Sinc-Galerkin method for solving linear sixth-order boundary-value problems

There are few techniques available to numerically solve sixth-order boundary-value problems with two-point boundary conditions. In this paper we show that the Sinc-Galerkin method is a very effective tool in numerically solving such problems. The method is then tested on examples with homogeneous and nonhomogeneous boundary conditions and a comparison with the modified decomposition method is made. It is shown that the Sinc-Galerkin method yields better results.

     

The synthesis and structure of potassium cyanotrimethylaluminate

The reaction of KCN with Al(CH₃)₃ to form K[Al(CH₃)₃CN] is greatly facilitated by the presence of an aromatic solvent: for p-xylene a solid complex, K[Al(CH₃)₃CN]·C₆H₄(CH₃)₂, has been isolated. The crystal structure of potassium cyanotrimethylaluminate has been determined from three-dimensional X-ray data measured by counter methods. K[Al(CH₃)₃CN] crystallizes in the monoclinic space group C2/c with cell dimensions a = 19.902(7), b = 9.211(4), c = 9.615(4) Å, β = 107.74(5)°, and p_calcd. = 1.09 g cm^?1 for Z = 8. Least squares refinement gave a conventional weighted R factor of 4.9% for 807 independent reflections. The monomeric [Al(CH₃)₃CN]^? units possess no crystallographic symmetry, and the packing in the unit cell is such that the nitrogen atoms on three such units approach the potassium atom to within 3.11 Å. The average aluminum-methyl carbon bond distance is 1.971 (7) Å, while the aluminum-cyano carbon distance is 2.047 (7) Å. This significant lengthening is attributed to partial electron deficiency in the aluminum-cyano carbon bond.     

The classical solution of the one-dimensional two-phase stefan problem with energy specification

Summary Existence and unicity for the solution of the one-dimensional two-phase Stefan problem with energy specification in the liquid phase is established via potential theoretic arguments employing the Schauder fixed point theorem and a contracting map.This work was supported in part by NSF Grant MCS-7801687.This work was carried out at UT-Austin while on sabbatical from the University of Adelaide.     

Six‐coordinate Co2+ with imidazole,NH3, and H2O ligands: Approaching spin crossover

Octahedral, six‐coordinate Co²⁺ can exist in two spin states: S = 3/2 and S = 1/2. The difference in energy between high spin (S = 3/2) and low spin (S = 1/2) is dependent on both the ligand mix and coordination stereochemistry. B3LYP calculations on combinations of neutral imidazole, NH₃, and H₂O ligands show that low‐spin isomers are stabilized by axial H₂O ligands and in structures that also include trans pairs of equatorial NH₃ and protonated imidazole ligands, spin crossover structures are predicted from spin state energy differences. Occupied Co d orbitals from the DFT calculations provide a means of estimating effective ligand strength for homoleptic and mixed ligand combinations. These calculations suggest that in a labile biological system, a spin crossover environment can be created. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Numerical Investigation of Graphene as a Back Surface Field Layer on the Performance of Cadmium Telluride Solar Cell

This paper numerically explores the possibility of ultrathin layering and high efficiency of graphene as a back surface field (BSF) based on a CdTe solar cell by Personal computer one-dimensional (PC1D) simulation. CdTe solar cells have been characterized and studied by varying the carrier lifetime, doping concentration, thickness, and bandgap of the graphene layer. With simulation results, the highest short-circuit current (I_sc = 2.09 A), power conversion efficiency (η = 15%), and quantum efficiency (QE~85%) were achieved at a carrier lifetime of 1 × 10³ μs and a doping concentration of 1 × 10¹⁷ cm⁻³ of graphene as a BSF layer-based CdTe solar cell. The thickness of the graphene BSF layer (1 μm) was proven the ultrathin, optimal, and obtainable for the fabrication of high-performance CdTe solar cells, confirming the suitability of graphene material as a BSF. This simulation confirmed that a CdTe solar cell with the proposed graphene as the BSF layer might be highly efficient with optimized parameters for fabrication.     

