this paper a lattice model for diffusional transport of particles in theinterphase cell nucleus is proposed. Dense networks of chromatin fibers arecreated by three different methods: randomly distributed, non-interconnectedobstacles, a random walk chain model, and a self avoiding random walk chainmodel with persistence length. By comparing a discrete and a continuous versionof the random walk chain model, we demonstrate that lattice discretization doesnot alter particle diffusion. The influence of the 3D geometry of the fibernetwork on the particle diffusion is investigated in detail, while varyingoccupation volume, chain length, persistence length and walker size. It isshown that adjacency of the monomers, the excluded volume effect incorporatedin the self avoiding random walk model, and, to a lesser extent, thepersistence length, affect particle diffusion. It is demonstrated how theintroduction of the effective chain occupancy, which is a convolution of thegeometric chain volume with the walker size, eliminates the conformationaleffects of the network on the diffusion, i.e., when plotting the diffusioncoefficient as a function of the effective chain volume, the data fall onto amaster curve.


Instruction: what is the prompt that generates the input?

Input: The damage spreading method (DS) provided a useful tool to obtain analyticalresults of the thermodynamics and stability of the 2D Ising model --amongstmany others--, but it suffered both from ambiguities in its results and fromlarge computational costs. In this paper we propose an alternative method, theso called self-overlap method, based on the study of correlation functionsmeasured at subsequent time steps as the system evolves towards itsequilibrium. Applying markovian and mean field approximations to a 2D Isingsystem we obtain both analytical and numerical results on the thermodynamicsthat agree with the expected behavior. We also provide some analytical resultson the stability of the system. Since only a single replica of the system needsto be studied, this method would seem to be free from the ambiguities thatafflicted DS. It also seems to be numerically more efficient and analyticallysimpler.


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Input: The magnetic focusing of electrons has proven its utility in fundamentalstudies of electron transport. Here we report the direct imaging of magneticfocusing of electron waves, specifically in a two-dimensional electron gas(2DEG). We see the semicircular trajectories of electrons as they bounce alonga boundary in the 2DEG, as well as fringes showing the coherent nature of theelectron waves. Imaging flow in open systems is made possible by a cooledscanning probe microscope. Remarkable agreement between experiment and theorydemonstrates our ability to see these trajectories and to use this system as aninterferometer. We image branched electron flow as well as the interference ofelectron waves. This technique can visualize the motion of electron wavesbetween two points in an open system, providing a straightforward way to studysystems that may be useful for quantum information processing and spintronics.


Instruction: what is the prompt that generates the input?

Input: We propose a gravitational dual of ``single-sector'' models of supersymmetrybreaking which contain no messenger sector and naturally explain the scale ofsupersymmetry breaking and the fermion mass hierarchy. In five dimensions thesemodels can be given a simple interpretation. Inspired by flux-backgroundsolutions of type IIB supergravity, a metric background that deviates fromAdS_5 in the IR breaks supersymmetry, while the fermion mass hierarchy resultsfrom the wavefunction overlap of bulk fermions with a UV-confined Higgs field.The first and second generation squarks and sleptons, which are localized nearthe IR brane, directly feel the supersymmetry breaking and obtain masses oforder 10 TeV. These are interpreted as composite states of the dual 4D theory.The gauginos and third generation squarks and sleptons are elementary statesthat obtain soft masses of order 1 TeV at the loop level via direct gaugemediation. This particle spectrum leads to distinctive signatures at the LHC,similar to the usual gauge mediation with a neutralino NLSP that decayspromptly to a gravitino LSP, but with lower event rates. Nevertheless we showthat with 1-10 fb^{-1} of LHC data "single-sector" models can easily bedetected above background and distinguished from conventional gravity and gaugemediation.


Instruction: what is the prompt that generates the input?

Input: We investigate the evolution of the electronic structure in SrRu_(1-x)Ti_xO_3as a function of x using high resolution photoemission spectroscopy, whereSrRuO3 is a weakly correlated metal and SrTiO3 is a band insulator. The surfacespectra exhibit a metal-insulator transition at x = 0.5 by opening up a softgap. A hard gap appears at higher x values consistent with the transportproperties. In contrast, the bulk spectra reveal a pseudogap at the Fermilevel, and unusual evolution exhibiting an apparent broadening of the coherentfeature and subsequent decrease in intensity of the lower Hubbard band with theincrease in x. Interestingly, the first principle approaches are found to besufficient to capture anomalous evolutions at high energy scale. Analysis ofthe spectral lineshape indicates strong interplay between disorder and electroncorrelation in the electronic properties of this system.


Instruction: what is the prompt that generates the input?

Input: In the Randall-Sundrum model, setting the ratio of up and down quark masses$m_u/m_d << 1$, relevant to the strong CP problem, does not require chiralsymmetry or fine-tuning, due to exponential bulk fermion profiles. We point outthat such geometric suppression of the mass of a fermion magnifies the massesof its corresponding Kaluza-Klein (KK) states. In this sense, these KK statesact as "microscopes" for probing light quark and lepton masses. In simplerealizations, this hypothesis can be testable at future colliders, like theLHC, by measuring the spectrum of level-1 KK fermions. The microscope can thenprovide an experimental test for the vanishing of $m_u$ in the ultraviolet,independently of non-perturbative determinations, by lattice simulations orother means, at hadronic scales. We also briefly comment on application of ourmicroscope idea to other fermions, such as the electron and neutrinos.


