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In 1973, Katona raised the problem of determining the maximum number of subsets in a separating cover on n elements. The answer to Katona's question turns out to be the inverse to the answer to a much simpler question: what is the largest integer which is the product of positive integers with sum n? We give a combinatorial explanation for this relationship, via Moon and Moser's answer to a question of Erdos: how many maximal independent sets can a graph on n vertices have? We conclude by showing how Moon and Moser's solution also sheds light on a problem of Mahler and Popken's about the complexity of integers.
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arxiv:0911.4204
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Measurements by the STAR collaboration of the cross section and transverse single spin asymmetry (SSA) of neutral pion production at large Feynman x (x_F) in pp-collisions at \sqrt{s}=200 GeV were reported previously. The x_F dependence of the asymmetry can be described by phenomenological models that include the Sivers effect, Collins effect or higher twist contributions in the initial and final states. Discriminating between the Sivers and Collins effects requires one to go beyond inclusive \pi^0 measurements. For the 2008 run, forward calorimetry at STAR was significantly extended. The large acceptance of the Forward Meson Spectrometer (FMS) allows us to look at heavier meson states and \pi^0-\pi^0 correlations. Recent results, the status of current analyses and near-term plans will be discussed.
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arxiv:0911.4388
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We calculate the complete one-loop quantum corrections to the helicity eigenstate chargino pair production cross sections in polarized electron positron collisions, within the Minimal Supersymmetric Standard Model. We calculate the non-QED corrections using the helicity amplitudes formalism, and Dimensional Regularization to deal with ultraviolet divergences. We calculate QED corrections using the dipole subtraction formalism to extract soft and collinear divergences in Bremsstrahlung, canceling them with the infrared divergences from virtual QED corrections. We show numerical results for the Focus Point scenario in mSUGRA, where we find important quantum corrections for differential cross sections with definite chargino helicities.
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arxiv:0911.4403
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The local motion of a null curve in Minkowski 3-space induces an evolution equation for its Lorentz invariant curvature. Special motions are constructed whose induced evolution equations are the members of the KdV hierarchy. The null curves which move under the KdV flow without changing shape are proven to be the trajectories of a certain particle model on null curves described by a Lagrangian linear in the curvature. In addition, it is shown that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlev\'e equation.
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arxiv:0911.4467
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It is known that $C(X)$ is algebraically closed if $X$ is a locally connected, hereditarily unicoherent compact Hausdorff space. For such spaces, we prove that if $F:C(X) \to C(X)$ is given by an everywhere convergent power series with coefficients in $C(X)$ and satisfies certain restrictions, then it has a root in $C(X)$. Our results generalizes the monic algebraic case.
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arxiv:0911.4469
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We present the Modular Algorithm for Relativistic Treatment of heavy IoN Interactions (MARTINI), an event generator for the hard and penetrating probes in high energy nucleus-nucleus collisions. The simulation consists of a time evolution model for the soft background, such as hydrodynamics, PYTHIA 8.1 to generate and hadronize the hard partons after the medium evolution, which is based on the McGill-AMY formalism and includes both radiative and elastic processes. MARTINI allows for the generation of full event configurations in the high transverse momentum region. We present results for the neutral pion and photon nuclear modification factor in Au+Au collisions at RHIC.
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arxiv:0911.4470
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We present a simplified model to study the orbital evolution of a young hot Jupiter inside the magnetospheric cavity of a proto-planetary disk. The model takes into account the disk locking of stellar spin as well as the tidal and magnetic interactions between the star and the planet. We focus on the orbital evolution starting from the orbit in the 2:1 resonance with the inner edge of the disk, followed by the inward and then outward orbital migration driven by the tidal and magnetic torques as well as the Roche-lobe overflow of the tidally inflated planet. The goal in this paper is to study how the orbital evolution inside the magnetospheric cavity depends on the cavity size, planet mass, and orbital eccentricity. In the present work, we only target the mass range from 0.7 to 2 Jupiter masses. In the case of the large cavity corresponding to the rotational period ~ 7 days, the planet of mass >1 Jupiter mass with moderate initial eccentricities (>~ 0.3) can move to the region < 0.03 AU from its central star in 10^7 years, while the planet of mass <1 Jupiter mass cannot. We estimate the critical eccentricity beyond which the planet of a given mass will overflow its Roche radius and finally lose all of its gas onto the star due to runaway mass loss. In the case of the small cavity corresponding to the rotational period ~ 3 days, all of the simulated planets lose all of their gas even in circular orbits. Our results for the orbital evolution of young hot Jupiters may have the potential to explain the absence of low-mass giant planets inside ~ 0.03 AU from their dwarf stars revealed by transit surveys.
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arxiv:0911.4532
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We derive a $\mathcal C^{k+\yt}$ H\"older estimate for $P\phi$, where $P$ is either of the two solution operators in Henkin's local homotopy formula for $\bar\partial_b$ on a strongly pseudoconvex real hypersurface $M$ in $\mathbf C^{n}$, $\phi$ is a $(0,q)$-form of class $\mathcal C^{k}$ on $M$, and $k\geq0$ is an integer. We also derive a $\mathcal C^{a}$ estimate for $P\phi$, when $\phi$ is of class $\mathcal C^{a}$ and $a\geq0$ is a real number. These estimates require that $M$ be of class $\mathcal C^{k+{5/2}}$, or $\mathcal C^{a+2}$, respectively. The explicit bounds for the constants occurring in these estimates also considerably improve previously known such results. These estimates are then applied to the integrability problem for CR vector bundles to gain improved regularity. They also constitute a major ingredient in a forthcoming work of the authors on the local CR embedding problem.
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arxiv:0911.4549
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New CCD photometry during 4 successive years from 2005 is presented for the eclipsing binary GW Cep, together with reasonable explanations for the light and period variations. All historical light curves, obtained over a 30-year interval, display striking light changes, and are best modeled by the simultaneous existence of a cool spot and a hot spot on the more massive cool component star. The facts that the system is magnetically active and that the hot spot has consistently existed on the inner hemisphere of the star indicate that the two spots are formed by (1) magnetic dynamo-related activity on the cool star and (2) mass transfer from the primary to the secondary component. Based on 38 light-curve timings from the Wilson-Devinney code and all other minimum epochs, a period study of GW Cep reveals that the orbital period has experienced a sinusoidal variation with a period and semi-amplitude of 32.6 yrs and 0.009 d, respectively. In principle, these may be produced either by a light-travel-time effect due to a third body or by an active magnetic cycle of at least one component star. Because we failed to find any connection between luminosity variability and the period change, that change most likely arises from the existence of an unseen third companion star with a minimum mass of 0.22 $M_\odot$ gravitationally bound to the eclipsing pair.
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arxiv:0911.4554
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We study real time dynamics of a Dp-brane orbiting a stack of NS5-branes. It is generally known that a BPS D-brane moving in the vicinity of NS5-branes becomes unstable due to the presence of tachyonic degree of freedom induced on the D-brane. Indeed, the D-brane necessarily falls into the fivebranes due to gravitational attraction and eventually collapses into a pressureless fluid. Such a decay of the D-brane is known to be closely related to the rolling tachyon problem. In this paper we show that in special cases the decay of D-brane caused by gravitational attraction can be avoided. Namely for certain values of energy and angular momentum the D-brane orbits around the fivebranes, maintaining certain distance from the fivebranes all the time, and the process of tachyon condensation is suppressed. We show that the tachyonic degree of freedom induced on such a D-brane really disappears and the brane returns to a stable D-brane.
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arxiv:0911.4557
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The energy eigenvalues and the corresponding eigenfunctions of the one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential are analytically obtained within the position-dependent mass formalism. The parametric generalization of the Nikiforov-Uvarov method is used in the calculations by choosing a mass distribution.
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arxiv:0911.4558
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In this article we encode Hadwiger's covering conjecture and Borsuk's partition conjecture into continuous functions defined on the spaces of convex bodies, propose a four-step program to approach them, and obtain some partial results.
