Solutions of the Dirac–Fock Equations for Atoms¶and Molecules

The Dirac-Fock equations are the relativistic analogue of the well-known Hartree-Fock equations. They are used in computational chemistry, and yield results on the inner-shell electrons of heavy atoms that are in very good agreement with experimental data. By a variational method, we prove the existence of infinitely many solutions of the Dirac-Fock equations "without projector", for Coulomb systems of electrons in atoms, ions or molecules, with Z h 124, N h 41, N h Z. Here, Z is the sum of the nuclear charges in the molecule, N is the number of electrons.     

Nature of urea-fluoride interaction: incipient and definitive proton transfer

1,3-bis(4-nitrophenyl)urea (1) interacts through hydrogen bonding with a variety of oxoanions in an MeCN solution to give bright yellow 1:1 complexes, whose stability decreases with the decreasing basicity of the anion (CH3COO- > C6H5COO- > H2PO4- > NO2- > HSO4- > NO3-). The [Bu4N][1.CH3COO] complex salt has been isolated as a crystalline solid and its molecular structure determined, showing the formation of a discrete adduct held together by two N-H...O hydrogen bonds of moderate strength. On the other hand, the F- ion first establishes a hydrogen-bonding interaction with 1 to give the most stable 1:1 complex, and then on addition of a second equivalent, induces urea deprotonation, due to the formation of HF2-. The orange-red deprotonated urea solution uptakes carbon dioxide from air to give the tetrabutylammonium salt of the hydrogencarbonate H-bond complex, [Bu4N][1.HCO3], whose crystal and molecular structures have been determined.     

Numerical Representations of Interval Orders

In the framework of the analysis of orderings whose associated indifference relation is not necessarily transitive, we study the structure of an interval order and its representability through a pair of real-valued functions. We obtain a list of characterizations of the existence of a representation, showing that the three main techniques that have been used in the literature to achieve numerical representations of interval orders are indeed equivalent.     

Mixing Closures for Conservation Laws in Stratified Flows

A closure for shocks involving the mixing of the fluids in two-layer stratified flows is proposed. The closure maximizes the rate of mixing, treating the dynamical hydraulic equations and entropy conditions as constraints. This closure may also be viewed as yielding an upper bound on the mixing rate by internal shocks. It is shown that the maximal mixing rate is accomplished by a shock moving at the fastest allowable speed against the upstream flow. Depending on whether the active constraint limiting this speed is the Lax entropy condition or the positive dissipation of energy, we distinguish precisely between internal hydraulic jumps and bores. Maximizing entrainment is shown to be equivalent to maximizing a suitable entropy associated to mixing. By using the latter, one can describe the flow globally by an optimization procedure, without treating the shocks separately. A general mathematical framework is formulated that can be applied whenever an insufficient number of conservation laws is supplemented by a maximization principle.     

Complexation of Hg2+ with α‐Lipoic and Dihydrolipoic Acids: Study by Differential Pulse Voltammetry on Rotating Au‐Disk Electrode and ESI‐MS

The complexation of the natural antioxidants α‐lipoic acid (ALA) and its reduced form dihydrolipoic acid (DHLA) with Hg²⁺ was investigated by a recently proposed differential pulse voltammetric (DPV) method using the rotating Au‐disk electrode. Complexation processes are proposed from the multivariate curve resolution by alternating least squares (MCR‐ALS) analysis of DPV titration data. Main complexes were both 1 : 1 Hg : ALA and Hg : DHLA, although the formation of 1 : 2 complexes can be also deduced. ALA and DHLA show different Hg²⁺‐binding patterns at different pH. Voltammetric findings are completed with the data obtained by electrospray ionization mass‐spectrometry (ESI‐MS), especially in negative mode.     

Stripping analysis of heavy metals in tap water using the bismuth film electrode

A commercially available screen-printed carbon electrode coated with an ex situ deposited bismuth film (BiSPCE) has been applied to the determination of Pb(II) and Zn(II) ions in tap water (Barcelona water distribution network) by means of stripping voltammetry (SV) and stripping chronopotentiometry (SCP). A good reproducibility of the measurements and a satisfactory agreement between SV and SCP data were observed for both heavy metal ions. Although, in principle, the procedure could be also suited to the determination of Cd(II), this species was not detected. The results were also consistent with the routine ICP-OES measurements of the water distribution company, thus confirming the potential usefulness of such BiSPCE disposable devices for the analysis of heavy metals in natural waters.      

Size-exclusion chromatographic protein refolding: fundamentals, modeling and operation

Size-exclusion chromatography (SEC) has proven its capability to refold a variety of proteins using a range of gel filtration column materials, demonstrated in the growing body of experimental evidence. However, little effort has been allocated to the development of mechanistic models describing size-exclusion chromatographic refolding reactors (SECRR). Mechanistic models are important since they provide a link between process variables like denatured and reduced protein feed concentration (C_f,D&;R), flow rate, column length, etc., and performance indicators like refolding yield (Y_N), thereby opening the possibility for in silico design of SECRRs. A critical step, in the formulation of such models, is the selection of an adequate reaction mechanism, which provides the direct link between the separation and the refolding yield. Therefore, in this work we present a methodology using a SEC refolding reactor model, supported by a library of reaction mechanisms, to estimate a suitable reaction scheme using experimental SEC refolding data. SEC refolding data is used since it provides information about the mass distribution of monomers and aggregates after refolding, information not readily available from batch dilution refolding data alone. Additionally, this work presents (1) a systematic analysis of the reaction mechanisms considered using characteristic time analysis and Damköhler maps, revealing (a) the direct effect of a given reaction mechanism on the shape of the SEC refolding chromatogram (number of peaks and resolution) and (b) the effect that the competition between convection, refolding and aggregation is likely to have on the SEC refolding yield; (2) a comparison between the SECR reactor and the batch dilution refolding reactor based on mechanistic modeling, quantitatively showing the advantages of the former over the latter; and (3) the successful application of the modeling based strategy to study the SEC refolding data of an industrially relevant protein. In principle, the presented modeling strategy can be applied to any protein refolded using any gel filtration material, providing the proper mass balances and activity measurements are available.     

Homogeneous diffusion in ℝ with power-like nonlinear diffusivity

We study the nonnegative solutions of the initial-value problem u_t=(u^r|u_x|^p-1u_x)_x,u(x, 0)L ¹(), where p>0, r+p>0. The local velocity of propagation of the solutions is identified as V = -v_x| v_x|^p-1 where v =cu (with r +p - 1)/p and c (r +p/(r +p- 1)) is the nonlinear potential. Our main result is the a priori estimate (v_x|v_x|^p-1)_x-