Instruction: what is the prompt that generates the input?

Input: The standard axiomatization of quantum mechanics (QM) is not fully explicitabout the role of the time-parameter. Especially, the time reference within theprobability algorithm (the Born Rule, BR) is unclear. Using a plausibleprinciple P1, about the role of probability in a physical theory, and a secondprinciple P2 affording a most natural way to make BR precise, a logicalconflict with the standard expression for the completeness of QM can bederived. Rejecting P1 is implausible. Rejecting P2 leads to unphysical resultsand to a conflict with a generalization of P2, a principle P3. It is thus madeplausible that the standard expression of QM completeness must be revised. Anabsolutely explicit form of the axioms is provided, including a precise form ofthe projection postulate. An appropriate expression for QM completeness,reflecting the restrictions of the Gleason and Kochen-Specker theorems isproposed.


Instruction: what is the prompt that generates the input?

Input: A wireless network in which packets are broadcast to a group of receiversthrough use of a random access protocol is considered in this work. Therelation to previous work on networks of interacting queues is discussed andsubsequently, the stability and throughput regions of the system are analyzedand presented. A simple network of two source nodes and two destination nodesis considered first. The broadcast service process is analyzed assuming achannel that allows for packet capture and multipacket reception. In this smallnetwork, the stability and throughput regions are observed to coincide. Thesame problem for a network with N sources and M destinations is considerednext. The channel model is simplified in that multipacket reception is nolonger permitted. Bounds on the stability region are developed using theconcept of stability rank and the throughput region of the system is comparedto the bounds. Our results show that as the number of destination nodesincreases, the stability and throughput regions diminish. Additionally, aprevious conjecture that the stability and throughput regions coincide for anetwork of arbitrarily many sources is supported for a broadcast scenario bythe results presented in this work.


Instruction: what is the prompt that generates the input?

Input: We present general relativistic correction terms appearing in Newton'sgravity to the second-order perturbations of cosmological fluids. In ourprevious work we have shown that to the second-order perturbations, the densityand velocity perturbation equations of general relativistic zero-pressure,irrotational, single-component fluid in a flat background coincide exactly withthe ones known in Newton's theory. Here, we present the general relativisticsecond-order correction terms arising due to (i) pressure, (ii)multi-component, (iii) background curvature, and (iv) rotation. In case ofmulti-component zero-pressure, irrotational fluids under the flat background,we effectively do not have relativistic correction terms, thus the relativisticresult again coincides with the Newtonian ones. In the other three cases wegenerally have pure general relativistic correction terms. In case of pressure,the relativistic corrections appear even in the level of background and linearperturbation equations. In the presence of background curvature, or rotation,pure relativistic correction terms directly appear in the Newtonian equationsof motion of density and velocity perturbations to the second order. In thesmall-scale limit (far inside the horizon), relativistic equations includingthe rotation coincide with the ones in Newton's gravity.


Instruction: what is the prompt that generates the input?

Input: The goal of this paper is to construct invariant dynamical objects for a (notnecessarily invertible) smooth self map of a compact manifold. We prove aresult that takes advantage of differences in rates of expansion in the termsof a sheaf cohomological long exact sequence to create unique lifts of finitedimensional invariant subspaces of one term of the sequence to invariantsubspaces of the preceding term. This allows us to take invariant cohomologicalclasses and under the right circumstances construct unique currents of a giventype, including unique measures of a given type, that represent those classesand are invariant under pullback. A dynamically interesting self map may have aplethora of invariant measures, so the uniquess of the constructed currents isimportant. It means that if local growth is not too big compared to the growthrate of the cohomological class then the expanding cohomological class givessufficient "marching orders" to the system to prohibit the formation of anyother such invariant current of the same type (say from some local dynamicalsubsystem). Because we use subsheaves of the sheaf of currents we giveconditions under which a subsheaf will have the same cohomology as the sheafcontaining it. Using a smoothing argument this allows us to show that the sheafcohomology of the currents under consideration can be canonically identifiedwith the deRham cohomology groups. Our main theorem can be applied in both thesmooth and holomorphic setting.


Instruction: what is the prompt that generates the input?

Input: In several classes of particle physics models -- ranging from the classicalMajoron models, to the more recent scenarios of late neutrino masses orMass-Varying Neutrinos -- one or more of the neutrinos are postulated to coupleto a new light scalar field. As a result of this coupling, neutrinos in theearly universe instead of streaming freely could form a self-coupled fluid,with potentially observable signatures in the Cosmic Microwave Background andthe large scale structure of the universe. We re-examine the constraints onthis scenario from the presently available cosmological data and investigatethe sensitivity expected from the Planck satellite. In the first case, we findthat the sensitivity strongly depends on which piece of data is used. The SDSSMain sample data, combined with WMAP and other data, disfavors the scenario ofthree coupled neutrinos at about the 3.5$\sigma$ confidence level, but alsofavors a high number of freely streaming neutrinos, with the best fit at 5.2.If the matter power spectrum is instead taken from the SDSS Large Red Galaxysample, best fit point has 2.5 freely streaming neutrinos, but the scenariowith three coupled neutrinos becomes allowed at $2\sigma$. In contrast, Planckalone will exclude even a single self-coupled neutrino at the $4.2\sigma$confidence level, and will determine the total radiation at CMB epoch to$\Delta N_\nu^{eff} = ^{+0.5}_{-0.3}$ ($1\sigma$ errors). We investigate therobustness of this result with respect to the details of Planck's detector.This sensitivity to neutrino free-streaming implies that Planck will be capableof probing a large region of the Mass-Varying Neutrino parameter space. Planckmay also be sensitive to a scale of neutrino mass generation as high as 1 TeV.


