Symmetric Markov chains in ℤd: How fast can they move?

Summary Consider a reversible Markov chain X _n which takes values in a subset of ^d. If the steps of the chain are uniformly bounded and the invariant measure satisfies a mild regularity condition, Varopoulos, Carne and Kesten have obtained estimates on \lambda n^{1/2} )$$ " align="middle" border="0"> which exhibit a Gaussian tail in but blow up as n. Following Kesten's approach we derive bounds which are uniform in n in some special cases. Our main result, however, is an example which shows that in general the estimates of Varopoulos, Carne and Kesten are essentially best possible.Research partially supported by an S.E.R.C. (U.K.) visiting fellowship and an operating grant from N.S.E.R.C. of Canada     

AN INEXPENSIVE STIRRING DEVICE FOR THE 'MERRY-GO-ROUND' PHOTOREACTOR FOR THE DETERMINATION OF REACTION QUANTUM YIELDS

A simple bar magnet is employed to effect stirring of the contents of reaction cells in a'merry-go-round'photoreactor.     

Synthesis and Inclusion Properties of the Host Compound 1,3-Dihydro-1,1,3,3-tetraphenylisobenzofuran. X-Ray Crystal Structures of the Free Host and of an Inclusion Compound with 1,4-Dioxane

A novel host molecule, 1, suitable for crystalline lattice-type inclusion, has been synthesized, and its cocrystal formation ability has been investigated. Host 1 proved to be of potential use for organic solvent separation and retrieval, and a promising auxiliary for solidification of certain odorous substances. The crystal structures of the solvent-free host 1, and its complex with 1,4-dioxane (1 : 1), have been determined by single crystal X-ray diffraction. The structure of 1 (guest-free) is triclinic, P , with a = 9.452(2), b = 10.359(3), c = 13.116(3) Å, = 101.80(2), = 106.53(1) and = 104.32(1)°. The spacious, propeller-like molecules are held together by weak van der Waals' forces. The dioxane inclusion compound is monoclinic, P21/a, with a = 15.050(1), b = 8.641(1) and c = 20.658(1) Å, and = 94.56(1)°, and contains two crystallographically independent guest molecules, both located around symmetry centres. The molecular packing seems to be governed by C—H···O type bonds (C···O = 3.31 and 3.48 Å) from the host to the dioxane oxygens.     

Fluctuating energy level Landau-Teller theory: application to the vibrational energy relaxation of liquid methanol

State-to-state vibrational energy relaxation (VER) rates of the OH-stretch fundamental to select vibrational modes of liquid methanol are presented. The rates are calculated via a modified, fluctuating Landau-Teller (FLT) theory approach, which allow for dynamical vibrational energy level shifts. These rates are then compared to previously published results from Gulmen and Sibert [J. Phys. Chem. A 2004, 108, 2389] for the traditional Landau-Teller (LT) method as well as results calculated through time-dependent perturbation theory (TD), which naturally allow for the fluctuation. For the first time, this method is applied to a polyatomic molecular system, and the FLT theory greatly reduces the discrepancy between the LT and TD results or, at a minimum, is comparable to the LT approach with very little additional computational cost.     

The Bond-Rotational Mobility of Guanidinium Ion

The NMR. spectrum of guanidinium ion 1 is studied in anisotropic liquid crystalline nematic solution. Assuming an HNH-angle of 120°, the distance ratio NH /NC = 0.784 is obtained, from which using NC = 1.330 Å (from X-ray data) NH = 1.043 Å results. An upper bound for the free energy of activation for bond rotation of ΔG⁺ ≤ 13 kcal/mol is deduced. The bondrotational mobility of 1 is also investigated using the MINDO/3-SCF-procedure. The results obtained for the three conceivable consecutive activation energies for bond-rotation indicate that the observed bond-rotational mobility of 1 does not involve cooperative two- or three-bond rotations. The ‘conjugative stabilization’ of 1 has been estimated to be of the order of 24–26 kcal/mol.     

