Liquid phase kinetic study of the formation and decomposition of methylsulfonyl and cyclohexylsulfonyl radicals in the cyclohexane–MeSO2C1-SO2 System at 150°

The thermally and radiolytically induced chain decomposition of methanesulfonyl chloride (MeSO₂Cl) in liquid cyclohexane (RH) was studied at 150°C. The main products, chlorocyclohexane, sulfur dioxide, and methane, are formed in almost equal yields, and a relatively small amount of methyl chloride is also observed. The formation and addition of SO₂ strongly inhibit the chain decomposition reaction. By kinetic analysis it is shown that the formation of the main products can be explained only in terms of a mechanism that postulates the decomposition of MeSO₂, and that the alternative mechanism of methane and SO₂ formation via the methanesulfinic acid is inconsistent with the kinetic behavior of the system. For the reactions Me + MeSO₂Cl → MeCl + MeSO₂(2b), Me + RH → MeH + R (4), and Me + CCl₄ → MeCCl₄ → MeCl + CCl₃ (15b) the following rate constant ratios are determined; k_2b/k₄=2.17±0.20 and k_2b/k_15b=2.63±0.52. For the reactions R + MeSO₂Cl → RCl + MeSO₂(2a) and R + CCl₄ → RCl + CCl₃ (15a), k_2a/k_15a is equal to 1.55±0.05. In addition the equilibrium constant K₇ for the reaction R + SO₂ ? RSO₂ (7) is estimated as being equal to (9.4±3) × 10³ mole/l.     

Attainable sets for linear stochastic control systems

Let x_t^u(w) be the solution process of the n-dimensional stochastic differential equation dx_t^u = [A(t)x_t^u + B(t) u(t)] dt + C(t) dW_t, where A(t), B(t), C(t) are matrix functions, W_t is a n-dimensional Brownian motion and u is an admissable control function. For fixed ? ? 0 and 1 ? δ ? 0, we say that x?Rⁿ is (?, δ) attainable if there exists an admissable control u such that P{x_t^u?S_?(x)} ? δ, where S_?(x) is the closed ?-ball in Rⁿ centered at x. The set of all (?, δ) attainable points is denoted by $\text{A}$(t). In this paper, we derive various properties of $\text{A}$(t) in terms of K(t), the attainable set of the deterministic control system $\text{x}\text{?}\text{= A(t)x + B(t)u}$. As well a stochastic bang-bang principle is established and three examples presented.     

The molecular structure of N-benzylidene-aniline

The molecular structure of N-benzylidene-aniline has been studied experimentally by the gas electron diffraction method, and also by molecular mechanics calculations. Both approaches gave the same results for the most stable conformer of the free molecule. The phenyl ring bonded to the carbon end of the CN bond was found to be coplanar with this bond, while the other phenyl ring was extensively (ca. 52°) rotated about the NΦ bond.     

The effect of temperature on formaldehyde photooxidation in oxygen-lean atmospheres

The photooxidation of formaldehyde in CH₂O? O₂, oxygen-lean mixtures was studied in the temperature range 298–378 K. H₂ and CO formation and the loss of O₂ proceed by a chain mechanism, which between 328 and 378 K follows the previously suggested kinetics [1] with one modification. The reaction HO₂ + CH₂O ? HO₂CH₂O (5) is now assumed to be reversible and ΔH is estimated to be between 14 and 19 kcal/mol. The relative yields of the chain formed H₂ and CO and of the consumed O₂ remained constant over the entire temperature range indicating that the relative efficiencies of the HO reactions: HO + CH₂O → H₂O HCO? (7), HO + CH₂O → H₂O + HCO (8) and HO + CH₂O → HOCH₂O (9) are temperature independent.     

n-point functions for the rectangular Ising ferromagnet

A new representation for then-point functions of the Planar Ising ferromagnet is given. Below the critical temperature the boundary conditions are toroidal; the state is a superposition of the extremal invariant ones, with equal weights.Supported by the Fonds National Suisse de la Recherche Scientifique, by the National Science Foundation Grant No. PHY 76-17191, and by the National Research Council of Canada Grant No. NRC A 9344     

On the impact and the separation approximations in the theory of multiphoton interactions ivith thermally perturbed systems

Criteria are provided for the factorization of thermal averages incuring in the calculation of cross-sections for several-photon processes, into produc     

Notes on ω- and τ-matrices

Results on ω- and τ-matrices are surveyed. The question whether an ω-matrix with positive leading principal minors is a τ-matrix is answered negatively. Other open questions are discussed. New conjectures and questions are introduced.