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arxiv:0911.4580
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When Inflation is embedded in a fundamental theory, such as string theory, it typically begins when the Universe is already substantially larger than the fundamental scale [such as the one defined by the string length scale]. This is naturally explained by postulating a pre-inflationary era, during which the size of the Universe grew from the fundamental scale to the initial inflationary scale. The problem then arises of maintaining the [presumed] initial spatial homogeneity throughout this era, so that, when it terminates, Inflation is able to begin in its potential-dominated state. Linde has proposed that a spacetime with compact negatively curved spatial sections can achieve this, by means of chaotic mixing. Such a compactification will however lead to a Casimir energy, which can lead to effects that defeat the purpose unless the coupling to gravity is suppressed. We estimate the value of this coupling required by the proposal, and use it to show that the pre-inflationary spacetime is stable, despite the violation of the Null Energy Condition entailed by the Casimir energy.
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arxiv:0911.4583
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We propose a novel method to reconstruct the spatio-temporal amplitude and phase of the electric field of ultrashort laser pulses using spatially-resolved spectral interferometry. This method is based on a fiber-optic coupler interferometer that has certain advantages in comparison with standard interferometer systems, such as it being alignment-free and selection of the reference beam at a single point. Our technique, which we refer to as STARFISH, offers compactness and simplicity. We report its application to the experimental characterization of chirped pulses and to spatio-temporal reconstructions of a convergent beam as well as plane-plane and spherical-plane waves interferences, which we check with our simulations.
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arxiv:0911.4589
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A scaling law analysis of the world data on inclusive large-pT hadron production in hadronic collisions is carried out. A significant deviation from leading-twist perturbative QCD predictions at next-to-leading order is reported. The observed discrepancy is largest at high values of xT=2pT/sqrt(s). In contrast, the production of prompt photons and jets exhibits the scaling behavior which is close to the conformal limit, in agreement with the leading-twist expectation. These results bring evidence for a non-negligible contribution of higher-twist processes in large-pT hadron production in hadronic collisions, where the hadron is produced directly in the hard subprocess rather than by gluon or quark jet fragmentation. Predictions for scaling exponents at RHIC and LHC are given, and it is suggested to trigger the isolated large-pT hadron production to enhance higher-twist processes.
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arxiv:0911.4604
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This paper presents an overview of the radiative transfer problem of calculating the spectral line intensity and polarization that emerges from a (generally magnetized) astrophysical plasma composed of atoms and molecules whose excitation state is significantly influenced by radiative transitions produced by an anisotropic radiation field. The numerical solution of this non-LTE problem of the 2nd kind is facilitating the physical understanding of the second solar spectrum and the exploration of the complex magnetism of the extended solar atmosphere, but much more could be learned if high-sensitivity polarimeters were developed also for the present generation of night-time telescopes. Interestingly, I find that the population ratio between the levels of some resonance line transitions can be efficiently modulated by the inclination of a weak magnetic field when the anisotropy of the incident radiation is significant, something that could provide a new diagnostic tool in astrophysics.
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arxiv:0911.4669
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We extend our previous work arXiv:1007.0053 on coherent-constructible correspondence for toric varieties to include toric Deligne-Mumford (DM) stacks. Following Borisov-Chen-Smith, a toric DM stack $\cX_\bSi$ is described by a "stacky fan" $\bSi=(N,\Si,\beta)$, where $N$ is a finitely generated abelian group and $\Si$ is a simplicial fan in $N_\bR=N\otimes_{\bZ}\bR$. From $\bSi$ we define a conical Lagrangian $\Lambda_\bSi$ inside the cotangent $T^*M_\bR$ of the dual vector space $M_\bR$ of $N_\bR$, such that torus-equivariant, coherent sheaves on $\cX_\bSi$ are equivalent to constructible sheaves on $M_\bR$ with singular support in $\LbS$.
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arxiv:0911.4711
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In this paper, we consider the $L_x^2$ solution $u$ to mass critical NLS $iu_t+\Delta u=\pm |u|^{\frac 4d} u$. We prove that in dimensions $d\ge 4$, if the solution is spherically symmetric and is \emph{almost periodic modulo scaling}, then it must lie in $H_x^{1+\eps}$ for some $\eps>0$. Moreover, the kinetic energy of the solution is localized uniformly in time. One important application of the theorem is a simplified proof of the scattering conjecture for mass critical NLS without reducing to three enemies(see the work of Killip-Tao-Visan, and Killip-Visan-Zhang). As another important application, we establish a Liouville type result for $L_x^2$ initial data with ground state mass. We prove that if a radial $L_x^2$ solution to focusing mass critical problem has the ground state mass and does not scatter in both time directions, then it must be global and coincide with the solitary wave up to symmetries. Here the ground state is the unique, positive, radial solution to elliptic equation $\Delta Q-Q+Q^{1+\frac 4d}=0$. This is the first rigidity type result in scale invariant space $L_x^2$.
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arxiv:0911.4746
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We have constructed a detailed spectral atlas covering the wavelength region 930A to 1225A for 10 sharp-lined B0-B9 stars near the main sequence. Most of the spectra we assembled are from the archives of the FUSE satellite, but for nine stars wavelength coverage above 1188A was taken from high-resolution IUE or echelle HST/STIS spectra. To represent the tenth star at type B0.2 V we used the Copernicus atlas of tau Sco. We made extensive line identifications in the region 949A to 1225A of all atomic features having published oscillator strengths at types B0, B2, and B8. These are provided as a supplementary data product - hence the term detailed atlas. Our list of found features totals 2288, 1612, and 2469 lines, respectively. We were able to identify 92%, 98%, and 98% of these features with known atomic transitions with varying degrees of certainty in these spectra. The remaining lines do not have published oscillator strengths. Photospheric lines account for 94%, 87%, and 91%, respectively, of all our iden- tifications, with the remainder being due to interstellar (usually molecular H2) lines. We also discuss the numbers of lines with respect to the distributions of various ions for these three most studied spectral subtypes. A table is also given of 167 least blended lines that can be used as possible diagnostics of physical conditions in B star atmospheres.
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arxiv:0911.4747
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In an intense laser field, an electron may decay by emitting a pair of photons. The two photons emitted during the process, which can be interpreted as a laser-dressed double Compton scattering, remain entangled in a quantifiable way: namely, the so-called concurrence of the photon polarizations gives a gauge-invariant measure of the correlation of the hard gamma rays. We calculate the differential rate and concurrence for a backscattering setup of the electron and photon beam, employing Volkov states and propagators for the electron lines, thus accounting nonperturbatively for the electron-laser interaction. The nonperturbative results are shown to differ significantly compared to those obtained from the usual double Compton scattering.
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arxiv:0911.4765
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Far-off-resonant pulsed laser fields produce negligible excitation between two atomic states but may induce considerable phase shifts. The acquired phases are usually calculated by using the adiabatic-elimination approximation. We analyze the accuracy of this approximation and derive the conditions for its applicability to the calculation of the phases. We account for various sources of imperfections, ranging from higher terms in the adiabatic-elimination expansion and irreversible population loss to couplings to additional states. We find that, as far as the phase shifts are concerned, the adiabatic elimination is accurate only for a very large detuning. We show that the adiabatic approximation is a far more accurate method for evaluating the phase shifts, with a vast domain of validity; the accuracy is further enhanced by superadiabatic corrections, which reduce the error well below $10^{-4}$. Moreover, owing to the effect of adiabatic population return, the adiabatic and superadiabatic approximations allow one to calculate the phase shifts even for a moderately large detuning, and even when the peak Rabi frequency is larger than the detuning; in these regimes the adiabatic elimination is completely inapplicable. We also derive several exact expressions for the phases using exactly soluble two-state and three-state analytical models.