Base- and light-assisted synthesis of anthracenes from 3-allylnaphthalene-2-carbaldehydes

The synthesis of substituted anthracenes from naphthalene precursors is described. The key step involved heating ortho-allyl substituted naphthalene-2-carbaldehydes and potassium t-butoxide in DMF with concomitant irradiation from a high pressure mercury lamp to afford anthracenes in yields of 76-98%.     

Tetrakis (methylidene)cyclobutane (‘[4]Radialene’): Electronic states of the molecular ion

The photoelectron spectrum of tetrakis (methylidene)cyclobutane ( 1 , ‘[4]radialene’) is reported. The electronic states of 1 ⁺ are assigned on the basis of model calculations and with reference to related systems. Jahn-Teller activity in the degenerate states is discussed. A failure of the simple LCBO-model for the π(e_g)-orbital of 1 is noted and traced to the fact that this orbital, though having a symmetry-equivalent π*-counterpart, does not interact with it. This feature is confined to [4n]radialenes; their total π-energies are therefore higher than those of the other members. It is shown that radialenes, in principle, do not constitute a class analogous to that of the linear polyenes as inferred earlier.     

UV/Vis-spektroskopische Untersuchungen an Cyclosilanderivaten

UV/Vis-spectra of Cyclosilanes (SiX ₂) _n withX=Cl, Br, I, OMe andn=4, 5, 6 are recorded and interpreted qualitatively. The spectra exhibit increasing influence of the substituents on the Si-Si-bond system within the rings in the order Cl OMe Br I. At the low energy side of the spectra weak absorption bands, possibly due to intramolecular charge transfer transitions, appear. The strong inductive effect of the electronegative substituents is documented by a marked increase of the first IP's compared to permethylcyclosilanes.

     

Determination of manganese in brain samples by slurry sampling graphite furnace atomic absorption spectrometry

A simple procedure for the determination of manganese in different sections of human brain samples by graphite furnace atomic absorption spectrometry has been developed. Brain sections included cerebellum, hypothalamus, frontal cortex, vermix and encephalic trunk. Two sample preparation procedures were evaluated, namely, slurry sampling and microwave-assisted acid digestion. Brain slurries (2% w/v) could be prepared in distilled, de-ionized water, with good stability for up to 30 min. Brain samples were also digested in a domestic microwave oven using 5 ml of concentrated HNO₃. A mixed palladium+magnesium nitrate chemical modifier was used for thermal stabilization of the analyte in the electrothermal atomizer up to pyrolysis temperatures of 1300 °C, irrespective of the matrix. Quantitation of manganese was conducted in both cases by means of aqueous standards calibration. The detection limits were 0.3 and 0.4 ng ml⁻¹ for the slurry and the digested samples, respectively. The accuracy of the procedure was checked by comparing the results obtained in the analysis of slurries and digested brain samples, and by analysis of the NIST Bovine Liver standard reference material (SRM 1577a). The ease of slurry preparation, together with the conventional set of analytical and instrumental conditions selected for the determination of manganese make such methodology suitable for routine clinical applications.     

Physical and Chemical Interaction of Homoconjugated Dienes with Tetracyanoethylene

EDA-complexes of bicyclo[2,2,n]alkadienes (n = 1, 2, 3, 4) ( 1 (n)-series), 1,4-cyclohexadiene ( 2 ) and various other cyclic monoenes, dienes and trienes as donors and tetracyanoethylene (TCNE) as acceptor were investigated. Spectroscopic and thermodynamic constants of the complexes were determined and correlated with the ionisation potentials (I^D) of the hydrocarbon donors obtained from PE. spectroscopy. The nature of the dominant energy contributions to the ground state and the two lowest CT-states of these weak complexes is discussed and structural conclusions are drawn. The role of the complexes in the addition reaction of the hydrocarbon components and TCNE is discussed. The homo Diels-Alder addition product of 1 (2) and TCNE, 9,9,10,10-tetracyanoquadricyclo[2,2,2,0^2,6,2^3,5]decane, and the ‘ene’-addition product of 2 and TCNE, 5-[1′,1′,2′,2′-tetracyanoethyl]-1,3-cyclohexadiene were prepared and characterized. Preliminary results for the mechanistic scheme governing the dehydrogenation of 2 by TCNE are reported.