Projective and affine connections on S and integrable systems

It is known that the Korteweg–de Vries (KdV) equation is a geodesic flow of an L² metric on the Bott–Virasoro group. This can also be interpreted as a flow on the space of projective connections on S¹. The space of differential operators Δ⁽ⁿ⁾=∂ⁿ+u₂∂ⁿ⁻²++u_n form the space of extended or generalized projective connections. If a projective connection is factorizable Δ⁽ⁿ⁾=(∂−((n+1)/2−1)p₁)(∂+(n−1)/2p_n) with respect to quasi primary fields p_i’s, then these fields satisfy ∑_i=1ⁿ((n+1)/2−i)p_i=0. In this paper we discuss the factorization of projective connection in terms of affine connections. It is shown that the Burgers equation and derivative non-linear Schrödinger (DNLS) equation or the Kaup–Newell equation is the Euler–Arnold flow on the space of affine connections.     

Predictions for the 4 GeV TJNAF inclusive electron scattering experiment and for FSI effects in EMC ratios

We express nuclear structure functions F_i^A as generalized convolutions of the structure function of a nucleon and of a nucleus, composed of point-nucleons. In computations of the latter we include final state interactions and results for F₂^A are compared with a few directly measured data on C and Fe. The above-mentioned F_i^A are primarily used for predictions of the TJNAF 89-008 inclusive scattering experiment of 4 GeV electrons on various targets. Those targets cover a broad angular, and correspondingly wide x, ² range, where the nucleon-inelastic part dominates large sections of the covered kinematics. The same model has been applied to the study of hitherto neglected final state interaction effects in the nuclear component in EMC ratios in the region 0.25 x 0.85.     

Saturation and BFKL dynamics in the HERA data at small-x

We show that the HERA data for the inclusive structure function F₂(x,Q²) for x10⁻² and 0.045Q²45 GeV² can be well described within the color dipole picture, with a simple analytic expression for the dipole–proton scattering amplitude, which is an approximate solution to the non-linear evolution equations in QCD. For dipole sizes less than the inverse saturation momentum 1/Q_s(x), the scattering amplitude is the solution to the BFKL equation in the vicinity of the saturation line. It exhibits geometric scaling and scaling violations by the diffusion term. For dipole sizes larger than 1/Q_s(x), the scattering amplitude saturates to one. The fit involves three parameters: the proton radius R, the value x₀ of x at which the saturation scale Q_s equals 1 GeV, and the logarithmic derivative of the saturation momentum λ. The value of λ extracted from the fit turns out to be consistent with a recent calculation using the next-to-leading order BFKL formalism.     

The deuteron A(Q) structure function and the neutron electric form factor

We have measured the deuteron A(Q²) structure function in the momentum transfer region between 1 and 18 fm⁻². The accuracy of the data ranges from 2 to 6%. These measurements allow a sensitive test of theoretical predictions. We find that meson-exchange currents and relativistic corrections significantly improve the agreement between experiment and theory. We investigate the sensitivity of A(Q²) to the nucleon-nucleon interaction and to the neutron electric form factor G_Eⁿ(Q²). Our analysis shows that G_Eⁿ(Q²) can be extracted from these data with a significantly improved accuracy. The model dependence of this analysis is discussed.     

General solutions of the Monge-Ampère equation in n-dimensional space

It is shown that the general solution of a homogeneous Monge-Ampère equation in n-dimensional space is closely connected with the exactly (but only implicitly) integrable system ∂ξ_j/∂x₀ + Σ_k=1ⁿ⁻¹ ξ_k ∂ξ_j/∂x_k = 0 Using the explicit form of solution of this system it is possible to construct the general solution of the Monge-Ampère equation.     

Defect structure of quenched γ-BICOVOX by combined X-ray and neutron powder diffraction

A detailed investigation of the defect structure of the Co doped BIMEVOX solid electrolyte, Bi₂V_{1 − x}Co_xO_{5.5 − 3x/2} (x = 0.1 and x = 0.2), quenched from high temperature, has been carried out using X-ray and neutron powder diffraction data measured at room temperature. The structure is built up from alternating layers of [Bi₂O₂]_n²ⁿ⁺ and [V_{1 − x}Co_xO_{3.5 − 3x/2}]_n²ⁿ⁻ with disorder limited to the vanadate layer. The ideal V/Co co-ordination is octahedral with corner sharing of equatorial oxygens. The refinements show that the true structure is distorted, with disorder in both apical and equatorial oxygens and oxygen vacancies concentrated in the equatorial positions. Detailed analysis of the oxygen site occupancies reveals two main types of V/Co co-ordination viz. distorted octahedral and distorted tetrahedral. The majority of the sites in both compositions are tetrahedral.     