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arxiv:0911.4812
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The coupled dark energy models, in which the quintessence scalar field nontrivially couples to the cold dark matter, have been proposed to explain the coincidence problem. In this paper we study the perturbations of coupled dark energy models and the effects of this interaction on the current observations. Here, we pay particular attention to its imprint on the late-time Integrated Sachs-Wolfe (ISW) effect. We perform a global analysis of the constraints on this interaction from the current observational data. Considering the typical exponential form as the interaction form, we obtain that the strength of interaction between dark sectors is constrained as $\beta<0.085$ at 95% confidence level. Furthermore, we find that future measurements with smaller error bars could improve the constraint on the strength of coupling by a factor two, when compared to the present constraints.
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arxiv:0911.4820
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This paper is concerned with the large time behavior of solutions to the Lifschitz-Slyozov-Wagner (LSW) system of equations. Point-wise in time upper and lower bounds on the rate of coarsening are obtained for solutions with fairly general initial data. These bounds complement the time averaged upper bounds obtained by Dai and Pego, and the point-wise in time upper and lower bounds obtained by Niethammer and Velasquez for solutions with initial data close to a self-similar solution.
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arxiv:0911.4935
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We determine the isomorphism classes of semisimple Hopf algebras of dimension 60 which are simple as Hopf algebras.
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arxiv:0911.4943
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We present a new, close relation between column densities of OH and CH molecules based on 16 translucent sightlines (six of them new) and confirm the theoretical oscillator strengths of the OH A--X transitions at 3078 and 3082 \AA (0.00105, 0.000648) and CH B--X transitions at 3886 and 3890 \AA, (0.00320, 0.00210), respectively. We also report no difference between observed and previously modelled abundances of the OH molecule.
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arxiv:0911.4945
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Efficient collection of fluorescence from trapped ions is crucial for quantum optics and quantum computing applications, specifically, for qubit state detection and in generating single photons for ion-photon and remote ion entanglement. In a typical setup, only a few per cent of ion fluorescence is intercepted by the aperture of the imaging optics. We employ a simple metallic spherical mirror integrated with a linear Paul ion trap to achieve photon collection efficiency of at least 10% from a single Ba$^+$ ion. An aspheric corrector is used to reduce the aberrations caused by the mirror and achieve high image quality.
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arxiv:0911.4958
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We have performed an experiment to demonstrate the approximate time reversal of a "chaotic" time evolution of atomic deBroglie waves. We use ultra cold atoms from a Bose-Einstein condensate in a quantum $\delta$-kicked rotor experiment, and show that an initial state can be approximately re-created even after a period of "chaotic" evolution (a number of kicks). As this mechanism only works for a very narrow range of momenta, the net effect is a narrowing of the momentum distribution after the kick sequence.
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arxiv:0911.4974
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We calculate the Ohmic and Hall conductivities from linear response theory in a system consisting of the intersection of Nc Dp-branes and Nf << N_c Dq-branes. Agreement is found between previous results found in a macroscopic approach comparing induced currents with external electric fields. The issue of how to deal with mixed operators is raised. The retarded Green's function is given by a matrix that can be computed from the boundary action similarly to the Green's function for uncoupled operators.
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arxiv:0911.4976
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By performing standard PUND (positive-up-negative-down), hysteresis-loop and dielectric measurements on the ferroelectric lead zirconate titanate (PZT) thin-film capacitors subject to bipolar/unipolar electrical cycling, we show that unipolar fatigue is evident though still less severe than bipolar fatigue conducted at the same voltage. That has been attributed to polarization retention (backswitching) induced by the residual depolarization field between the monopolar pulses where the applied field is lower than the depolarization field, and explained using the LPD-SICI model (LPD-SICI stands for local phase decomposition caused by switching-induced charge injection). The conventional view that switching does not occur during unipolar electrical cycling may need to be corrected. PUND results recorded using the pulses of the same voltage as those for repetitive fatigue cycling are not reliable if the voltage is lower than 2Vc (Vc is the saturated coercive voltage). Dielectric measurements or hysteresis-loop measurements at higher voltages (e.g. 4Vc) are more reliable ways to evaluate the degree of fatigue and could provide more valuable information in such situations. Finally, dielectric results have been used to estimate the effective thickness di of the fatigue-induced degraded (pyrochlorelike) interfacial layer after bipolar/unipolar fatigue, which has not been done so far to our best knowledge. The fact that di is still much less than the film thickness even after the most severe bipolar fatigue strongly suggests that polarization fatigue in ferroelectrics is an interface effect, not a bulk one.
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arxiv:0911.5009
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We have measured the specific heat of zincblende ZnS for several isotopic compositions and over a broad temperature range (3 to 1100 K). We have compared these results with calculations based on ab initio electronic band structures, performed using both LDA and GGA exchange- correlation functionals. We have compared the lattice dynamics obtained in this manner with experimental data and have calculated the one-phonon and two-phonon densities of states. We have also calculated mode Grueneisen parameters at a number of high symmetry points of the Brillouin zone. The electronic part of our calculations has been used to investigate the effect of the 3d core electrons of zinc on the spin-orbit splitting of the top valence bands. The effect of these core electrons on the band structure of the rock salt modification of ZnS is also discussed.
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arxiv:0911.5022
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We compute the K-theory of ring C*-algebras for polynomial rings over finite fields. The key ingredient is a duality theorem which we had obtained in a previous paper. It allows us to show that the K-theory of these algebras has a ring structure and to determine explicit generators. Our main result also reveals striking similarities between the number field case and the function field case.
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arxiv:0911.5023
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The {\em longest common subsequence (LCS)} problem is a classic and well-studied problem in computer science. LCS is a central problem in stringology and finds broad applications in text compression, error-detecting codes and biological sequence comparison. However, in numerous contexts, words represent cyclic sequences of symbols and LCS must be generalized to consider all circular shifts of the strings. This occurs especially in computational biology when genetic material is sequenced form circular DNA or RNA molecules. This initiates the problem of {\em longest common cyclic subsequence (LCCS)} which finds the longest subsequence between all circular shifts of two strings. In this paper, we give an $O(n^2)$ algorithm for solving LCCS problem where $n$ is the number of symbols in the strings.
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arxiv:0911.5031
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We give an example showing that the Kobayashi-Royden pseudometric for a non-taut domain is, in general, not the derivative of the Lempert function.
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arxiv:0911.5071
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Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative geometry like maps, partitions, Hurwitz numbers, intersection numbers, Gromov-Witten invariants... The problem is thus to understand what they count, or in other words, given a spectral curve, construct an enumerative geometry problem. This is what we do in a semi-heuristic approach in this article. Starting from a spectral curve, i.e. an integrable system, we use its flat connection and flat coordinates, to define a family of worldsheets, whose enumeration is indeed solved by the topological recursion and symplectic invariants. In other words, for any spectral curve, we construct a corresponding string theory, whose target space is a submanifold of the Jacobian.
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arxiv:0911.5096
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Self-regulation of living tissue as an example of self-organization phenomena in hierarchical systems of biological, ecological, and social nature is under consideration. The characteristic feature of these systems is the absence of any governing center and, thereby, their self-regulation is based on a cooperative interaction of all the elements. The work develops a mathematical theory of a vascular network response to local effects on scales of individual units of peripheral circulation.
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arxiv:0911.5131
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In this paper, we analyze the performance of an electro-optic modulator based on a single quantum dot strongly coupled to a nano-resonator, where electrical control of the quantum dot frequency is achieved via quantum confined Stark effect. Using realistic system parameters, we show that modulation speeds of a few tens of GHz are achievable with this system, while the energy per switching operation can be as small as 0.5 fJ. In addition, we study the non-linear distortion, and the effect of pure quantum dot dephasing on the performance of the modulator.
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arxiv:0911.5207
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We show that the duality symmetry of the BFKL equation can be interpreted as a symmetry under rotation of the BFKL Kernel in the transverse space from s-channel (color dipole model) to t-channel (reggeized gluon formulation). We argue that the duality symmetry holds also in the non-forward case due to a very special structure of the non-forward BFKL Kernel, which can be written as a sum of three forward BFKL Kernels. The duality symmetry is established by identifying the dual coordinates with the transverse coordinates of a non-diagonal dipole scattered off the target.
