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Sufficient Conditions for Maximally Edge-connected and Super-edge-connected Digraphs Depending on the Size

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Acta Mathematica Sinica,English Series 2019年第12期35卷 1861-1870页

作者： Sebastian MILZ lutz volkmann Lehrstuhl Ⅱ für Mathematik RWTH Aachen University

Let D be a finite and simple digraph with vertex set V(D).The minimum degreeδof a digraph D is defined as the minimum value of its out-degrees and its *** D is a digraph with minimum degreeδand edge-connectivity λ,then λ≤δ.A digraph is maximally edge-connected ifλ=δ.A digraph is called super-edge-connected if every minimum edge-cut consists of edges incident to or from a vertex of minimum *** this note we show that a digraph is maximally edge-connected or super-edge-connected if the number of arcs is large enough.

关键词： Digraphs edge-connectivity maximally edge-connected digraphs super-edge-connected digraphs

The Roman k-domatic Number of a Graph

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Acta Mathematica Sinica,English Series 2011年第10期27卷 1899-1906页

作者： Seyed Mahmoud SHEIKHOLESLAMI lutz volkmann Department of Mathematics Azarbaijan University of Tarbiat MoaUem Tabriz 53714-161 L R. Iran and School of Mathematics Institute for Research in Fundamental Sciences ( IPM) Lehrstuhl H fiir Mathematik RWTH Aachen University 52056 Aachen Germany

Let k be a positive integer. A Roman k-dominating function on a graph G is a labeling f ： V（G） → {0, 1, 2} such that every vertex with label 0 has at least k neighbors with label 2. A set {f1, f2,..., fd} of distinct Roman k-dominating functions on G with the property that ∑di=1 fi（v） ≤ 2 for each v C V（G）, is called a Roman k-dominating family （of functions） on G. The maximum number of functions in a Roman k-dominating family on G is the Roman k-domatic number of G, denoted by dkR（G）. Note that the Roman 1-domatic number dlR（G） is the usual Roman domatic number dR（G）. In this paper we initiate the study of the Roman k-domatic number in graphs and we present sharp bounds for dkR（G）. In addition, we determine the Roman k-domatic number of some graphs. Some of our results extend those given by Sheikholeslami and volkmann in 2010 for the Roman domatic number.

关键词： Roman domination number Roman domatic number Roman k-domination number Ro- man k-domatic number

Total Restrained Bondage in Graphs

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Acta Mathematica Sinica,English Series 2013年第6期29卷 1033-1042页

作者： Nader JAFARI RAD Roslan HASNI Joanna RACZEK lutz volkmann Department of Mathematics Shahrood University of Technology Department of Mathematics Faculty of Science and Technology University Malaysia Terengganu Department of Mathematics Gdansk University of Technology Lehrstuhl II fr Mathematik RWTH Aachen University

A subset S of vertices of a graph G with no isolated vertex is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V （G） S is also adjacent to a vertex in V （G） S. The total restrained domination number of G is the minimum cardinality of a total restrained dominating set of G. In this paper we initiate the study of total restrained bondage in graphs. The total restrained bondage number in a graph G with no isolated vertex, is the minimum cardinality of a subset of edges E such that G E has no isolated vertex and the total restrained domination number of G E is greater than the total restrained domination number of G. We obtain several properties, exact values and bounds for the total restrained bondage number of a graph.

关键词： Domination total restrained domination bondage

有向图是极大连通的和超连通的充分条件（英文）

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中国科学技术大学学报 2018年第8期48卷 612-617页

作者：洪振木福克曼.鲁茨徐俊明安徽财经大学金融学院安徽蚌埠233030 亚琛工业大学数学系中国科学技术大学数学科学学院安徽合肥230026

设D是顶点集为V(D)的有限简单有向图.V(D)中的顶点v的度d(v)被定义为v的出度d+(v)和入度d-(v)中的最小值.如果有向图D的最小度为δ,连通度为κ,则κ≤δ.如果κ=δ,则称有向图是极大连通的.对极大连通的有向图D的每个最小点割S,如果D-S... 详细信息

