The molecular Zeeman effect in HCP,HCN, and HCCBr and a comparison with similar molecules

The molecular Zeeman effect has been observed in the J = 0 → 1 ΔM = 0, and ± 1 transitions in H¹²CP, D¹²CP, H¹²C¹⁵N, H¹²C¹²C⁷⁹Br, and H¹²C¹²C⁸¹ Br giving the molecular g-values, magnetic susceptibility anisotropies, and corresponding molecular quadrupole moments. The results are g_⊥(HCP) = ?0.0430 ± 0.0010, g_⊥(DCP) = ?0.0353 ± 0.0010, x_⊥ - x_| = (8.4 ± 0.9) × 10^?6 erg/G² mole and Q_|(HCP) = (4.4 ± 1.2) × 10^?26 esu; g_⊥(HC¹⁵N) = ?0.0904 ± 0.0003, x_⊥ - x_| = (7.2 ± 0.4) × 10^?6 erg/G² mole, and Q_|(HC¹⁵N) = (3.1 ± 0.6) × 10^?26 esu; g_⊥(HCC⁷⁹Br) = ?0.00395 ± 0.00032, g_⊥(HCC⁸¹Br) = ?0.00388 ± 0.00014, x_⊥ - x_| = (9.5 ± 0.9) × 10^?6 erg/G² mole, and Q_| = (8.5 ± 1.1) × 10^?26 esu. The results in HCN agree very well with an earlier prediction of the magnetic properties. The new results presented here are compared to other members in the acetylene and cyanide series of molecules and we conclude that the sign of the g-value in acetylene should be positive.The deuterium nuclear quadrupole coupling constant was also determined in DCP to be x_D = 233 ± 40 kHz.     

The affine geometry of the Lanczos H-tensor formalism

We identify the fiber-bundle-with-connection structure that underlies the Lanczos H-tensor formulation of Riemannian geometrical structure. We consider linear connections to be type (1,2) affine tensor fields, and we sketch the structure of the appropriate fiber bundle that is needed to describe the differential geometry of such affine tensors, namely the affine frame bundleA ₁ ² M with structure groupA ₁ ² (4) =GL(4) T ₁ ^{2 4} over spacetimeM. Generalized affine connections on this bundle are in 1-1 correspondence with pairs(, K) onM, where thegl(4)-component denotes a linear connection and the T ₁ ^{2 4}-componentK is a type (1,3) tensor field onM. We show that the Lanczos H-tensor arises from a gauge fixing condition on this geometrical structure. The resulting translation gauge, theLanczos gauge, is invariant under the transformations found earlier by Lanczos. The other Lanczos variablesQ _mandq are constructed in terms of the translational component of the generalized affine connection in the Lanczos gauge. To complete the geometric reformulation we reconstruct the Lanczos Lagrangian completely in terms of affine invariant quantities. The essential field equations derived from ourA ₁ ² (4)-invariant Lagrangian are the Bianchi and Bach-Lanczos identities for four-dimensional Riemannian geometry.     

Use of principal components analysis for displaying variation between pyrograms of micro-organisms

Principal components analysis is used to display variations between batches of pyrograms of micro-organisms represented by sets of peak heights. Although it is not usually suitable for discriminating genus or species groups, it provides a means of detecting aberrant analyses, unsuspected trends in the data and of assessing reproducibility. It can also provide information relating specific peaks or sets of peaks to clusters of samples.These uses of principal components analysis are not confined to pyrolysis—gas—liquid chromatography; the technique can be applied widely to quantitative chromatographic and mass spectrometric data.     

On the quasistatic effective elastic moduli for elastic waves in three-dimensional phononic crystals

Effective elastic moduli for 3D solid–solid phononic crystals of arbitrary anisotropy and oblique lattice structure are formulated analytically using the plane-wave expansion (PWE) method and the recently proposed monodromy-matrix (MM) method. The latter approach employs Fourier series in two dimensions with direct numerical integration along the third direction. As a result, the MM method converges much quicker to the exact moduli in comparison with the PWE as the number of Fourier coefficients increases. The MM method yields a more explicit formula than previous results, enabling a closed-form upper bound on the effective Christoffel tensor. The MM approach significantly improves the efficiency and accuracy of evaluating effective wave speeds for high-contrast composites and for configurations of closely spaced inclusions, as demonstrated by three-dimensional examples.     

HEAT TRANSFER REGIMES IN THE COOLANT PASSAGES OF A DIESEL ENGINE CYLINDER HEAD

An investigation aimed at identifying the heat transfer regimes present in the valve bridge coolant passages of a diesel engine cylinder head is reported. An inverse heat conduction method utilizing experimental results along with a finite-element model was developed and applied. The sensitivity of the results to uncertain boundary conditions is discussed and found to be minimal. Locations where local boiling occurs were identified.     

Synthesis of the heterocyclic core of martinelline and martinellic acid

A Povarov reaction, between an aromatic imine derived from cinnamaldehyde and a cyclic enamide, was employed to rapidly construct the tricyclic core of the alkaloids martinelline and martinellic acid. The cycloaddition was completely regioselective though the exo/endo selectivity was poor. The diastereoisomers were readily separated by flash chromatography and the relative stereochemistry of the exo-isomer confirmed by single crystal X-ray crystallography. This intermediate was converted to the central core of the aforementioned alkaloids in five additional synthetic operations.     

Cells in Sol-Gels I: A Cytocompatible Route for the Production of Macroporous Silica Gels

A novel, high hydrolysis ratio sol-gel route for the biocompatible production of macroporous silica gels is presented. This route exploits the two step nature of the gelation reaction to remove undesired alcohol by-products from an acidic aqueous sol prior to gelation. These alcohol-free sols will gel when the pH is raised to the physiologic range in a two-step, acid/base catalyzed process. Furthermore, monolithic macroporous samples can be produced in a controlled manner by introducing water-soluble organic polymers into the sol.     

Diffusivity of a random walk on random walks

We consider a random walk with the constraint that each coordinate of the walk is at distance one from the following one. In this paper, we show that this random walk is slowed down by a variance factor with respect to the case of the classical simple random walk without constraint. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 267–283, 2015