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arxiv:0911.5279
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We study renormalization group flows in the Lifshitz-like $N$-flavour four fermi model discussed in 0905.2928. In the large-$N$ limit, a nontrivial flow occurs in only one of all possible marginal couplings and one relevant coupling, which provides the scale for Lorentz invariance violations. We discuss in detail the phase diagram and RG flows in the space of couplings, which includes the Lifshitz fixed point, the free field fixed point and a new fixed point characterized by $z=1$ scaling and a violation of Lorentz invariance, which cannot be tuned away by adjusting a parameter. In the broken symmetry phase, the model flows from the $z=3$ Lifshitz-like fixed point in the ultraviolet to this new fixed point in the infrared. However, in a modified version of the present model, which has an effective ultraviolet cut-off much smaller than the Lorentz invariance violating scale, the infrared behaviour is governed by an approximately Lorentz invariant theory, similar to the low energy limit of the usual relativistic Nambu$-$Jona-Lasinio model. Such a modified model could be realized by a supersymmetric version of the present model.
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arxiv:0911.5316
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Stein's method is applied to obtain a general Cramer-type moderate deviation result for dependent random variables whose dependence is defined in terms of a Stein identity. A corollary for zero-bias coupling is deduced. The result is also applied to a combinatorial central limit theorem, a general system of binary codes, the anti-voter model on a complete graph, and the Curie-Weiss model. A general moderate deviation result for independent random variables is also proved.
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arxiv:0911.5373
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We study resonant tunneling through a layered medium with a negative index medium (NIM) slab as a constituent layer. We demonstrate large delays in transmission mediated by the surface and the guided modes of the structure with low losses. We show how important it is to include NIM dispersion for correct assessment of the nature and magnitude of the delay. We also point out the role of NIM absorption for the feasibility of such compact delay devices.
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arxiv:0911.5374
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Rough set theory, a mathematical tool to deal with inexact or uncertain knowledge in information systems, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to coverings. Recently, some topological concepts such as neighborhood have been applied to covering rough sets. In this paper, we further investigate the covering rough sets based on neighborhoods by approximation operations. We show that the upper approximation based on neighborhoods can be defined equivalently without using neighborhoods. To analyze the coverings themselves, we introduce unary and composition operations on coverings. A notion of homomorphismis provided to relate two covering approximation spaces. We also examine the properties of approximations preserved by the operations and homomorphisms, respectively.
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arxiv:0911.5394
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We apply the heat kernel method (using Avramidi's non-recursive technique) to the study of the effective action of chiral matter in a complex representation of an arbitrary gauge sector coupled to background U(1) supergravity. This generalizes previous methods, which restricted to 1) real representations of the gauge sector in traditional Poincar\'e supergravity or 2) vanishing supergravity background. In this new scheme, we identify a classical ambiguity in these theories which mixes the supergravity U(1) with the gauge U(1). At the quantum level, this ambiguity is maintained since the effective action changes only by a local counterterm as one shifts a U(1) factor between the supergravity and gauge sectors. An immediate application of our formalism is the calculation of the one-loop gauge, Kahler, and reparametrization anomalies of chiral matter coupled to minimal supergravity from purely chiral loops. Our approach gives an anomaly whose covariant part is both manifestly supersymmetric and non-perturbative in the Kahler potential.
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arxiv:0911.5426
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Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation procedure is proposed and evaluated for a model system where a-priori information about the Hamiltonian's structure is available.
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arxiv:0911.5429
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We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The algorithm product-decomposes $U$ in a chosen operator basis by identifying a certain symmetry of $U$ that is intimately related to the number of gates in the decomposition. We illustrate the algorithm by first obtaining a polynomial decomposition in the Pauli basis of the $n$-qubit Quantum State Transfer unitary by Di Franco et. al. (Phys. Rev. Lett. 101, 230502 (2008)) that transports quantum information from one end of a spin chain to the other; and then implement it in Nuclear Magnetic Resonance to demonstrate that the decomposition is experimentally viable and well-scaled. We furthur experimentally test the resilience of the state transfer to static errors in the coupling parameters of the simulated Hamiltonian. This is done by decomposing and simulating the corresponding imperfect unitaries.
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arxiv:0911.5467
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Using the equation of state of asymmetric nuclear matter that has been recently constrained by the isospin diffusion data from intermediate-energy heavy ion collisions, we have studied the transition density and pressure at the inner edge of neutron star crusts, and they are found to be 0.040 fm^{-3} <= \rho_{t}<= 0.065 fm^{-3} and 0.01 MeV/fm^{3} <= P_{t} <= 0.26 MeV/fm^{3}, respectively, in both the dynamical and thermodynamical approaches. We have further found that the widely used parabolic approximation to the equation of state of asymmetric nuclear matter gives significantly higher values of core-crust transition density and pressure, especially for stiff symmetry energies. With these newly determined transition density and pressure, we have obtained an improved relation between the mass and radius of neutron stars based on the observed minimum crustal fraction of the total moment of inertia for Vela pulsar.
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arxiv:0911.5470
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In this paper, we study the hyperbolic geometry of noncommutative balls generated by the joint operator radius $\omega_\rho$, $\rho\in (0,\infty]$, for $n$-tuples of bounded linear operators on a Hilbert space. In particular, $\omega_1$ is the operator norm, $\omega_2$ is the joint numerical radius, and $\omega_\infty$ is the joint spectral radius. We provide mapping theorems, von Neumann inequalities, and Schwarz type lemmas for free holomorphic functions on noncommutative balls, with respect to the hyperbolic metric $\delta_\rho$, the Carath\' eodory metric $d_K$, and the joint operator radius $\omega_\rho$.
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arxiv:0911.5489
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We present near-infrared imaging and spectroscopic high spatial resolution observations of the SMC region N88 containing the bright, excited, extincted and compact H II region N88A of size ~ 1 pc. To investigate its stellar content and reddening, N88 was observed using spectroscopy and imagery in the JHKs- and L'-band at a spatial resolution of ~ 0.1-0.3", using the VLT UT4 equipped with the NAOS adaptive optics system. In order to attempt to establish if the origin of the infra-red (IR) excess is due to bright nebulosity, circumstellar material and/or local dust, we used Ks vs J-K colour-magnitude (CM) and JHK colour-colour (CC) diagrams, as well as L' imagery.Our IR-data reveal in the N88 area an IR-excess fraction of geq 30 per cent of the detected stars,as well as an unprecedently detailed morphology of N88A. It consists of an embedded cluster of ~3.5" (~ 1 pc) in diameter, of at least thirteen resolved stars superposed with an unusual bright continuum centered on a very bright star. The four brightest stars in this cluster lie red-ward of H-K geq 0.45 mag, and could be classified as young stellar object (YSO) candidates. Four other probable YSO candidates are also detected in N88 along a south-north bow-shaped thin H2 filament at ~ 7" east of the young central bright star. At 0.2" east of this star, a heavily embedded core is detected that could be a massive class I protostar candidate. The 2.12 mu H2 image of N88A resembles a shell of diameter ~ 3" ~ 0.9 pc) centered on the bright star. The line ratios of H2 2-1 S(1) and 1-0 S(0) relative to 1-0 S(1), as well as the presence of high v lines, are indicative of photodissociation regions, rather than shocks.
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arxiv:0911.5490
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We use exact numerical diagonalization in the search of fractional quantum Hall states with non-Abelian quasiparticle statistics. For the (most promising) states in a partially filled second Landau level, the search is narrowed to the range of filling factors $7/3 <\nu_e<8/3$. In this range, the analysis of energy spectra and correlation functions, calculated including finite width and Landau level mixing, supports the prominent non-Abelian candidates at $\nu_e=5/2$ (paired Moore--Read "pfafian" state) and 12/5 (clustered Read--Rezayi "parafermion" state). Outside of this range, the noninteracting composite fermion model with four attached flux quanta is validated, yielding the family of quantum liquids with fractional, but Abelian statistics. The borderline $\nu_e=7/3$ state is shown to be adiabatically connected to the Laughlin liquid, but its short-range correlations are significantly different.
