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11.
12.
Esa Järvenpää Maarit Järvenpää Antti Käenmäki Tapio Rajala Sari Rogovin Ville Suomala 《Mathematische Zeitschrift》2010,266(1):83-105
Let X be a metric measure space with an s-regular measure μ. We prove that if A ì X{A\subset X} is r{\varrho} -porous, then dimp(A) £ s-crs{{\rm {dim}_p}(A)\le s-c\varrho^s} where dimp is the packing dimension and c is a positive constant which depends on s and the structure constants of μ. This is an analogue of a well known asymptotically sharp result in Euclidean spaces. We illustrate by an example that the
corresponding result is not valid if μ is a doubling measure. However, in the doubling case we find a fixed N ì X{N\subset X} with μ(N) = 0 such that
dimp(A) £ dimp(X)-c(log\tfrac1r)-1rt{{\rm {dim}_p}(A)\le{\rm {dim}_p}(X)-c(\log \tfrac1\varrho)^{-1}\varrho^t} for all r{\varrho} -porous sets A ì X\ N{A \subset X{\setminus} N} . Here c and t are constants which depend on the structure constant of μ. Finally, we characterize uniformly porous sets in complete s-regular metric spaces in terms of regular sets by verifying that A is uniformly porous if and only if there is t < s and a t-regular set F such that A ì F{A\subset F} . 相似文献
13.
Tapio Rajala Karl-Theodor Sturm 《Calculus of Variations and Partial Differential Equations》2014,50(3-4):831-846
We prove that in metric measure spaces where the entropy functional is \(K\) -convex along every Wasserstein geodesic any optimal transport between two absolutely continuous measures with finite second moments lives on a non-branching set of geodesics. As a corollary we obtain that in these spaces there exists only one optimal transport plan between any two absolutely continuous measures with finite second moments and this plan is given by a map. The results are applicable in metric measure spaces having Riemannian Ricci curvature bounded below, and in particular they hold also for Gromov-Hausdorff limits of Riemannian manifolds with Ricci curvature bounded from below by some constant. 相似文献
14.
Most branch-and-bound algorithms in global optimization depend on convex underestimators to calculate lower bounds of a minimization objective function. The $\alpha $ BB methodology produces such underestimators for sufficiently smooth functions by analyzing interval Hessian approximations. Several methods to rigorously determine the $\alpha $ BB parameters have been proposed, varying in tightness and computational complexity. We present new polynomial-time methods and compare their properties to existing approaches. The new methods are based on classical eigenvalue bounds from linear algebra and a more recent result on interval matrices. We show how parameters can be optimized with respect to the average underestimation error, in addition to the maximum error commonly used in $\alpha $ BB methods. Numerical comparisons are made, based on test functions and a set of randomly generated interval Hessians. The paper shows the relative strengths of the methods, and proves exact results where one method dominates another. 相似文献
15.
Bernas A Kumar N Mäki-Arvela P Laine E Holmbom B Salmi T Murzin DY 《Chemical communications (Cambridge, England)》2002,(10):1142-1143
Development of a new heterogeneous catalytic pathway for isomerization of linoleic acid to conjugated linoleic acids at mild reaction conditions over Ni/H-MCM-41 in a soluted system. 相似文献
16.
17.
Andreas Lundell Joakim Westerlund Tapio Westerlund 《Journal of Global Optimization》2009,43(2-3):391-405
In this paper some transformation techniques, based on power transformations, are discussed. The techniques can be applied to solve optimization problems including signomial functions to global optimality. Signomial terms can always be convexified and underestimated using power transformations on the individual variables in the terms. However, often not all variables need to be transformed. A method for minimizing the number of original variables involved in the transformations is, therefore, presented. In order to illustrate how the given method can be integrated into the transformation framework, some mixed integer optimization problems including signomial functions are finally solved to global optimality using the given techniques. 相似文献
18.
The diffraction of sound from an edge of a thin chipboard panel was measured in an anechoic chamber, and compared to simulations based on the diffraction formulation developed by Svensson et al. [Svensson UP, Fred RI, Vanderkooy J. An analytic secondary source model of edge diffraction impulse responses. J Acoust Soc Am 1999;106(5):2331-44]. The measurements and simulations were performed for a line of receiver positions below the panel to include cases for which the direct sound had an unobstructed propagation path to the receivers, as well as cases for which the direct sound was occluded by the panel. Comparison of the measured and simulated responses is provided in both the time and frequency-domains, and shows that the differences between them are small over the entire audible frequency range. This case study verifies that the applied diffraction-modeling method gives accurate results, and that the assumptions of ideal source and wedge characteristics inherent in the method do not preclude its use in simulations of realistic scenarios. 相似文献
19.
Ögmundur Vidar Rúnarsson Clemens Malainer Hákon Steinsson Tapio Nevalainen 《European Polymer Journal》2010,46(6):1251-1267
Quaternary N-(2-(N,N,N-tri-alkyl ammoniumyl and 2-pyridiniumyl) acetyl) derivatives of chitosan polymer, chitooligomer, and glucosamine (monomer) were synthesized for the purpose of investigating the structure activity relationship (SAR) for the antibacterial effect. Novel methods were used in the synthesis. The final chitosan and chitooligomer derivatives could thus be obtained in two steps without prior protection of the hydroxyl groups. However, in order to obtain chitosan derivatives with the bulky N,N-dimethyl-N-dodecyl- and N,N-dimethyl-N-butyl side chains three steps were needed, starting from 3,6-O-di-tert-butyldimethylsilyl chitosan (3,6-O-di-TBDMS chitosan) as the key intermediate. The quaternary ammoniumyl acetyl derivatives of glucosamine were synthesized from glucosamine or tetra-O-acetylglucosamine. N,N,N-trimethyl chitosan (TMC) was used as reference compound for investigation of antibacterial activity. Clinical Laboratory Standard Institute (CLSI) protocols were used to determine MIC and MLC for activity against clinically important Gram-positive strains Staphylococcus aureus (ATCC 25923), and S. aureus (MRSA) (ATCC 43300), and Gram-negative strains of Escherichia coli (ATCC 25922), P. aeriginosa (ATCC 27853) and Enterococcus facialis (ATCC 29212). The MIC values for the compounds ranged from 8 to ?8192 mg/L. In general the N-(2-(N,N-dimethyl-N-dodecyl ammoniumyl) acetyl) derivatives of chitooligomer and glucosamine monomer were more active against bacteria than derivatives with shorter alkyl chains. In contrast the N-(2-(N,N-dimethyl-N-dodecyl ammoniumyl) acetyl) derivatives of chitosan were less active than derivatives with N-(2-N,N,N-trimetylammoniumyl) acetyl or N-(2-(N-pyridiniumyl) acetyl) quaternary moiety. N,N,N-trimethyl chitosan (TMC) was the most active compound in this study. 相似文献
20.
A recent study on perceptual difference in simulated concert halls showed that a concert hall renders stronger sound with more bass when the temporal envelope of a signal is preserved in the reflections [Lokki et al., J. Acoust. Soc. Am. 129, EL223-EL228 (2011)]. In the same study the lateral reflections were shown to contribute to the perceived envelopment and openness. Moreover, the listening test results suggest that lateral reflections contribute to perception of sound source distance. Here, it is shown that lateral reflections are beneficial due to their increasing effect on binaural loudness-the phenomenon known well in psychoacoustics, but not in architectural acoustics. The reflections from the side are amplified more than median plane reflections, in particular at high frequencies, due to the shape of the human head. 相似文献