Direct transformation of variational problems into Cauchy systems. I. Scalar-quadratic case

This series of papers addresses three interrelated problems: the solution of a variational minimization problem, the solution of integral equations, and the solution of an initial-valued system of integro-differential equations. It will be shown that a large class of minimization problems requires the solution of linear Fredholm integral equations. It has also been shown that the solution of a linear Fredholm integral equation is identical to the solution of a Cauchy system. In this paper, we bypass the Fredholm integral equations and show that the minimization problem directly implies a solution of a Cauchy system. This first paper in the series looks only at quadratic functionals and scalar functions.This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-77-3383.     

Apparent Molar Volume, Heat Capacity, and Conductance of Lithium Bis(trifluoromethylsulfone)imide in Glymes and Other Aprotic Solvents

Lithium bis(trifluoromethylsulfone)imide (LiTFSI) is a promising electrolyte for high-energy lithium batteries due to its high solubility in most solvents and electrochemical stability. To characterize this electrolyte in solution, its conductance and apparent molar volume and heat capacity were measured over a wide range of concentration in glymes, tetraethylsulfamide (TESA), acetonitrile, -butyrolactone, and propylene carbonate at 25°C and were compared with those of LiClO₄ in the same solvents. The glymes or n(ethylene glycol) dimethyl ethers (nEGDME), which have the chemical structure CH₃–O–(CH₂–CH₂–O) _n –CH₃ for n = 1 to 4, are particularly interesting since they are electrochemically stable, have a good redox window, and are analogs of the polyethylene oxides used in polymer-electrolyte batteries. TESA is a good plasticizer for polymer-electrolyte batteries. Whenever required, the following properties of the pure solvents were measured: compressibilities, expansibilities, temperature and pressure dependences of the dielectric constant, acceptor number, and donor number. These data were used in particular to calculate the limiting Debye-Hückel parameters for volumes and heat capacities. The infinite dilution properties of LiTFSI are quite similar to those of other lithium salts. At low concentrations, LiTFSI is strongly associated in the glymes and moderately associated in TESA. At intermediate concentrations, the thermodynamic data suggests that a stable solvate of LiTFSI in EGDME exists in the solution state. At high concentrations, the thermodynamic properties of the two lithium salts approach those of the molten salts. These salts have a reasonably high specific conductivity in most of the solvents. This suggests that the conductance of ions at high concentration in solvents of low dielectric constant is due to a charge transfer process rather than to the migration of free ions.     

Cathode of a fuel cell with a solid polymer electrolyte: Calculating overall currents in the presence of a gas-diffusion layer

Mathematical apparatus, which makes it possible to perform calculations of the current-voltage characteristics of cathodes of fuel cells with a solid polymer electrolyte in conditions where there are present extraneous diffusion restrictions is proposed. In so doing, the partial pressure of oxygen and the absolute pressure of gas in the gas chamber may assume any values. First of all presented are the results of calculations of the current-voltage characteristics intrinsic to active layers of the air and oxygen cathodes, which are performed under the assumption that the extraneous diffusion restrictions are absent altogether. Thereafter, in the same conditions (at the same parameters that characterize the active layer of a cathode), obtained are results of a calculation of the current-voltage characteristics inherent in the air and oxygen cathodes in the presence of extraneous diffusion restrictions. Afterward there is performed an analysis of the way a gas-diffusion layer restricts the process of generation of current in a cathode and of what measures should be taken in order for the extraneous diffusion restrictions to become less significant.     

金属团簇MoS4Cu4(SCN)2(NC5H5)6的皮秒光学非线性特性和光限幅特性研究

由于激光技术的快速发展，新型超快可调谐波长的高功率激光器更多的在民用和军事上应用。快速的非线性光学器件的需求越来越多。近10年，人们投入大量研究寻找超快光学非线性材料，同时寻找快速响应、高线性透过率和低非线性透过率以及高损伤阈值的光限幅材料，研究发现金属酞菁化合物、金属卟啉化合物以及富勒烯衍生物具有良好的光限幅效果和强的光学非线性特性。     