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arxiv:0911.5500
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In the present paper we give an explicit formula which allows us immediately to describe a unique Gauss circuit on a framed 4-valent graph (a graph with a structure of opposite edges) from an arbitrary Euler tour on the graph whenever the Gauss circuit exists. This formula only depends on the adjacency matrix of an Euler tour and also tells us whether there exists a Gauss tour on a framed 4-valent graph or not. It turns out that the results are also valid for all symmetric matrices (not just realisable by a chord diagram).
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arxiv:0911.5504
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In this paper, we analyze the quantum phases of multiple component Bose-Hubbard model in optical superlattices, using a mean-field method, the decoupling approximation. We find that the phase diagrams exhibit complected patterns and regions with various Charge Density Wave (CDW) for both one- and two- component cases. We also analyze the effective spin dynamics for the two-component case in strong-coupling region at unit filling, and show the possible existence of a Spin Density Wave (SDW) order.
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arxiv:0911.5536
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We report an indication (3.22 sigma) of ~ 1860 Hz quasi-periodic oscillations from a neutron star low-mass X-ray binary 4U 1636-536. If confirmed, this will be by far the highest frequency feature observed from an accreting neutron star system, and hence could be very useful to understand such systems. This plausible timing feature was observed simultaneously with lower (~ 585 Hz) and upper (~ 904 Hz) kilohertz quasi-periodic oscillations. The two kilohertz quasi-periodic oscillation frequencies had the ratio of ~ 1.5, and the frequency of the alleged ~ 1860 Hz feature was close to the triple and the double of these frequencies. This can be useful to constrain the models of all the three features. In particular, the ~ 1860 Hz feature could be (1) from a new and heretofore unknown class of quasi-periodic oscillations, or (2) the first observed overtone of lower or upper kilohertz quasi-periodic oscillations. Finally we note that, although the relatively low significance of the ~ 1860 Hz feature argues for caution, even a 3.22 sigma feature at such a uniquely high frequency should be interesting enough to spur a systematic search in the archival data, as well as to scientifically motivate sufficiently large timing instruments for the next generation X-ray missions.
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arxiv:0911.5574
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A new structural model of Au induced Si(553) surface is proposed. The model accounts for recently experimentally found value of the Au coverage, i.e. 0.48 monolayer, which suggests formation of two gold chains on each Si(553) terrace. The resulting structural model, like the models of other vicinal Si surfaces, features the honey-comb chain, but there is no buckling at step edge, which is observed on Si(335)-Au and Si(557)-Au surfaces. The present model is more stable than the models with single Au chain only, and agrees very well with existing experimental data. In particular, calculated band structure, featuring two metallic bands coming from hybridization of the gold in both chains with neighboring Si atoms, perfectly matches the photoemission data. Moreover, theoretical scanning tunneling microscopy topography remains in excellent agreement with the experiment.
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arxiv:0911.5576
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The general solution to the reflection equation associated with the jordanian deformation of the SL(2) invariant Yang R-matrix is found. The same K-matrix is obtained by the special scaling limit of the XXZ-model with general boundary conditions. The Hamiltonian with the boundary terms is explicitly derived according to the Sklyanin formalism. We discuss the structure of the spectrum of the deformed XXX-model and its dependence on the boundary conditions.
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arxiv:0911.5592
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Characterizing the surfaces of rocky exoplanets via the scattered light will be an essential challenge to investigate the existence of life on habitable exoplanets. We present a simple reconstruction method for fractional areas of different surface types from photometric variations, or colors, of a second Earth. We create mock light curves for Earth without clouds using empirical data. Then these light curves are fitted to the isotropic scattering model consisting of 4 surface types: ocean, soil, snow and vegetation. In an idealized situation where the photometric errors are only photon shot noise, we are able to reproduce the fractional areas of those components fairly well. We may be even able to detect a signature of vegetation from the distinct feature of photosynthesis on the Earth, known as the red edge. In our reconstruction method, Rayleigh scattering due to the atmosphere has an important effect, and for terrestrial exoplanets with atmosphere similar to our Earth, it is possible to estimate the presence of oceans and an atmosphere simultaneously.
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arxiv:0911.5621
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We grew the single crystal of stoichiometric Tm5Si2.0Ge2.0 using a Bridgeman method and performed XRD, EDS, magnetization, ac and dc magnetic susceptibilities, specific heat, electrical resistivity and XPS experiments. It crystallizes in orthorhombic Sm5Ge4-type structure. The mean valence of Tm ions in Tm5Si2.0Ge2.0 is almost trivalent. The 4f states is split by the crystalline electric field. The ground state exhibits the long range antiferromagnetic order with the ferromagnetically coupled magnetic moments in the ac plane below 8.01 K, while the exited states exhibit the reduction of magnetic moment and magnetic entropy and -log T-behaviors observed in Kondo materials.
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arxiv:0911.5640
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The study of quasi-K\"ahler Chern-flat almost Hermitian manifolds is strictly related to the study of anti-bi-invariant almost complex Lie algebras. In the present paper we show that quasi-K\"ahler Chern-flat almost Hermitian structures on compact manifolds are in correspondence to complex parallelisable Hermitian structures satisfying the second Gray identity. From an algebraic point of view this correspondence reads as a natural correspondence between anti-bi-invariant almost complex structures on Lie algebras to bi-invariant complex structures. Some natural algebraic problems are approached and some exotic examples are carefully described.
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arxiv:0911.5655
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The hadron-quark phase transition in the interior of compact stars is investigated, when the transition proceeds through a mixed phase. The hadronic phase is described in the framework of relativistic mean-field theory, when also the scalar-isovector delta-meson mean-field is taken into account. The changes of the parameters of phase transition caused by the presence of delta-meson field are explored. The results of calculation of structure of the mixed phase (Glendenning construction) are compared with the results of usual first-order phase transition (Maxwell construction).
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arxiv:0912.0018
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We create a model for recovering the intrinsic, absorption-corrected surface brightness distribution of a galaxy and apply the model to the M31. We construct a galactic model as a superposition of axially symmetric stellar components and a dust disc to analyse the intrinsic absorption efects. Dust column density is assumed to be proportional to the far-infrared flux of the galaxy. Along each line of sight, the observed far-infrared spectral energy distribution is approximated with modified black body functions considering dust components with different temperatures, allowing to determine the temperatures and relative column densities of the dust components. We apply the model to the nearby galaxy M31 using the Spitzer Space Telescope far-infrared observations for mapping dust distribution and temperature. A warm and a cold dust component are distinguished. The temperature of the warm dust in M31 varies between 56 and 60 K and is highest in the spiral arms; the temperature of the cold component is mostly 15-19 K and rises up to about 25 K at the centre of the galaxy. The intensity-weighted mean temperature of the dust decreases from T ~32 K at the centre to T ~20 K at R ~7 kpc and outwards. We also calculate the intrinsic UBVRIL surface brightness distributions and the spatial luminosity distribution. The intrinsic dust extinction in the V-colour rises from 0.25 mag at the centre to 0.4-0.5 mag at R = 6-13 kpc and decreases smoothly thereafter. The calculated total extinction-corrected luminosity of M31 is L_B = (3.64 pm 0.15) 10^10L_sun, corresponding to an absolute luminosity M_B = (-20.89 pm 0.04) mag. Of the total B-luminosity, 20% (0.24 mag) is obscured from us by the dust inside M31. The intrinsic shape of the bulge is slightly prolate in our best-fit model.
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arxiv:0912.0124
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Using a geometric averaging procedure applied to a non-affine linear connection, we prove that for a narrow one particle distribution function and in the ultra-relativistic limit, a bunch of point charged particles can be described by a Charged Cold Fluid Model, without additional hypothesis on the moments.
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arxiv:0912.0183
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This paper is concerned with solutions to a one dimensional linear diffusion equation and their relation to some problems in stochastic control theory. A stochastic variational formula is obtained for the logarithm of the solution to the diffusion equation, with terminal data which is the characteristic function of a set. In this case the terminal data for the control problem is singular, and hence standard theory does not apply. The variational formula is used to prove convergence in the zero noise limit of the cost function for the stochastic control problem and its first derivatives, to the corresponding quantities for a classical control problem.
