On Bianchi type-I vacuum solutions inR+R 2 theories of gravitation. II. The axially symmetric anisotropic case

The field equations following from a LagrangianL(1/L)(–g)^1/2[(1/2)R+l ²(R _lk R ^lk +R ²)] will be considered for Bianchi type-I homogeneous models. Thereby the special case,+3=0, is considered qualitatively for axially symmetric anisotropic metrics. Generically, the solutions have both past and future singularities, but it will be proven by topological arguments that the two-dimensional space of solutions possesses a one-parameter subspace of solutions with a behavior similar to the Kasner solution.     

Exact scalar field cosmologies in a higher derivative theory

We obtain exact cosmological solutions of a higher derivative theory described by the Lagrangian L=R+2αR ² in the presence of interacting scalar field. The interacting scalar field potential required for a known evolution of the FRW universe in the framework of the theory is obtained using a technique different from the usual approach to solve the Einstein field equations. We follow here a technique to determine potential similar to that used by Ellis and Madsen in Einstein gravity. Some new and interesting potentials are noted in the presence of R ² term in the Einstein action for the known behaviours of the universe. These potentials in general do not obey the slow rollover approximation.     

Electronic absorption spectrum of CO+ in an ion beam

The He+He⁺¹ interactions have been studied, as a function of the internuclear separation R, in terms of the electronic forces acting on the nuclei and the change in the charge distribution. The analysis reveals that at large R the atomic densities are polarized inwards, causing an attractive force on each nucleus, while at small R the difference in the nature of the interactions in the ²Σ_u and ²Σ_g systems is noted. It is seen that the He+He⁺¹ (²Σ_u) interaction is less attractive than the He⁺¹+He⁺¹ interaction at lower values of R.     

Hydrothermal reactions of simple molecules by real-time infrared spectroscopy

Abstract

The relative roles of the materials of construction of the reactor (stainless steel or titanium) and the effects of Group 1 cations are discussed in terms of their effect on the rate of decarboxylation of acetic acid derivatives, RCO₂H. Past work indicates that the reaction container composition has a very large effect when R is CH3—. A smaller but significant effect is seen when R is electron neutral (i.e., R=H). When R is electron Withdrawing the rate depends less on the reactor type than the nature of R. The effect of the counter ion M on the rate of decarboxylation of monovalent malonate salts, HC&CHzC02M, is discussed for M=Li⁺, Na⁺, K⁺, Rb⁺, and Cs⁺. The rate generally increases with the ionic radius except that the Rb⁺ salt exhibits the fastest rate. Preliminary explanations are given.     

Four-Vertex Theorems, Sturm Theory and Lagrangian Singularities

We prove that the vertices of a curve γ⊂R ⁿ are critical points of the radius of the osculating hypersphere. Using Sturm theory, we give a new proof of the (2k+2)-vertex theorem for convex curves in the Euclidean space R ^2k . We obtain a very practical formula to calculate the vertices of a curve in R ⁿ . We apply our formula and Sturm theory to calculate the number of vertices of the generalized ellipses in R ^2k . Moreover, we explain the relations between vertices of curves in Euclidean n-space, singularities of caustics and Sturm theory (for the fundamental systems of solutions of disconjugate homogeneous linear differential operators L:C ^∞(S ¹)→C ^∞(S ¹)).     

Bounds on non-leading QCD effects in a quark model for inclusive reactions

We study the possible effect of QCD in the proton wave function in a quark model for inclusive processesA+B→C+X pursued by us. The assumption is the validity of the conjecture of Lepage and Brodsky in QCD on such effects. Our results obey the perturbative expectation, |R _g tan² φ|<1. Symmetric version of the model is, however, found to be at variance with most of the inclusive data as well as with some known phenomenology. If the dynamics of the underlying theory generate Regge-like symmetry breaking approximately, the model is phenomenologically viable, and the non-leading QCD effects become reasonable in size. Phenomenological necessity of the admixtures of (56, 0⁺)*, (70, 0⁺) and (56, 2⁺) in the nucleon wave function is also discussed in the present analysis.     

