scholarly journals A robust version of Freiman's 3k–4 Theorem and applications

2018 ◽  
Vol 166 (3) ◽  
pp. 567-581 ◽  
Author(s):  
XUANCHENG SHAO ◽  
WENQIANG XU
Keyword(s):  
Sobolev Inequality ◽  
Robust Version ◽  
Structure Theorems ◽  
Restricted Sumset ◽  
Special Case

AbstractWe prove a robust version of Freiman's 3k – 4 theorem on the restricted sumset A+ΓB, which applies when the doubling constant is at most (3+$\sqrt{5}$)/2 in general and at most 3 in the special case when A = −B. As applications, we derive robust results with other types of assumptions on popular sums, and structure theorems for sets satisfying almost equalities in discrete and continuous versions of the Riesz–Sobolev inequality.

scholarly journals Generalized n-circular projections on JB*-triples and Hilbert C0(Ω)-modules

2017 ◽  
Vol 4 (1) ◽  
pp. 109-120
Author(s):  
Dijana Ilišević ◽  
Chih-Neng Liu ◽  
Ngai-Ching Wong
Keyword(s):  
Banach Space ◽  
Hilbert Spaces ◽  
Orthogonal Projections ◽  
Geometric Properties ◽  
C Algebras ◽  
Structure Theorems ◽  
Special Case

Abstract Being expected as a Banach space substitute of the orthogonal projections on Hilbert spaces, generalized n-circular projections also extend the notion of generalized bicontractive projections on JB*-triples. In this paper, we study some geometric properties of JB*-triples related to them. In particular, we provide some structure theorems of generalized n-circular projections on an often mentioned special case of JB*-triples, i.e., Hilbert C*-modules over abelian C*-algebras C0(Ω).

scholarly journals On semigroups of endomorphisms of generalized Boolean rings

1974 ◽  
Vol 18 (4) ◽  
pp. 411-418 ◽  
Author(s):  
Douglas B. Smith ◽  
Jiang Luh
Keyword(s):  
Boolean Rings ◽  
Structure Theorems ◽  
Paper Structure ◽  
Special Case

Magill in [4] first proved that two Boolean rings are isomorphic if and only if their respective endomorphism semigroups are isomorphic. His proof, however, relied on topological techniques. More recently Maxson has published a proof of the above using purely algebraic techniques [5]. In this paper, structure theorems are given which allow us to extend the above result to thepk-rings of Foster [1]. As a special case, the result is shown to apply also top-rings. An example is given to show that a further extension toJ-rings is impossible.

Existence results for Schrödinger–Choquard–Kirchhoff equations involving the fractional p-Laplacian

2019 ◽  
Vol 12 (3) ◽  
pp. 253-275 ◽  
Author(s):  
Patrizia Pucci ◽  
Mingqi Xiang ◽  
Binlin Zhang
Keyword(s):  
Variational Principle ◽  
Sobolev Inequality ◽  
Mountain Pass Theorem ◽  
Growth Conditions ◽  
Existence Results ◽  
Kirchhoff Equations ◽  
Superlinear Growth ◽  
Nonnegative Solutions ◽  
Carathéodory Function ◽  
Special Case

AbstractThe paper is concerned with existence of nonnegative solutions of a Schrödinger–Choquard–Kirchhoff-type fractional p-equation. As a consequence, the results can be applied to the special case(a+b\|u\|_{s}^{p(\theta-1)})[(-\Delta)^{s}_{p}u+V(x)|u|^{p-2}u]=\lambda f(x,u)% +\Bigg{(}\int_{\mathbb{R}^{N}}\frac{|u|^{p_{\mu,s}^{*}}}{|x-y|^{\mu}}\,dy% \Biggr{)}|u|^{p_{\mu,s}^{*}-2}u\quad\text{in }\mathbb{R}^{N},where\|u\|_{s}=\Bigg{(}\iint_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^{p}}{|x-y|^{N+ps}}% \,dx\,dy+\int_{\mathbb{R}^{N}}V(x)|u|^{p}\,dx\Biggr{)}^{\frac{1}{p}},{a,b\in\mathbb{R}^{+}_{0}}, with {a+b>0}, {\lambda>0} is a parameter, {s\in(0,1)}, {N>ps}, {\theta\in[1,N/(N-ps))}, {(-\Delta)^{s}_{p}} is the fractional p-Laplacian, {V:\mathbb{R}^{N}\rightarrow\mathbb{R}^{+}} is a potential function, {0<\mu<N}, {p_{\mu,s}^{*}=(pN-p\mu/2)/(N-ps)} is the critical exponent in the sense of Hardy–Littlewood–Sobolev inequality, and {f:\mathbb{R}^{N}\times\mathbb{R}\rightarrow\mathbb{R}} is a Carathéodory function. First, via the Mountain Pass theorem, existence of nonnegative solutions is obtained when f satisfies superlinear growth conditions and λ is large enough. Then, via the Ekeland variational principle, existence of nonnegative solutions is investigated when f is sublinear at infinity and λ is small enough. More intriguingly, the paper covers a novel feature of Kirchhoff problems, which is the fact that the parameter a can be zero. Hence the results of the paper are new even for the standard stationary Kirchhoff problems.

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.

Decanting the Rabelaisian Casks: Accessing Neoplatonic Poetic Fury in Baudelaire's ‘L'Âme du vin’

2016 ◽  
Vol 55 (3) ◽  
pp. 263-279
Author(s):  
Robert J. Hudson ◽  
Kristen Foote
Keyword(s):  
Nineteenth Century ◽  
Old Regime ◽  
Robust Version ◽  
Poetic Inspiration ◽  
Fleurs Du Mal

In one of the lesser-studied sections of Baudelaire's Les Fleurs du Mal, ‘Le Vin’, the poet offers a key to understanding the transcendence necessary for common post-Revolution Parisians to attain the proper poetic inspiration to create elevated verse. Divine or poetic Fury, a theoretically more robust version of other nineteenth-century ideas of intoxication, is at the heart of the section's threshold poem, ‘L'Âme du vin’, and establishes a bridge in Les Fleurs du mal linking the modern terrestrial wanderings of the ‘Tableaux parisiens’ to the celestial flights of the ‘Fleurs du mal’. Developed from Plato's Ion and Gallically codified by Rabelais, these theories filter to the aesthete Baudelaire, who decants this aged wine into a nineteenth-century vessel that lays old regime vertical hierarchies on their side and offers poetic intoxication to all who are willing to labour to become vessels of inspiration themselves.

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.

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