Instruction: what is the prompt that generates the input?

Input: A library of C functions yielding exact solutions of potential and fluxinfluences due to uniform surface distribution of singularities on flattriangular and rectangular elements has been developed. This library, ISLES,has been used to develop the neBEM solver that is both precise and fast insolving a wide range of problems of scientific and technological interest. Herewe present the exact expressions proposed for computing the influence ofuniform singularity distributions on triangular elements and illustrate theiraccuracy. We also present a study concerning the time taken to evaluate theselong and complicated expressions \textit{vis a vis} that spent in carrying outsimple quadratures. Finally, we solve a classic benchmark problem inelectrostatics, namely, estimation of the capacitance of a unit square plateraised to unit volt. For this problem, we present the estimated values ofcapacitance and compare them successfully with some of the most accurateresults available in the literature. In addition, we present the variation ofthe charge density close to the corner of the plate for various degrees ofdiscretization. The variations are found to be smooth and converging. This isin clear contrast to the criticism commonly leveled against usual BEM solvers.


Instruction: what is the prompt that generates the input?

Input: Red supergiant stars represent a key phase in the evolution of massive stars.Recent radiative hydrodynamic simulations suggest that their atmospheres may bethe location of large-scale convective motions. As supergiant convection isexpected to generate supersonic motions and shocks, we seek constraints onthese atmospheric motions and their possible relation with mass-loss rates. Wepresent high-resolution, visible spectroscopy of a sample of red supergiants(spectral type M I) and analyse them with a tomographic technique. We observesteep velocity gradients, characterising both upward and downward supersonicmotions, which are time variable on time scales of a few hundred days. Theseconvective motions will generate turbulent pressure, which will stronglydecrease the effective gravity. We suggest that this decrease, combined withradiative pressure on molecular lines, initiate the mass loss in red supergiantstars.


Instruction: what is the prompt that generates the input?

Input: A state of an excitonic insulator with the electric current is studied.Initially, in the metallic phase, the electrons and holes are assumed to bemoving in the opposite directions, so as the electric current exists. Thisstate is supported by an external condition (the specimen is in an electriccircuit with the current). When the temperature decreases, the transition tothe ordering state due to formation of the electron--hole pairs is possible(similar to the ordinary state of the excitonic insulator). The properties ofthe state at zero temperature are investigated. The spectrum of elementaryexcitations has a gap, and so the conclusion can be made that obtained state issuperconducting one. Thus, depending on the external conditions, excitonicinsulator behaves itself like the insulator or superconductor. That is correctin the limit of strong overlapping of the electron--hole pairs.


Instruction: what is the prompt that generates the input?

Input: We observed 34 comets using the 24 micron camera on the Spitzer SpaceTelescope. Each image contains the nucleus and covers at least 10^6 km of eachcomet's orbit. Debris trails due to mm-sized or larger particles were foundalong the orbits of 27 comets; 4 comets had small-particle dust tails and aviewing geometry that made debris trails impossible to distinguish; and only 3had no debris trail despite favorable observing conditions. There are now 30Jupiter-family comets with known debris trails, of which 22 are reported inthis paper for the first time. The detection rate is >80%, indicating thatdebris trails are a generic feature of short-period comets. By comparison toorbital calculations for particles of a range of sizes ejected over 2 yr priorto observation, we find that particles comprising 4 debris trails are typicallymm-sized while the remainder of the debris trails require particles larger thanthis. The lower-limit masses of the debris trails are typically 10^11 g, andthe median mass loss rate is 2 kg/s. The mass-loss rate in trail particles iscomparable to that inferred from OH production rates and larger than thatinferred from visible-light scattering in comae.


Instruction: what is the prompt that generates the input?

Input: We present the first X-ray detection of the very young pulsar PSR J1357-6429(characteristic age of 7.3 kyr) using data from the XMM-Newton and Chandrasatellites. We find that the spectrum is well described by a power-law plusblackbody model, with photon index Gamma=1.4 and blackbody temperature kT=160eV. For the estimated distance of 2.5 kpc, this corresponds to a 2-10 keVluminosity of about 1.2E+32 erg/s, thus the fraction of the spin-down energychanneled by PSR J1357-6429 into X-ray emission is one of the lowest observed.The Chandra data confirm the positional coincidence with the radio pulsar andallow to set an upper limit of 3E+31 erg/s on the 2-10 keV luminosity of acompact pulsar wind nebula. We do not detect any pulsed emission from thesource and determine an upper limit of 30% for the modulation amplitude of theX-ray emission at the radio frequency of the pulsar.


Instruction: what is the prompt that generates the input?

Input: We investigate one of the consequences of the twisted Poincare symmetry. Wederive the charge conservation law and show that the equivalence principle issatisfied in the canonical noncommutative spacetime. We applied the twistedPoincare symmetry to the Weinberg's analysis. To this end, we generalize ourearlier construction of the twisted S matrix \cite{Bu}, which apply thenoncommutativity to the fourier modes, to the massless fields of integer spins.The transformation formula for the twisted S matrix for the massless fields ofinteger spin has been obtained. For massless fields of spin 1, we obtain theconservation of charge, and the universality of coupling constant for masslessfields of spin 2, which can be interpreted as the equality of gravitationalmass and inertial mass, i.e., the equivalence principle.


