Nitrogen‐Doped Carbon Nanotube‐Based Bilayer Thin Film as Transparent Counter Electrode for Dye‐Sensitized Solar Cells (DSSCs)

Carbon nanotubes (CNTs) have been widely considered as one of the promising candidates for replacing fluorine‐doped tin oxide (FTO)/platinum (Pt) electrodes to reduce the fabrication cost of dye‐sensitized solar cells (DSSCs). Here, we report that a bilayer transparent film containing N‐doped CNTs (which are highly catalytic) and normal CNTs (which are highly conductive) as a counter electrode in DSSCs results in efficiencies up to 2.18 %, yet still maintains a good transparency with a transmittance of approximately 57 % at 550 nm.     

Calibration of STUD+ Parameters to Achieve Optimally Efficient Broadband Adiabatic Decoupling in a Single Transient

To provide the most efficient conditions for spin decoupling with least RF power, master calibration curves are provided for the maximum centerband amplitude, and the minimum amplitude for the largest cycling sideband, resulting from STUD+ adiabatic decoupling applied during a single free induction decay. The principal curve is defined as a function of the four most critical experimental input parameters: the maximum amplitude of the RF field,RF_max, the length of the sech/tanh pulse,T_p, the extent of the frequency sweep,bwdth,and the coupling constant,J_o. Less critical parameters, the effective (or actual) decoupled bandwidth,bw_eff, and the sech/tanh truncation factor, β, which become more important asbwdthis decreased, are calibrated in separate curves. The relative importance of nine additional factors in determining optimal decoupling performance in a single transient are considered. Specific parameters for efficient adiabatic decoupling can be determined via a set of four equations which will be most useful for¹³C decoupling, covering the range of one-bond¹³C¹H coupling constants from 125 to 225 Hz, and decoupled bandwidths of 7 to 100 kHz, with a bandwidth of 100 kHz being the requirement for a 2 GHz spectrometer. The four equations are derived from a recent vector model of adiabatic decoupling, and experiment, supported by computer simulations. The vector model predicts an inverse linear relation between the centerband and maximum sideband amplitudes, and it predicts a simple parabolic relationship between maximum sideband amplitude and the productJ_oT_p. The ratiobwdth/(RF_max)²can be viewed as a characteristic time scale, τ_c, affecting sideband levels, with τ_c≈T_pgiving the most efficient STUD+ decoupling, as suggested by the adiabatic condition. Functional relationships betweenbwdthand less critical parameters,bw_effand β, for efficient decoupling can be derived from Bloch-equation calculations of the inversion profile for a single sech/tanh pulse. Residual splitting of the centerband, normally associated with incomplete or inefficient decoupling, is not seen in sech/tanh decoupling and therefore cannot be used as a measure of adiabatic decoupling efficiency. The calibrated experimental performance levels achieved in this study are within 20% of theoretical performance levels derived previously for ideal sech/tanh decoupling at high power, indicating a small scope for further improvement at practical RF power levels. The optimization procedures employed here will be generally applicable to any good combination of adiabatic inversion pulse and phase cycle.     

Exponential polynomials as solutions of certain nonlinear difference equations

Recently, C.-C. Yang and I. Laine have investigated finite order entire solutions f of nonlinear differential-difference equations of the form fn + L(z, f ) = h, where n ≥ 2 is an integer. In particular, it is known that the equation f(z)2 + q(z)f (z + 1) = p(z), where p(z), q(z) are polynomials, has no transcendental entire solutions of finite order. Assuming that Q(z) is also a polynomial and c ∈ C, equations of the form f(z)n + q(z)e Q(z) f(z + c) = p(z) do posses finite order entire solutions. A classification of these solutions in terms of growth and zero distribution will be given. In particular, it is shown that any exponential polynomial solution must reduce to a rather specific form. This reasoning relies on an earlier paper due to N. Steinmetz.     

The preparation and reduction of 5-cyano-3-indolylketones. Synthesis of 5-cyanotryptamines

The acylation of indoles under acidic conditions has been studied. Stannic chloride was shown to be an effective catalyst for the preparation of some 3-acylindoles, notably 5-cyano-3-indolylketones. The various 5-cyano -3 - indolylketones were reduced with sodium borohydride to yield either the 5-cyano-3-carbinols or 5-cyano-3-alkylindoles. 5-Cyanotryptamines were obtained by reduction of appropriate α-dialkylamino and α-azidoketones. A cleavage reaction of the carbinols involving loss of the 3-side chain to yield 5-cyanoindole is also described.     

The Iwasawa Main Conjectures for GL2

We prove the one-, two-, and three-variable Iwasawa-Greenberg Main Conjectures for a large class of modular forms that are ordinary with respect to an odd prime p. The method of proof involves an analysis of an Eisenstein ideal for ordinary Hida families for GU(2,2).