Classical Hamiltonian perturbation theory without secular terms or small denominators

We consider perturbation theory in ? for the classical Hamiltonian H = H₀ + ?H₁, where H₀ gives rise to a known motion and ? is small. First we demonstrate how the usual secular terms and small denominators arise from a straightforward expansion in ? and argue that they are artifacts of the method. Then we present an alternative perturbation theory based on an analysis of the operator (s ? L)^?1, where s is a complex number and L is the Liouville operator corresponding to H. This perturbation series contains neither secular terms nor small denominators. In the case of almost multiply periodic systems we show, to lowest non-trivial order in ?, how our series reproduces the standard results both in the resonant and nonresonant regions — all in one analytic formula. As a final exercise we demonstrate that energy is conserved at order ?ⁿ⁺¹ when the accuracy of the theory is order ?ⁿ.     

Brownian motion on a manifold as a limit of Brownian motions with drift

Let ?ⁿ be n-dimensional Euclidean space and let M ? ?ⁿ be a smooth compact m-dimensional Riemannian manifold (without boundary) embedded in ?ⁿ. By a Brownian motion on M we mean a Markovian process whose transition semigroup is defined by the generator ?½Δ_M, where Δ_M stands for the Laplace-Beltrami operator on M (see, e.g., [2]). This note extends a series of papers in which a measure generated by a Brownian motion on M on the space of trajectories (with values in M) can be represented as the weak limit of measures on the space of trajectories in the ambient space ?ⁿ (see [7–10]). Namely, we claim that a sequence of diffusion processes on ?n which are Brownian motions with drift (in the direction of the manifold) with infinitely increasing modulus converges in distribution to a Brownian motion on the manifold.     

On the vacuum rearrangement in massless chromodynamics

It is shown that in the weak coupling limit the Bethe-Salpeter equation of massless chromodynamics admits a colourless tachyon solution when the number of quark multiplets n ? n_c, where for the colour group SU(N) the critical value n_c ≈ 0.14 N³/(N² ? 1). When n ? n_c, the vacuum rearrangement results in the gluons acquiring a mass; n > n_c all particles remain massless.     

The influence of PEO on the synthesis and electrochemical properties of VO2 and V3O7·nH2O nanobelts as a cathode for lithium battery

In this paper, we report the hydrothermal synthesis of VO₂, poly(ethylene oxide) (PEO)/VO₂,V₃O₇·nH₂O and PEO/V₃O₇·nH₂O nanobelts by using 1,2-propylene carbonate (1,2-PC (C₄H₆O₃)) and poly(ethylene glycol) (PEG) as templates, respectively. Structure and morphology of the samples were investigated by XRD, FTIR, SEM, and TEM. The vanadium oxide (VO₂) nanobeltcomposite show the initial specific capacity 152?mA?h?g^?1, whereas PEO/VO₂ shows 182?mA?h?g^?1. The pure V₃O₇·nH₂O nanobelts shows the initial specific capacity 192?mA?h?g^?1, while PEO/V₃O₇·nH₂O nanobelts show 297?mA?h?g^?1. It was found that PEO/VO₂ and PEO/V₃O₇·nH₂O nanocomposites show better cyclic performance and high discharge stability compared to pure vanadium oxide nanomaterials. The role of the polymeric PEO component of the hybrid material seems to be the stabilization and improvement of the specific capacity due to probable homogeneous distribution between the nanobelts. The TEM images indicate that PEO works as a surfactant to decrease the dimensions of nanobelts.     

Effect of different doped elements on visible light absorption and ultraviolet light emission on Er3+:Y3Al5O12

In this progress report, seven kinds of novel carefully designed and fabricated up-conversion luminescence agents, Er³⁺:Y₃Al₅O₁₂, Er³⁺:Yb_nY_3?nAl₅O₁₂, Er³⁺:Y₃B_aAl_5?aO₁₂, Er³⁺:Y₃Ga_bAl_5?bO₁₂, Er³⁺:Y₃Al₅N_xO_12?x, Er³⁺:Y₃Al₅F_yO_12?y and Er³⁺:Yb_nY_3?nB_aGa_bAl_5?a?bN_xF_yO_12?x?y, are successfully synthesized using sol–gel methods. After that, their corresponding photocatalysts, Er³⁺:Y₃Al₅O₁₂/TiO₂, Er³⁺:Yb_nY_3?nAl₅O₁₂/TiO₂, Er³⁺:Y₃B_aAl_5?aO₁₂/TiO₂, Er³⁺:Y₃Ga_bAl_5?bO₁₂/TiO₂, Er³⁺:Y₃Al₅N_xO_12?x/TiO₂, Er³⁺:Y₃Al₅F_yO_12?y/TiO₂ and Er³⁺:Yb_nY_3?nB_aGa_bAl_5?a?bN_xF_yO_12?x?y/TiO₂, are also prepared by sol–gel coating process. The obtained up-conversion luminescence agents and photocatalysts were characterized by using XRD, XPS, SEM, UV–vis and fluorescence spectrophotometer. Synchronously, several kinds of organic dyes are used to test their photocatalytic degradation using prepared photocatalysts. It indicates that the up-conversion luminescence ability of Er³⁺:Y₃Al₅O₁₂ can be improved obviously through doping of some elements. And then, the photocatalytic activity of TiO₂ is markedly enhanced by modified up-conversion luminescence agents which can transform much visible light into ultraviolet light.     

