High order stiffly stable composite multistep methods for numerical integration of stiff differential equations

Let \(\dot y\) =f(y,t) withy(t ₀)=y ₀ possess a solutiony(t) fort≧t ₀. Sett _n=t ₀+nh, n=1, 2,.... Lety ₀ denote the approximate solution ofy(t _n) defined by the composite multistep method with \(\dot y_n \) =f(y _n ,t _n ) andN=1, 2,.... It is conjectured that the method is stiffly stable with orderp=l for alll≧1 and shown to be so forl=1,..., 25. The method is intrinsically efficient in thatl future approximate solution values are established simultaneously in an iterative solution process with only one function evaluation per iteration for each of thel future time points. Step and order control are easily implemented, in that the approximate solution at only one past point appears in each component multistep formula of the method and in that the local truncation error for the first component multistep formula of the method is easily evaluated as $$T^{[l]} = \frac{h}{{t_{Nl} - t_{(N - 1)l - 1} }}\{ y_{Nl}^{PRED} - y_{Nl} \} ,$$ wherey _Nl ^PRED denotes the value att _Nl of the Lagrange interpolating polynomial passing through the pointsy _(N?1)l+j att _(N?1)l+j withj=?1, 0,...,l ? 1.     

Organic salts as powerful lanthanide shift donors

The interaction of Eu(fod)₃ with organic salts is studied.     

Evidence for molecular reorientations on a surface: Coadsorption of CO and Na on Ru(001)

Evidence is presented for a local interaction between CO and Na adsorbed on Ru(001). For low coverages of Na (θ_Na ? 0.15 ML) and saturation coverages of CO at 80 K. a fraction of the CO molecules undergo a substantial change in bonding configuration: molecular CO bound perpendicular to the Ru(001) surface changes to an “inclined” configuration in the presence of low coverages of Na.     

ESCA study of fractional monolayer quantities of chemisorbed gases on tungsten

X-ray photoelectron spectroscopy (ESCA) has been used in a study of CO and O₂ chemisorbed on a polycrystalline tungsten sample. Working under ultra-high vacuum conditions, the surface was cleaned and then covered with known monolayer and fractional monolayer quantities of adsorbed CO and O₂. The O(ls) and C(ls) spectral features were detected, and the influence of an adsorbed layer on the tungsten spectral features was determined. A chemical shift of 3.4 eV in the O(ls) line from chemisorbed CO is related to the different modes of bonding of CO to tungsten. A model calculation of the photoelectron yields expected from an adsorbed monolayer is in good agreement with the experimental results.     

Reflection and forcing in E-recursion theory

E-recursive enumerability is compared via forcing to Σ₁ definability. It is shown that for every countable E-closed ordinal κ there is a set of reals, X, so that L_κ[X] is the least E-closed structure over X.     

Evidence for the conformation of H2O adsorbed on Ru(001)

The electron stimulated desorption ion angular distributions (ESDIAD) method has been used to study the adsorption of H₂O by Ru(001). The results indicate that chemisorbed, undissociated H₂O is bonded to Ru via the oxygen atom, and that interactions between neighboring molecules occur as coverage increases. The utility of ESDIAD for structure determination in the absence of long range order is demonstrated.