Improving constants of strong convexity in linear stochastic programming

We derive formulas for constants of strong convexity (CSCs) of expectation functions encountered in two-stage stochastic programs with linear recourse. One of them yields a CSC as the optimal value of a certain quadratically constrained quadratic program, another one in terms of the thickness of the feasibility polytope of the dual problem associated to the recourse problem. CSCs appear in Hoelder-type estimates relating the distance of optimal solution sets of stochastic programs to a suitable distance of underlying probability distributions.     

Range-Renewal Processes: SLLNs and Power Laws*

Given n samples(viewed as an n-tuple) of a γ-regular discrete distribution π,in this article the authors concern with the weighted and unweighted graphs induced by the n samples. They first prove a series of SLLN results(of Dvoretzky-Erd¨os’ type). Then they show that the vertex weights of the graphs under investigation obey asymptotically power law distributions with exponent 1 + γ. They also give a conjecture that the degrees of unweighted graphs would exhibit asymptotically power law distribu...     

A strong limit theorem for generalized Cantor-like random sequences

ＡＳＴＲＯＮＧＬＩＭＩＴＴＨＥＯＲＥＭＦＯＲＧＥＮＥＲＡＬＩＺＥＤＣＡＮＴＯＲ－ＬＩＫＥ　ＲＡＮＤＯＭ　ＳＥＱＵＥＮＣＥＳＬＩＵＷＥＮ（刘文）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＰｈｙｓｉｃｓ,ＨｅｂｅｉＵｎｉｖｅｒｓｉｔｙｏｆＴｅ...     

Curves of marginal stability, and weak- and strong-coupling BPS spectra in N = 2 supersymmetric QCD

We explicitly determine the global structure of the SL(2, ) bundle over the Coulomb branch of the moduli space of asymptotically free N = 2 supersymmetric Yang-Mills theories with gauge group SU(2) when massless hypermultiplets are present. For each relevant number of flavours, we show that there is a curve of marginal stability of the Coulomb branch, diffeomorphic to a circle, across which the BPS spectrum is discontinuous. We determine rigorously and completely the BPS spectra inside and outside the curve. In all cases, the spectrum inside the curve consists of only those BPS states that are responsible for the singularities of the low energy effective action (in addition to the massless abelian gauge multiplet which is always present). The predicted decay patterns across the curve of marginal stability are perfectly consistent with all quantum numbers carried by the BPS states. As a byproduct, we also show that the electric and magnetic quantum numbers of the massless states at the singularities proposed by Seiberg and Witten are the only possible ones.     

弱碱性和强碱性阴离子交换树脂的离子交换平衡的比较SO_4~(2-)-Cl~--NO_3~-体系

本文详细地比较了在弱碱性和强碱性阴离子交换树脂上,SO_4~(2-)-Cl~-、NO_3~--Cl~-及NO_3~--SO_4~(2-)二元交换的等温线和修正选择系数。实验测定及理论计算了上述三种二元交换反应的标准自由能的改变量。测得了在弱碱性树脂上的SO_4~(2-)-Cl~--NO_3~-三元交换的等温线。适用于强酸性和强碱性树脂的从二元交换平衡数据推算三元交换平衡数据的方法推广应用于弱碱性树脂。     

铂电极上溶液酸碱性的电位溶出法响应

提出了一个广谱测定强酸、强碱溶液浓度的方法。用铂电极作工作电极，电位溶出法对溶液酸碱性产生响应。通过调节沉积时间和沉积电位，利用电位溶出法可以检测溶液酸、大致 的浓度范围为2．5mol/L H^ -1.0mol/L OH^-。详细研究了不同测定范围的实验条件，以及溶出过程的响应机理。在不同酸碱性溶液中电沉积产生的氢吸附于电极表面，溶出过程中被溶液中的氧氧化成氢离子，从而产生电位平台。该平台的出现还与随后的电极表面金属／金属氧化物电对电位值有关。     

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.