设D是顶点集为V(D)的有限简单有向图.V(D)中的顶点v的度d(v)被定义为v的出度d+(v)和入度d-(v)中的最小值.如果有向图D的最小度为δ,连通度为κ,则κ≤δ.如果κ=δ,则称有向图是极大连通的.对极大连通的有向图D的每个最小点割S,如果D-S要么是非强连通的且至少有一个平凡的强连通分支,要么是平凡的,则称D是超连通的.通过弧数给出有向图或二部有向图在最小度给定时是极大连通的或超连通的充分条件,并举例说明这些条件中的下界是紧的.

关键词：有向图连通度极大连通超连通

Structural pavement assessment in Germany

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Frontiers of Structural and Civil Engineering 2018年第2期12卷 183-191页

作者： lutz PINKOFSKY Dirk JANSEN Bundesanstalt fur Straflenwesen (Federal Highway Research Institute) BASt Bruederstrasse 53 51427 Bergisch Gladbach Germany

The aging structure as well as the considerable increase of heavy-traffic load on Germany＇s motorways and trunk roads encourages the use of innovative, sound and reliable methods for the structural assessment on network level as well as on project level. Essential elements for this are data, which allow a reliable assessment. For a holistic approach to structural pavement assessment performance orientated measurements will be necessary. In combination with functional parameters as well as write-down models, strategically motivated decision making processes will be useful combined with technically motivated decision processes. For the application at the network level, the available methods for performance orientated measurements are still challenging, as they are based either on testing drill-cores or on non- traffic speed methods. In recent years significant innovation steps have been made to bring traffic speed bearing capacity measurements and methods for evaluating pavement structures on the road. The paper summarizes the actual assessment procedures in Germany as well as the ongoing work on the development and implementation of new methods and techniques.

关键词： pavement assessment Germany structure system

Simple and fast prediction of train-induced track forces,ground and building vibrations

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Railway Engineering Science 2020年第3期28卷 232-250页

作者： lutz Auersch Federal Institute of Materials Research and Testing D-12200 BerlinGermany

A simple and fast prediction scheme is presented for train-induced ground and building *** models such as(one-dimensional)transfer matrices are used for the vehicle–track–soil interaction and for the building–soil *** wave propagation through layered soils is approximated by a frequency-dependent homogeneous *** prediction is divided into the parts“emission”(excitation by railway traffic),“transmission”(wave propagation through the soil)and“immission”(transfer into a building).The link between the modules is made by the excitation force between emission and transmission,and by the free-field vibration between transmission and *** formula for the simple vehicle–track,soil and building models are given in this *** behaviour of the models is demonstrated by typical examples,including the mitigation of train vibrations by elastic track elements,the low-and high-frequency cut-offs characteristic for layered soils,and the interacting soil,wall and floor resonances of multi-storey *** is shown that the results of the simple prediction models can well represent the behaviour of the more time-consuming detailed models,the finite-element boundary-element models of the track,the wavenumber integrals for the soil and the three-dimensional finite-element models of the *** addition,measurement examples are given for each part of the prediction,confirming that the methods provide reasonable *** the prediction models are fast in calculation,many predictions can be done,for example to assess the environmental effect along a new railway *** simple models have the additional advantage that the user needs to know only a minimum of ***,the prediction is fast and user-friendly,but also theoretically and experimentally well-founded.