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arxiv:0912.0185
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In this article, we provide an application of hypergeometric evaluation identities, including a strange valuation of Gosper, to prove several supercongruences related to special valuations of truncated hypergeometric series. In particular, we prove a conjecture of van Hamme.
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arxiv:0912.0197
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Hermann Schwarz, while studying complex analysis, introduced the geometric interpretation for the Poisson kernel in 1890. We shall see here that the geometric interpretation can be useful to develop a new approach to some old classical problems as well as to obtain several new results, mostly related to hyperbolic geometry. For example, we obtain One Radius Theorem saying that any two radial eigenfunctions of a Hyperbolic Laplacian assuming the value 1 at the origin can not assume any other common value within some interval [0, p], where the length of this interval depends only on the location of the eigenvalues on the complex plane and does not depend on the distance between them.
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arxiv:0912.0223
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We study the equation of state of neutron matter using a family of unitarity potentials all of which are constructed to have infinite $^1S_0$ scattering lengths $a_s$. For such system, a quantity of much interest is the ratio $\xi=E_0/E_0^{free}$ where $E_0$ is the true ground-state energy of the system, and $E_0^{free}$ is that for the non-interacting system. In the limit of $a_s\to \pm \infty$, often referred to as the unitary limit, this ratio is expected to approach a universal constant, namely $\xi\sim 0.44(1)$. In the present work we calculate this ratio $\xi$ using a family of hard-core square-well potentials whose $a_s$ can be exactly obtained, thus enabling us to have many potentials of different ranges and strengths, all with infinite $a_s$. We have also calculated $\xi$ using a unitarity CDBonn potential obtained by slightly scaling its meson parameters. The ratios $\xi$ given by these different unitarity potentials are all close to each other and also remarkably close to 0.44, suggesting that the above ratio $\xi$ is indifferent to the details of the underlying interactions as long as they have infinite scattering length. A sum-rule and scaling constraint for the renormalized low-momentum interaction in neutron matter at the unitary limit is discussed.
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arxiv:0912.0273
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Spatio-temporal models are widely used for inference in statistics and many applied areas. In such contexts interests are often in the fractal nature of the sample surfaces and in the rate of change of the spatial surface at a given location in a given direction. In this paper we apply the theory of Yaglom (1957) to construct a large class of space-time Gaussian models with stationary increments, establish bounds on the prediction errors and determine the smoothness properties and fractal properties of this class of Gaussian models. Our results can be applied directly to analyze the stationary space-time models introduced by Cressie and Huang (1999), Gneiting (2002) and Stein (2005), respectively.
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arxiv:0912.0285
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A long XMM-Newton observation of the mini-BAL QSO PG 1126-041 allowed us to detect a highly ionized phase of X-ray absorbing gas outflowing at v~15000 km/s. Physical implications are briefly discussed.
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arxiv:0912.0333
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We study the Brown-York quasilocal energy for regular black holes. We also express the identity that relates the difference of the Brown-York quasilocal energy and the Komar charge at the horizon to the total energy of the spacetime for static and spherically symmetric black hole solutions in a convenient way which permits us to understand why this identity is not satisfied when we consider nonlinear electrodynamics. However, we give a relation between quantities evaluated at the horizon and at infinity when nonlinear electrodynamics is considered. Similar relations are obtained for more general static and spherically symmetric black hole solutions which include solutions of dilaton gravity theories.
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arxiv:0912.0334
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The strange and antistrange quark distributions of the nucleon are less constrained by experimental data than the non-strange quark sea. The combination of light quark sea distributions, $\Delta(x)=\dbar(x)+\ubar(x)-s(x)-\sbar(x)$, originates mainly from non-perturbative processes and can be calculated using non-perturbative models of the nucleon. We have calculated $\Delta(x)$ using the meson cloud model, which, when combined with the relatively well known non-strange light antiquark distributions obtained from global analysis of available experimental data, enables us to make new estimates of the total strange sea distributions of the nucleon and the strange sea suppression factor.
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arxiv:0912.0351
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Ferroelectric domains were investigated using piezoresponse force microscopy in superlattices composed of multiferroic BiFeO3 and SrTiO3 layers. Compared to single BiFeO3 thin films, a reduction in the domains size and a suppression of the in-plane orientation of domains are observed in a superlattice of (BiFeO3)4(SrTiO3)8, suggesting a constrained ferroelectric domain orientation along the out-of-plane <001> direction. Such modification of domain size and orientation in BiFeO3-based heterostructures could play a vital role on engineering the domains and domain wall mediated functional properties necessary for device applications
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arxiv:0912.0358
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We present a new determination of the solar nitrogen abundance making use of 3D hydrodynamical modelling of the solar photosphere, which is more physically motivated than traditional static 1D models. We selected suitable atomic spectral lines, relying on equivalent width measurements already existing in the literature. For atmospheric modelling we used the co 5 bold 3D radiation hydrodynamics code. We investigated the influence of both deviations from local thermodynamic equilibrium (non-LTE effects) and photospheric inhomogeneities (granulation effects) on the resulting abundance. We also compared several atlases of solar flux and centre-disc intensity presently available. As a result of our analysis, the photospheric solar nitrogen abundance is A(N) = 7.86 +/- 0.12.
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arxiv:0912.0375
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We study the problem of the existence of filtered multiplicative bases of a restricted enveloping algebra u(L), where L is a finite-dimensional and p-nilpotent restricted Lie algebra over a field of positive characteristic p.
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arxiv:0912.0387
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The SIM Lite mission will undertake several planet surveys. One of them, the Deep Planet Survey, is designed to detect Earth-mass exoplanets in the habitable zones of nearby main sequence stars. A double blind study has been conducted to assess the capability of SIM to detect such small planets in a multi-planet system where several giant planets might be present. One of the tools which helped in deciding if the detected planets were actual was an orbit integrator using the publicly available HNBody code so that the orbit solutions could be analyzed in terms of temporal stability over many orbits. In this contribution, we describe the implementation of this integrator and analyze the different blind test solutions. We discuss also the usefulness of this method given that some planets might be not detected but still affect the overall stability of the system.
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arxiv:0912.0404
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Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in C^n whose differentials have one-dimensional family of resonances in the first m eigenvalues, m <= n (but more resonances are allowed for other eigenvalues). Next, we provide invariants and give conditions for the existence of basins of attraction. Finally, we give applications and examples demonstrating the sharpness of our conditions.
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arxiv:0912.0428
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We investigate spin dynamics of a two-component Bose-Einstein condensates with weak Josephson coupling. Analytical expressions of atom-number squeezing and bipartite entanglement are presented for atom-atom repulsive interactions. For attractive interactions, there is no number squeezing; however, the squeezing parameter is still useful to recognize the appearance of Schr\"{o}dinger's cat state.
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arxiv:0912.0444
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For noncommutative variables x,y an expansion of log(exp(x)exp(y)) in powers of x+y is obtained.Each term of the series is given by an infinite sum in powers of x-y.The series is represented by diagrams.
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arxiv:0912.0486
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There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a new approach to calculate averages over ratios of characteristic polynomials. At first sight paradoxically, one can coin our approach "supersymmetry without supersymmetry" because we use structures from supersymmetry without actually mapping onto superspaces. We address two kinds of integrals which cover a wide range of applications for random matrix ensembles. For probability densities factorizing in the eigenvalues we find determinantal structures in a unifying way. As a new application we derive an expression for the k-point correlation function of an arbitrary rotation invariant probability density over the Hermitian matrices in the presence of an external field.
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arxiv:0912.0654
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We study the generalized Hankel transform of the family of sequences satisfying the recurrence relation $a_{n+1} = \bigl(\alpha + \frac{\beta}{n+\gamma}\bigr) a_n$. We apply the obtained formula to several particular important sequences. Incidentally, we find a connection between some well known formulas that had previously arisen in literature in dissimilar settings. Additionally, given a non-zero sequence satisfying the above recurrence, we evaluate the Hankel transform of the sequence of its reciprocals.