The ΔNγ electromagnetic transition form factors GM(q) and GE(q)

A parameter-free, nonperturbative calculation of the ΔNγ electromagnetic transition amplitudes GM*(q2), GE*(q2), and the resonant multipole ratio REM(q2)≡E1+3/2(q2)/M1+3/2(q2) is performed in terms of the well-known nucleon isovector Sachs form factor GMV. Our methods are fully relativistic with conservation of the electromagnetic current guaranteed. We find that GM*(q2) decreases more rapidly than the nucleon dipole form factor when −q21 GeV2/c2 and that REM(q2) remains small even for very high four-momentum transfer implying that the perturbative QCD prediction REM(q2)→1 is purely asymptotic and is valid only for extremely high |q2|.     

A measurement of the photon structure function F2 at Q = 6.8 GeV

The photon structure function F₂^γ has been measured at an average Q² value of 6.8 GeV² using data collected by the AMY detector at the TRISTAN e⁺e⁻ collider. The measured F₂^γ is compared with several QCD-based parton density models.     

应用分子子图指数估计与预测烷烃核磁共振碳谱位移和

系统地研究了核磁共振碳谱(¹³C NMR)与化学位移规律及其定量构谱关系(QSSR).本文研究了一组多元素分子子图指数矢量(VMSG),并发现它与烷烃化学位移和(CCSA)有很好线性相关性.采用多元线性回归(MVLR)进行准确估计与预测,结果良好.     

应用分子子图指数估计与预测烷烃核磁共振碳谱位移和

系统地研究了核磁共振碳谱(¹³C NMR)与化学位移规律及其定量构谱关系(QSSR).本文研究了一组多元素分子子图指数矢量(VMSG),并发现它与烷烃化学位移和(CCSA)有很好线性相关性.采用多元线性回归(MVLR)进行准确估计与预测,结果良好.     

Interprétation de la susceptibilité magnétique de l'oxysulfure de samarium par un modèle de champ cristallin

The paramagnetic susceptibility of polycrystalline samarium oxysulfide has been measured between 3° and 300°K. The data are interpreted with an approximation to the crystal potential of the form

V_c = _JV₂⁰O₂⁰ + β_JV₄⁰O₄⁰ + β_JV₄³O₄³

and correction taking into account exchange is made. The energy levels and crystal fields parameters have been calculated. Fluorescence studies of Gd₂O₂S: Sm³⁺ and Y₂O₂S: Sm³⁺ have confirmed these results.     

A hybrid mode of one- and two-surface multipactor on grooved dielectric surface

A hybrid mode of one- and two-surface multipactor on the grooved dielectric surface is studied in detail using both an analytical approach and two-dimensional particle-in-cell(2D PIC) simulations. When the groove width L eE_0/(4πm_ef~2),there are one-surface multipactor and one-order two-surface multipactor on the grooved dielectric surface, and only one slope of the groove has the multipactor anytime. When L eE0/(4πme f~2), both slopes may have the multipactors. The electron surface density of the multipactor discharge has a sharp increase at the length L = eE_0/(4πm_ef~2).     

Magnetic properties and percolation threshold in diluted B-spinel ZnCr2xAl2−2xS4: a study through high-temperature expansions

By making use of high-temperature series expansions (HTSE) of the correlation functions, we study the thermal and disorder variation of the short-range order (SRO) in the particular B-spinel ZnCr_2xAl_2−2xS₄. We developed the HTSE for the q-dependent static structure factor S(q) to the order 6 in reciprocal temperature including both the nearest- and next-nearest-neighbour interactions J₁ and J₂, respectively. Respecting the experimental fact that the broad diffuse peak of the neutron is situated at the particular wave vector q₀=[0 0 0.79] and is insensitive to the temperature for a given ratio of dilution x, we have estimated the thermal variation of J₁ and J₂ in the case of the pure compound.

The bond percolation threshold x_p of the ZnCr_2xAl_2−2xS₄ is determined by studying the disorder variation of the correlation length ξ. The x_p is considered as the concentration at which ξ vanishes. The obtained values are x_p=0.27 when only J₁ is considered and 0.23 when both J₁ and J₂ are taken into account.     

