scholarly journals Discrete Quantitative Nodal Theorem

10.37236/9944 ◽  
2021 ◽  
Vol 28 (3) ◽  
Author(s):  
László Lovász
Keyword(s):  
Common Generalization ◽  
Eigenvalues Of The Laplacian ◽  
Special Case

We prove a theorem that can be thought of as a common generalization of the Discrete Nodal Theorem and (one direction of) Cheeger's Inequality for graphs. A special case of this result will assert that if the second and third eigenvalues of the Laplacian are at least $\varepsilon$ apart, then the subgraphs induced by the positive and negative supports of the eigenvector belonging to $\lambda_2$ are not only connected, but edge-expanders (in a weighted sense, with expansion depending on $\varepsilon$).

scholarly journals Detachments Preserving Local Edge-Connectivity of Graphs

1999 ◽  
Vol 6 (35) ◽  
Author(s):  
Tibor Jordán ◽  
Zoltán Szigeti
Keyword(s):  
Edge Connectivity ◽  
Common Generalization ◽  
Connectivity Augmentation ◽  
Local Edge ◽  
Positive Integers ◽  
Special Case

Let G = (V +s,E) be a graph and let S = (d1, ..., dp) be a set of positive integers with<br />Sum dj = d(s). An S-detachment splits s into a set of p independent vertices s1, ..., sp with<br />d(sj) = dj, 1 <= j <= p. Given a requirement function r(u, v) on pairs of vertices of V , an<br />S-detachment is called r-admissible if the detached graph G' satisfies lambda_G' (x, y) >= r(x, y)<br />for every pair x, y in V . Here lambda_H(u, v) denotes the local edge-connectivity between u and v<br />in graph H.<br />We prove that an r-admissible S-detachment exists if and only if (a) lambda_G(x, y) >= r(x, y),<br />and (b) lambda_G−s(x, y) >= r(x, y) − Sum |dj/2| hold for every x, y in V .<br />The special case of this characterization when r(x, y) = lambda_G(x, y) for each pair in V was conjectured by B. Fleiner. Our result is a common generalization of a theorem of W. Mader on edge splittings preserving local edge-connectivity and a result of B. Fleiner on detachments preserving global edge-connectivity. Other corollaries include previous results of L. Lov´asz and C.J.St.A. Nash-Williams on edge splittings and detachments, respectively. As a new application, we extend a theorem of A. Frank on local edge-connectivity augmentation to the case when stars of given degrees are added.

THE Qn,k,m GRAPH: A COMMON GENERALIZATION OF VARIOUS POPULAR INTERCONNECTION NETWORKS

2013 ◽  
Vol 23 (03) ◽  
pp. 1350011 ◽  
Author(s):  
EDDIE CHENG ◽  
NART SHAWASH
Keyword(s):  
Interconnection Networks ◽  
Cayley Graphs ◽  
Alternating Group ◽  
Star Graph ◽  
Strong Connectivity ◽  
Common Generalization ◽  
Arrangement Graph ◽  
Special Case ◽  
Alternating Group Graph

The star graph and the alternating group graph were introduced as competitive alternatives to the hypercube, and they are indeed superior over the hypercube under many measures. However, they do suffer from scaling issues. To address this, different generalizations, namely, the (n,k)-star graph and the arrangement graph were introduced to address this shortcoming. From another direction, the star graph was recognized as a special case of Cayley graphs whose generators can be associated with a tree. Nevertheless, all these networks appear to be very different and yet share many properties. In this paper, we will solve this mystery by providing a common generalization of all these networks. Moreover, we will show that these networks have strong connectivity properties.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

Determination of the phase structure of polymerblends by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 492-493
Author(s):  
Dr. G. Kaemof
Keyword(s):  
Screw Extruder ◽  
Electron Microscopic ◽  
Thin Sections ◽  
Single Screw Extruder ◽  
Transmission Electron ◽  
The Matrix ◽  
Twin Screw ◽  
Special Case ◽  
Microscopic Investigations

A mixture of polycarbonate (PC) and styrene-acrylonitrile-copolymer (SAN) represents a very good example for the efficiency of electron microscopic investigations concerning the determination of optimum production procedures for high grade product properties.The following parameters have been varied:components of charge (PC : SAN 50 : 50, 60 : 40, 70 : 30), kind of compounding machine (single screw extruder, twin screw extruder, discontinuous kneader), mass-temperature (lowest and highest possible temperature).The transmission electron microscopic investigations (TEM) were carried out on ultra thin sections, the PC-phase of which was selectively etched by triethylamine.The phase transition (matrix to disperse phase) does not occur - as might be expected - at a PC to SAN ratio of 50 : 50, but at a ratio of 65 : 35. Our results show that the matrix is preferably formed by the components with the lower melting viscosity (in this special case SAN), even at concentrations of less than 50 %.