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arxiv:0912.0684
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In this paper we analyze the Hilbert boundary-value problem of the theory of analytic functions for an $(N+1)$-connected circular domain. An exact series-form solution has already been derived for the case of continuous coefficients. Motivated by the study of the Hall effect in a multiply connected plate we extend these results by examining the case of discontinuous coefficients. The Hilbert problem maps into the Riemann-Hilbert problem for symmetric piece-wise meromorphic functions invariant with respect to a symmetric Schottky group. The solution to this problem is derived in terms of two analogues of the Cauchy kernel, quasiautomorphic and quasimultiplicative kernels. The former kernel is known for any symmetry Schottky group. We prove the existence theorem for the second, quasimultiplicative, kernel for any Schottky group (its series representation is known for the first class groups only). We also show that the use of an automorphic kernel requires the solution to the associated real analogue of the Jacobi inversion problem which can be bypassed if we employ the quasiautomorphic and quasimultiplicative kernels. We apply this theory to a model steady-state problem on the motion of charged electrons in a plate with $N+1$ circular holes with electrodes and dielectrics on the walls when the conductor is placed at right angle to the applied magnetic field.
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arxiv:0912.0696
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The low-energy singlet dynamics of the Quantum Heisenberg Antiferromagnet on the Kagome lattice is described by a quantitative Quantum Dimer Model. Using advanced numerical tools, the latter is shown to exhibit Valence Bond Crystal order with a large 36-site unit cell and hidden degeneracy between even and odd parities. Evidences are given that this groundstate lies in the vicinity of a $\mathbb{Z}_2$ dimer liquid region separated by a Quantum Critical Point. Implications regarding numerical analysis and experiments are discussed.
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arxiv:0912.0724
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Consider a planar, bounded, $m$-connected region $\Omega$, and let $\bord\Omega$ be its boundary. Let $\mathcal{T}$ be a cellular decomposition of $\Omega\cup\bord\Omega$, where each 2-cell is either a triangle or a quadrilateral. From these data and a conductance function we construct a canonical pair $(S,f)$ where $S$ is a genus $(m-1)$ singular flat surface tiled by rectangles and $f$ is an energy preserving mapping from ${\mathcal T}^{(1)}$ onto $S$.
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arxiv:0912.0740
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In this paper we demonstrate atomic-scale lithography on hydrogen terminated Ge(001. The lithographic patterns were obtained by selectively desorbing hydrogen atoms from a H resist layer adsorbed on a clean, atomically flat Ge(001) surface with a scanning tunneling microscope tip operating in ultra-high vacuum. The influence of the tip-to-sample bias on the lithographic process have been investigated. Lithographic patterns with feature-sizes from 200 nm to 1.8 nm have been achieved by varying the tip-to-sample bias. These results open up the possibility of a scanning-probe lithography approach to the fabrication of future atomic-scale devices in germanium.
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arxiv:0912.0754
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We present a systematic study of the influence of the encapsulation temperature on dopant confinement and electrical properties of Ge:P delta-doped layers. For increasing growth temperature we observe an enhancement of the electrical properties accompanied by an increased segregation of the phosphorous donors, resulting in a slight broadening of the delta-layer. We demonstrate that a step-flow growth achieved at 530 C provides the best compromise between high crystal quality and minimal dopant redistribution, with an electron mobility ~ 128 cm^2/Vs at a carrier density 1.3x10^14 cm-2, and a 4.2 K phase coherence length of ~ 180 nm.
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arxiv:0912.0755
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The spreading of a bilayer gold film propagating outward from gold clusters, which are pinned to clean Si(111), is imaged in real time by low energy electron microscopy. By monitoring the evolution of the boundary of the gold film at fixed temperature, a linear dependence of the spreading radius on time is found. The measured spreading velocities in the temperature range of 800 < T < 930 K varied from below 100 pm/s to 50 nm/s. We show that the spreading rate is limited by the reaction to form Au silicide, and the spreading velocity is likely regulated by the reconstruction of the gold silicide that occurs at the interface.
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arxiv:0912.0761
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Development of computer technology in chemistry, bring many application of chemistry. Not only the application to visualize the structure of molecule but also to molecular dynamics simulation. One of them is Gromacs. Gromacs is an example of molecular dynamics application developed by Groningen University. This application is a non-commercial and able to work in the operating system Linux. The main ability of Gromacs is to perform molecular dynamics simulation and minimization energy. In this paper, the author discusses about how to work Gromacs in molecular dynamics simulation of some protein. In the molecular dynamics simulation, Gromacs does not work alone. Gromacs interact with pymol and Grace. Pymol is an application to visualize molecule structure and Grace is an application in Linux to display graphs. Both applications will support analysis of molecular dynamics simulation.
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arxiv:0912.0893
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We study the stability of anyonic models on lattices to perturbations. We establish a cluster expansion for the energy of the perturbed models and use it to study the stability of the models to local perturbations. We show that the spectral gap is stable when the model is defined on a sphere, so that there is no ground state degeneracy. We then consider the toric code Hamiltonian on a torus with a class of abelian perturbations and show that it is stable when the torus directions are taken to infinity simultaneously, and is unstable when the thin torus limit is taken.
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arxiv:0912.0945
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We show that the behaviour of analytic eigenbranches of a Schr\"odinger operator depends on the way eigenfunctions concentrate in the phase space.
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arxiv:0912.1027
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The visible diameter of Sun oscilates with a period of 160 min. The same type of periodicity is also found in a huge number of solar radiation parameters. To elucidate the origin of these longitudinal radial pulsations we have used the equation for the equilibrium of inner layers which, after linearization, turned into the harmonic oscilator equation. The latter equation allows radial pulsations whose period and wave length were calculated using regresion expresions for the gas presure and density in various layers. The radial pulsations originate at the surface of active zone and propagate til the litosphere, where they undergo full inner reflection producing undersurface stationary waves with a period of 150-160 min.
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arxiv:0912.1211
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The accurate modeling of gravitational radiation is a key issue for gravitational wave astronomy. As simulation codes reach higher accuracy, systematic errors inherent in current numerical relativity wave-extraction methods become evident, and may lead to a wrong astrophysical interpretation of the data. In this paper, we give a detailed description of the Cauchy-characteristic extraction technique applied to binary black hole inspiral and merger evolutions to obtain gravitational waveforms that are defined unambiguously, that is, at future null infinity. By this method we remove finite-radius approximations and the need to extrapolate data from the near zone. Further, we demonstrate that the method is free of gauge effects and thus is affected only by numerical error. Various consistency checks reveal that energy and angular momentum are conserved to high precision and agree very well with extrapolated data. In addition, we revisit the computation of the gravitational recoil and find that finite radius extrapolation very well approximates the result at $\scri$. However, the (non-convergent) systematic differences to extrapolated data are of the same order of magnitude as the (convergent) discretisation error of the Cauchy evolution hence highlighting the need for correct wave-extraction.
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arxiv:0912.1285
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We perform a detailed phenomenological analysis of how well hadronization in nuclear environments can be described in terms of effective fragmentation functions. The medium modified fragmentation functions are assumed to factorize from the partonic scattering cross sections and evolve in the hard scale in the same way as the standard or vacuum fragmentation functions. Based on precise data on semi-inclusive deep-inelastic scattering off nuclei and hadron production in deuteron-gold collisions, we extract sets of effective fragmentation functions for pions and kaons at NLO accuracy. The obtained sets provide a rather accurate description of the kinematical dependence of the analyzed cross sections and are found to differ significantly from standard fragmentation functions both in shape and magnitude. Our results support the notion of factorization and universality in the studied nuclear environments, at least in an effective way and within the precision of the available data.