Hall coefficient in solution for a simple dynamical model

A model Liouville equation is proposed for a system composed of an ion moving in a solvent fluid. Using this model, explicit results are obtained for the Ohmic conductivityL and the Hall conductivityh. These results are then used to calculate the Hall coefficientR = ehL^–2, which is a measure of the effect of non-Brownian motion, for several charge carriers of interest. Our results are in agreement with earlier findings based on a stochastic model which predictR > 1 for H⁺(aq). Our results also indicate thatR 1 for charge carriers such as Na⁺, Cl^–, and K⁺ which have a mass greater than that of a solvent molecule (here taken as 18 amu).This research was supported in part by grants from the National Science Foundation and by the Research Foundation of the State University of New York.     

Determination and analysis of opiates in complex mixtures by surface-ionization mass spectrometry

The results of studies of the analytical opportunities of surface-ionization mass spectrometry (SIMS) for high-sensitivity and selective detection and analysis of opiate mixtures—natural opium, crude heroin, and narcotic analgesic omnopon—are presented. The experiments were carried out using an MX-1320 chemical mass spectrometer modernized for studying surface ionization (SI). It was ascertained that the opiate mixtures are ionized by highly efficient surface ionization. The bands of M⁺ (for papaverine), (M-H)⁺, (M-H-2nH)⁺, (M-R)⁺, and (M-R-2nH)⁺ ions, where M is a molecule, H is a hydrogen atom, R is a radical, are observed in the mass spectra; they are the sum of the SI mass spectra of components of the mixtures. The series of bands of ions with m/z of 144 and 146 that is characteristic of SI-morphinelike molecules is the main one in the mass spectrum of crude heroin, while for omnopon and natural opium this series is the main at low temperatures of a thermionic emitter (up to ∼900 K). At high temperatures of the thermionic emitter, the band series with m/z of 218 and 220 is the main series. Studies of natural opium, crude heroin, and omnopon have shown that the SIMS method allows analyzing mixtures without preliminary chromatographic separation thereof. The study also contains the results of comparative analyses of opiate mixtures by SIMS and chromate- and mass spectrometry (HP-6890) with electronic ionization.     

NMR 1 J(HD) coupling in HD as a function of interatomic distance in the presence of an external magnetic field

A theoretical study has been made of the dependence of the ¹ J(HD) coupling in HD on the interatomic distance R in the presence of a static uniform magnetic field B ₀. The behaviour of all coupling terms arising from Ramsey's magnetic electron-nucleus interactions, Fermicontact (FC), spin-dipolar (SD) and paramagnetic (PSO) and diamagnetic (DSO) spin-orbital interactions is analysed qualitatively for large R. It is concluded that the PSO, DSO and SD terms become negligibly small as R increases. Detailed calculations were carried out for the FC term following two different approaches: detailed full CI calculations within a non-perturbative approach; and explicit diagonalization of the Hamiltonian operator restricted to the subspace spanned by the ¹Σ⁺;_g and the ³Σ⁺;_u states. Within the approximations considered, the FC term of ¹ J(HD) is found to be independent of B ₀ and to increase by several orders of magnitude, in agreement with previous results by Bacskay, G. B., 1995, Chem. Phys. Lett., 242, 507, until a critical distance R(B ₀) is reached, beyond which it almost vanishes. The quenching of the coupling at R(B ₀) is due to the splitting of the ³Σ⁺;_u state in the presence of the field B ₀. The stronger the field the shorter is R(B ₀).     

Evidence for a relativistic electron-pair model of nuclear particles

A positroniumlike, relativistic electron-pair model previously found to describe the properties of the pion and hadron resonances is tested for its prediction of the hadron-to-muon production ratioR in high-energye ⁺ e ^– collisions. It is found that the model leads to the observed magnitude ofR and its stepwise increase with energy. The model predicts a series of further rises ofR as the available energy is increased, beginning at about 7.9 Gev.     