关键词： Railway-induced vibration Ground vibration Layered soil Building response Excitation forces Track and vehicle irregularities

Electrolyser design controls position-divergent C–H carboxylation

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Science China Chemistry 2023年第6期66卷 1549-1550页

作者： Max Surke Rong Zhao lutz Ackermann Institut für Organische und Biomolekulare Chemie Georg-August-Universitot GottingenTammannstraBe 237077 GotingenGermany Wohler Research Institute for Sustainable Chemistry Georg-August-Universitot GottingenTammannstraBe 237077 GotingenGermany German Center for Cardiovascular Research(DZHK) Potsdamer StraBe 5810785 BerlinGermany

In recent years,molecular electrochemistry has undergone a remarkable renaissance to surface as a sustainable strategy for organic synthesis and catalysis,gaining considerable momentum by the use of renewable forms of energy[1,2].Modern organic electrochemistry has the unique power to control chemo-,regio-,and position-selectivities through the judicious choice of the electrode material,the applied potential or an additional catalyst,among others[1,2].Despite the major advances in molecular electrochemistry,these approaches continue to predominantly rely on non-renewable fossil resources.

关键词： electrochemistry momentum catalysis

Development of a classification system based on corneal biomechanical properties using artificial intelligence predicting keratoconus severity

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Eye and Vision 2021年第3期8卷 203-213页

作者： Robert Herber lutz E.Pillunat Frederik Raiskup Department of Ophthalmology University Hospital Carl Gustav CarusUniversitätsklinikum Carl Gustav Carus an der Technischen Universität DresdenFetscherstraße 74TU 01307 DresdenGermany

Background:To investigate machine-learning(ML)algorithms to differentiate corneal biomechanical properties between different topographical stages of keratoconus(KC)by dynamic Scheimpflug tonometry(CST,Corvis ST,Oculus,Wetzlar,Germany).In the following,ML models were used to predict the severity in a training and validation ***:Three hundred and eighteen keratoconic and one hundred sixteen healthy eyes were included in this monocentric and cross-sectional pilot *** corneal response(DCR)and corneal thickness related(pachymetric)parameters from CST were chosen by appropriated selection techniques to develop a ML *** stage of KC was determined by the topographical keratoconus classification system(TKC,Pentacam,Oculus).Patients who were classified as TKC 1,TKC 2 and TKC 3 were assigned to subgroup mild,moderate,and advanced *** patients were classified as TKC 1-2,TKC 2-3 or TKC 3-4,they were assigned to subgroups according to the normative range of further corneal indices(index of surface variance,keratoconus index and minimum radius).Patients classified as TKC 4 were not included in this study due to the limited amount of *** discriminant analysis(LDA)and random forest(RF)algorithms were used to develop the classification *** were divided into training(70%of cases)and validation(30%of cases)***:LDA model predicted healthy,mild,moderate,and advanced KC eyes with a sensitivity(S_(n))/specificity(S_(p))of 82%/97%,73%/81%,62%/83%and 68%/95%from a validation dataset,*** the RF model,a S_(n)/S_(p) of 91%/94%,80%/90%,63%/87%,72%/95%could be reached for predicting healthy,mild,moderate,and advanced KC eyes,*** overall accuracy of LDA and RF was 71%and 78%,*** accuracy for KC detection including all subgroups of KC severity was 93%in both ***:The RF model showed good accuracy in predicting healthy eyes and various stages of *** accuracy was superior with respec

关键词： Artificial intelligence Corneal biomechanics Corvis ST Grading Keratoconus Machine learning

Nickela-electrocatalyzed sulfide and phosphine oxygenations with water

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Science China Chemistry 2021年第6期64卷 873-874页

作者： Long Yang Johanna Frey lutz Ackermann Institut für Organische und Biomolekulare Chemie Georg-August-Universität GöttingenTammannstrasse 2Göttingen 37077Germany Wöhler Research Institute for Sustainable Chemistry(WISCh) Georg-August-Universität GöttingenTammannstrasse 2Göttingen 37077Germany

Molecular electrochemistry has emerged as an environmentally-friendly *** major recent momentum was gained in electrocatalyzed bond activations by earth-abundant 3 d transition metals[1],cost-effective nickela-electrocatalysis continuous to be underdevelopment for electrocatalysis[2].Nickel is an essential component of metalloproteins involved in catalytic aerobic oxygenation processes,for which nickel-dioxygen species were proposed as the key catalytic species[3].

关键词： catalyzed nickel Nickel