On the existence of hydrodynamic fluctuation forces

The form of fluctuating hydrodynamic forces has been derived recently [R.B. Jones, Physica 105A (1981) 395] from the stochastic fluid equations of Landau and Lifshitz. We show by general physical arguments as well as by a direct calculation that such forces do not exist in the classical limit.     

The approximation of flows

Let U, V be two strongly continuous one-parameter groups of bounded operators on a Banach space $\text{X}$ with corresponding infinitesimal generators S, T. We prove the following: ∥U_t, ? V_t ∥ = O(t), t → 0, if and only if U = V; ∥U_t ? V_t∥ = O(t^α), t → 0; with 0 ? α ? 1, if and only if $\text{S = Ω(T + P)Ω}{}^{\mathrm{?1}}$, where Ω, P, are bounded operators on $\text{X}$ such that $\text{∥U}{}_{\mathrm{t}}\text{Ω ? ΩU}{}_{\mathrm{t}}\text{∥ = O(t}{}^{\mathrm{\alpha }}\text{), ∥U}{}_{\mathrm{t}}\text{P ? PU}{}_{\mathrm{t}}\text{∥ = ?O(t}{}^{\mathrm{\alpha }}\text{), t → 0; ∥U}{}_{\mathrm{t}}\text{? V}{}_{\mathrm{t}}\text{∥ = O(t)}$ if and only if $\text{S}{}^1\text{? T}{}^1$ has a bounded extension to $\text{X}$¹. Further results of this nature are inferred for semigroups, reflexive spaces, Hilbert spaces, and von Neumann algebras.     

Thermodynamic properties of a fluid of hard spheres with water-like dipole and quadrupole moments

The thermodynamic properties of a fluid of hard spheres with dipole and tetrahedral quadrupole moments are investigated using thermodynamic perturbation theory. The drpole-quadrupole coupling is found to be very important at values of the multipole moments that are close to those of water.     

Sodium hydrogen telluride as a useful nucleophilic reagent for the cleavage of epoxides and of quaternary ammonium salts

Sodium hydrogen telluride opens many epoxides cleanly by an SN₂ process to give telluro-alcohols, which by reduction with nickel boride afford alcohols. An intermediate telluro-alcohol was converted to olefin in high yield by treatment with $\text{p}$-toluene-sulphonyl chloride in pyridine. Quaternary ammonium salt are also cleaved efficiently by sodium hydrogen telluride.     

Intense shake-up satellites in the XPS spectra of planar and sterically hindered N-piperidyl-nitrobenzenes and -nitrothiophens

The shake-up satellites present in the O_1s and N_1s energy regions of the XPS spectra of the planar 4-N-piperidyl-nitrobenzene (1) and 2-N-piperidyl-5-nitrothiophen (3), and of the sterically hindered 2-N-piperidyl-nitrobenzene (2), 2-N-piperidyl-3-nitrothiophen (4) and 3-N-piperidyl-2-nitrothiophen (5) and, for comparison, of 2-bromo-3-nitrothiophen (6) have been analyzed with the help of CNDO/S CI calculations. The spectra of the planar derivatives closely resemble these of the related compounds previously analysed, the main satellites deriving from the transition between the highest occupied molecular orbital (HOMO, localized at the donor-ring moiety) towards the lowest unoccupied one (LUMO, localized at the nitro group). Calculations indicate that in the ortho derivatives new relaxation processes are allowed upon N_1s/NO₂ ionization. In 2, where the angle of rotation θ is closer to 90° than 60°, the NR ₂ lone-pair orbital relaxes through space towards the core-ionized N/NO₂ atom. In 4 and 5, where 45° ? θ ? 60°, both through-ring and through-space relaxations are present. The assignment of the main N_1s/NO₂ line in 1 is discussed.     

Local Lower Bounds on Heat Kernels

We analyze convolution semigroups on a regular measure space which satisfies the local doubling property. We assume the kernels are bounded and symmetric with the characteristic small-time, volume-dependent, singularity. Then, using a weak conservation property, we deduce local lower bounds with a comparable singularity.Applications are given to a wide range of subelliptic and strongly elliptic self-adjoint, or near self-adjoint, operators on Lie groups.     

Selective reduction of the N-O bond in n-oxides and in nitrones by sodium hydrogen telluride

Sodium hydrogen telluride reduces $\text{tert}$.-amine $\text{N}$-oxides to the corresponding amines in very high yield, but does not reduce sulphoxides. This reagent also reduces nitrones to $\text{sec}$.-amines at pH6 and to imines at alkaline pH (10–11).     

Striking contrasts in stereoselectivities of spiro-claisen rearrangements of pyranosides versus carbocycles.

Structurally equivalent derivatives of pyranosides and cyclohexanes undergo the spiro-Claisen rearrangement with different stereochemical results. A rationalization for the course observed with the pyranosides is suggested, which invokes interaction of the oxygen lone pair with a (developing) electron deficient centre at the spiro carbon.