Instruction: what is the prompt that generates the input?

Input: We identify plain evaporation of ions as the fundamental loss mechanism outof a multipole ion trap. Using thermalized negative Cl- ions we find that theevaporative loss rate is proportional to a Boltzmann factor. This thermodynamicdescription sheds new light on the dynamics of particles in time-varyingconfining potentials. It specifically allows us to extract the effective depthof the ion trap as the activation energy for evaporation. As a function of therf amplitude we find two distinct regimes related to the stability of motion ofthe trapped ions. For low amplitudes the entire trap allows for stable motionand the trap depth increases with the rf field. For larger rf amplitudes,however, rapid energy transfer from the field to the ion motion can occur atlarge trap radii, which leads to a reduction of the effective trapping volume.In this regime the trap depth decreases again with increasing rf amplitude. Wegive an analytical parameterization of the trap depth for various multipoletraps that allows predictions of the most favorable trapping conditions.


Instruction: what is the prompt that generates the input?

Input: We present the analysis of the source counts in the XMM-COSMOS survey usingdata of the first year of XMM-Newton observations. The survey covers ~2 deg^2within the region of sky bounded by 9^h57.5^m<R.A.<10^h03.5^m;1^d27.5^m<DEC<2^d57.5^m with a total net integration time of 504 ks. Using amaximum likelihood algorithm we detected a total of 1390 sources at least inone band. Using Monte Carlo simulations to estimate the sky coverage weproduced the logN-logS relations. These relations have been then derived in the0.5--2 keV, 2--10 keV and 5--10 keV energy bands, down to flux limits of7.2x10^-16 erg cm^-2 s^-1, 4.0x10^-15 erg cm^-2 s^-1 and 9.7x10^-15 erg cm^-2s^-1, respectively. These relations have been compared to previous X-ray surveyand to the most recent X-ray background model finding an excellent agreement.The slightly different normalizations observed in the source counts of COSMOSand previous surveys can be largely explained as a combination of low countingstatistics and cosmic variance introduced by the large scale structure.


Instruction: what is the prompt that generates the input?

Input: We report on the statistics of strong (W_r > 0.15 A) C IV absorbers atz=1.5-3.5 toward high-redshift gamma-ray bursts (GRBs). In contrast with arecent survey for strong Mg II absorption systems at z < 2, we find that thenumber of C IV absorbers per unit redshift dN/dz does not show a significantdeviation from previous surveys using quasi-stellar objects (QSOs) asbackground sources. We find that the number density of C IV toward GRBs isdN/dz(z~1.5)= 2.2 +2.8/-1.4, dN/dz(z~2.5)= 2.3 +1.8/-1.1 and dN/dz(z~3.5)= 1.1+2.6/-0.9. These numbers are consistent with previous C IV surveys using QSOspectra. Binning the entire dataset, we set a 95% c.l. upper limit to theexcess of C IV absorbers along GRB sightlines at twice the incidence observedalong QSO sightlines. Furthermore, the distribution of equivalent widths of theGRB and QSO samples are consistent with being drawn from the same parentpopulation. Although the results for Mg II and C IV absorbers along GRBsightlines appear to contradict one another, we note that the surveys arenearly disjoint: the C IV survey corresponds to higher redshift and more highlyionized gas than the Mg II survey. Nevertheless, analysis on larger statisticalsamples may constrain properties of the galaxies hosting these metals (e.g.mass, dust content) and/or the coherence-length of the gas giving rise to themetal-line absorption.


Instruction: what is the prompt that generates the input?

Input: Human beings like to believe they are in control of their destiny. Thisubiquitous trait seems to increase motivation and persistence, and is probablyevolutionarily adaptive. But how good really is our ability to control? Howsuccessful is our track record in these areas? There is little understanding ofwhen and under what circumstances we may over-estimate or even lose our abilityto control and optimize outcomes, especially when they are the result ofaggregations of individual optimization processes. Here, we demonstrateanalytically using the theory of Markov Chains and by numerical simulations intwo classes of games, the Minority game and the Parrondo Games, that agents whooptimize their strategy based on past information actually perform worse thannon-optimizing agents. In other words, low-entropy (more informative)strategies under-perform high-entropy (or random) strategies. This provides aprecise definition of the "illusion of control" in set-ups a priori defined toemphasize the importance of optimization.


Instruction: what is the prompt that generates the input?

Input: We contrast two sets of conditions that govern the transition in whichclassical dynamics emerges from the evolution of a quantum system. The firstwas derived by considering the trajectories seen by an observer (dubbed the``strong'' transition) [Bhattacharya, et al., Phys. Rev. Lett. 85: 4852(2000)], and the second by considering phase-space densities (the ``weak''transition) [Greenbaum, et al., Chaos 15, 033302 (2005)]. On the face of itthese conditions appear rather different. We show, however, that in thesemiclassical regime, in which the action of the system is large compared to$\hbar$, and the measurement noise is small, they both offer an essentiallyequivalent local picture. Within this regime, the weak conditions dominatewhile in the opposite regime where the action is not much larger than Planck'sconstant, the strong conditions dominate.


