Quasi sure analysis and Stratonovich anticipative stochastic differential equations

Summary Consider a stochastic differential equation on ^d with smooth and bounded coefficients. We apply the techniques of the quasi-sure analysis to show that this equation can be solved pathwise out of a slim set. Furthermore, we can restrict the equation to the level sets of a nondegenerate and smooth random variable, and this provides a method to construct the solution to an anticipating stochastic differential equation with smooth and nondegenerate initial condition.     

η5-cyclopentadienyl-η5-syn-1-methylpentadienylrhodium and iridium cations - preparation and reactions with nucleophiles

η⁵-cyclopentadienyl-η⁵-syn-1-methylpentadienyliridium(I) hexafluorophosphate, a novel complex containing an open chain pentadienyl ligand, has been prepared $\text{via}$ protonation of η⁵-cyclopentadienyl-η⁴-hexa-2,4-dien-1-ol iridium. It and the corresponding rhodium salt are attacked by methoxide ion at the central 3-position of the dienyl group to give 1,4-diene complexes. This contrasts with nucleophilic attack on pentadienyltricarbonyliron cations which occurs at the terminal positions of the dienyl group.     

Exact solution (within a double-zeta basis set) of the schrodinger electronic equation for water

Using recently developed theoretical techniques it has been possible to achieve an exact variational solution of the Schrödinger equation within a modest basis set or one-eleltron functions. The full configuration interaction for this system included a total of 256473 ¹A₁ spin-and space-adapted configurations. Comparison with many-body perturbation theory proves to be quite interesting.     

Synthesis, crystal structure, and properties of MnNCN, the first carbodiimide of a magnetic transition metal

Synthesis, single-crystal structure determination, and magnetic properties are reported for manganese carbodiimide, MnNCN. The presumably unstable but inert phase adopts the trigonal system (R3m) with a = 3.3583(4) A, c = 14.347(2) A, V = 140.13(3) A3, and Z = 3. Divalent manganese is octahedrally coordinated by nitrogen atoms at 2.26 A, and the NCN(2-) unit adopts the linear [N=C=N](2-) carbodiimide shape with two C=N double bonds of 1.23 A. MnNCN contains high-spin Mn(II) with five unpaired electrons and behaves like an antiferromagnet with an ordering temperature below 30 K.     

Selective modification of the 2-position of pyridoxol

Pyridoxol, protected by acetylation of the hydroxyl groups, has been converted to its N-oxide which upon reaction with perfluoroacetie anhydride yields a 2-nor-2-hydroxymethylpyridoxol derivative as an intermediate. This compound undergoes acyl migration from the 3-position. Protection of the pyridoxol hydroxyls by benzylalion followed by the same treatment yields the unrearranged α²-hydroxy derivative. This compound has been converted to a series of α²-substituted pyridoxols (X = -Cl, -Br, -OCOCH₃, -OCH₃, -OC₂H₅).     

Equivalence and conservation rules for the total integral cross section in molecular collisions

The rule of conservation of the total integral cross section o_Tj) is described in a general way using the opacity function. An equivalence rule which states that at the same initial kinetic energy, the total integral cross section from the initial state j is equal to that from the initial state j, i.e., o_Tj) is also presented. Both rules are demonstrated with numerical examples in the He + H₂ collision system and counter-examples are also presented. Possible uses of the rules in the inversion of the intermolecular surface and as an experimental tool are also discussed.     

MECHANISMS OF 1,2-DIOXETANE DECOMPOSITION: THE ROLE OF ELECTRON TRANSFER

Abstract— The chemiluminescence from the cleavage of a number of 1,6-diaryl-2,5,7,8-tetraoxabicyclo[4.2.0]octanes 1 has been examined. The ease of oxidation of (object) the aryl moiety strongly influences both the stability and chemiluminescence efficiency of these 1,2-dioxetanes. When Ar is difficult to oxidize, 1 is comparable in stability to simple. alkyl-substituted 1,2-dioxe-tanes and affords triplet excited states in moderate yield. Both biradical and concerted cleavage mechanisms have been suggested to explain this behavior. However, when Ar is a readily oxidized group, 1 is substantially destahilized and gives excited singlet states in high yield. In this instance 1 is analogous to a number of bioluminescent systems. Cleavage mechanisms involving intramolecular electron transfer are proposed to account for this observation. In certain cases thermolysis of 1 occurs by both types of mechanism in competition, and the electron transfer mechanism may be selectively catalyzed by polar, protic media.     

Regioselective hydroborations of methylvinylchlorosilanes

The regioselectivity of the hydroboration of the methylchlorovinylsilanes, Cl_nMe_3?nSiCHCH₂ (n= 0 ? 3), has been investigated using BH₃←THF, 9-BBN, disiamyl- and dicyclohexylborane. Methylation of the adducts with methylmagnesium bromide is complicated by formation of tetraalkylboronates. Alkaline hydrogen peroxide oxidation of the boronates gives reasonable yields of the corresponding α- and β-trimethylsilylethanols forn= 0 and 1. Forn= 2 and 3, conversion of the adducts to the corresponding α- and β- deuteroethylsilanes by treatment with excess sodium methoxide in methanol-0-d provides a more effective means of derivatization. Addition of the alkenes,n= 2 or 3, to excess BH₃←THF givesca. 90% of the α-boro-organo-chlorosilanes. For all of the alkenes, the dialkylboranes giveca. 80% of the β-boron adducts.     

Benzothiazolium derivatives. III. Nucleophilic substitution reactions of benzothiazolium salts

The reactions of 2,3-dihydrothiazolo[2,3-b]benzothiazolium bromide 1 (A^? ?Br^?) with certain nucleophilic reagents have been performed for the purpose of ascertaining the reaction pathways and identifying the group that is displaced from the central carbon atom of the dithiocarbamate system. The nature of complex salt-like intermediates formed initially from 1 (A^? ?Br^?) has been studied and confirmed. For comparison, a number of nucleophilic substitution reactions of 2-methylthio-3-methylbenzothiazolium iodide 17 and 2-dimethylamino-3-methylbenzothiazolium perchlorate 18 have been examined.