Generalizations of the Hohenberg-Kohn theorem: I. Legendre transform constructions of variational principles for density matrices and electron distribution functions

Given a general, N-particle Hamiltonian operator, analogs of the Hohenberg-Kohn theorem are derived for functions that are more general than the particle density, including density matrices and the diagonal elements thereof. The generalization of Lieb's Legendre transform ansatz to the generalized Hohenberg-Kohn functional not only solves the upsilon-representability problem for these entities, but, more importantly, also solves the N-representability problem. Restricting the range of operators explored by the Legendre transform leads to a lower bound on the true functional. If all the operators of interest are incorporated in the restricted maximization, however, the variational principle dictates that exact results are obtained for the systems of interest. This might have important implications for practical work not only for density matrices but also for density functionals. A follow-up paper will present a useful alternative approach to the upsilon- and N-representability problems based on the constrained search formalism.     

Bacterial cellulose/triethanolamine based ion-conducting membranes

New bacterial cellulose (BC)–triethanolamine (TEA) ion-conducting membranes have been prepared and characterized. The samples were obtained by soaking BC membranes in triethanolamine aqueous solutions and drying. The scanning electron microscopy pictures revealed that the incorporation of TEA in BC membranes covers the cellulose microfibrils. Raman spectra exhibited BC and TEA characteristic group frequencies and thermal analysis evidenced an influence of TEA content on the sample thermal stability. The ion-conductivity as a function of the temperature showed an Arrhenius behavior increasing from 1.8 × 10^?5 S/cm at room temperature to 7.0 × 10^?4 S/cm at 80 °C for the BC–TEA 1 M sample.     

Local order around rare earth ions during the devitrification of oxyfluoride glasses

Erbium L(3)-edge extended x-ray absorption fine structure (EXAFS) measurements were performed on rare earth doped fluorosilicate and fluoroborate glasses and glass ceramics. The well known nucleating effects of erbium ions for the crystallization of cubic lead fluoride (based on x-ray diffraction measurements) and the fact that the rare earth ions are present in the crystalline phase (as indicated by Er(3+) emission spectra) seem in contradiction with the present EXAFS analysis, which indicates a lack of medium range structural ordering around the Er(3+) ions and suggests that the lead fluoride crystallization does not occur in the nearest neighbor distance of the rare earth ion. Molecular dynamics simulations of the devitrification process of a lead fluoride glass doped with Er(3+) ions were performed, and results indicate that Er(3+) ions lower the devitrification temperature of PbF(2), in good agreement with the experimental results. The genuine role of Er(3+) ions in the devitrification process of PbF(2) has been investigated. Although Er(3+) ions could indeed act as seeds for crystallization, as experiments suggest, molecular dynamics simulation results corroborate the experimental EXAFS observation that the devitrification does not occur at its nearest neighbor distance.     

Thermal lens spectrometric determination of hexavalent chromium

The applicability of thermal lens spectrometry (TLS) for quantification and routine determination of hexavalent chromium was investigated by using a collinear dual beam thermal lens spectrometer. In aqueous solutions the LOD of 0.1 μg l⁻¹ was obtained for Cr(VI) by using 160 mW laser power. The performance of the technique was verified by the determination of hexavalent chromium in standard reference water samples (NIST SRM 1643a and NIST SRM 1643c) and comparing the results for Cr(VI) in CCA (Cr, Cu, As)-treated timber extracts to concentrations obtained by atomic absorption spectrometry (AAS). Good agreement between the TLS results and reported values for Cr(VI) in SRMs as well as AAS results for Cr(VI) in CCA-treated timbers confirmed that TLS is a reliable and accurate analytical technique applicable for the determination of Cr(VI) in aqueous solutions at concentration levels 0.5–100 μg l⁻¹.     

A new multidimensional integral relationship between heat flux and temperature for direct internal assessment of heat flux

This paper derives a new integral relationship between heat flux and temperature in a transient, two-dimensional heat conducting half space. A unified mathematical treatment is proposed that is extendable to higher-dimensional and finite-region geometries. The analytic expression provides the local heat flux perpendicular to the front surface solely based on an embedded line of temperature sensors parallel to the surface. The relationship does not require apriori knowledge of the surface boundary condition. A new sensor strategy is analytically conceived based on the integral relationship for estimating the local, in-depth heat flux without surface instrumentation. It should further be clarified that the integral relationship requires only knowledge of the local, in-depth temperature and heating/cooling rate (time rate of change of temperature). The resulting formulation is mildly ill-posed and either requires digital filtering of the temperature signal to remove high frequency components of noise or the development of direct heating/cooling rate sensors. This paper (a) develops the new mathematical relationship; (b) demonstrates that the proposed relationship reduces to well-known (i) one-dimensional results under the appropriate assumptions; and, (ii) two-dimensional surface results; and, (c) provides a simple numerical example validating the concept.     

On RSA moduli with almost half of the bits prescribed

We show that using character sum estimates due to H. Iwaniec leads to an improvement of recent results about the distribution and finding RSA moduli M=pl, where p and l are primes, with prescribed bit patterns. We are now able to specify about n bits instead of about n/2 bits as in the previous work. We also show that the same result of H. Iwaniec can be used to obtain an unconditional version of a combinatorial result of W. de Launey and D. Gordon that was originally derived under the Extended Riemann Hypothesis.     

Spectral narrowing and manipulation in an optical parametric oscillator using periodically poled lithium niobate electro-optic polarization-mode converters

We report a unique spectral narrowing and manipulation technique in an optical parametric oscillator (OPO) realized by an integrated periodically poled lithium niobate comprising an optical parametric gain medium sandwiched by two electro-optic polarization-mode converters (EO PMCs). We achieved a manipulation of the gain spectrum of the OPO via EO and/or temperature control of the EO PMCs, in which we obtained single to multiple signal spectral peaks from the OPO with a spectral width reduced by up to 10 times and peak intensity increased by up to 6 times in comparison with the original signal. Fast EO tuning of the narrowed signal spectral peak has also been demonstrated.     

Multivariate Regular Variation of Discrete Mass Functions with Applications to Preferential Attachment Networks

Regular variation of a multivariate measure with a Lebesgue density implies the regular variation of its density provided the density satisfies some regularity conditions. Unlike the univariate case, the converse also requires regularity conditions. We extend these arguments to discrete mass functions and their associated measures using the concept that the mass function can be embedded in a joint density function with continuous arguments. We give two different conditions, monotonicity and convergence on the unit sphere, both of which can make the discrete function embeddable. Our results are then applied to the preferential attachment network model, and we conclude that the joint mass function of in- and out-degree is embeddable and thus regularly varying.