Mo(W)-Cu(Ag)-S簇合物的非线性光学性能研究

本文介绍了非线性光学性测试中的Ｚ－扫描方法。总结了Ｍｏ（Ｗ）－Ｃｕ（Ａｇ）－Ｓ簇合物的光限制效应、非线性吸收和非线性折射等光学性质。讨论了簇合物结构与光学性能的关系。     

Evaluation of single-ion conductances in nonaqueous solvents at 25°C by the use of tetrabutylammonium tetrabutylboride as a reference electrolyte

Precise conductances for tetrabutylammonium tetrabutylboride (Bu₄NBBu₄) at 25°C have been measured in a number of nonaqueous solvents, and the data have been analyzed by the 1957 Fuoss-Onsager conductance equation. Limiting ion conductances for the Bu₄N⁺ ion at infinite dilution ₀(Bu ₄ N ⁺) in various solvents have been evaluated by dividing ₀ values of the salt into two equal parts. The ₀(Bu ₄ N ⁺) values so obtained are in fairly good agreement (within±0.1–3.5%) with the corresponding values determined from direct transference number measurements in these solvents.     

Induced Absorption of C60 and a Water-Soluble C60-Derivative in SiO2 Sol-Gel Matrices

Porous sol-gel glasses, either impregnated with pure C₆₀ or doped with a methanofullerene derivative, have been studied and induced absorption or reverse saturable absorption (RSA) has been observed in both types of solid materials. The samples impregnated by pure C₆₀ mainly contain well-dispersed fullerene molecules. Unlike crystalline films of C₆₀, their absorption dynamics can be well described by a 5-level model, developed for non-interacting C₆₀-molecules in solutions. Methanofullerene samples, on the other hand, show signs of micellar aggregation and therefore RSA dynamics that are influenced by solid state effects. We observe an important decrease of transmission at high fluences for both kinds of samples, a shortened singlet-state lifetime to that observed in solution, but nonetheless, a triplet yield, that cannot be considered as negligible. In the case of pure C₆₀ in a sol-gel matrix, we can explain the faster de-excitation dynamics, relative to behavior in solution, mainly by the absence of stabilizing aromatic solvents and also by the interaction of the amorphous environment with the molecules. Concerning the methanofullerene samples, the acceleration of the de-excitation dynamics can be principally attributed to solid-state effects due to the micellar aggregation.     

Electrical Conductance and Volumetric Studies in Aqueous Solutions of DL-Pyroglutamic Acid

Conductivity measurements of DL-pyroglutamic acid and sodium pyroglutamate in dilute aqueous solutions were performed in the 288.15–323.15 K temperature range. The limiting molar conductances of pyroglutamate anion, λ^o(pGlu⁻, T) and the dissociation constants of pyroglutamic acid, K(T) were derived from the Onsager, and the Quint and Viallard conductivity equations. Densities of aqueous solutions with molalities lower than 0.5 mol-kg⁻¹ were determined at 5 K intervals from T = 288.15 K to 333.15 K. Densities served to evaluate the apparent molar volumes, V_2,φ(m, T), the cubic expansion coefficients, α (m,T) and the changes of the isobaric heat capacities with respect to pressure, (∂ C_P/∂ P)_T,m. They were correlated qualitatively with the changes in the structure of water when pyroglumatic acid is dissolved in it.     

Preparation and Optical Limiting Properties of Polyurethane Containing Long Conjugated Chromophores

Two functional polyurethanes (P1 and P2) bearing a large π electron conjugated chromophoric pendant were synthesized and characterized by FT‐IR, ¹H‐NMR and UV‐Vis absorption spectra. Their optical limiting properties were evaluated. The results show that P1 and P2 show novel optical limiting properties, which are assigned to a long π electron conjugated chromophoric pendant. It was found that their optical limiting properties were affected simultaneously by solution concentration and P2 displays a better optical limiting property than P1 at the same solution transmittance, although that P1 has larger χ⁽³⁾ (4.28×10^?11 esu) than P2 (0.87×10^?11 esu), and their optical limiting mechanism is investigated.     

The convergence on spectrum of sample covariance matrices for information-plus-noise type data

In this paper,we consider the limiting spectral distribution of the information-plusnoise type sample covariance matrices Cn =1/N (Rn + σXn) (Rn + σXn)*,under the assumption that the entries of Xn are ...