Reactions of hexamethylditin with alkylmercury salts I. Stoichiometry and rate step

Hexamethylditin in methanol solution reacts rapidly with mercuric chloride to yield mercury and trimethyltin chloride. With alkylmercuric salts the reaction is complex, yielding tetraalkyltin and/or dialkylmercury, depending upon the reactivity of the alkylmercuric salt. An electrophilic substitution mechanism involving trimethylstannyl mercurials as transient intermediates is suggested. The reaction of hexaalkylditin with diarylmercury is suggested to follow a homolyric pathway.     

A practical synthesis of (+/-)-alpha-isosparteine from a tetraoxobispidine core

[reaction: see text] The title alkaloid was synthesized in racemic form from 3,7-diallyl-2,4,6,8-tetraoxo-3,7-diazabicyclo[3.3.1]nonane (7) by a regioselective diallylation reaction followed by double ring-closing olefin metathesis and exhaustive reduction. Tetraoxobispidine 7 was itself prepared in three simple operations from dimethyl malonate. The entire sequence to alpha-isosparteine was conducted on a multigram scale and proceeded without recourse to chromatography.     

Homomorphisms on some function algebras

In this note we prove, for some classes of real locally convex spacesE including all complete Schwartz spaces, that every non-zero homomorphism on the algebraC (E) ofC -functions onE is given by a point evaluation at some point ofE.     

Comparison methods for a class of function valued stochastic partial differential equations

Summary A comparison theorem is derived for a class of function valued stochastic partial differential equations (SPDE's) with Lipschitz coefficients driven by cylindrical and regular Hilbert space valued Brownian motions. Moreover, we obtain necessary and sufficient conditions for the positivity of the mild solutions of the SPDE's where the sufficiency follows from the comparison theorem. Thereby it is, e.g., possible to identify a class of SPDE's, which can serve as stochastic space-time models for the density of particles. As a consequence we can construct unique mild solutions of SPDE's on the cone of positive functions with non-Lipschitz drift parts including the case of arbitrary polynomialsR(x) withR(O)O and leading negative coefficient.This research was supported by a grant from ONR     

Experiments in Solving Mixed Integer Programming Problems on a Small Array of Transputers

The time-consuming process of solving large-scale Mixed Integer Programming problems using the branch-and-bound technique can be speeded up by introducing a degree of parallelism into the basic algorithm. This paper describes the development and implementation of a parallel branch-and-bound algorithm created by adapting a commercial MIP solver. Inherent in the design of this software are certain ad hoc methods, the use of which are necessary in the effective solution of real problems. The extent to which these ad hoc methods can successfully be transferred to a parallel environment, in this case an array of at most nine transputers, is discussed. Computational results on a variety of real integer programming problems are reported.     

Macdonald polynomials from Sklyanin algebras: A conceptual basis for thep-adics-quantum group connection

We establish a previously conjectured connection betweenp-adics and quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra and its generalizations, the conceptual basis for the Macdonald polynomials, which interpolate between the zonal spherical functions of related real andp-adic symmetric spaces. The elliptic quantum algebras underlie theZ _n -Baxter models. We show that in then limit, the Jost function for the scattering offirst level excitations in the 1+1 dimensional field theory model associated to theZ _n -Baxter model coincides with the Harish-Chandra-likec-function constructed from the Macdonald polynomials associated to the root systemA ₁. The partition function of theZ ₂-Baxter model itself is also expressed in terms of this Macdonald-Harish-Chandrac-function, albeit in a less simple way. We relate the two parametersq andt of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular thep-adic regimes in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of q-deforming Euler products.Work supported in part by the NSF: PHY-9000386     

The microwave spectrum of thioformaldehyde,CD2S,and CH2S: Average structure,dipole moments,and 33S quadrupole coupling

Microwave transitions up to J = 53 in the ground vibrational state of deuterothioformaldehyde, CD₂S, were studied between 8 and 40 GHz. A detailed centrifugal distortion analysis yields accurate constants for comparison with force field values. The isotopic species ¹³CH₂S, CH₂³⁴S, CH₂³³S, ¹³CD₂S, CD₂³⁴S, and CD₂³³S were studied in natural abundance. Accurate average zero-point structures were determined for both CD₂S and CH₂S:

$\text{CH}{}_2\text{S}\text{CS}\text{=1.6138(4)}\text{CH}\text{= 1.0962(6)}\text{A}\text{?}\text{∠}\text{HCH}\text{=116° 16(6)′,}\text{CD}{}_2\text{S}\text{CS}\text{=1.6136(4)}\text{CD}\text{= 1.0931(4)}\text{A}\text{?}\text{∠}\text{DCD}\text{=116° 25(5)′}$

Changes in the zero-point geometry for deuterium substitution were established. Quadrupole fine structure arising from the ³³S nucleus has been measured in CH₂³³S and CD₂³³S. Analysis gives the following coupling constants (for both molecules) as χ_aa = ?11.7 and χ_bb - χ_cc = 88.1 MHz. The dipole moment of CD₂S was measured to be 1.6588(8)D and an accurate comparison with CH₂S was made; the ratio of dipole moments $\text{CD}{}_2\text{S}\text{CH}{}_2\text{S}$ was found to be 1.0062(4). The spectroscopic and bonding properties of CH₂S will be compared with formaldehyde and other molecules.     

Configurationally and conformationally homogeneous cyclic n-aryl sulfimides—IV : Synthesis,configuration and stereochemistry of the rearrangement of 1,3-di-thiane-1-N-p-chlorophenylimides

1,3-Dithiane-1-N-p-chlorophenylimides (1,4-9) were prepared and their configuration and conformation was determined by ¹H and ¹³C NMR. The compounds were rearranged to the corresponding 2-(2'-amino-5'-chlorophenyl)-1, 3-dithianes (1U,4U,9U). The rearrangement reactions took place with ?95% stereospecifity. The mechanism of the reaction was investigated with the aid of analogs specifically deuterated at C-2.     

Vibrational spectroscopy of 3,4-difluorocyclobutenes: cis-d0, trans-d0 and trans-d4 species

Infrared and Raman spectra were recorded for cis-3,4-difluorocyclobutene (cDFCB) and trans-3,4-difluorocyclobutene-d4. Unscaled density functional theory (DFT) calculations of frequencies and intensities at the B3LYP/6-311++G(d,p) level supported the complete assignment of the vibrational fundamentals. The previous assignment of fundamentals of trans-3,4-difluorocyclobutene was revised. An unusual blue shift occurs for the methylenic CH-stretching frequencies of cis-3,4-difluorocyclobutene in going from the gas phase to the liquid phase. This hydrogen bond effect is related to similar observations recently reported and interpreted. The blue shift does not occur for the vinylic CH bonds of the cis isomer and does not occur for either type of CH bond in the trans isomer.