Instruction: what is the prompt that generates the input?

Input: Using the tight-binding model with long-range Coulomb interactions betweenelectrons, we study some of the electronic properties of graphene. The Coulombinteractions are treated with the renormalized-ring-diagram approximation. Byself-consistently solving the integral equations for the Green function, wecalculate the spectral density. The obtained result is in agreement withexperimental observation. In addition, we also compute the density of states,the distribution functions, and the ground-state energy. Within the presentapproximation, we find that the imaginary part of the self-energy fixed at theFermi momentum varies as quadratic in energy close to the chemical potential,regardless the system is doped or not. This result appears to indicate that theelectrons in graphene always behave like a moderately correlated Fermi liquid.


Instruction: what is the prompt that generates the input?

Input: We show that the globular cluster mass function (GCMF) in the Milky Waydepends on cluster half-mass density (rho_h) in the sense that the turnovermass M_TO increases with rho_h while the width of the GCMF decreases. We arguethat this is the expected signature of the slow erosion of a mass function thatinitially rose towards low masses, predominantly through cluster evaporationdriven by internal two-body relaxation. We find excellent agreement between theobserved GCMF -- including its dependence on internal density rho_h, centralconcentration c, and Galactocentric distance r_gc -- and a simple model inwhich the relaxation-driven mass-loss rates of clusters are approximated by-dM/dt = mu_ev ~ rho_h^{1/2}. In particular, we recover the well-knowninsensitivity of M_TO to r_gc. This feature does not derive from a literal``universality'' of the GCMF turnover mass, but rather from a significantvariation of M_TO with rho_h -- the expected outcome of relaxation-drivencluster disruption -- plus significant scatter in rho_h as a function of r_gc.Our conclusions are the same if the evaporation rates are assumed to dependinstead on the mean volume or surface densities of clusters inside their tidalradii, as mu_ev ~ rho_t^{1/2} or mu_ev ~ Sigma_t^{3/4} -- alternativeprescriptions that are physically motivated but involve cluster properties(rho_t and Sigma_t) that are not as well defined or as readily observable asrho_h. In all cases, the normalization of mu_ev required to fit the GCMFimplies cluster lifetimes that are within the range of standard values(although falling towards the low end of this range). Our analysis does notdepend on any assumptions or information about velocity anisotropy in theglobular cluster system.


Instruction: what is the prompt that generates the input?

Input: In this article we analyze the impact of B-physics and Higgs physics at LEPon standard and non-standard Higgs bosons searches at the Tevatron and the LHC,within the framework of minimal flavor violating supersymmetric models. TheB-physics constraints we consider come from the experimental measurements ofthe rare B-decays b -> s gamma and B_u -> tau nu and the experimental limit onthe B_s -> mu+ mu- branching ratio. We show that these constraints are severefor large values of the trilinear soft breaking parameter A_t, rendering thenon-standard Higgs searches at hadron colliders less promising. On the contrarythese bounds are relaxed for small values of A_t and large values of theHiggsino mass parameter mu, enhancing the prospects for the direct detection ofnon-standard Higgs bosons at both colliders. We also consider the availableATLAS and CMS projected sensitivities in the standard model Higgs searchchannels, and we discuss the LHC's ability in probing the whole MSSM parameterspace. In addition we also consider the expected Tevatron collidersensitivities in the standard model Higgs h -> b bbar channel to show that itmay be able to find 3 sigma evidence in the B-physics allowed regions for smallor moderate values of the stop mixing parameter.


Instruction: what is the prompt that generates the input?

Input: We reanalyse leptogenesis via the out-of-equilibrium decay of the lightestright-handed neutrino in type II seesaw scenarios, taking into accountflavour-dependent effects. In the type II seesaw mechanism, in addition to thetype I seesaw contribution, an additional direct mass term for the lightneutrinos is present. We consider type II seesaw scenarios where thisadditional contribution arises from the vacuum expectation value of a Higgstriplet, and furthermore an effective model-independent approach. Weinvestigate bounds on the flavour-specific decay asymmetries, on the mass ofthe lightest right-handed neutrino and on the reheat temperature of the earlyuniverse, and compare them to the corresponding bounds in the type I seesawframework. We show that while flavour-dependent thermal type II leptogenesisbecomes more efficient for larger mass scale of the light neutrinos, and thebounds become relaxed, the type I seesaw scenario for leptogenesis becomes moreconstrained. We also argue that in general, flavour-dependent effects cannot beignored when dealing with leptogenesis in type II seesaw models.


Instruction: what is the prompt that generates the input?

Input: The search for MSSM Higgs bosons will be an important goal at the LHC. Weanalyze the search reach of the CMS experiment for the heavy neutral MSSM Higgsbosons with an integrated luminosity of 30 or 60 fb^-1. This is done bycombining the latest results for the CMS experimental sensitivities based onfull simulation studies with state-of-the-art theoretical predictions of MSSMHiggs-boson properties. The results are interpreted in MSSM benchmark scenariosin terms of the parameters tan_beta and the Higgs-boson mass scale, M_A. Westudy the dependence of the 5 sigma discovery contours in the M_A-tan_betaplane on variations of the other supersymmetric parameters. The largest effectsarise from a change in the higgsino mass parameter mu, which enters both viahigher-order radiative corrections and via the kinematics of Higgs decays intosupersymmetric particles. While the variation of $\mu$ can shift theprospective discovery reach (and correspondingly the ``LHC wedge'' region) byabout Delta tan_beta = 10, we find that the discovery reach is rather stablewith respect to the impact of other supersymmetric parameters. Within thediscovery region we analyze the accuracy with which the masses of the heavyneutral Higgs bosons can be determined. We find that an accuracy of 1-4% shouldbe achievable, which could make it possible in favourable regions of the MSSMparameter space to experimentally resolve the signals of the two heavy MSSMHiggs bosons at the LHC.


