Lucas Mol  Ortrud R. Oellermann 《Journal of Graph Theory》2019,91(4):326-352

This article focuses on properties and structures of trees with maximum mean subtree order in a given family; such trees are called optimal in the family. Our main goal is to describe the structure of optimal trees in and , the families of all trees and caterpillars, respectively, of order . We begin by establishing a powerful tool called the Gluing Lemma, which is used to prove several of our main results. In particular, we show that if is an optimal tree in or for , then every leaf of is adjacent to a vertex of degree at least . We also use the Gluing Lemma to answer an open question of Jamison and to provide a conceptually simple proof of Jamison's result that the path has minimum mean subtree order among all trees of order . We prove that if is optimal in , then the number of leaves in is and that if is optimal in , then the number of leaves in is . Along the way, we describe the asymptotic structure of optimal trees in several narrower families of trees.  相似文献   

    

Florian Barbero  Christophe Paul  Michał Pilipczuk 《Journal of Graph Theory》2019,90(4):484-496

We prove that the strong immersion order is a well-quasi-ordering on the class of semicomplete digraphs, thereby strengthening a result of Chudnovsky and Seymour (2011, J. Comb. Theory, Series B, 101, 47–53) that this holds for the class of tournaments.  相似文献   

    

P. Constantinou  S. Franz  L. Ludwig  C. Xenophontos 《Numerical Methods for Partial Differential Equations》2019,35(1):114-127

We consider fourth‐order singularly perturbed problems posed on smooth domains and the approximation of their solution by a mixed Finite Element Method on the so‐called Spectral Boundary Layer Mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at an exponential rate when the error is measured in the energy norm. Numerical examples illustrate our theoretical findings.  相似文献   

    

《Applied Mathematics Letters》2019

Under some assumptions we find a general solution of the factorization problem for a family of second order difference equations.  相似文献   

    

Ann‐Christin Pppler  Michael M. Lübtow  Jonas Schlauersbach  Johannes Wiest  Lorenz Meinel  Robert Luxenhofer 《Angewandte Chemie (International ed. in English)》2019,58(51):18540-18546

Detailed insight into the internal structure of drug‐loaded polymeric micelles is scarce, but important for developing optimized delivery systems. We observed that an increase in the curcumin loading of triblock copolymers based on poly(2‐oxazolines) and poly(2‐oxazines) results in poorer dissolution properties. Using solid‐state NMR spectroscopy and complementary tools we propose a loading‐dependent structural model on the molecular level that provides an explanation for these pronounced differences. Changes in the chemical shifts and cross‐peaks in 2D NMR experiments give evidence for the involvement of the hydrophobic polymer block in the curcumin coordination at low loadings, while at higher loadings an increase in the interaction with the hydrophilic polymer blocks is observed. The involvement of the hydrophilic compartment may be critical for ultrahigh‐loaded polymer micelles and can help to rationalize specific polymer modifications to improve the performance of similar drug delivery systems.  相似文献   

    

《Computational Biology and Chemistry》2019

The extraction of vein traits from venation networks is of great significance to the development of a variety of research fields, such as evolutionary biology. However, traditional studies normally target to the extraction of reticulate structure traits (ReSTs), which is not sufficient enough to distinguish the difference between vein orders. For hierarchical structure traits (HiSTs), only a few tools have made attempts with human assistance, and obviously are not practical for large-scale traits extraction. Thus, there is a necessity to develop the method of automated vein hierarchy classification, raising a new challenge yet to be addressed. We propose a novel vein hierarchy classification method based on directional morphological filtering to automatically classify vein orders. Different from traditional methods, our method classify vein orders from highly dense venation networks for the extraction of traits with ecological significance. To the best of our knowledge, this is the first attempt to automatically classify vein hierarchy. To evaluate the performance of our method, we prepare a soybean transmission image dataset (STID) composed of 1200 soybean leaf images and the vein orders of these leaves are manually coarsely annotated by experts as ground truth. We apply our method to classify vein orders of each leaf in the dataset. Compared with ground truth, the proposed method achieves great performance, while the average deviation on major vein is less than 5 pixels and the average completeness on second-order veins reaches 54.28%.  相似文献   

    

Jieni Li  Henan Li  Lai Liu  Huizhen Yao  Bingbing Tian  Chenliang Su  Haizhe Zhong  Ye Wang  Lifu Zhang  Yumeng Shi 《化学:亚洲杂志》2019,14(16):2861-2868

Organometallic halide perovskites have attracted great research interest as light‐active materials for use in optoelectronics. Here, we report a high‐performance photoconductor based on a methylammonium lead iodide (MAPbI₃) film that was prepared from a methylamine‐treated MAPbI₃/PbI₂ perovskite film. An ultrahigh responsivity of 3.6 A W^?1 and detectivity of 5.4×10¹² Jones were obtained for the film under 0.5 mW cm^?2 white‐light illumination. In addition, under 420 nm light irradiation, the film exhibited its highest responsivity and detectivity of 30 A W^?1 and 2.4×10¹⁴ Jones, respectively. The excellent photo‐response performance results from the improved electronic quality and suppressed nonradiative recombination channels of the treated perovskite thin film.  相似文献   

    

Upkar Kumar  Aurlien Cuche  Jadab Sharma  Antoine Moreau  Grard Colas des Francs  Christian Girard  Erik Dujardin 《Advanced Optical Materials》2019,7(11)

Sub‐micrometric and ultrathin gold cavities sustain several high order planar plasmon resonances in the visible to near‐infrared spectral window that open new perspectives for the realization of self‐assembled metasurfaces or integrated components for nano‐optics. This article investigates in detail the far‐field spectral features of these multimodal crystalline gold nanoprisms, deposited on either dielectric (glass) or metallic substrates (Au, Al) by dark‐field scattering spectroscopy. Relying on the computation of the plasmonic density of states, the signature of each planar resonance is de‐convoluted from the experimental global response of single cavities as a function of the cavity size and the substrate nature. The redshifting dispersion of each resonance is extracted from this decomposition analysis and agrees with predictions from a Green dyadic method based numerical tool. In addition, in the presence of a metallic film, a characteristic redshift or blueshift of the global response is observed for each cavity that results from a metal‐specific redistribution of the resonances. The fine spectral tuning of high order plasmonic resonances achieved here reveals the potential of the metal–insulator–metal gap geometry for a static modal engineering within ultrathin gold cavities.  相似文献   

    

H. Sabiki  M. Rhoudaf  R. Elarabi 《复变函数与椭圆型方程》2019,64(1):143-170

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《Journal of Chemometrics》2018,32(8)

As shallow architecture is inefficient in terms of computational elements, some incipient fault features can be characterized through the composition of many nonlinearities, ie, with deep network. In this paper, a novel approach is developed for multivariate statistical process monitoring based on higher‐order correlations. First, the correlations among monitoring variables can be learned by a multilayer learning framework hierarchically: The higher the number of layers to be stacked, the more nonlinear and abstract features can be characterized. Second, 3 monitoring statistics, SRE, M², and C, are presented to monitor whether the process is remaining in control, and they are instructive for the identification of fault types. Moreover, only normal data are used in training phase; this can avoid the unbalance problem of different types of fault data. These capabilities of the proposed approach are illustrated with two industrial benchmarks, Tennessee Eastman process and Metal Etch process.  相似文献