Kinetics and thermodynamics of reversible disproportionation–comproportionation in redox triad oxoammonium cations – nitroxyl radicals – hydroxylamines

Kinetics and equilibrium of the acid‐catalyzed disproportionation of cyclic nitroxyl radicals R₂NO^? to oxoammonium cations R₂NO⁺ and hydroxylamines R₂NOH is defined by redox and acid–base properties of these compounds. In a recent work (J. Phys. Org. Chem. 2014, 27, 114‐120), we showed that the kinetic stability of R₂NO^? in acidic media depends on the basicity of the nitroxyl group. Here, we examined the kinetics of the reverse comproportionation reaction of R₂NO⁺ and R₂NOH to R₂NO^? and found that increasing in –I‐effects of substituents greatly reduces the overall equilibrium constant of the reaction K₄. This occurs because of both the increase of acidity constants of hydroxyammonium cations K_3H+ and the difference between the reduction potentials of oxoammonium cations E_R2NO+/R2NO? and nitroxyl radicals E_R2NO?/R2NOH. pH dependences of reduction potentials of nitroxyl radicals to hydroxylamines E_1/3Σ and bond dissociation energies D(O–H) for hydroxylamines R₂NOH in water were determined. For a wide variety of piperidine‐ and pyrrolidine‐1‐oxyls values of pK_3H+ and E_R2NO+/R2NO? correlate with each other, as well as with the equilibrium constants K₄ and the inductive substituent constants σ_I. The correlations obtained allow prediction of the acid–base and redox characteristics of redox triads R₂NO^?–R₂NO⁺–R₂NOH. Copyright © 2014 John Wiley & Sons, Ltd.     

Boson—Fermion Correspondence on the Circle via Quantum Stochastic Calculus

The quantum stochastic differential formula dB = (–1)dA, known to relateboson and fermion fields A and B, respectively, on the Fock space over L ²(R₊),is shown to hold in a modified form in a Fock space associated with the nontrivialcomplex line bundle over the circle S ¹.     

Calculation of the photoionization with deexcitation cross sections of He and helium-like ions

We discuss the results of the calculation of the photoionization with deexcitation of excited He and helium-like ions Li⁺ and B³⁺ at high but nonrelativistic photon energies θ. Several lower ¹ S and ³ S states are considered. We present and analyze the ratios R _d ⁺ * of the cross sections of photoionization with deexcitation, σ _(d) ⁺ *(θ), and of the photoionization with excitation, σ⁺*(θ). The dependence of R _d ⁺ * on the excitation of the target object and the charge of its nucleus is presented. In addition to theoretical interest, the results obtained can be verified using long-lived excited states such as 2³ S of He. The text was submitted by authors in English.     

A rotationally-resolved Rydberg transition of I2

Rotationally-resolved bands leading to a Rydberg state R 0 _u ⁺ of molecular I₂ are observed in a two-stage, three-photon transition from the ground state. The R 0 _u ⁺ state interacts homogeneously with high vibrational levels, ν_F ≈ 200–250, of an ionic state F 0 _u ⁺, the perturbation being directed by the vibrational overlap integrals towards even-numbered vibrational levels of R. Spectral constants of R 0 _u ⁺ are (in cm^-1): T _e = 61665·15, ω_e = 209.29, ω_e x _e = 0·859, B _e = 0·03842 and α_e = 1·6 × 10^-4. The electronic matrix element for the R, F interaction (excluding one deviant result) is |W _e| = 107 ± 1 cm^-1; thus W _e/ω_e ≈ 0·5, corresponding to ‘intermediate’ coupling. Energy considerations indicate that R should be assigned to the 0 _u ⁺ state of either the configuration (2430 Π_1/2g )6pσ _u , or of (2421 ⁴Σ _u ^-)6sσ _g . This state is the first extra-valence state of I₂ to be rotationally analysed.     

Influence of the Structure of the MEu(PO3)4 Crystals on Their Luminescent Properties

The influence of the M⁺ cations of alkali metals on the luminescent properties of the Meu(PO₃)₄ crystals, where M represents Li, Na, K, Rb, and Cs, is considered. The nonlinear dependences of the spectral position of the barycenters in the J components of the ⁷ F term of Eu³⁺ on the ionic radius R(M⁺), which are individual in the series of crystals of chain and cyclic structure, have been revealed. It is shown that the liability of the ligands of the europium complex in MeEu(PO₃)₄ to the polarizing action of the cations of alkali metals is manifested as an intermediate dependence of the luminescence lifetime of Eu³⁺ on R(M⁺).     