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arxiv:0912.1311
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We consider large deviations for nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on $\mathbb{Z}^d$. There exist variational formulae for the quenched and averaged rate functions $I_q$ and $I_a$, obtained by Rosenbluth and Varadhan, respectively. $I_q$ and $I_a$ are not identically equal. However, when $d\geq4$ and the walk satisfies the so-called (T) condition of Sznitman, they have been previously shown to be equal on an open set $\mathcal{A}_{\mathit {eq}}$. For every $\xi\in\mathcal{A}_{\mathit {eq}}$, we prove the existence of a positive solution to a Laplace-like equation involving $\xi$ and the original transition kernel of the walk. We then use this solution to define a new transition kernel via the h-transform technique of Doob. This new kernel corresponds to the unique minimizer of Varadhan's variational formula at $\xi$. It also corresponds to the unique minimizer of Rosenbluth's variational formula, provided that the latter is slightly modified.
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arxiv:0912.1429
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Let S be a finite subset of a field. For multivariate polynomials the generalized Schwartz-Zippel bound [2], [4] estimates the number of zeros over Sx...xS counted with multiplicity. It does this in terms of the total degree, the number of variables and |S|. In the present work we take into account what is the leading monomial. This allows us to consider more general point ensembles and most importantly it allows us to produce much more detailed information about the number of zeros of multiplicity r than can be deduced from the generalized Schwartz-Zippel bound. We present both upper and lower bounds.
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arxiv:0912.1436
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Absorption and emission in inorganic bipolar solar cells based on low dimensional structures exhibiting the effects of quantum confinement is investigated in the framework of a comprehensive microscopic theory of the optical and electronic degrees of freedom of the photovoltaic system. In a quantum-statistical treatment based on non-equilibrium Green's functions, the optical transition rates are related to the conservation of electronic currents, providing a quantum version of the balance equations describing the operation of a photovoltaic device. The generalized Planck law used for the determination of emission from an excited semiconductor in quasi-equilibrium is replaced by an expression of extended validity, where no assumptions on the distribution of electrons and photons are made. The theory is illustrated by the numerical simulation of single quantum well diodes at the radiative limit.
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arxiv:0912.1450
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The path packing problem is stated finding the maximum number of edge-disjoint paths between predefined pairs of nodes in an undirected multigraph. Such a multigraph together with predefined node pairs is often called a network.
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arxiv:0912.1452
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In this paper we show that there are "E_0 many" orbit inequivalent free actions of the free groups F_n, $2\leq n\leq\infty$, by measure preserving transformations on a standard Borel probability space. In particular, there are uncountably many such actions.
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arxiv:0912.1506
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QCD_{AS}, a variant of large N_c QCD in which quarks transform under the color two-index antisymmetric representation, reduces to standard QCD at N_c = 3 and provides an alternative to the usual large N_c extrapolation that uses fundamental representation quarks. Previous strong plausibility arguments assert that the QCD_{AS} baryon mass scales as N_c^2; however, the complicated combinatoric problem associated with quarks carrying two color indices impeded a complete demonstration. We develop a diagrammatic technique to solve this problem. The key ingredient is the introduction of an effective multi-gluon vertex: a "traffic circle" or "roundabout" diagram. We show that arbitrarily complicated diagrams can be reduced to simple ones with the same leading N_c scaling using this device, and that the leading contribution to baryon mass does, in fact, scale as N_c^2.
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arxiv:0912.1566
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The investigation of the endpoint region of the tritium beta decay spectrum is still the most sensitive direct method to determine the neutrino mass scale. In the nineties and the beginning of this century the tritium beta decay experiments at Mainz and Troitsk have reached a sensitivity on the neutrino mass of 2 eV/c^2 . They were using a new type of high-resolution spectrometer with large sensitivity, the MAC-E-Filter, and were studying the systematics in detail. Currently, the KATRIN experiment is being set up at Forschungszentrum Karlsruhe, Germany. KATRIN will improve the neutrino mass sensitivity by one order of magnitude down to 0.2 eV/c^2, sufficient to cover the degenerate neutrino mass scenarios and the cosmologically relevant neutrino mass range.
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arxiv:0912.1619
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In this paper is extended the original theorem by Fueter-Sce (assigning an $\mathbb R_{0,m}$-valued monogenic function to a $\mathbb C$-valued holomorphic function) to the higher order case. We use this result to prove Fueter's theorem with an extra monogenic factor $P_k(x_0,\underline x)$.
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arxiv:0912.1635
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The Darboux transformation on matrix solutions to the generalized coupled dispersionless integrable system based on some non-abelian Lie group, is studied and the solutions are shown to be expressed in terms of quasideterminants. As an explicit example, the Darboux transformation on scalar solutions to the system based on the Lie group SU(2) is discussed in detail and the solutions are shown to be expressed as ratios of determinants.
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arxiv:0912.1671
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Recent experiments on ultracold Bose gases in two dimensions have provided evidence for the existence of the Berezinskii-Kosterlitz-Thouless (BKT) phase via analysis of the interference between two independent systems. In this work we study the two-dimensional quantum degenerate Bose gas at finite temperature using the projected Gross-Pitaevskii equation classical field method. While this describes the highly occupied modes of the gas below a momentum cutoff, we have developed a method to incorporate the higher momentum states in our model. We concentrate on finite-sized homogeneous systems in order to simplify the analysis of the vortex pairing. We determine the dependence of the condensate fraction on temperature and compare this to the calculated superfluid fraction. By measuring the first order correlation function we determine the boundary of the Bose-Einstein condensate and BKT phases, and find it is consistent with the superfluid fraction decreasing to zero. We reveal the characteristic unbinding of vortex pairs above the BKT transition via a coarse-graining procedure. Finally, we model the procedure used in experiments to infer system correlations [Hadzibabic et al., Nature 441, 1118 (2006)], and quantify its level of agreement with directly calculated in situ correlation functions.
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arxiv:0912.1675
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This paper builds on our earlier proposal for construction of a positive inner product for pseudo-Hermitian Hamiltonians and we give several examples to clarify our method. We show through the example of the harmonic oscillator how our construction applies equally well to Hermitian Hamiltonians which form a subset of pseudo-Hermitian systems. For finite dimensional pseudo-Hermitian matrix Hamiltonians we construct the positive inner product (in the case of $2\times 2$ matrices for both real as well as complex eigenvalues). When the quantum mechanical system cannot be diagonalized exactly, our construction can be carried out perturbatively and we develop the general formalism for such a perturbative calculation systematically (for real eigenvalues). We illustrate how this general formalism works out in practice by calculating the inner product for a couple of ${\cal PT}$ symmetric quantum mechanical theories.
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arxiv:0912.1678
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The magnetic field of the classical T Tauri star V2129 Oph can be modeled approximately by superposing slightly tilted dipole and octupole moments, with polar magnetic field strengths of 0.35kG and 1.2kG respectively (Donati et al. 2007). Here we construct a numerical model of V2129 Oph incorporating this result and simulate accretion onto the star. Simulations show that the disk is truncated by the dipole component and matter flows towards the star in two funnel streams. Closer to the star, the flow is redirected by the octupolar component, with some of the matter flowing towards the high-latitude poles, and the rest into the octupolar belts. The shape and position of the spots differ from those in a pure dipole case, where crescent-shaped spots are observed at the intermediate latitudes. Simulations show that if the disk is truncated at the distance of 6.2 R_* which is comparable with the co-rotation radius, 6.8 R_*, then the high-latitude polar spots dominate, but the accretion rate obtained from the simulations is about an order of magnitude lower than the observed one. The accretion rate matches the observed one if the disk is disrupted much closer to the star, at 3.4 R_*. However, the octupolar belt spots strongly dominate. Better match has been obtained in experiments with a dipole field twice as strong. The torque on the star from the disk-magnetosphere interaction is small, and the time-scale of spin evolution, 2 x10^7-10^9 years is longer than the 2x10^6 years age of V2129 Oph. The external magnetic flux of the star is strongly influenced by the disk: the field lines connecting the disk and the star inflate and form magnetic towers above and below the disk. The potential (vacuum) approximation is still valid inside the Alfv\'en (magnetospheric) surface where the magnetic stress dominates over the matter stress.
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arxiv:0912.1681
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