On the algebraic structure ofN=2 string theory

InN=2 string theory the chiral algebra expresses the generations and anti-generations of the theory and the Yukawa couplings among them and is thus crucial to the phenomenological properties of the theory. Also the connection with complex geometry is largely through the algebras. These algebras are systematically investigated in this paper. A solution for the algebras is found in the context of rational conformal field theory based on Lie algebras. A statistical mechanics interpretation for the chiral algebra is given for a large family of theories and is used to derive a rich structure of equivalences among the theories (dihedralities). The Poincaré polynomials are shown to obey a resolution series which cast these in a form which is a sum of complete intersection Poincaré polynomials. It is suggested that the resolution series is the proper tool for studying allN=2 string theories and, in particular, exposing their geometrical nature.     

How likely is Polya's drunkard to stay in x⩾ y⩾z?

In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay inxyz. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844....     

Comparison between potentiostatic and galvanostatic intermittent titration techniques for determination of chemical diffusion coefficients in ion-insertion electrodes

Using well-cycled, thin composite graphite electrodes we analyze carefully the limitations of potentiostatic and galvanostatic intermittent titration techniques (PITT and GITT, respectively) for determination of the differential (incremental) intercalation capacitance, C_dif, and the chemical diffusion coefficient, D, of Li ions in these ion-insertion electrodes (IIEs). We demonstrate the superiority of the GITT over PITT to determine these quantities as the former technique allows for a more accurate determination of C_dif and hence D which closely approach to the spinodal domain related to the first-order phase transition during ion-insertion. We show that GITT is also more effective in eliminating the parasitic contributions of background currents to the total measured response. A pronounced difference in the initial, intrinsic kinetics of formation of a new phase in the bulk of the old one has been observed depending on the direction of titration (phases less saturated with Li are formed faster during deintercalation than the Li-rich phases in the course of intercalation).     

The crystal structure of the inorganic surface films formed on Mg and Li intercalation compounds and the electrode performance

A crystallographic approach was applied to elucidate the influence of the nature of the surface films on the electrochemical behavior of Li and Mg intercalation compounds. This paper presents two examples: (1) protection of graphite electrodes by Li₂CO₃ surface films, and (2) the unique electrochemical behavior of Mg-containing Chevrel phases (MgCP) obtained by different synthetic routes. In the former case, the elucidation of the protection mechanism and the explanation of the high performance of such protected electrodes are based on the analysis of possible Li-ion motion in the carbonate crystal structure. In the latter case, a combination of synthesis, electrochemistry and XRD analysis was used to explain an unusual phenomenon: the difference between the excellent electrochemical behavior of the Chevrel phase (CP) based on Cu-leached Cu₂Mo₆S₈ (CuCP), and the poor electrochemical activity of the high-temperature synthesized MgCP, with the same phase composition. It is shown that this phenomenon is caused by MgO formation on the surface of the latter material. The different surface chemistry of the MgCPs obtained by the two different synthetic routes was substantiated by revealing the correlation between the electrochemical activity and the chemical stability of these materials under ambient atmosphere conditions. Dedicated to Prof. Mikhail A. Vorotyntsev on the occasion of his 60th birthday.     

Molten salt synthesis (MSS) of Cu2Mo6S8—New way for large-scale production of Chevrel phases

The Chevrel phase (CP), Mo₆S₈, was found to be an excellent cathode material for rechargeable magnesium batteries. Mo₆S₈ is obtained by a leaching process of Cu₂Mo₆S₈, which removes the copper. A new method of Cu₂Mo₆S₈ production was developed. In contrast to the well-known solid-state synthesis of CP, the method is based on the reaction in a molten salt media (KCl). A fast kinetics of this reaction allows using less active, but more convenient precursors (sulfides instead of sulfur), decreasing temperature and synthesis duration, as well as operation in the inert atmosphere instead of dynamic evacuated systems. It was shown that the composition and the electrochemical behavior of the products obtained by MSS and by the solid-state synthesis are identical. Thus, the molten salt method is extremely attractive for the large-scale production of the active materials for Mg batteries.     

Effect of the Structure of Nonuniform Conducting Polymer Films on Their Electrochemical Impedance Response

Electrochemical impedance spectroscopy is used to characterize thin p-doped polypyrrole (PPy) films in propylene carbonate (PC) solutions and poly(trifluorophenyl)thiophene (PTFPT), in solutions based on sulfolane (SF). It appears that the latter film is much less swelled compared to the former one. One consequence of this difference is that the PTFPT film shows a much higher bulk resistance compared to that for the PPy film. Another important consequence is that the swelling of the PTFPT film is essentially physically non-homogeneous. Two parallel, uncoupled paths, with different chemical diffusion coefficients, model the experimental results adequately. In order to quantify the impedance spectra for both polymer films, we use a model proposed by Rubinstein et al. explaining the difference in the diffusion coefficients of Ru(bpy)^3+/2+ ₃ within a thin Nafion film. The model can also predict the impedance spectra for composite powdery electrodes containing different particle sizes, such as composite cathodes and graphite anodes used in lithium batteries.     

Aerobic Iron‐Based Cross‐Dehydrogenative Coupling Enables Efficient Diversity‐Oriented Synthesis of Coumestrol‐Based Selective Estrogen Receptor Modulators

An iron‐based cross‐dehydrogenative coupling (CDC) approach was applied for the diversity‐oriented synthesis of coumestrol‐based selective estrogen receptor modulators (SERMs), representing the first application of CDC chemistry in natural product synthesis. The first stage of the two‐step synthesis of coumestrol involved a modified aerobic oxidative cross‐coupling between ethyl 2‐(2,4‐dimethoxybenzoyl)acetate and 3‐methoxyphenol, with FeCl₃ (10 mol %) as the catalyst. The benzofuran coupling product was then subjected to sequential deprotection and lactonization steps, affording the natural product in 59 % overall yield. Based on this new methodology other coumestrol analogues were prepared, and their effects on the proliferation of the estrogen receptor (ER)‐dependent MCF‐7 and of the ER‐independent MDA‐MB‐231 breast cancer cells were tested. As a result, new types of estrogen receptor ligands having an acetamide group instead of the 9‐hydroxyl group of coumestrol were discovered. Both 9‐acetamido‐coumestrol and 8‐acetamidocoumestrol were found more active than the natural product against estrogen‐dependent MCF‐7 breast cancer cells, with IC₅₀ values of 30 and 9 nM , respectively.