强扰动能区非全裸C$lt;sup$gt;$lt;i$gt;q$lt;/i$gt;+$lt;/sup$gt;，O$lt;sup$gt;$lt;i$gt;q$lt;/i$gt;+$lt;/sup$gt;($lt;i$gt;q$lt;/i$gt;=1—4)与He原子碰撞过程中截面比的实验研究

利用兰州大学2×1.7 MV串列加速器离子-原子碰撞实验终端上产生的单核子能量为20—500 keV的C^q+和O^q+（q=1—4）离子与He原子碰撞.采用符合测量方法和多参数数据获取系统得到了散射离子与反冲离子电荷态的二维谱,从而分别得到直接电离、入射离子俘获电子和入射离子损失电子截面与总截面的截面比R^direct, R^capture和R^loss,并对强扰动能区的各个反应道之间竞争关系及同一反应道在不同碰撞体系中所表现出的实验规律进行了比较和定性分析. 关键词： 离子-原子碰撞 截面比 竞争关系 强扰动区     

Ab initio configuration interaction study on the electronic structure of the X2Σ+, B2Σ+ and 32Σ+ states of SiO+

The energy levels and electronic structure of the X²Σ⁺, B²Σ⁺ and 3²Σ⁺ states of SiO⁺ are studied using ab initio configuration interaction (CI) calculations at and around their equilibrium internuclear distances R _e. Spectroscopic constants and the vertical excitation energy from the SiO⁺ X²Σ⁺ state are predicted for the 3²Σ⁺ state. Based on the calculated CI wavefunctions, avoided crossings of the potential energy curve for the 3²Σ⁺ state and a near-degeneracy effect in the avoided crossing region are examined. The effects of the mixing of excited configuration state functions in the total electronic wavefunctions for the 1–3 ²Σ⁺ states are investigated by analysing correlation energies in terms of the contributions from classes of excited configurations. The importance of both the near-degeneracy effect and the correlation energy effect in describing correctly the electronic structure of the 3 ²Σ⁺ state in the neighbourhood of its R _e is discussed.     

Padé approximation methods applied to the intermolecular force series

The H(1s)-H⁺, He-He, H(1s)-H(1s) and H(1s)-H(2s) interactions are considered as model systems for investigating the use of the Padé approximation method in summing the R ^-1 intermolecular force series. Various Padé approximants and partial sums of the R ^-1 expansions of the second-order Coulomb interaction energies are compared with the corresponding non-expanded results for each interaction. The computations are based on Unsöld's average energy approximation and on exact results for the H(1s)-H interaction. The results indicate that the Padé approximation method is a simple, useful way to remove some of the difficulties associated with the slow rate of convergence of the R ^-1 force series but that it does not alleviate the problems associated with the asymptotic divergent nature of the series. The results for the H(1s)-H⁺ interaction illustrate a possible difficulty in using Unsöld's method in the calculation of interaction energies.     

The influence of the proton affinity of molecules that form proton disolvates on disolvate hydrogen bridge parameters

The optimum structures of thirty three proton disolvates (B…H…B)⁺ and (B…H…S)⁺ containing O…H⁺…O, N…H⁺…N, and N…H⁺…O hydrogen bridges were calculated by the density functional theory method (B3LYP/6-31++G(d, p)). The bridge parameters are compared with the proton affinities (PAs) of B and S molecules. Several dependences between the PA or ΔPA = PA_B ? PA_S values and the R _OO, R _NN, and R _NO distances were established. It follows from these results that the proton affinity of oxygen-or nitrogen-containing molecules that form (B…H…B)⁺ and (B…H…S)⁺ ions is an important but not the only factor determining the geometric parameters of hydrogen bridges in them. The dependences obtained can be used to estimate the length of the central fragment of proton disolvates if the PA values of molecules in the disolvates are known. They also allow the degree of proton transfer (the R _N…H and R _H…O distances) to be estimated for N…H⁺…O bridges.