Fixed subgroups are compressed in surface groups

For a compact surface Σ (orientable or not, and with boundary or not), we show that the fixed subgroup, Fix ℬ, of any family ℬ of endomorphisms of π1(Σ) is compressed in π1(Σ), i.e. rk ( Fix ℬ) ≤ rk (H) for any subgroup Fix ℬ ≤ H ≤ π1(Σ). On the way, we give a partial positive solution to the inertia conjecture, both for free and for surface groups. We also investigate direct products, G, of finitely many free and surface groups, and give a characterization of when G satisfies that rk ( Fix ϕ) ≤ rk (G) for every ϕ ∈ Aut (G).

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Fixed subgroups in direct products of surface groups of Euclidean type

Communications in Algebra ◽

10.1080/00927872.2020.1726939 ◽

2020 ◽

Vol 48 (7) ◽

pp. 3003-3010 ◽

Cited By ~ 1

Author(s):

Jianchun Wu ◽

Enric Ventura ◽

Qiang Zhang

Keyword(s):

Surface Groups ◽

Direct Products ◽

Fixed Subgroups ◽

Euclidean Type

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Shakespeare Afoot

10.1093/oso/9780198793755.003.0003 ◽

2018 ◽

Author(s):

John Kerrigan

Keyword(s):

Early Modern ◽

Richard Iii ◽

Midsummer Night's Dream ◽

As You Like It ◽

A Midsummer Night's Dream ◽

History Of ◽

The Way

That Shakespeare adds a limp to the received characterization of Richard III is only the most conspicuous instance of his interest in how actors walked, ran, danced, and wandered. His attention to actors’ footwork, as an originating condition of performance, can be traced from Richard III through A Midsummer Night’s Dream and As You Like It into Macbeth, which is preoccupied with the topic and activity all the way to the protagonist’s melancholy conclusion that ‘Life’s but a walking shadow, a poor player | That struts and frets his hour upon the stage’. Drawing on classical and early modern accounts of how people walk and should walk, on ideas about time and prosody, and the experience of disability, this chapter cites episodes in the history of performance to show how actors, including Alleyn, Garrick, and Olivier, have worked with the opportunities to dramatize footwork that are provided by Shakespeare’s plays.

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Compact Differences of Composition Operators on Bergman Spaces Induced by Doubling Weights

Journal of Geometric Analysis ◽

10.1007/s12220-021-00724-y ◽

2021 ◽

Author(s):

Bin Liu ◽

Jouni Rättyä ◽

Fanglei Wu

Keyword(s):

Bergman Space ◽

Open Problem ◽

Lebesgue Space ◽

Composition Operators ◽

Bergman Spaces ◽

Weighted Bergman Space ◽

Carleson Measures ◽

Doubling Weights ◽

The Way

AbstractBounded and compact differences of two composition operators acting from the weighted Bergman space $$A^p_\omega $$ A ω p to the Lebesgue space $$L^q_\nu $$ L ν q , where $$0<q<p<\infty $$ 0 < q < p < ∞ and $$\omega $$ ω belongs to the class "Equation missing" of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proofs a new description of q-Carleson measures for $$A^p_\omega $$ A ω p , with $$p>q$$ p > q and "Equation missing", involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space $$A^p_\alpha $$ A α p with $$-1<\alpha <\infty $$ - 1 < α < ∞ to the setting of doubling weights. The case "Equation missing" is also briefly discussed and an open problem concerning this case is posed.

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cis-Tetrachlorido-bis(indazole)osmium(iv) and its osmium(iii) analogues: paving the way towards the cis-isomer of the ruthenium anticancer drugs KP1019 and/or NKP1339

Dalton Transactions ◽

10.1039/c7dt02194a ◽

2017 ◽

Vol 46 (35) ◽

pp. 11925-11941 ◽

Cited By ~ 4

Author(s):

Gabriel E. Büchel ◽

Susanne Kossatz ◽

Ahmad Sadique ◽

Peter Rapta ◽

Michal Zalibera ◽

...

Keyword(s):

Anticancer Drugs ◽

Synthesis And Characterization ◽

Cis Isomer ◽

The Way

The synthesis and characterization of cis-[OsIVCl4(κN2-1H-indazole)2] and its 1e-reduced analog are reported.

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Identification and Characterization of Monomeric, Volatile SiCl3NH2 as Product of the Reaction Between SiCl4 and NH3: An Important Intermediate on the Way to Silicon Nitride?

