Strong coupling expansion for classical statistical dynamics

We discuss the simple, randomly driven systemdx/dt = –x –x³ +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)ⁿ, whereR is the internal Reynolds number ()^1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp ²/2 +m ² x ²/2 +vx ⁴ +x ⁶/2, we evaluate the path integral on a lattice by assuming that thex ⁶ term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)^1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy.     

Evaluation of behaviour of linear monoamines CH3-(CH2)n−1-NH2 (n=1-6) in ion chromatography

This paper reports the results on a study of ion chromatography (IC) behaviour on strong cationic exchange column of CH₃-(CH₂)_n−1-NH₂ (n=1-6) type linear monoamines. The eluents were mixtures of HCl-NaCl, HNO₃-NaNO₃, HClO₄-NaClO₄, H₂SO₄-Na₂SO₄, HClO₄-NaClO₄-CH₃CN. Amines were revealed with an amperometric detector. The influence of different counter-ions on retention factors, k′, is discussed. Relationships between k′ and pE (E=sum of Na⁺ and H⁺ concentrations), and length of alkylic chain, and sensitivity coefficient S, are reported and discussed. The addition of acetonitrile (ACN) in the eluent was also taken into account. Suitable considerations are derived from these data. An example of monoamines separation is given.     

Survey of ligand field parameters of strong field d complexes obtained from the g matrix

Using a newly proposed approach involving an internally consistent set of equations, the ligand field parameters Δ/ξ, V/ξ and k are obtained from literature values of the g matrix for strong field d⁵ systems of various conformations in which |Δ/ξ|≤10. Qualitative analysis of the observed results is done using the Angular Overlap Model, AOM.     

The ν(OH/OD) band shape of strong hydrogen bonded dimers of phosphinic acids. Phenomenology and formation models

The infrared spectra of phosphinic acid R₂POOH dimers (R=CH₃, CH₂Cl, C₆H₅) have been studied in CCl₄ and CH₂Cl₂ solutions (T=300 K). The infrared spectra of deuterated R₂POOD dimers (R=CH₃, CH₂Cl) were also studied in the gas phase (T=400–550 K) and solid state (T=100–300 K). They are compared with previously studied spectra of the light (non-deuterated) dimers in the gas phase, in the solid state and in low-temperature argon matrices (T=12–30 K) in the 4000–400 cm⁻¹ spectral region. It is found that the strong and broad ν(OH) dimer bands have similar shapes, nearly equal values of bandwidth and low-frequency shift, and possess the Hadzi ABC structure irrespective of the type of acid, significant differences of dimerization enthalpies, influence of solvent, the type of H-bonded complexes (cyclic dimers in the gas phase, in solutions, and in inert matrices, and infinite chains in the solid state), and temperature in the range 12–600 K. Isotopic ratio of the first moments of light and deuterated acid bands has been measured. Analysis of the ν(OH/OD) band of hydrogen bonded dimers of phosphinic acids shows that the interaction between the two intermolecular bonds O–HOP in a cyclic complex plays virtually no role in the mechanism of the ν(OH/OD) band formation; the shape of ν(OH/OD) band is controlled mainly by the POOH(D)O fragment; and the band shape of strong hydrogen bonded complexes is formed by a number of vibrational transitions from the ground state to different combination levels in the region 3500–1500 cm⁻¹.     

随机变量序列加权和的强收敛性

本文讨论了一般随机变量序列加权和的强收敛性．作为推论，得到一类鞅差序列加权和的收敛定理和若干经典的独立随机变量序列的强大数定律；已有的若干结论是本文结果的特例．     

同分布NA列Jamison型加权和强稳定的充要条件

本文将Ｊａｍｉｓｏｎ等（１９６５）关于ｉｉｄ列加权和强稳定的充分性结果推广到ＮＡ列的场合并且得到了ＮＡ列Ｊａｍｉｓｏｎ型加权和强稳定的必要性结果。     

Weak Graph Map Homotopy and Its Applications∗

The authors introduce a notion of a weak graph map homotopy (they call it M-homotopy), discuss its properties and applications. They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001. The difference between them is that the weak graph map homotopy transformation is defined in terms of maps, while the graph homotopy transformation is defined by means of combinatorial operations. They discuss its advantages over the graph homotopy transformation. As its applications, they investigate the mapping class group of a graph and the 1-order MP-homotopy group of a pointed simple graph. Moreover, they show that the 1-order MP-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.     

强碱性阴离子交换树脂分离富集土壤中的钼

研究了以强碱性阴离子交换树脂为固定相的离子交换色谱法分离富集土壤中钼,实现了钼与其他常见金属元素离子的选择性分离,富集在色谱柱上的钼以0.5mol.L^-1NH4NO3＋2mol.L^-1HNO3洗脱并用富氧火焰原子吸收光谱法进行测定,钼的回收率为99%—101.3%。     

Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels

Photons propagating in strong magnetic fields are subject to a phenomenon called the “vacuum birefringence” where refractive indices of two physical modes both deviate from unity and are different from each other. We compute the vacuum polarization tensor of a photon in a static and homogeneous magnetic field by utilizing Schwinger’s proper-time method, and obtain a series representation as a result of double integrals analytically performed with respect to proper-time variables. The outcome is expressed in terms of an infinite sum of known functions which is plausibly interpreted as summation over all the Landau levels of fermions. Each contribution from infinitely many Landau levels yields a kinematical condition above which the contribution has an imaginary part. This indicates decay of a sufficiently energetic photon into a fermion–antifermion pair with corresponding Landau level indices. Since we do not resort to any approximation, our result is applicable to the calculation of refractive indices in the whole kinematical region of a photon momentum and in any magnitude of the external magnetic field.     

An Efficient and Environment Friendly Procedure for the Synthesis of Arylmethylenemalononitrile Catalyzed by Strong Base Anion‐Exchange Resin in Water

Abstract

Knoevenagel condensation of malononitrile with aromatic aldehydes catalyzed by strong base anion‐exchange resin in water results arylmethylenemalononitrile in 74–98% yield at room temperature.