Instruction: what is the prompt that generates the input?

Input: Using in-medium hadron properties according to the Brown-Rho scaling due tothe chiral symmetry restoration at high densities and considering naturalnessof the coupling constants, we have newly constructed several relativisticmean-field Lagrangians with chiral limits. The model parameters are adjustedsuch that the symmetric part of the resulting equation of state at supra-normaldensities is consistent with that required by the collective flow data fromhigh energy heavy-ion reactions, while the resulting density dependence of thesymmetry energy at sub-saturation densities agrees with that extracted from therecent isospin diffusion data from intermediate energy heavy-ion reactions. Theresulting equations of state have the special feature of being soft atintermediate densities but stiff at high densities naturally. With theseconstrained equations of state, it is found that the radius of a 1.4$M_\odot$canonical neutron star is in the range of 11.9 km$\leq$R$\leq$13.1 km, and themaximum neutron star mass is around 2.0$M_\odot$ close to the recentobservations.


Instruction: what is the prompt that generates the input?

Input: We analyze the small-scale clustering in "MegaZ-LRG", a largephotometric-redshift catalogue of Luminous Red Galaxies extracted from theimaging dataset of the Sloan Digital Sky Survey. MegaZ-LRG, presented in acompanion paper, spans the redshift range 0.4 < z < 0.7 with an r.m.s. redshifterror dz ~ 0.03(1+z), covering 5,914 deg^2 to map out a total cosmic volume 2.5h^-3 Gpc^3. In this study we use 380,000 photometric redshifts to measuresignificant deviations from the canonical power-law fit to the angularcorrelation function in a series of narrow redshift slices, in which weconstruct volume-limited samples. These deviations are direct signatures of themanner in which these galaxies populate the underlying network of dark matterhaloes. We cleanly delineate the separate contributions of the "1-halo" and"2-halo" clustering terms and fit our measurements by parameterizing the halooccupation distribution N(M) of the galaxies. Our results are successfully fitby a "central" galaxy contribution with a "soft" transition from zero to onegalaxies, combined with a power-law "satellite" galaxy component, the slope ofwhich is a strong function of galaxy luminosity. The large majority of galaxiesare classified as central objects of their host dark matter haloes rather thansatellites in more massive systems. The effective halo mass of MegaZ-LRGgalaxies lies in the range log_10 (M_eff / h^-1 M_sol) = 13.61 - 13.8(increasing with redshift, assuming large-scale normalization sigma_8 = 0.8)for corresponding number densities in the range n_g = 5.03 - 0.56 x 10^-4 h^3Mpc^-3. Our results confirm the usefulness of the halo model for gainingphysical insight into the patterns of galaxy clustering.


Instruction: what is the prompt that generates the input?

Input: This thesis considers two different aspects of string theory, the tensionlesslimit of the string and supersymmetric sigma models. The tensionless limit isused to find a IIB supergravity background generated by a tensionless string.Quantization of the tensionless string in a pp-wave background is performed andthe tensionless limit is found to commute with quantization. Further, the sigmamodel with N=(2,2) extended world-sheet supersymmetry is considered and therequirement on the target space to have a bi-Hermitean geometry is reviewed. Itis shown that the equivalence between bi-Hermitean geometry and generalizedKahler follows, in this context, from the equivalence between the Lagrangian-and Hamiltonian formulation of the model. Moreover, the explicit T-dualitytransformation in the Hamiltonian formulation of the sigma model is constructedand shown to be a symplectomorphism. Under certain assumptions, the amount ofextended supersymmetry present in the sigma model is shown to be preservedunder T-duality. Further, by requiring N=(2,2) extended supersymmetry in afirst order formulation of the sigma model an intriguing geometrical structurearises and in a special case generalized complex geometry is found to becontained in the new framework.


Instruction: what is the prompt that generates the input?

Input: A problem which has recently attracted research attention is that ofestimating the distribution of flow sizes in internet traffic. On high trafficlinks it is sometimes impossible to record every packet. Researchers haveapproached the problem of estimating flow lengths from sampled packet data intwo separate ways. Firstly, different sampling methodologies can be tried tomore accurately measure the desired system parameters. One such method is thesample-and-hold method where, if a packet is sampled, all subsequent packets inthat flow are sampled. Secondly, statistical methods can be used to ``invert''the sampled data and produce an estimate of flow lengths from a sample.  In this paper we propose, implement and test two variants on thesample-and-hold method. In addition we show how the sample-and-hold method canbe inverted to get an estimation of the genuine distribution of flow sizes.Experiments are carried out on real network traces to compare standard packetsampling with three variants of sample-and-hold. The methods are compared fortheir ability to reconstruct the genuine distribution of flow sizes in thetraffic.


Instruction: what is the prompt that generates the input?

