Open orbits in linear chain mercury compounds

Open orbits have been found in the linear chain mercury compound Hg_3?δAsF₆ by the induced torque method with magnetic fields between 2.0 and 8.5T. There is a primary open orbit along the [001] direction. Higher-order open orbits are observed and result from magnetic breakdown. The orbits are explained by the cylindrical Fermi surface formed from coupled, one-dimensional bands.     

Studies of phthalic acid and related compounds by positive- and negative-ion chemical ionization tandem mass spectrometry (± CI/MS/MS)

The positive- and negative-ion chemical ionization (± CI) behavior of phthalic acid and four related compounds (phthalic anhydride, phthalide, biphthalyl, and anthraquinone-2-carboxyIic acid) are characterized by tandem mass spectrometry with low-energy collisionally activated dissociation. Principal fragmentation pathways have been established, and molecular and fragment ions arising from these compounds have been differentiated from adduct and dimer ions, as well as from ions due to impurities. The ubiquitous nature of these compounds in analytical samples makes it important to identify the corresponding ions, and thus to be able to exclude them from consideration in the identification of other sample components.     

Specific heat,electrical resistance,and other properties of superconducting Pd-H alloys

Specific heat and electrical resistance measurements have been carried out in the ～1.2 to 4.2 K range for a series of Pd-H alloys having H/Pd atomic ratios in the ～0.82 to 0.88 range. Superconductive transitions in the resistance were observed; the specific heat data exhibited broad, yet very pronounced peaks with characteristics that depended strongly upon hydrogen concentration. A fairly successful theoretical fitting of the specific heat data was carried out on the basis of the assumption that Pd-H alloys are simply inhomogeneous BCS superconductors. Data for the dependence of the superconducting transition temperature upon hydrogen concentration were derived from both the specific heat and electrical resistance measurements. An interesting scaling feature of the specific heat data is discussed. A search for a possible interrelationship between the superconductive properties and an exothermic process which occurs in Pd-H alloys yielded negative results. A marked suppression of superconductive effects was observed in Pd-H alloys based on one particular Pd ingot; this was probably due to Fe impurities.     

Profit maximization from the sales of products which have limited lifetimes in a fixed price market

The optimization of profit resulting from the sales of products which have limited lifetimes is discussed. The factors considered in the analysis are selling price, cost price, disposal price and loss of goodwill. Demand which is considered to be stochastic is represented by an exponential distribution function. It is found that the factors most influential in the determination of expected profit are the cost price to produce the product and the administrative cost involved in the disposal of the product after its useful lifetime has been exceeded.     

A topological study of the geometry of AF6E molecules: weak and inactive lone pairs

The geometries of AF6E molecules, which may have either an O(h) or a C(3v) geometry, have been studied by means of the electron localization function. Our results show that when the molecule has a C(3v) geometry, there is a valence-shell monosynaptic V(A) basin corresponding to the presence of a lone pair in the valence shell of the central atom A. The population of this basin is, however, extensively delocalized so that the electron density has a core-valence basin character, which is consistent with an earlier suggestion of a weakly active lone pair that gives a C(3v) distorted octahedral molecule rather than the valence-shell electron-pair repulsion predicted pentagonal-pyramid geometry. In contrast, the molecules with O(h) geometry do not have a monosynaptic valence-shell basin, but they have a larger core. These results provide confirmation of a previous suggestion that in AX6E (X = Cl, Br, I) molecules with the O(h) geometry the ligands X are sufficiently closely packed around the central atom A so as to leave no space in the valence shell for the lone pair E, which remains part of the core. Among the corresponding fluorides, only BrF6- has the O(h) geometry, while the others have the C(3v) geometry because there is sufficient space in the valence shell to accommodate the lone pair, the presence of which distorts the O(h) geometry to C(3v). The energies of the O(h) and C(3v) geometries have been shown to be very similar so the observed geometries are a consequence of a very fine balance between ligand-ligand repulsions and the energy gained by the expansion of the two nonbonding electrons into the valence shell.     

Corrections to eikonal models for hadron-nucleus scattering at high and intermediate energies

Corrections to eikonal amplitudes for hadron-nucleus scattering are calculated for realistic optical potentials at medium and high energies. The corrections, involving only one-dimensional integrals, are found to provide rapid convergence towards the exact results. In contrast to the lowest-order eikonal approximation, the corrections lead to a sensitivity of the calculated cross section to the sign of the real part of the optical potential.     

Logarithmic Growth for Matrix Martingale Transforms

An example is given of an operator weight W that satisfies thedyadic operator Hunt–Muckenhoupt–Wheeden condition for which there exists a dyadic martingale transform on L² (W) that is unbounded. The constructionrelates weighted boundedness to the boundedness of dyadic vectorHankel operators.     

Subpicosecond electro-optic measurement of relativistic electron pulses

Time-resolved measurements of the transverse electric field associated with relativistic electron bunches are presented. Using an ultrafast electro-optic sensor close to the electron beam, the longitudinal profile of the electric field was measured with subpicosecond time resolution and without time-reversal ambiguity. Results are shown for two cases: inside the vacuum beam line in the presence of wake fields, and in air behind a beryllium window, effectively probing the near-field transition radiation. Especially in the latter case, reconstruction of the longitudinal electron bunch shape is straightforward.