On the thermodynamic formalism for the gauss map

We study the generalized transfer operator ? _β f(z)= \(\sum\limits_{n = 1}^\infty {\left( {\frac{1}{{z + n}}} \right)^{2\beta } \times f\left( {1/\left( {z + n} \right)} \right)} \) of the Gauss mapTx=(1/x) mod 1 on the unit interval. This operator, which for β=1 is the familiar Perron-Frobenius operator ofT, can be defined for Re β>1/2 as a nuclear operator either on the Banach spaceA _∞(D) of holomorphic functions over a certain discD or on the Hilbert space ? _Reβ ⁽²⁾ (H _-1/2 of functions belonging to some Hardy class of functions over the half planeH _?1/2. The spectra of ? _β on the two spaces are identical. On the space ? _Reβ ⁽²⁾ (H _-1/2 ? _β is isomorphic to an integral operatorK _β with kernel the Bessel function \(\mathfrak{F}_{2\beta - 1} (2\sqrt {st} )\) and hence to some generalized Hankel transform. This shows that ? _β has real spectrum for real β>1/2. On the spaceA _∞(D) the operator ? _β can be analytically continued to the entire β-plane with simple poles atβ=β _k =(1-k)/2,k=0, 1, 2,..., and residue the rank 1 operatorN ^(k) f=1/2(1/K!)f ^(k)(0) . From this similar analyticity properties for the Fredholm determinant det (1-? _β ) of ? _β and hence also for Ruelle's zeta function follow. Another application is to the function \(\zeta _{\rm M} (\beta ) = \sum\limits_{n = 1}^\infty {\left[ n \right]^\beta } \) , where [n] denotes the irradional [n]=(n+(n ²+4)^1/2)/2.ζ _M (β) extends to a meromorphic function in the β-plane with the only poles at β=±1 both with residue 1.     

Light-Front Zero-Mode Issue for the Transition Form Factors Between Pseudoscalar and Vector Mesons

We study the light-front zero-mode contribution to the transition form factors (g, f, a _±, T _i ) (i = 1, 2, 3) for the exclusive semileptonic P → V ?ν _? and rare P → V ? ⁺?^? decays using a covariant fermion field theory model in (3+1) dimensions. While the zero-mode contribution in principle depends on the form of the vector meson vertex Γ ^μ  = γ ^μ ? (2k ? P _V ) ^μ /D, the six form factors (g, f, a ₊, T ₁, T ₂, T ₃) are found to be free from the zero mode if the denominator D contains the term proportional to the light-front longitudinal momentum fraction factor (1/x) ⁿ of the struck quark with the power n > 0. Although the form factor a _? is not free from the zero mode, the zero-mode contribution comes only either from the simple vertex Γ ^μ  = γ ^μ term or from the other term just with a constant D (i.e. n = 0). We identify the zero-mode operator that is convoluted with the initial- and final-state valence wave functions to generate the zero-mode contribution to a _?.     

Observation of nuclear rotational spectra in pion capture on 165Ho and 175Lu

In X-ray spectra of pionic atoms of ¹⁶⁵Ho and ¹⁷⁵Lu we observed nuclear γ-rays of Dy and Yb isotopes, respectively, arising from the pion capture reactions ¹⁶⁵Ho(π^?,xn^165?xDy¹, and ¹⁷⁵Lu(π^?xn^175? Yb¹, where x = 1, 3, 5, 7, 9, 11.     

Measurement of 232Th(n, γ) and 232Th({n}, {2n}) cross-sections at neutron energies of 13.5, 15.5 and 17.28?MeV using neutron activation techniques

The ²³²Th(n, ??) reaction cross-section at average neutron energies of 13.5, 15.5 and 17.28?MeV from the ⁷Li(p, n) reaction has been determined for the first time using activation and off-line ??-ray spectrometric technique. The ²³²Th(n, 2n) cross-section at 17.28?MeV neutron energy has also been determined using the same technique. The experimentally determined ²³²Th(n, ??) and ²³²Th(n, 2n) reaction cross-sections from the present work were compared with the evaluated data of ENDF/BVII and JENDL-4.0 and were found to be in good agreement. The present data, along with literature data in a wide range of neutron energies, were interpreted in terms of competition between ²³²Th(n, ??), (n, f), (n, nf) and (n, xn) reaction channels. The ²³²Th(n, ??) and ²³²Th(n, 2n) reaction cross-sections were also calculated theoretically using the TALYS 1.2 computer code and were found to be in good agreement with the experimental data from the present work but were slightly higher than the literature data at lower neutron energies.     

