Dual Forms on Supermanifolds and Cartan Calculus

We introduce and study the complex of “stable forms” on supermanifolds. Stable forms on a supermanifold M are represented by Lagrangians of “copaths” (formal systems of equations, which may or may not specify actual surfaces) on M×ℝ ^D . Changes of D give rise to stability isomorphisms. The resulting (direct limit) {Cartan-de Rham} complex made of stable forms extends both in positive and negative degree. Its positive half is isomorphic to the complex of forms defined as Lagrangians of paths, studied earlier. Including the negative half is crucial, in particular, for homotopy invariance. For stable forms we introduce (non-obvious) analogs of exterior multiplication by covectors and contraction with vectors and find the anticommutation relations that they obey. Remarkably, the version of the Clifford algebra so obtained is based on the super anticommutators rather than the commutators and (before stabilization) it includes some central element σ. An analog of Cartan's homotopy identity is proved, which also contains this “stability operator”σ. Received: 3 January 2000 / Accepted: 15 September 2001     

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.     

The adsorption of no on Ni(111); an esdiad/leed study

The ESDIAD method (electron stimulated desorption ion angular distributions) has been combined with LEED (low energy electron diffraction) in a study of the adsorption of NO on Ni(111). For adsorption at 80 K, NO appears to be bonded with its molecular axis perpendicular to the Ni(111) surface at all coverages. Heating the 80 K layer leads to a striking structural change which we interpret as the formation of inclined or bent NO in the range 120 ? T ? 250 K. Upon adsorption at 150 K, only the bent form of NO is present at low coverages; at higher coverages at 150 K, the perpendicular form appears, in agreement with recent electron energy loss spectroscopy (EELS) data of Lehwald, Yates, and Ibach. When NO is coadsorbed with p(2 × 2) oxygen, the perpendicular form of NO dominates at all coverages and temperatures studied. Dissociated NO adsorbed at steps and defect sites on Ni(111) produces a welldefined hexagonal ESDIAD pattern.     

Nonlinear eigenvalue problems with positively convex operators

We consider the equation u = λAu (λ > 0), where A is a forced isotone positively convex operator in a partially ordered normed space with a complete positive cone K. Let Λ be the set of positive λ for which the equation has a solution u?K, and let Λ₀ be the set of positive λ for which a positive solution—necessarily the minimum one—can be obtained by an iteration u_n = λAu_n?1, u₀ = 0. We show that if K is normal, and if Λ is nonempty, then Λ₀ is nonempty, and each set Λ₀, Λ is an interval with $\text{inf}\text{(Λ}{}_0\text{) =}\text{inf}\text{(Λ) = 0}\text{and sup}\text{(Λ}{}_0\text{) =}\text{sup}\text{(Λ) (= λ1,}\text{say}\text{)}$; but we may have λ1 ? Λ₀ and λ1 ? Λ. Furthermore, if A is bounded on the intersection of K with a neighborhood of 0, then Λ₀ is nonempty. Let u⁰(λ) = lim_n→∞(λA)ⁿ(0) be the minimum positive fixed point corresponding to λ ? Λ₀. Then u⁰(λ) is a continuous isotone convex function of λ on Λ₀.     

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.