A fuzzy approach to the transportation problem

The transportation problem with fuzzy supply values of the deliverers and with fuzzy demand values of the receivers is analysed. For the solution of the problem the technique of parametric programming is used. This makes it possible to obtain not only the maximizing solution (according to the Bellman-Zadeh criterion) but also other alternatives close to the optimal solution.     

Bootstrapping the change-point of a hazard rate

This paper concerns the asymptotic validity of the bootstrap method in a non-regular model. Specifically, it is shown that the parametric bootstrap of the change-point parameter in the change-point hazard rate model works.     

Complexity results for multicriterial and parametric network flows using a pathological graph of Zadeh

For two classes of network flow problems a worst-case analysis is given depending on the number of vertices of a pathological graph of Zadeh. Firstly, an exponential number of breakpoints in the optimal value function of the maximal flow problem in generalized networks with parametric capacities is demonstrated. Secondly, it is shown that the bicriterial min-cost flow has, in the worst case. an exponential number of efficient extreme point solutions in the objective space.

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Zusammenfassung Für zwei Klassen von Netzwerkflußproblemen wird eine worst-case Analyse in Abhängigkeit von der Anzahl der Knoten eines pathologischen Graphen von Zadeh vorgenommen. Demnach besitzt das Maximalflußproblem in verallgemeinerten Netzwerken mit parametrischen Kapazitätsbeschränkungen eine exponentielle Anzahl von Knickstellen in der Optimalwertfunktion. und kostenminimale Flüsse haben bereits für zwei Kriterien eine exponentielle Zahl von effizienten Eckpunkten im Bildbereich.

     

Graphical Criticism: Some Historical Notes

This article proposes a bootstrap local bandwidth selector for estimating nonparametric additive models. The selector is derived from a bootstrap approximation of the conditional mean squared error, based on a wild bootstrap resampling scheme applied to the estimated residuals. The selector is computed exactly (without involving Monte Carlo approximations) and in practice can be evaluated for many additive estimation methods, including backfitting (bivariate), marginal integration, and mixed methods. We study the consistency of the bootstrap approximation and also carry out an empirical simulation study to explore the performance of the proposed selector in comparison with others. The graphical tool SiZer Map enables us to make meaningful comparisons between local and global selectors.     

New method for measuring beam profiles using a parametric X-ray pinhole camera

We propose a new method for measuring electron beam profiles using parametric X-ray radiation. In this method, a pinhole is placed between the source of parametric X-ray radiation and a two-dimensional X-ray detector, and the beam profile can be reconstructed on the detector, i.e., based on the principle of a pinhole camera. The profiles are in good agreement with the results obtained using a standard method with optical transition radiation. This method may prove useful to measure profiles of electron beams with short bunch lengths in recent advanced linear accelerators.     

Parametric Analysis for a Single Collapsing Bubble

This work presents a sensitivity analysis for cavitation processes, studying in detail the effect of various model parameters on the bubble collapse. A complete model (Hauke et al. Phys Rev E 75:1–14, 2007) is used to obtain how different parameters influence the collapse in SBSL experiments, providing some clues on how to enhance the bubble implosion in real systems. The initial bubble radius, the frequency and the amplitude of the pressure wave are the most important parameters determining under which conditions cavitation occurs. The range of bubble sizes inducing strong implosions for different frequencies is computed; the initial radius is the most important parameter characterized the intensity of the cavitation processes. However, other parameters like the gas and liquid conductivity or the liquid viscosity can have an important effect under certain conditions. It is shown that mass transfer processes play an important role in order to correctly predict the trends related with the effect of the liquid temperature, which translates into the bubble dynamics. Moreover, under some particular circumstances, evaporation can be encountered during the bubble collapse; this can be profitably exploited in order to feed reactants when the most extreme conditions inside the bubbles are reached. Thus, this paper aims at providing a global assessment of the effect of the different parameters on the entire cycle of a single cavitating spherical bubble immersed in an ultrasonic field. This work has been partially supported by Ministerio de Ciencia y Tecnologia, under grant number CTM2004-06184-C02-02.     

小波包分解及其参数模型

本文在小波包分析的基础之上，实现了适合于一维信号分析的小波分解算法，并将小波包分析理论和参数模型有机地结合了起来，构造了小波包参数模型。     

Approximation of circular arcs by parametric polynomial curves

In this paper the approximation of circular arcs by parametric polynomial curves is studied. If the angular length of the circular arc is h, a parametric polynomial curve of arbitrary degree \(n \in {\mathbb{N}}\) , which interpolates given arc at a particular point, can be constructed with radial distance bounded by h ²ⁿ . This is a generalization of the result obtained by Lyche and Mørken for odd n.     

Boundedness and continuity of Marcinkiewicz integrals associated to homogeneous mappings on Triebel-Lizorkin spaces

We establish the boundedness and continuity of parametric Marcinkiewicz integrals associated to homogeneous compound mappings on Triebel-Lizorkin spaces and Besov spaces. Here the integral kernels are provided with some rather weak size conditions on the unit sphere and in the radial direction. Some known results are naturally improved and extended to the rough case.     

Entanglement in optical parametric down-conversion with losses and noise

We show that radiation generated in optical parametric down-conversion with losses and noise is entangled for all times if the coupling coefficient is higher than half of damping constant and the product of damping constant and mean number of noise photons. For the process stimulated by means of chaotic light there is a saturable bound of its intensity for the generation of nonclassical light. Otherwise the quantum behaviour and entanglement are fully reduced. Under some restrictions for noise nonclassical light can also be generated at and below the threshold.