Phenothiazine–BODIPY–Fullerene Triads as Photosynthetic Reaction Center Models: Substitution and Solvent Polarity Effects on Photoinduced Charge Separation and Recombination

Novel photosynthetic reaction center model compounds of the type donor₂–donor₁–acceptor, composed of phenothiazine, BF₂‐chelated dipyrromethene (BODIPY), and fullerene, respectively, have been newly synthesized using multistep synthetic methods. X‐ray structures of three of the phenothiazine‐BODIPY intermediate compounds have been solved to visualize the substitution effect caused by the phenothiazine on the BODIPY macrocycle. Optical absorption and emission, computational, and differential pulse voltammetry studies were systematically performed to establish the molecular integrity of the triads. The N‐substituted phenothiazine was found to be easier to oxidize by 60 mV compared to the C‐substituted analogue. The geometry and electronic structures were obtained by B3LYP/6‐31G(dp) calculations (for H, B, N, and O) and B3LYP/6‐31G(df) calculations (for S) in vacuum, followed by a single‐point calculation in benzonitrile utilizing the polarizable continuum model (PCM). The HOMO?1, HOMO, and LUMO were, respectively, on the BODIPY, phenothiazine and fullerene entities, which agreed well with the site of electron transfer determined from electrochemical studies. The energy‐level diagram deduced from these data helped in elucidating the mechanistic details of the photochemical events. Excitation of BODIPY resulted in ultrafast electron transfer to produce PTZ–BODIPY^.+–C₆₀^.?; subsequent hole shift resulted in PTZ^.+–BODIPY–C₆₀^.? charge‐separated species. The return of the charge‐separated species was found to be solvent dependent. In nonpolar solvents the PTZ^.+–BODIPY–C₆₀^.? species populated the ³C₆₀* prior to returning to the ground state, while in polar solvent no such process was observed due to relative positioning of the energy levels. The ¹BODIPY* generated radical ion‐pair in these triads persisted for few nanoseconds due to electron transfer/hole‐shift mechanism.     

Nickel‐Catalyzed α‐Carbonylalkylarylation of Vinylarenes: Expedient Access to γ,γ‐Diarylcarbonyl and Aryltetralone Derivatives

We report a Ni‐catalyzed regioselective α‐carbonylalkylarylation of vinylarenes with α‐halocarbonyl compounds and arylzinc reagents. The reaction works with primary, secondary, and tertiary α‐halocarbonyl molecules, and electronically varied arylzinc reagents. The reaction generates γ,γ‐diarylcarbonyl derivatives with α‐secondary, tertiary, and quaternary carbon centers. The products can be readily converted to aryltetralones, including a precursor to Zoloft, an antidepressant drug.     

Continuous sample paths in quantum field theory

Nelson's free Markoff field on ? ^l+1 is a natural generalization of the Ornstein-Uhlenbeck process on ?¹, mapping a class of distributions φ(x,t) on ? ^l ×?¹ to mean zero Gaussian random variables φ with covariance given by the inner product \(\left( {\left( {m^2 - \Delta - \frac{{\partial ^2 }}{{\partial t^2 }}} \right)^{ - 1} \cdot , \cdot } \right)_2 \) . The random variables φ can be considered functions φ〈q〉=∝ φ(x,t)q(x,t)d x dt on a space of functionsq(x,t). In the O.U. case,l=0, the classical Wiener theorem asserts that the underlying measure space can be taken as the space of continuous pathst →q(t). We find analogues of this, in the casesl>0, which assert that the underlying measure space of the random variables φ which have support in a bounded region of ? ^l+1 can be taken as a space of continuous pathst →q(·,t) taking values in certain Soboleff spaces.     

An exact solution to the multi-dimensional line transfer equation

The theory of generalized analytic functions is used to obtain an exact closed form analytical solution to a transfer problem for spectral line radiation in a multi-dimensional atmosphere. The multi-dimensional full-space and half-space Green's functions so obtained are quite general and may be used, along with the corresponding orthogonality relationships, to obtain solutions to any general multi-dimensional radiative transfer problem involving model two-level atoms. An application of the method using perturbation techniques is illustrated.