Lie 2-Bialgebras

In this paper, we study Lie 2-bialgebras, paying special attention to coboundary ones, with the help of the cohomology theory of L _∞-algebras with coefficients in L _∞-modules. We construct examples of strict Lie 2-bialgebras from left-symmetric algebras (also known as pre-Lie algebras) and symplectic Lie algebras (also called quasi-Frobenius Lie algebras).     

Spectral and scattering theory for a class of strongly oscillating potentials

Following a recent investigation by Pearson [23] on scattering theory for some class of oscillating potentials, we consider the Schrödinger operator inL ²(IR ⁿ ) given by:H =-e ^?U?·e ^2U ?e ^?U +e ^?2U (F + (?·Q)). HereU andF are real functions ofx, andQ is a IR ⁿ -valued function ofx, such that:

1. U is bounded, and the local singularities ofF andQ ² are controlled in a suitable sense by the kinetic energy,
2. U, Q, andF tend to zero at infinity faster than ‖x‖^?1. We defineH by a method of quadratic forms and derive the usual results of scattering theory, namely: the absolutely continuous spectrum is [0, ∞) and the singular continuous spectrum is empty, the wave operators exist and are asymptotically complete. This enlarges the class of already studied strongly oscillating potentials that give rise to the scattering and spectral properties mentioned above.

     

Raman scattering by zigzag fluoropolymer molecules

The Raman spectra of ultrafine powders consisting of F(CF₂)_nF fluoropolymer zigzag molecules treated as a one-dimensional nanocrystal are investigated. These spectra are compared with the Raman spectra of C_nF_2n+1Br compounds (n=6–10 and 14) and fluoroplastics. It is found that the frequencies of optical vibrations of F(CF₂)_nF fluoropolymer molecules are shifted by more than 10 cm^?1 with respect to the relevant frequencies of C₆F₁₃Br molecules. The length of nanoparticles comprising an organofluoric ultrafine powder is estimated to be L=2–2.5 nm. This estimate is obtained from the measured frequency shifts in terms of the vibrational theory for a crystalline diatomic chain of finite length.     

Electrochemical properties of Li[CnF2n+1BF3] as electrolyte salts for lithium-ion cells

The fundamental electrochemical properties of lithium perfluoroalkyltrifluoroborates Li[C_nF_2n+1BF₃] (n = 1∼4) were evaluated as electrolyte salts for lithium-ion battery in comparison with LiBF₄ and LiPF₆. Li[C_nF_2n+1BF₃] showed higher electrolytic conductivities than LiBF₄ in aprotic solvents. In these series, the conductivities decreased with the perfluoroalkyl group being longer, and Li[C₂F₅BF₃] exhibited a comparable conductivity to LiPF₆. The relationship between the conductivity and the anion size showed that the anion with a moderate size is in favor of obtaining high conductivities. The limiting oxidation potentials determined by linear sweep voltammetry demonstrated that Li[C_nF_2n+1BF₃] were less resistant against oxidation than LiBF₄. The HOMO energies and ionization energies of [C_nF_2n+1BF₃]⁻ calculated by ab initio molecular orbital (MO) theory and density functional theory (DFT) supported this observation, however, there was no accuracy to explain the effect of the chain length of perfluoroalkyl groups on the limiting oxidation potentials. The cell performances of a LiC₆/Li_0.5CoO₂ cell using Li[C₂F₅BF₃] were comparable to those using LiPF₆ at room temperature, however, it deteriorated at elevated temperature due to the reaction on the cathode.     

Coherent-anomaly method in self-avoiding walk problems

Self-avoiding walk (SAW), being a nonequilibrium cooperative phenomenon, is investigated with a finite-order-restricted-walk (finite-ORW or FORW) coherent-anomaly method (CAM). The coefficient β_1r in the asymptotic form C_nr≅ β_1r λⁿ_1r for the total number C_nr of r- ORW's with respect to the step number n is investigated for the first time. An asymptotic form for SAW's is thus obtained form the series of FORW approximants, C_nr≅ br^gμⁿ(1 + a/r)ⁿ, as the envelope curve C_n≅b(ae/g)^gμⁿn^g. Numerical results are given by C_n≅1.424n^0.27884.1507ⁿ and C_n≅1.179n^0.158710.005ⁿ for the plane triangular lattice and f.c.c. lattice, respectively. A good coincidence of the total numbers estimated from the above simple formulae with exact enumerations for finite-step SAW's implies that the essential nature of SAW (non-Markov process) can be understood from FORW (Markov process) in the CAM framework.     