Input: Hayashi and Carthew (Nature 431 [2004], 647) have shown that the packing ofcone cells in the Drosophila retina resembles soap bubble packing, and thatchanging E- and N-cadherin expression can change this packing, as well as cellshape.  The analogy with bubbles suggests that cell packing is driven by surfaceminimization. We find that this assumption is insufficient to model theexperimentally observed shapes and packing of the cells based on their cadherinexpression. We then consider a model in which adhesion leads to a surfaceincrease, balanced by cell cortex contraction. Using the experimentallyobserved distributions of E- and N-cadherin, we simulate the packing and cellshapes in the wildtype eye. Furthermore, by changing only the correspondingparameters, this model can describe the mutants with different numbers ofcells, or changes in cadherin expression.


Instruction: what is the prompt that generates the input?

Input: We present a ground based photometry of the low-temperature contact binary BBPeg. We collected all times of mid-eclipses available in literature andcombined them with those obtained in this study. Analyses of the data indicatea period increase of 3.0(1) x 10^{-8} days/yr. This period increase of BB Pegcan be interpreted in terms of the mass transfer 2.4 x 10^{-8} Ms yr^{-1} fromthe less massive to the more massive component. The physical parameters havebeen determined as Mc = 1.42 Ms, Mh = 0.53 Ms, Rc = 1.29 Rs, Rh = 0.83 Rs, Lc =1.86 Ls, and Lh = 0.94 Ls through simultaneous solution of light and of theradial velocity curves. The orbital parameters of the third body, that orbitsthe contact system in an eccentric orbit, were obtained from the periodvariation analysis. The system is compared to the similar binaries in theHertzsprung-Russell and Mass-Radius diagram.


Instruction: what is the prompt that generates the input?

Input: We define angles from-to and between infinite dimensional subspaces of aHilbert space, inspired by the work of E. J. Hannan, 1961/1962 for generalcanonical correlations of stochastic processes. The spectral theory ofselfadjoint operators is used to investigate the properties of the angles,e.g., to establish connections between the angles corresponding to orthogonalcomplements. The classical gaps and angles of Dixmier and Friedrichs arecharacterized in terms of the angles. We introduce principal invariantsubspaces and prove that they are connected by an isometry that appears in thepolar decomposition of the product of corresponding orthogonal projectors.Point angles are defined by analogy with the point operator spectrum. We boundthe Hausdorff distance between the sets of the squared cosines of the anglescorresponding to the original subspaces and their perturbations. We show thatthe squared cosines of the angles from one subspace to another can beinterpreted as Ritz values in the Rayleigh-Ritz method, where the formersubspace serves as a trial subspace and the orthogonal projector of the lattersubspace serves as an operator in the Rayleigh-Ritz method. The Hausdorffdistance between the Ritz values, corresponding to different trial subspaces,is shown to be bounded by a constant times the gap between the trial subspaces.We prove a similar eigenvalue perturbation bound that involves the gap squared.Finally, we consider the classical alternating projectors method and proposeits ultimate acceleration, using the conjugate gradient approach. Thecorresponding convergence rate estimate is obtained in terms of the angles. Weillustrate a possible acceleration for the domain decomposition method with asmall overlap for the 1D diffusion equation.


Instruction: what is the prompt that generates the input?

Input: We apply the technique of parameter-splitting to existing cosmological datasets, to check for a generic failure of dark energy models. Given a dark energyparameter, such as the energy density Omega_Lambda or equation of state w, wesplit it into two meta-parameters with one controlling geometrical distances,and the other controlling the growth of structure. Observational data spanningType Ia Supernovae, the cosmic microwave background (CMB), galaxy clustering,and weak gravitational lensing statistics are fit without requiring the twometa-parameters to be equal. This technique checks for inconsistency betweendifferent data sets, as well as for internal inconsistency within any one dataset (e.g., CMB or lensing statistics) that is sensitive to both geometry andgrowth. We find that the cosmological constant model is consistent with currentdata. Theories of modified gravity generally predict a relation between growthand geometry that is different from that of general relativity.Parameter-splitting can be viewed as a crude way to parametrize the space ofsuch theories. Our analysis of current data already appears to put sharp limitson these theories: assuming a flat universe, current data constrain thedifference Omega_Lambda(geom) - Omega_Lambda(grow) to be -0.0044 +/- 0.0058(68% C.L.); allowing the equation of state w to vary, the difference w(geom) -w(grow) is constrained to be 0.37 +/- 0.37 (68% C.L.). Interestingly, theregion w(grow) > w(geom), which should be generically favored by theories thatslow structure formation relative to general relativity, is quite restricted bydata already. We find w(grow) < -0.80 at 2 sigma. As an example, the best-fitflat Dvali-Gabadadze-Porrati (DGP) model approximated by our parametrizationlies beyond the 3 sigma contour for constraints from all the data sets.


Instruction: what is the prompt that generates the input?

Input: Let $X$ be a compact K\"ahler manifold and $\om$ a smooth closed form ofbidegree $(1,1)$ which is nonnegative and big. We study the classes ${\mathcalE}_{\chi}(X,\om)$ of $\om$-plurisubharmonic functions of finite weightedMonge-Amp\`ere energy. When the weight $\chi$ has fast growth at infinity, thecorresponding functions are close to be bounded.  We show that if a positive Radon measure is suitably dominated by theMonge-Amp\`ere capacity, then it belongs to the range of the Monge-Amp\`ereoperator on some class ${\mathcal E}_{\chi}(X,\om)$. This is done byestablishing a priori estimates on the capacity of sublevel sets of thesolutions.  Our result extends U.Cegrell's and S.Kolodziej's results and puts them into aunifying frame. It also gives a simple proof of S.T.Yau's celebrated a priori${\mathcal C}^0$-estimate.


