Transportation problems which can be solved by the use of hirsch-paths for the dual problems

Balinski uses his signature method for the proof of the Hirsch-conjecture for dual transportation polyhedra to obtain an efficient algorithm for the assignment problem. We will show how to extend this method to other primal transportation problems, including transportation problems with unit demands. We then prove that Balinski's assignment algorithm is equivalent, cycle by cycle, to that of Hung and Rom. We demonstrate that, under some assumptions for our probability model, a modification of the latter algorithm has an average complexity of O(n ²logn) and present some computational results confirming this. We also present results that indicate that this modification compares favorably with Balinski's algorithm and other codes. Research of both authors supported, in part, by grants of the Alexander von Humboldt-Stiftung. Supported, in part, by NSF grant DMS-8504050.     

Spectral functions at small energies and the electrical conductivity in hot quenched lattice QCD

In lattice QCD, the maximum entropy method can be used to reconstruct spectral functions from Euclidean correlators obtained in numerical simulations. We show that at finite temperature the most commonly used algorithm, employing Bryan's method, is inherently unstable at small energies and gives a modification that avoids this. We demonstrate this approach using the vector current-current correlator obtained in quenched QCD at finite temperature. Our first results indicate a small electrical conductivity above the deconfinement transition.     

Nuclear spin ferromagnetic phase transition in an interacting two dimensional electron gas

Electrons in a two-dimensional semiconducting heterostructure interact with nuclear spins via the hyperfine interaction. Using a a Kondo lattice formulation of the electron-nuclear-spin interaction, we show that the nuclear-spin system within an interacting two-dimensional electron gas undergoes a ferromagnetic phase transition at finite temperatures. We find that electron-electron interactions and non-Fermi liquid behavior substantially enhance the nuclear-spin Curie temperature into the mK range with decreasing electron density.     

XPS study on silica-bismuthate glasses and glass ceramics

X-ray photoelectron spectroscopy (XPS) was used to evidence the effect of the Bi₂O₃ to SiO₂ ratio and of partial crystallisation on the electronic charge density around the atoms entering silica-bismuthate glasses of nominal composition 0.01Fe₂O₃⋅0.99[xSiO₂⋅(100−x)Bi₂O₃] with . The core level spectra show significant composition dependent changes in binding energy, and the full width at half maximum of photoelectron peaks both of cations and of oxygen atoms. The analysis reveals changes in electron density correlated with the ionic and covalent character of the samples. The shift in binding energy suggests charge transfer from silicon and oxygen atoms to bismuth atoms. Contrary to the expected behaviour in conventional silicate oxide systems, the results indicate an increase of ionicity for silicon and of covalency for bismuth atoms. The same evolution of ionicity/covalency is observed after partial crystallisation.     

Diode-pumped efficient slab laser with two Nd:YLF crystals and second-harmonic generation by slab LBO

We demonstrate a diode-pumped electro-optical Q-switched slab laser with a high optical efficiency, high pulse energy, and short pulse width with two Nd:YLF crystals inside one resonator. The single compact slab resonator can generate a 1D top-hat beam at both the far field and the near field. With a slab-geometry-design lithium triborate (LBO) crystal, efficient critical phase-matching second-harmonic generation for a 1D top-hat beam with multiple transverse modes is achieved.     

Creating second-order nonlinearity in pure synthetic silica optical fibers by thermal poling

A twin-hole optical fiber with pure synthetic silicate glass between the two electrode holes was thermally poled. The induced second-order nonlinearity (SON) was located at the core-cladding interface sections that were nearly parallel to the poling electric field. The polarization dependence of the induced SON suggests that nonlinearity was due to the presence of a space-charge field, which was probably formed by electron migration among the defects located at the core-cladding interface. The magnitude of the induced SON was measured to be approximately 0.06 pm /V.     

A solution for the narrow rectangular punch

This paper considers the problem of a rectangular flat ended punch acting on an elastic half-space. An approximate solution is generated through application of the elastic line integral equations. The results produced by this method are then compared with another approximate solution already available.

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Zusammenfassung Dieser Aufsatz behandelt das Problem eines starren, flachen Stempels mit rechteckigen Grundriss, der in einen elastischen Halbraum gepresst wird. Eine Näherungslösung wird erzeugt mittels der Integralgleichung des elastischen Linienkontakts. Die auf dieser Weise gewonnene Ergebnisse werden mit einer schon bekannten Näherungslösung verglichen.

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Résumé Dans ce rapport, on considère le problème d'un cachet rigide à base plane rectangulaire qui est poussée dans une semi-espace élastique. Une solution approximative est générée par application de l'équation integrale du contact élastique de ligne. Les résultats produits par cette méthode sont comparés à une solution approximative déjà connue.

     

Variable Order and Distributed Order Fractional Operators

Many physical processes appear to exhibit fractional order behavior thatmay vary with time or space. The continuum of order in the fractionalcalculus allows the order of the fractional operator to be considered asa variable. This paper develops the concept of variable and distributedorder fractional operators. Definitions based on the Riemann–Liouvilledefinition are introduced and the behavior of the new operators isstudied. Several time domain definitions that assign different argumentsto the order q in the Riemann–Liouville definition are introduced. Foreach of these definitions various characteristics are determined. Theseinclude: time invariance of the operator, operator initialization,physical realization, linearity, operational transforms, and memorycharacteristics of the defining kernels.A measure (m ₂) for memory retentiveness of the order history isintroduced. A generalized linear argument for the order q allows theconcept of `tailored' variable order fractional operators whose m ₂ memory may be chosen for a particular application. Memory retentiveness (m ₂) andorder dynamic behavior are investigated and applications are shown.The concept of distributed order operators where the order of thetime based operator depends on an additional independent (spatial)variable is also forwarded. Several definitions and their Laplacetransforms are developed, analysis methods with these operators aredemonstrated, and examples shown. Finally operators of multivariable anddistributed order are defined and their various applications areoutlined.