Conformally covariant nonlinear equations on tensor-spinors

We prove that to each conformally covariant equation on tensor-spinors on a Riemannian or pseudo-Riemannian manifold with spin structure one can add a nonlinear term without losing the property of conformal covariance. It follows in particular that, on a manifold of dimension n, the nonlinear Dirac equation, Pψ + λ|ψ|^1/(n?1)ψ = 0, where P is the Dirac operator and λ is a constant, is conformally covariant. This generalizes a result of Gürsey [1]. Some results of Ørsted [2], concerning a nonlinear equation associated with the Laplacian on function, and of Branson, concerning distinguished nonlinearities associated with his modified Laplacian on differential forms [3] are also derived as particular cases of this general result.     

An operatorially solved model of massless two-dimensional quantum chromodynamics

An operator solution is constructed in (1,1) dimensions to the massless quantum chromodynamics of n fermion quarks and n² ? 1 vector boson gluons with local colour SU(n) symmetry. The interacting quark field is a confined SU(n) Thirring field with zero Abelian coupling. The colour gluons are dependent Lie fields obeying the gluon-free fermionic current identity. Explicit local infinitesimal operator colour transformations (with an arbitrary coordinate-independent Lorentz vector coefficient defining the gauge) are given and the requirement of proper colour covariance linked to the vanishing of the coloured quark source currents and hence to the absence of coloured quark-composite states. The status of Noether's theorem is also clarified.     

Critical correlation function to order ϵ3

The zero-field, two-point correlation function of an n-vector system in d = 4 ? ?dimensions is calculated to order ?³ for T ? T_c, using a dispersion theory approach to the scaling function g(g²ξ²)     

Characteristics of molybdenum oxide and chromium oxide cathodes in primary and secondary organic electrolyte lithium batteries. Part II. Transport properties

Utilization and rate performance of metal chalcogenide host lattice cathodes depend on transport properties of phases Li_nMCh_x, i.e., on their electronic and Li⁺ conductivity. On the other hand, liquid phase Li⁺ diffusion in pores of the electrodes or rates of charge transfer and phase change reactions may also be limiting under certain conditions. For phases Li_nMO_x (M=Cr, Mo) and in particular for the model substance Li_nMoO₃ parameters controlling utilization and rate performance were followed during discharge and recharge, i,e., in dependence of composition and history. The main results can be summarized as below: Chemical diffusion coefficients D?_Li+in Li_nCrO_x and Li_nMoO₃ have their maxima close to n ca. 0.5 and drop sharply for n&>;1 - in the layered phase Li_nMoO₃, Li⁺ mobility is paralleled by the interplanar distance; D?_Li+ in discharged Li_nCrO_x and Li_nMoO₃ partly recovers during recharge, but never reaches the top values of the 1st discharge - this is related with irreversible structural disintegration of the host matrix; At the end of discharge (n ca. 1.5) a porous layer of a final discharge product is formed on Li_nCrO_x and Li_nMoO₃ particles. This layer is electronically insulating and Li⁺ transport through this layer is predominantly by liquid phase diffusion in the pores; The electrochemical intercalation of Li⁺ into Li_nCrO_x or Li_nMoO₃ is a 1st order reaction with respect to Li⁺ concentration in the electrolyte.     

Recent Progress in Ab-initio Four-Body Scattering Calculations

In the first part of the contribution, we discuss the results of a recent benchmark calculation of n ? ³H and p ? ³He phase-shifts below the trinucleon disintegration thresholds. Three different methods—Alt, Grassberger and Sandhas, Hyperspherical Harmonics, and Faddeev–Yakubovsky—have been used and their results are compared. For both n ? ³H and p ? ³He we observe a rather good agreement between the three different theoretical methods. In the second part of the contribution, we study the longitudinal asymmetry ${A_z^{n^3{\rm He}}}$ in the ³He(n, p)³H reaction in order to obtain information about the parity-violating components of the nucleon–nucleon interaction.     

Experimental Study of Photon Induced Reactions on 3He and 4He at Low Energies

Data are reported for the photodisintegration cross section of the reaction ³He(??, p)²H at ten energies between 7.0 and 16.0?MeV. Very preliminary data are presented for the reaction ⁴He(??, p)³H between 22.0 and 29.5?MeV in 0.5?MeV energy steps, and for the reaction ⁴He(??, n)³He at three energies around 28.0?MeV. High-pressure He/Xe gas scintillators served as target and detector. Our data are in better agreement with recent theoretical calculations than the majority of the existing data for all three reactions, but differ significantly from recent data taken with a mono-energetic photon beam and a time-projection chamber.     

The stark effect in the 6snf Rydberg series of barium

The polarizabilities of the barium 6snf ³ F ₂ levels with principal quantum numbern ranging from 11 to 40 have been measured in a high resolution laser-atomic-beam experiment. In Coulomb approximation the contributions to the polarizabilities of all known even-parity levels connected with the³ F ₂ levels via the electric dipole operator have been calculated. In this way information on the to a large extent unknown 6sng ³ G ₃ Rydberg series is extracted. The results support earlier observations of a perturbation of this series in betweenn = 18 and 19, but no evidence has been found for a perturbation nearn = 14.