Euclidean nonlinear classical field equations with unique vacuum

We study the real, Euclidean, classical field equation $$(\mu ^2 + \Delta )\varphi + \lambda F(\varphi ) = f,\mu ^2 > 0$$ where φ: ? ^d →? is suitably small at infinity. We study existence and regularity assuming that λ≧0,F∈C ^∞(?), andaF(a)≧0?a∈∝. These hypotheses allow strongly nonlinearF and nonunique solutions forf≠0. WhenF′≧0, we prove uniqueness, various contractivity properties, analytic dependence on the coupling constant λ, and differentiability in the external sourcef. For applications in the loop expansion in quantum field theory, it is useful to know that φ is in the Schwartz classL wheneverf is, and we provide a proof of this fact. The technical innovations of the problem lie in treating the noncompactness of R ^d , the strong nonlinearity ofF, and the polynomial weights in the seminorms definingL.     

Chemical effect on FKα X-ray satellites produced by 6 MeV/amu p,α and C4+

The excitation conditions where both direct Coulomb and shake-off processes concur to multiply ionize fluorineK andL shells were adopted in this experiment; 6MeV/amu p,α and C⁴⁺ impacts. The ion induced FKα satellites, measured for a series of F bearing compounds, showed significant chemical effects on their intensity distributions. Such effects are explained well with an FL-vacancy rearrangement model. Without any theoretical prediction, rearrangement probabilities or widths of FL shells were estimated by use of a reference compound with high ionicity, i.e. NaF. A linear relationship between FL widths and covalencies of compounds was found for a wide variety of fluorides. For the same compounds, the absolute values of the FL-vacancy rearrangement probabilities or the FL-shell widths obtained here were the same as those estimated from pure direct Coulomb and pure shake-off excitations, respectively. Other models than theL-vacancy rearrangement's are also discussed and eliminated.     

Radiation transfer in an anisotropically scattering plane-parallel medium with space-dependent albedo ω(x)

A method of analysis is presented for solving radiation-transfer problems involving space-dependent albedo ω(x) for an absorbing, emitting and anisotropically scattering plane-parallel medium with reflecting boundaries. The albedo is represented in terms of Legendre polynomials in the form ω(x) = Σ^R_r=0D_rP_r(x/L), where x is the optical variable, L is the half optical-thickness of the slab, P_r(x/L) are the Legendre polynomials and D_r are known expansion coefficients. The effects of spatial variation of albedo on the reflectivity and transmissivity of a medium having a slab geometry are examined for the cases of both forward and backward anisotropic scattering over a wide range of system variables. The effects of ω(x) on the angular distribution of radiation are also shown for some representative cases.     

Molecular field theory analysis of R2Fe17C (R=PR,Nd, Gd,Tb, Dy,Ho, Er)

The temperature dependence of magnetization is analysed for R₂Fe₁₇C via the two-sublattice molecular field theory. The molecular field coefficients n_FF, n_RF and n_RR are obtained, by which T_C was calculated. Using the least-squares method, the fitted-form of H_R(T) varying with temperature for each compound is presented. The results are analysed. In addition, the parameters F=M_Fe²(0)n_FF/T_C was calculated for each R₂Fe₁₇C. By F, some phenomena different from the normal view were explained.     

Does a generic connection depend continuously on its curvature?

For a principal bundle with semi-simple structure group over a smooth four-dimensional base manifold, the set of connections (gauge potentials)A which are uniquely determined by their curvature (field or field strength)F is generic in the set of all potentials, endowed with the WhitneyC ^∞ topology. However, the operator taking each such fieldF to its potentialA is not continuous. Partial negative results are given concerning the existence of a smaller generic set on which this operator is continuous.     

Lifting classes of principal bundles

Given a principal G-bundle P over X, we define a particularly suitable equivalence relation between liftings of P with respect to a group morphism σ:M→G. Supposing that σ has a central kernel C, we obtain a free operation of H¹(X$\text{C}$) (with coefficients in the sheaf of C-valued functions) on the set of lifting classes of P, which is natural under change of groups and base spaces. It is simply transitive, if in addition σ is an epimorphism; otherwise we classify its orbits by sections in the associated bundle P × _G(G/σM).For $\text{C=}\text{Z}{}_{\mathrm{n}}$ we relate the lifting classes to similar classes of n-th roots of associated line bundles. In the differentiable case and for an epimorphism σ with discrete kernel, there is a natural lifting of partial principal connections in each of these lifting classes. Finally, we indicate some applications to geometric quantization.     

The electrooptic effect in NH4IO3

The static electrooptic coefficients of NH₄IO₃ at room temperature are r₄₃ = 4.9, r₆₁ = 1.0, r₁₂n²₁ ? r₃₂n³₃ = 59.6, r₂₂n³₂ ? r₃₂n³₃ = 116.8 [ X 10^-12m/V]. The electrooptic effect depends on temperature and shows two ph ase transitions at 82.5°C and near 120°C.     

