Singular Matched Eigenfunction Expansions for Stokes Flow around a Corner

A singular matched eigenfunction expansion method is describedfor solving Stokes flow around a corner. The flow region isdecomposed into a number of simpler rectangular subregions;this enables the stream function to be represented by meansof an expansion of Papkovich-Fadle eigenfunctions in each ofthese subregions. The coefficients in these expansions are obtainedby matching them across common interfaces in a weak sense. Theresulting solution is used in a post-processing technique todetermine the coefficients in the known locally convergent expansionof the stream function at reentrant and salient corners. A smallnumber of terms in this expansion is necessary to produce accurateapproximations.     

Fourier Series Solutions to Poisson's Equation in Rectangularly Decomposable Regions

Fourier senes solutions to Poisson problems defined in rectangularlydecomposable regions are found by matching solutions in a weaksense across the interfaces dividing subregions. The matchingprocess produces an infinite system of algebraic equations forthe unknown expansion coefficients. Complex analysis is usedto investigate theoretically the conditioning of the coefficientmatrix for both the C⁰ and C¹ matching problems. The formeris shown to be not well-defined whereas the latter is extremelywell-conditioned. Furthermore, the analysis of the coefficientmatrix for the weak C¹ problem suggests a rapidly convergentiterative method for solving the truncated algebraic systemfor the expansion coefficients. Accurate approximations areobtained after a handful of iterations and with few degreesof freedom.     

A Consistent System of Curved Electron Arrows

Many students of organic chemistry find it difficult to properly use electron arrows. Traditional arrows do not end at one type of location. Whereas the vast majority end at an atom, an arrow that indicates formation of a bond points to a bond instead. Rethinking electron arrows leads to the following four rules, which form a consistent system:1. An electron arrow always begins at an electron pair, either bonding or nonbonding. One arrow begins at the nucleophilic electron pair, if any.2. An electron pair always remains attached to an atom, normally indicated by its arrow.3. An electron arrow always ends at an atom, not at a bond. One arrow ends at the electrophilic atom, if an.4. In a series of arrows for one mechanistic step, a succeeding arrow begins by the atom where the preceding arrow ends.This system of electron arrows is superior because the rules can be more generally applied, the arrows reflect the nucleophilicity of electron pairs, the arrows carry more meaning, the arrows in a series flow more directly from one to the next, and the arrows clearly prescribe products.     

Complexation of hydrogen by lithium: structures,energies and vibrational spectra of Li+ (H2) n (n = 1–4), Li-H(H2) m and Li-H + (H2) m (m = 1–3)

The interaction of metals with hydrogen is of importance in several areas of technology. Lithium-hydrogen complexes are particularly amenable to theoretical study. Although no stable compound of the Li atom and H₂ has been found, a weak dative interaction forms between the σ bond of H₂ and the positively charged Li atom for Li⁺, Li-H⁺, and Li-H. At least four H₂ molecules can be complexed by Li⁺, and three by Li-H⁺ and Li-H. The presence of the Li ion does not substantially weaken the H₂ bond, nor is the energy of dissociation affected; however, the Li ion does form stable complexes with the dissociated H atoms.     

On the Legendre Coefficients of a General-Order Derivative of an Infinitely Differentiable Function

An expression relating the Legendre coefficients of a generalderivative of an infinitely differentiable function in termsof the Legendre coefficients of the function is proved.     

PHOTOCHEMICAL REDUCTION OF 5-BROMOURACIL BY CYSTEINE DERIVATIVES AND COUPLING OF 5-BROMOURACIL TO CYSTINE DERIVATIVES

Irradiation of pH 7, aqueous solutions of 5-bromouracil (BU) in the presence of cysteine peptide-like derivatives at 308 nm using a XeCl excimer laser yielded initial formation of only uracil (U) and the corresponding cystine derivative. Continued irradiation yielded an S-uracilylcysteinyl adduct as well as additional U and cystine derivative. Similar irradiation of a solution of BU and a cystine derivative yielded initial formation of U and the S-uracilylcysteinyl adduct. Formation of these products as well as secondary products of uracil photochemistry was observed upon irradiation of the respective solutions with 254 nm light. With 308 nm laser excitation, U-Cys adduct formation and reduction of BU to U are proposed to occur via initial electron transfer from the disulfide of the cystine derivative to triplet BU. The quantum yield of BU destruction with 308 nm excitation in the presence of cystine derivative is 1.1 X 10(-3). Reaction of triplet BU with the cysteine derivative does not yield U-Cys adduct but U and cystine derivative. A possible byproduct of reduction of triplet BU to U by a cysteinyl residue in a protein BU-DNA complex is a sulphenyl bromide which might yield a protein-DNA crosslink via nucleophilic substitution on sulfur by a nucleophilic site in DNA.     

DEVELOPMENT AND EVALUATION OF A SYSTEM DYNAMICS MODEL FOR INVESTIGATING AGRICULTURALLY DRIVEN LAND TRANSFORMATION IN THE NORTH CENTRAL UNITED STATES

Land transformation from grassland to cropland in the Northern Great Plains (NGP) has become a growing concern among many stakeholders. A growing body of work has sought to determine the amount and rate of land use change with less emphasis on the systemic structures or feedback processes of land use decisions. This paper presents the development of a system dynamics simulation model to integrate ecological, economic, and social components influencing land use decisions, including cattle ranching, cropland production, rural communities, land quality, and public policies. Evaluation indicated that the model satisfactorily predicted historical land, agricultural commodity, and rural community data from the model structure. Reference modes for key variables, including the farmland area, were characterized by a bias correction of 0.999, root mean squared error of prediction of 0.053, R² of 0.921, and concordance correlation coefficient of 0.0959. The model was robust under extreme and varying sensitivity tests, as well as adequately predicting land use under changing system context. The model's major contributions were the inclusion of decision‐making feedbacks from economic and social signals with connectivity to land quality and elasticity values that drive land transformation. Limitations include lack of spatial input and output capabilities useful for visual interfacing.     

The near infrared overtone spectrum of propyne taken by diode laser in the 12700 cm−1region

Detailed regions of the near infrared spectrum of propyne between 12737 cm-¹ and 12778cm-¹ have been measured using a simple and inexpensive home-made laser diode spectrometer. This part of the spectrum covers the overlapping 3v₁ + v₃ + v₅ and 3v₁ + v₃ + v₅ + v₁₀—v₁₀ bands. Combining a global fit and an individual profile analysis made possible the determination of the vibrational and rotational constants in each band and in some cases the resolution of the individual K structure in each transition cluster.     

Accurate ab initio anharmonic force field and heat of formation for silane

From large basis set coupled cluster calculations and a minor empirical adjustment, an anharmonic force field for silane has been derived that is consistently of spectroscopic quality (±1 cm^?1 on vibrational fundamentals) for all isotopomers of silane studied. Inner-shell polarization functions have an appreciable effect on computed properties and even on anharmonic corrections. From large basis set coupled cluster calculations and extrapolations to the infinite-basis set limit, we obtain TAE₀ = 303.80 ± 0.18 kcal mol^?1, which includes an anharmonic zero-point energy (19.59 kcal mol^?1), inner-shell correlation (—0.36 kcal mol^?1), scalar relativistic corrections (— 0.70 kcal mol^?1) and atomic spin-orbit corrections (—0.43 kcal mol^?1). In combination with the recently revised ΔH ^o _{f, o}[Si(g)], we obtain ΔH ^o _f.o[SiH₄(g)] = 9.9 ± 0.4 kcal mol^?1 in between the two established experimental values.