Nuclear properties of Z=114 isotopes and shell structure of ~(298)114

The two-neutron separation energies(S_(2n)) and α-decay energies(Q_α) of the Z=114 isotopes are calculated by the deformed Skyrme-Hartree-Fock-Bogoliubov(SHFB) approach with the SLy5,T22,T32 and T43 interactions.It is found that the tensor force effect on the bulk properties is weak and the shell closure at N=184 is seen evidently with these interactions by analyzing the S_(2n) and Q_α evolutions with neutron number N.Meanwhile,the single-particle energy spectra of ~(298)114 are studied using the spherical SHFB approach with these interactions to furthermore examine the shell structure of the magic nucleus ~(298)114.It is shown that the shell structure is almost not changed by the inclusion of the tensor force in the Skyrme interactions.Finally,by examining the energy splitting of the three pairs of pseudospin partners for the protons and neutrons of ~(298)114,it is concluded that the pseudospin symmetry of the neutron states is preserved better than that of the proton states and not all of the pseudospin symmetries of the proton and neutron states are influenced by the tensor force.     

Ca$lt;sub$gt;2$lt;/sub$gt;Si（O$lt;sub$gt;4-$lt;i$gt;x$lt;/i$gt;$lt;/sub$gt;N$lt;sub$gt;$lt;i$gt;x$lt;/i$gt;$lt;/sub$gt;）：Eu$lt;sup$gt;2+$lt;/sup$gt;绿色荧光粉的制备及其发光性能

利用在Ca-Si-O干凝胶前驱体中添加Si₃N₄的方法于非还原气氛下合成了含N固溶体Ca₂Si（O_4-xN_x）：Eu²⁺绿色荧光粉. 通过X射线衍射仪、扫描电子显微镜以及荧光分光光度计分别分析了产物的物相结构、颗粒形貌和发光性能. 结果显示,Si₃N₄与前驱体的混合物在非还原气氛（纯氮气）下于1100℃焙烧后获得含N固溶体Ca₂Si（O_4-xN_x）：Eu²⁺荧光粉,特别是其中Eu³⁺被还原为Eu²⁺,产物的晶体结构与βup -Ca₂SiO₄相一致. Ca₂Si（O_4-xN_x）：Eu²⁺能够被270–400 nm 范围内的紫外线有效激发,其发射光谱呈宽带发射. 随着N含量的增加,发射峰出现一定程度红移（501–504 nm）,而且发光强度显著提高. 当Eu²⁺浓度为0.25 mol%时发光强度达最大值,浓度超过0.25 mol%时,发光强度显著降低,出现浓度猝灭 效应. 关键词： 白光LED 荧光粉 溶胶凝胶法 3N₄')" href="#">Si₃N₄     

Octet baryons in the independent-quark-model approach based on the dirac equation with a power-law potential

Several properties of octet baryons such as (i) the magnetic moment, (ii) (G_A/G_v)_n for neutron β-decay and (iii) the charge radius of the proton have been calculated in a simple independent-quark model under the assumption that the individual constituent quarks are confined, in first approximation, by a relativistic power-law potential V_q(r)=(1+β)(a^v+1r^v+V₀) with a, v>0. In view of the simplicity of the model, the results obtained are quite encouraging.     

Measurement of spin-lattice relaxation times of C in organic solids

A transient nuclear Overhauser effect (NOE) makes measurements of the ¹³C spin-lattice relaxation times in organic solids complicated. Extended Solomon equations are applied in order to describe ¹³C spin-lattice relaxation with ¹H r.f. field irradiation. Spin-lattice relaxation under r.f. irradiation is shown to be generally a triple-exponential process, but it can be reduced to be single-exponential under stronger r.f. field irradiation as well as in the absence of ¹H initial magnetizations. Based on numerical calculations, the difference between spin-lattice relaxation curves obeying T₁^C < T₁^H and those obeying T₁^C < T₁^H is clearly indicated. The methyl group resonances in solid-state -valine are examined, and the experimental results agree well with the theoretical results.     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.     

NFX(X=-1,0,+1)分子离子基态的结构与势能函数

用密度泛函理论的B3LYP方法,分别以6-311++g(df,3pd),6-311g(3d,3p)和6-311++g(3df,3pd)为基函数对NF分子、NF⁺和NF^-离子基态进行几何优化和频率计算,并进行单点能扫描计算.用最小二乘法拟合得到NF^X(X=-1,0,+1)分子离子基态的Murrell-Sorbie势能函数.利用得到的解析势能函数计算出的NF分子和NF⁺离子基态光谱常数(B_e,α_e,ω_e,ω_eχ_e)与实验值符合很好.首次得到NF^-离子基态的光谱常数(B_e,α_e,ω_e,ω_eχ_e)和力常数(f₂,f₃,f₄),为NF-离子基态的后期研究提供理论参考.