Optimal bounds for the pion form factor from analyticity and experimental data

Optimal bounds for the pion electromagnetic form factor F(t) below threshold and on the pion mean-square charge radius 〈r_π²〉 = 6F'(0) are derived. Use is made of analyticity arguments and of experimental data on F(t) from e⁺e^? → π⁺π^? as well as e^?p → e^?nπ⁺. The method accounts in an approximate way for the statistical errors of the experimental information. Numerical results for F(t) are calculated for the CEA as well as the DESY electroproduction data.     

Formation of binary clusters by molecular ion irradiation

In the present study, we have observed silicon–carbon cluster ions (Si_nC_m⁺) emitted from a Si(1 0 0) surface under irradiation of reactive molecular ions, such as C₆F₅⁺, at 4 keV, 1 μA/cm². The cluster Si_n up to n=8 and “binary” cluster Si_nC up to n=6 are clearly detected for the C₆F₅⁺ irradiation. Stoichiometric clusters (Si_nC_m n=m) except SiC⁺ and other binary clusters which contain more than two carbon atoms (m≥2) were scarcely observed. The observed clusters show a yield alternation between odd and even n. The intensities of Si₄, Si₆ and Si₅C clusters are relatively higher than those of the neighboring clusters. In the case of Si₅C, it is considered that doped carbon atom acts as silicon atom. These results imply that the recombination through the nascent cluster emission and subsequent decomposition takes place during the cluster formation.     

Compatibility with Cap-Products in Tsygan’s Formality and Homological Duflo Isomorphism

In this paper we prove, with details and in full generality, that the isomorphism induced on tangent homology by the Shoikhet-Tsygan formality L _∞-quasi-isomorphism for Hochschild chains is compatible with cap-products. This is a homological analogue of the compatibility with cup-products of the isomorphism induced on tangent cohomology by Kontsevich formality L _∞-quasi-isomorphism for Hochschild cochains. As in the cohomological situation our proof relies on a homotopy argument involving a variant of Kontsevich eye. In particular, we clarify the rôle played by the I-cube introduced in Calaque and Rossi (SIGMA 4, paper 060, 17 2008). Since we treat here the case of a most possibly general Maurer–Cartan element, not forced to be a bidifferential operator, we take this opportunity to recall the natural algebraic structures on the pair of Hochschild cochain and chain complexes of an A _∞-algebra. In particular we prove that they naturally inherit the structure of an A _∞-algebra with an A _∞-(bi)module.     

A theorem on the existence of dyon solutions

We prove the existence of finite energy dyon solutions to Yang-Mills-Higgs equations satisfying the Julia-Zee ansatz, and the generalization to SU(N) gauge groups. This rigorously establishes the existence of a model for the particles having electric and magnetic charge conjectured by Schwinger. We also prove that the solutions are real analytic on (0, ∞) and C^∞ at r = 0. To establish our result we prove a new abstract theorem that allows one to study singular constrained minimization problems without the introduction of Lagrange multipliers.     

Bounds on the Spectral Shift Function and the Density of States

We study spectra of Schrödinger operators on ? ^d . First we consider a pair of operators which differ by a compactly supported potential, as well as the corresponding semigroups. We prove almost exponential decay of the singular values μ _n of the difference of the semigroups as n→∞ and deduce bounds on the spectral shift function of the pair of operators. Thereafter we consider alloy type random Schrödinger operators. The single site potential u is assumed to be non-negative and of compact support. The distributions of the random coupling constants are assumed to be Hölder continuous. Based on the estimates for the spectral shift function, we prove a Wegner estimate which implies Hölder continuity of the integrated density of states.     

Collisional depolarization and redistribution of laser radiation in near resonance with a2 P 3/2↔2 S 1/2 transition

We have investigated experimentally and theoretically the spectral distribution and collisional depolarization of laser light near resonant to the Na transition 3² S _1/2?3² P _3/2 scattered from a Na/Ar mixture in a cell (n _Na≈4.0×10¹⁰cm^?3,n _Ar≈1.0×10¹⁷cm^?3). In particular, at excitation intensity of ≈3mW/mm² and bandwidth of <10 MHz, intensityI _F and linear polarization degreeP _F of theD ₂-fluorescence component of the scattered spectrum have been measured as functions of the laser detuningΔλ _L from theD ₂-resonance within two regions: 1) ¦Δλ _L ¦-Doppler-width; 2) 20≧¦Δλ _L ¦/Δλ _D ≧1. Within the first region the influence of hyperfine splitting as well as pumping of the hyperfine and Zeeman sublevels of 3² S _1/2 was studied in detail. Using an overall, total collision cross section for depolarization of 3² P _3/2 state atoms, calculations on the basis of the theory of redistribution reproduce qualitatively, but in a consistent manner, the experimental functionsI _F(Δλ_L) andP _F (Δλ _L ). The possibility to derive differential cross sections fromP _F (Δλ_L) is discussed.