Instruction: what is the prompt that generates the input?

Input: After the work of Gladman et al. (1998), it is now assessed that manyirregular satellites are orbiting around Uranus. Despite many studies have beenperformed in past years, very few is know for the light-curves of these objectsand inconsistencies are present between colours derived by different authors.This situation motivated our effort to improve both the knowledge of coloursand light curves. We present and discuss time series observations of Sycorax,Prospero, Stephano, Setebos and Trinculo, five faint irregular satellites ofUranus, carried out at VLT, ESO Paranal (Chile) in the nights between 29 and 30July, 2005 and 25 and 30 November, 2005. We derive light curves for Sycorax andProspero and colours for all of these these bodies. For Sycorax we obtaincolours B-V =0.839 +/- 0.014, V-R = 0.531 +/- 0.005 and a light curve which issuggestive of a periodical variation with period about 3.6 hours and amplitudeabout 0.067 +/- 0.004 mag. The periods and colours we derive for Sycorax are inagreement with our previous determination in 1999 using NTT. We derive also alight-curve for Prospero which suggests an amplitude of about 0.2 mag and aperiodicity of about 4 hours. However, the sparseness of our data, prevents amore precise characterization of the light-curves, and we can not determinewether they are one-peaked or two-peaked. Hence, these periods and amplitudeshave to be considered preliminary estimates. As for Setebos, Stephano andTrinculo the present data do not allow to derive any unambiguous periodicity,despite Setebos displays a significant variability with amplitude about aslarge as that of Prospero. Colours for Prospero, Setebos, Stephano and Trinculoare in marginal agreement with the literature.


Instruction: what is the prompt that generates the input?

Input: Low energy supersymmetric models provide a solution to the hierarchy problemand also have the necessary ingredients to solve two of the most outstandingissues in cosmology: the origin of dark matter and baryonic matter. One of themost attractive features of this framework is that the relevant physicalprocesses are related to interactions at the weak scale and therefore may betested in collider experiments in the near future. This is true for the MinimalSupersymmetric Standard Model (MSSM) as well as for its extension with theaddition of one singlet chiral superfield, the so-called nMSSM. It has beenrecently shown that within the nMSSM an elegant solution to both the problem ofbaryogenesis and dark matter may be found, that relies mostly on the mixing ofthe singlet sector with the Higgs sector of the theory. In this work we reviewthe nMSSM model constraints from cosmology and present the associated colliderphenomenology at the LHC and the ILC. We show that the ILC will efficientlyprobe the neutralino, chargino and Higgs sectors, allowing to confrontcosmological observations with computations based on collider measurements. Wealso investigate the prospects for a direct detection of dark matter and theconstraints imposed by the current bounds of the electron electric dipolemoment in this model.


Instruction: what is the prompt that generates the input?

Input: We investigate the effect of planetary rotation on the transit spectrum of anextrasolar giant planet. During ingress and egress, absorption features arisingfrom the planet's atmosphere are Doppler shifted by of order the planet'srotational velocity (~1-2 km/s) relative to where they would be if the planetwere not rotating. We focus in particular on the case of HD209458b, which oughtto be at least as good a target as any other known transiting planet. ForHD209458b, this shift should give rise to a small net centroid shift of ~60cm/s on the stellar absorption lines. Using a detailed model of thetransmission spectrum due to a rotating star transited by a rotating planetwith an isothermal atmosphere, we simulate the effect of the planet's rotationon the shape of the spectral lines, and in particular on the magnitude of theirwidth and centroid shift. We then use this simulation to determine the expectedsignal-to-noise ratio for distinguishing a rotating from a non-rotating planet,and assess how this S/N scales with various parameters of HD209458b. We findthat with a 6 m telescope, an equatorial rotational velocity of ~2 km/s couldbe detected with a S/N~5 by accumulating the signal over many transits over thecourse of several years. With a 30 m telescope, the time required to make sucha detection reduces to less than 2 months.


Instruction: what is the prompt that generates the input?

Input: We carry out the non-perturbative renormalization of the chromo-magneticoperator in Heavy Quark Effective Theory. At order 1/m of the expansion, theoperator is responsible for the mass splitting between the pseudoscalar andvector B mesons. We obtain its two-loop anomalous dimension in a Schr"odingerfunctional scheme by successive one-loop conversions to the lattice MS schemeand the MS-bar scheme. We then compute the scale evolution of the operatornon-perturbatively in the N_f=0 theory between $\mu \approx 0.3$ GeV and $\mu\approx 100$ GeV, where contact is made with perturbation theory. The overallrenormalization factor that converts the bare lattice operator to itsrenormalization group invariant form is given for the Wilson gauge action andtwo standard discretizations of the heavy-quark action. As an application, wefind that this factor brings the previous quenched predictions of the B* - Bmass splitting closer to the experimental value than found with a perturbativerenormalization. The same renormalization factor is applicable to thespin-dependent potentials of Eichten and Feinberg.