The prime orbit theorem for quasihyperbolic toral automorphisms

For a toral automorphism which is ergodic, but not necessarily hyperbolic, we derive asymptotic formulae for the number of closed orbits by analogy with the Prime Number Theorem. A new proof of the uniform distribution of periodic points is also given.     

The Determination of the Optimum Joint Replenishment Policy for a Group of Discount-Connected Stock Lines

This paper investigates the situation where a joint replenishment order for a group of stock lines from a common supplier qualifies for a quantity discount provided the total order equals a specified number of units. It is assumed that, when any line in the group reaches its reorder point, an order of this size is made for the whole group and it is the problem of how to determine the optimum order "mix" which is considered here. In the case of a group consisting of two lines only, an analytical solution is derived which, assuming Poisson sales-rates, gives the individual stock levels for which the expected number of sales between successive replenishments is maximized for a given total stock. However, for groups of more than two lines, it was necessary to resort to numerical methods and a computer program is described which uses a quasi dynamic-programming approach to determine the optimum set of individual stocks for any given set of sales-rates and total stock. Based on the results from this program, a "ready reckoner" has been constructed which permits an easy look-up to obtain the optimum allocation of any given total stock between the lines of a group of any size and sales-rates. Finally, the possible extension of this approach to other multi-item inventory problems is discussed.     

An investigation of the 144Sm(α, 3He)145Sm reaction

The ¹⁴⁴Sm(α, ³He)¹⁴⁵Sm stripping reaction has been studied up to 3 MeV excitation energy with a 40 MeV α-beam. Angular distributions have been recorded, and spectroscopic factors are deduced using a standard DWBA procedure. The reaction favours high-l transfers, and is found to be very useful for the investigation of large-j states. From a comparison with the spectroscopic factors known from the ¹⁴⁴Sm(d, p)¹⁴⁵Sm reaction the normalization factor for the (α, ³He) reaction is found to depend strongly on the optical model parameters and on the transferred angular momentum l.     

Interactions of 10.6 GeV/nucleon gold nuclei in nuclear emulsion

Stacks of nuclear emulsion were exposed at the Brookhaven AGS to a 10.6 GeV/n beam of gold nuclei in the BNL 868 experiment. A preliminary analysis of the main features of the interactions of these nuclei is reported here and compared with those observed previously at lower energies,E<1 GeV/n. The multiplicity and pseudo-rapidity distributions of the singly charged particles emitted both in central and in minimum bias samples of interactions have been analyzed in order to look for any non random effects indicative of the nuclear state during the interactions. The fragmentation characteristics of the gold projectiles appear to be different at 10.6 GeV/n from those at ≦1 GeV/n incident energy. Fission of the gold projectiles, which was relatively frequent at low energy, is almost entirely suppressed. Some of alpha particles from the projectile are emitted with very large transverse momenta. In gold-emulsion interactions the residual target nuclei are significantly smaller than in oxygen and sulfur interactions in emulsion.

     

An inelastic neutron scattering study of C2H2 adsorbed on type 13X zeolites

The inelastic neutron scattering spectra of C₂H₂ and C₂D₂ adsorbed on a Ag⁺ exchanged 13X zeolite (0–800 cm^?1) and of C₂H₂ on the Na⁺ form (0–300 cm^?1) have been obtained. For the Na-13X system no distinct vibrational modes were observed, however for the Ag-13X systems the low frequency intramolecular modes of the adsorbed gas and some of the vibrations of the adsorbed gas relative to the surface have been assigned. From the deuteration shifts it appears that C₂H₂ and C₂D₂, adsorbed on Ag-13X, are non-linear.     

Inelastic neutron scattering spectra of alkali metal (Na,K) bifluorides: The harmonic overtone of v3

Inelastic neutron scattering spectra of MFHF (M  Na and K) have been measured up to energy transfers of ca. 4000 cm^?1 Both 0 → 1 and 0 → 2 transitions of the bending (v₂), and antisymmetric stretching (v₃) modes were observed. A normal harmonic (i.e. no quartic contribution) model for the dynamics of the bifluoride ion is entirely consistent with our observations. Evidence of phonon dispersion was observed in the band shape of v₃, but no structure attributable to the LO mode could be found. The similarity of the band shapes of v₃ for both NaFHF and KFHF is interpreted in terms of a very short range coupling mechanism.     

Lamellar crystalline self-assembly behaviour and solid lipid nanoparticles of a palmityl prodrug analogue of Capecitabine--a chemotherapy agent

An amphiphile prodrug, 5′-deoxy-5-fluoro-N⁴-(palmityloxycarbonyl) cytidine or 5′-deoxy-5-fluoro-N⁴-(hexadecanaloxycarbonyl) cytidine (5-FCPal), consisting of the same head group as the commercially available chemotherapeutic agent Capecitabine, linked to a palmityl hydrocarbon chain via a carbamate bond is reported. Thermal analysis of this prodrug indicates that it melts at ∼115 °C followed quickly by degradation beginning at ∼120 °C. The neat solid 5-FCPal amphiphile acquires a lamellar crystalline arrangement with a d-spacing of 28.6 ± 0.3 Å, indicating interdigitation of the hydrocarbon chains. Under aqueous conditions, solid 5-FCPal is non-swelling and no lyotropic liquid crystalline phase formation is observed. In order to assess the in vitro toxicity and in vivo efficacy in colloidal form, solid lipid nanoparticles (SLNs) with an average size of ∼700 nm were produced via high pressure homogenization. The in vitro toxicity of the 5-FCPal SLNs against several different cancer and normal cell types was assessed over a 48 h period, and IC₅₀ values were comparable to those observed for Capecitabine. The in vivo efficacy of the 5-FCPal SLNs was then assessed against the highly aggressive mouse 4T1 breast cancer model. To do so, the prodrug SLNs were administered orally at 3 different dosages (0.1, 0.25, 0.5 mmol/mouse/day) and compared to Capecitabine delivered at the same dosages. After 21 days of receiving the treatments, the 0.5 mmol dose of 5-FCPal exhibited the smallest average tumour volume. Since 5-FCPal is activated in a similar manner to Capecitabine via a 3 step enzymatic pathway with the final step occurring preferentially at the tumour site, formulation of the prodrug into SLNs combines the advantage of selective, localized activation with the sustained release properties of nanostructured amphiphile self-assembly and multiple payload materials thereby potentially creating a more effective anticancer agent.