Molecular flow and wall collision age distributions

The use of storage cells has become a standard technique for internal gas targets in conjunction with high energy storage rings. In case of spin-polarized hydrogen and deuterium gas targets the interaction of the injected atoms with the walls of the storage cell can lead to depolarization and recombination. Thus the number of wall collisions of the atoms in the target gas is important for modeling the processes of spin relaxation and recombination. It is shown in this article that the diffusion process of rarefied gases in long tubes or storage cells can be described with the help of the one-dimensional diffusion equation. Mathematical methods are presented that allow one to calculate collision age distributions (CAD) and their moments analytically. These methods provide a better understanding of the different aspects of diffusion than Monte Carlo calculations. Additionally it is shown that measurements of the atomic density or polarization of a gas sample taken from the center of the tube allow one to determine the possible range of the corresponding density weighted average values along the tube. The calculations are applied to the storage cell geometry of the HERMES internal polarized hydrogen and deuterium gas target. Received 9 July 2001 and Received in final form 18 September 2001     

A semiempirical model for the two-center repulsion integrals in the NDDO approximation

A self-consistent formalism is proposed for the two-center electron repulsion integrals in the NDDO approximation, based on their expansion in terms of multipole-multipole interactions and free from adjustable parameters.     

Protein Conformational Flexibility from Structure‐Free Analysis of NMR Dipolar Couplings: Quantitative and Absolute Determination of Backbone Motion in Ubiquitin

A robust procedure for the determination of protein‐backbone motions on time scales of pico‐ to milliseconds directly from residual dipolar couplings has been developed that requires no additional scaling relative to external references. The results for ubiquitin (blue in graph: experimental N? HN order parameters) correspond closely to the amplitude, nature, and distribution of motion found in a 400 ns molecular‐dynamics trajectory of ubiquitin (red).

     

C-H activation and C=C double bond formation reactions in iridium ortho-methyl arylphosphane complexes

The Vaska-type iridium(I) complex [IrCl(CO){PPh(2)(2-MeC(6)H(4))}(2)] (1), characterized by an X-ray diffraction study, was obtained from iridium(III) chloride hydrate and PPh(2)(2,6-MeRC(6)H(3)) with R=H in DMF, whereas for R=Me, activation of two ortho-methyl groups resulted in the biscyclometalated iridium(III) compound [IrCl(CO){PPh(2)(2,6-CH(2)MeC(6)H(3))}(2)] (2). Conversely, for R=Me the iridium(I) compound [IrCl(CO){PPh(2)(2,6-Me(2)C(6)H(3))}(2)] (3) can be obtained by treatment of [IrCl(COE)(2)](2) (COE=cyclooctene) with carbon monoxide and the phosphane in acetonitrile. Compound 3 in CH(2)Cl(2) undergoes intramolecular C-H oxidative addition, affording the cyclometalated hydride iridium(III) species [IrHCl(CO){PPh(2)(2,6-CH(2)MeC(6)H(3))}{PPh(2)(2,6-Me(2)C(6)H(3))}] (4). Treatment of 2 with Na[BAr(f) (4)] (Ar(f)=3,5-C(6)H(3)(CF(3))(2)) gives the fluxional cationic 16-electron complex [Ir(CO){PPh(2)(2,6-CH(2)MeC(6)H(3))}(2)][BAr(f) (4)] (5), which reversibly reacts with dihydrogen to afford the delta-agostic complex [IrH(CO){PPh(2)(2,6-CH(2)MeC(6)H(3))}{PPh(2)(2,6-Me(2)C(6)H(3))}][BAr(f)(4)] (6), through cleavage of an Ir-C bond. This species can also be formed by treatment of 4 with Na[BAr(f)(4)] or of 2 with Na[BAr(f)(4)] through C-H oxidative addition of one ortho-methyl group, via a transient 14-electron iridium(I) complex. Heating of the coordinatively unsaturated biscyclometalated species 5 in toluene gives the trans-dihydride iridium(III) complex [IrH(2)(CO){PPh(2)(2,6-MeC(6)H(3)CH=CHC(6)H(3)Me-2,6)PPh(2)}][BAr(f) (4)] (7), containing a trans-stilbene-type terdentate ligand, as result of a dehydrogenative carbon-carbon double bond coupling reaction, possibly through an iridium carbene species.     

Program explanations and causal relevance

Frank Jackson and Philip Pettit have defended a non-reductive account of causal relevance known as the ‘program explanation account’. Allegedly, irreducible mental properties can be causally relevant in virtue of figuring in non-redundant program explanations which convey information not conveyed by explanations in terms of the physical properties that actually do the ‘causal work’. I argue that none of the possible ways to spell out the intuitively plausible idea of a program explanation serves its purpose, viz., defends non-reductive physicalism against Jaegwon Kim’s Causal Exclusion Argument according to which non-reductive physicalism is committed to epiphenomenalism because irreducible mental properties are ‘screened off’ from causal relevance by their physical realizers. Jackson and Pettit’s most promising explication of a program explanation appeals to the idea of invariance of effect under variation of realization, but I show that invariance of effect under variation of realization is neither necessary nor sufficient for causal relevance.     

Nonvanishing derivatives and normal families

We consider the differential operators Ψ _k , defined by Ψ₁(y) =y and Ψ _k+1(y)=yΨ _k y+d/dz(Ψ _k (y)) fork ∈ ℕ fork∈ ℕ. We show that ifF is meromorphic in ℂ and Ψ _k F has no zeros for somek≥3, and if the residues at the simple poles ofF are not positive integers, thenF has the formF(z)=((k-1)z+a)/(z ²+β z+γ) orF(z)=1/(az+β) where α, β, γ ∈ ℂ. If the residues at the simple poles ofF are bounded away from zero, then this also holds fork=2. We further show that, under suitable additional conditions, a family of meromorphic functionsF is normal if each Ψ _k (F) has no zeros. These conditions are satisfied, in particular, if there exists δ>0 such that Re (Res(F, a)) <−δ for all polea of eachF in the family. Using the fact that Ψ _k (f ^′/f) =f ^(k)/f, we deduce in particular that iff andf ^(k) have no zeros for allf in some familyF of meromorphic functions, wherek≥2, then {f ^′/f :f ∈F} is normal. The first author is supported by the German-Israeli Foundation for Scientific Research and Development G.I.F., G-643-117.6/1999, and INTAS-99-00089. The second author thanks the DAAD for supporting a visit to Kiel in June–July 2002. Both authors thank Günter Frank for helpful discussions.     

Absence of shocks in an initially dilute collisionless plasma

The Cauchy Problem for the relativistic Vlasov-Maxwell equations is studied in three space dimensions. It is assumed that the initial data satisfy the required constraints and have compact support. If in addition the data have sufficiently smallC ² norm, then a uniqueC ¹ solution to this system is shown to exist on all of spacetime.Research supported in part by NSF DMS 85-20662 and NSF DMS 84-20957     

PHOTOCHEMISTRY OF ALL-TRANS- AND 13-CIS-14,15-DIDEUTERIORETINAL

Abstract— All- trans - and 13- cis -14,15-dideuterioretinal were synthesized and their solution photochemistry examined. Quantum yields of trans → cis or cis → trans photoisomerization and the number and ratio of primary photoproducts, determined by high pressure liquid chromatographic analysis, are essentially identical to that of their corresponding retinal isomer. The C-14, C-15 carbon-hydrogen modes play no particularly important role in the deactivation of electronically excited linear polyenes related to retinal.