Optimal and better transport plans

We consider the Monge-Kantorovich transport problem in a purely measure theoretic setting, i.e. without imposing continuity assumptions on the cost function. It is known that transport plans which are concentrated on c-monotone sets are optimal, provided the cost function c is either lower semi-continuous and finite, or continuous and may possibly attain the value ∞. We show that this is true in a more general setting, in particular for merely Borel measurable cost functions provided that {c=∞} is the union of a closed set and a negligible set. In a previous paper Schachermayer and Teichmann considered strongly c-monotone transport plans and proved that every strongly c-monotone transport plan is optimal. We establish that transport plans are strongly c-monotone if and only if they satisfy a “better” notion of optimality called robust optimality.     

Cohen-Macaulayness and computation of Newton graded toric rings

Let H⊆Z^d be a positive semigroup generated by A⊆H, and let K[H] be the associated semigroup ring over a field K. We investigate heredity of the Cohen-Macaulay property from K[H] to both its A-Newton graded ring and to its face rings. We show by example that neither one inherits in general the Cohen-Macaulay property. On the positive side, we show that for every H there exist generating sets A for which the Newton graduation preserves Cohen-Macaulayness. This gives an elementary proof for an important vanishing result on A-hypergeometric Euler-Koszul homology. As a tool for our investigations we develop an algorithm to compute algorithmically the Newton filtration on a toric ring.     

MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems

We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations on a graph. We propose an instantaneous control approach in which suitable Euler discretizations yield systems of ordinary differential equations on a graph. This networked system of ordinary differential equations is shown to be well-posed and affine-linear solutions of these systems are derived analytically. As a consequence, finite-dimensional mixed-integer linear optimization problems are obtained for every time step that can be solved to global optimality using general-purpose solvers. We illustrate our approach in practice by presenting numerical results on a realistic gas transport network.     

Nonparametric inference of gradual changes in the jump behaviour of time-continuous processes

In applications the properties of a stochastic feature often change gradually rather than abruptly, that is: after a constant phase for some time they slowly start to vary. In this paper we discuss statistical inference for the detection and the localization of gradual changes in the jump characteristic of a discretely observed Ito semimartingale. We propose a new measure of time variation for the jump behaviour of the process. The statistical uncertainty of a corresponding estimate is analysed by deriving new results on the weak convergence of a sequential empirical tail integral process and a corresponding multiplier bootstrap procedure.     

聚丙烯微孔膜表面修饰的葡聚糖固定化研究

糖以各种形式广泛存在于自然界,在人类的许多生理过程中起着不可或缺的重要作用．它具有优良的亲水性和生物特异性．研究表日月,将含糖单体接枝到聚丙烯微孔膜表面或通过共聚引入聚丙烯腈超滤膜,能显著提高常规高分子分离膜的抗污染能力和表面生物相容性,从而扩大其应用范围．     

Development and test of a numerical model for pulse thermography in civil engineering

Pulse thermography of concrete structures is used in civil engineering for detecting voids, honeycombing and delamination. Quantitatively realistic numerical 3D simulation is difficult due to the arising boundary layer at the heated surface and unreliable information about material parameters and environmental conditions. We address both issues by a semi-analytic reformulation of the heat transport problem and by parameter identification. Numerical results are compared with measurements of a test specimen.     

Characterization of active phosphorus surface sites at synthetic carbonate-free fluorapatite using single-pulse 1H, 31P, and 31P CP MAS NMR

The chemically active phosphorus surface sites defined as PO(x), PO(x)H, and PO(x)H2, where x = 1, 2, or 3, and the bulk phosphorus groups of PO4(3-) at synthetic carbonate-free fluorapatite (Ca5(PO4)3F) have been studied by means of single-pulse 1H,31P, and 31P CP MAS NMR. The changes in composition and relative amounts of each surface species are evaluated as a function of pH. By combining spectra from single-pulse 1H and 31P MAS NMR and data from 31P CP MAS NMR experiments at varying contact times in the range 0.2-3.0 ms, it has been possible to distinguish between resonance lines in the NMR spectra originating from active surface sites and bulk phosphorus groups and also to assign the peaks in the NMR spectra to the specific phosphorus species. In the 31P CP MAS NMR experiments, the spinning frequency was set to 4.2 kHz; in the single-pulse 1H MAS NMR experiments, the spinning frequency was 10 kHz. The 31P CP MAS NMR spectrum of fluorapatite at pH 5.9 showed one dominating resonance line at 2.9 ppm assigned to originate from PO4(3-) groups and two weaker shoulder peaks at 5.4 and 0.8 ppm which were assigned to the unprotonated PO(x) (PO, PO2-, and PO3(2-)) and protonated PO(x)H (PO2H and PO3H-) surface sites. At pH 12.7, the intensity of the peak representing unprotonated PO(x) surface sites has increased 1.7% relative to the bulk peak, while the intensity of the peaks of the protonated species PO(x)H have decreased 1.4% relative to the bulk peak. At pH 3.5, a resonance peak at -4.5 ppm has appeared in the 31P CP MAS NMR spectrum assigned to the surface species PO(x)H2 (PO3H2). The results from the 1H MAS and 31P CP MAS NMR measurements indicated that H+, OH-, and physisorbed H2O at the surface were released during the drying process at 200 degrees C.     

Analytical relation between effective mode field area and waveguide dispersion in microstructure fibers

For optical fibers exhibiting a radially symmetric refractive index profile, there exists an analytical relation that connects waveguide dispersion and the Petermann-II mode field radius. We extend the usefulness of this relation to the nonradially symmetric case of microstructure fibers in the anomalous dispersion regime, yielding a simple relation between dispersion and effective mode field area. Assuming a Gaussian mode distribution, we derive a fundamental upper limit for the effective mode field area that is required to obtain a certain amount of anomalous waveguide dispersion. This relation is demonstrated to show excellent agreement for fiber designs suited for supercontinuum generation and soliton lasers in the near infrared.     

Interaction-induced resonance in conductance and thermopower of quantum wires

We study the effect of electron-electron interaction on the transport properties of short clean quantum wires adiabatically connected to reservoirs. Interactions lead to resonances in a multichannel wire at particular values of the Fermi energy. We investigate in detail the resonance in a two-channel wire. The (negative) conductance correction peaks at the resonance, and decays exponentially as the Fermi energy is tuned away, the resonance width being given by the temperature. Likewise, the thermopower shows a characteristic structure, which is surprisingly well approximated by the so-called Mott formula. Finally, fourfold splitting of the resonance in a magnetic field provides a unique signature of the effect.