Test Validation Without Measurement

2016 ◽  
Vol 32 (3) ◽  
pp. 204-214 ◽  
Author(s):  
Emilie Lacot ◽  
Mohammad H. Afzali ◽  
Stéphane Vautier
Keyword(s):  
Test Data ◽  
Test Scores ◽  
Scientific Explanation ◽  
Test Validation ◽  
Clinical Tests ◽  
Ethical Perspective ◽  
Power Of Test ◽  
Memory Accuracy ◽  
Social Uses ◽  
Special Case

Abstract. Test validation based on usual statistical analyses is paradoxical, as, from a falsificationist perspective, they do not test that test data are ordinal measurements, and, from the ethical perspective, they do not justify the use of test scores. This paper (i) proposes some basic definitions, where measurement is a special case of scientific explanation; starting from the examples of memory accuracy and suicidality as scored by two widely used clinical tests/questionnaires. Moreover, it shows (ii) how to elicit the logic of the observable test events underlying the test scores, and (iii) how the measurability of the target theoretical quantities – memory accuracy and suicidality – can and should be tested at the respondent scale as opposed to the scale of aggregates of respondents. (iv) Criterion-related validity is revisited to stress that invoking the explanative power of test data should draw attention on counterexamples instead of statistical summarization. (v) Finally, it is argued that the justification of the use of test scores in specific settings should be part of the test validation task, because, as tests specialists, psychologists are responsible for proposing their tests for social uses.

Impact of Digitalization on Service Work in Knowledge-Intensive Business Services: An Empirical Study in Tax Consultancies

2019 ◽  
Vol 3 (4) ◽  
pp. 209-222
Author(s):  
Philipp K. Görs ◽  
Henning Hummert ◽  
Anne Traum ◽  
Friedemann W. Nerdinger
Keyword(s):  
Work Engagement ◽  
Service Work ◽  
Psychological Consequences ◽  
Business Services ◽  
Knowledge Intensive Business Services ◽  
Positive Effects ◽  
Knowledge Intensive ◽  
The Impact ◽  
Positive Effect ◽  
Special Case

Digitalization is a megatrend, but there is relatively little knowledge about its consequences for service work in general and specifically in knowledge-intensive business services (KIBS). We studied the impact of digitalization on psychological consequences for employees in tax consultancies as a special case of KIBS. We compare two tax consulting jobs with very different job demands, those of tax consultants (TCs) and assistant tax consultants (ATCs). The results show that the extent of digitalization at the workplace level for ATCs correlates significantly positively with their job satisfaction. For TCs, the same variable correlates positively with their work engagement. These positive effects of digitalization are mediated in the case of ATCs by the impact on important job characteristics. In the case of TCs, which already have very good working conditions, the impact is mediated by the positive effect on self-efficacy. Theoretical and practical consequences of these results are discussed.

Nonwovens: Global Trends in World Economy, European Foreign Trade, and Selected Case Studies from Poland and Asian Brics Countries

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zofia Wysokińska ◽  
Tomasz Czajkowski ◽  
Katarzyna Grabowska
Keyword(s):  
Case Studies ◽  
World Economy ◽  
World Market ◽  
Global Trends ◽  
Textile Materials ◽  
Brics Countries ◽  
Recent Trends ◽  
Almost All ◽  
Special Case

AbstractNonwovens are one of the most versatile textile materials and have become increasingly popular in almost all sectors of the economy due to their low manufacturing costs and unique properties. In the next few years, the world market of nonwovens is predicted to grow by 7%–8% annually (International Nonwovens & Disposables Association [INDA], European Disposables and Nonwovens Association [EDANA], and Markets and Markets). This article aims to analyze the most recent trends in the global export and import of nonwovens, to present two case studies of Polish companies that produce them, and to present one special case study of the market of nonwoven geotextiles in China and India, which are the Asian transition economies among the BRICS countries (Brazil, Russia, India, China, and South Africa).

Sign in / Sign up

Export Citation Format

Share Document