ChemInform ◽

10.1002/chin.200322023 ◽

2003 ◽

Vol 34 (22) ◽

Author(s):

Hans-Joerg Himmel ◽

Nils Schiefenhoevel ◽

Michael Binnewies

Keyword(s):

Silicon Nitride ◽

Important Intermediate ◽

Identification And Characterization ◽

The Way

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Point configurations, phylogenetic trees, and dissimilarity vectors

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.2021244118 ◽

2021 ◽

Vol 118 (12) ◽

pp. e2021244118

Author(s):

Alessio Caminata ◽

Noah Giansiracusa ◽

Han-Bom Moon ◽

Luca Schaffler

Keyword(s):

Phylogenetic Trees ◽

Geometric Interpretation ◽

Explicit Characterization ◽

Point Configurations ◽

Definition Of ◽

Tropical Basis ◽

The Way

In 2004, Pachter and Speyer introduced the higher dissimilarity maps for phylogenetic trees and asked two important questions about their relation to the tropical Grassmannian. Multiple authors, using independent methods, answered affirmatively the first of these questions, showing that dissimilarity vectors lie on the tropical Grassmannian, but the second question, whether the set of dissimilarity vectors forms a tropical subvariety, remained opened. We resolve this question by showing that the tropical balancing condition fails. However, by replacing the definition of the dissimilarity map with a weighted variant, we show that weighted dissimilarity vectors form a tropical subvariety of the tropical Grassmannian in exactly the way that Pachter and Speyer envisioned. Moreover, we provide a geometric interpretation in terms of configurations of points on rational normal curves and construct a finite tropical basis that yields an explicit characterization of weighted dissimilarity vectors.

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Possible Worlds in Translation: Coleman Barks’s Rendition of a Story from Rumi’s Masnavi

Primerjalna književnost ◽

10.3986/pkn.v44.i3.07 ◽

2021 ◽

Vol 44 (3) ◽

Author(s):

Vahid Medhat ◽

Hossein Pirnajmuddin ◽

Pyeaam Abbasi

Keyword(s):

Internal Structure ◽

English Translation ◽

Possible Worlds ◽

Translation Studies ◽

Original Text ◽

Main Character ◽

Source Text ◽

Narrative Worlds ◽

The Way

This article applies the theory of possible worlds to the field of translation studies by examining the narrative worlds of original and translated texts. Specifically, Marie-Laure Ryan’s characterization of possible worlds provides an account of the internal structure of the textual universe and the progression of the plot. Based on this account, one of the stories from Rumi’s Masnavi is compared to Coleman Barks’s English translation. The possible worlds of the characters and the unfolding of the plots in both texts are examined to assess the degree of compatibility between the textual universes of the original and the translated texts and how significant this might be. It also examines how readers reconstruct the narrative worlds projected by the two texts. The analysis reveals some inconsistencies in the way the textual universes of the original and translated texts are furnished and in the way readers reconstruct the narrative worlds of the two texts. The inability of translation to fully render the main character results in some loss in terms of the pungency and pithiness of the original text. It is also shown that the source text presents a richer domain of the virtual in comparison, suggesting a higher degree of tellability in the textual universe of the Masnavi’s narrative.

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Novel Mega Best-Seller Karya Luluk HF Mariposa dalam Kajian Resepsi Sastra

MEDAN MAKNA: Jurnal Ilmu Kebahasaan dan Kesastraan ◽

10.26499/mm.v19i2.3603 ◽

2021 ◽

Vol 19 (2) ◽

pp. 152

Author(s):

Tania Intan ◽

Muhamad Adji

Keyword(s):

Aggressive Behavior ◽

Research Data ◽

The Novel ◽

Research Results ◽

Female Protagonist ◽

Data Source ◽

The Difference ◽

Horizon Of Expectations ◽

The Way

This study discusses the reception of readers of the mega best-seller novel entitled Mariposa by Luluk HF. The purpose of this study is to (1) describe the reader's responses, (2) describe the horizon of readers' expectations, and (3) describe the factors that cause differences in responses and the horizon of expectations of readers of Mariposa's novel. The method applied is descriptive qualitative. This study uses a reception aesthetic approach that seeks to find consistent reception patterns as a reflection of the way the reader responds to the text. The research data consisted of texts containing the responses of twenty respondents from the data source in the form of the Goodreads reader site. The research results obtained are as follows. First, not all readers respond positively to the intrinsic elements of the novel, especially the characterization of the female protagonist who is considered to show aggressive behavior with a love motive. Second, most of the horizons of readers' expectations do not match the reality in Mariposa. Readings are generally motivated by curiosity because of the hyperbolic labeling of the novel, recommendations from friends, and the discourse of filming the novel. Third, the factors that cause the difference or suitability of the horizon of readers' expectations for the Mariposa novel are knowledge of literature, knowledge of life, and experience of reading literary works.

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Vertex-Transitive Direct Products of Graphs

The Electronic Journal of Combinatorics ◽

10.37236/6999 ◽

2018 ◽

Vol 25 (2) ◽

Cited By ~ 1

Author(s):

Richard H. Hammack ◽

Wilfried Imrich

Keyword(s):

Direct Product ◽

Direct Products ◽

Odd Cycle ◽

Vertex Transitive ◽

Odd Cycles

It is known that for graphs $A$ and $B$ with odd cycles, the direct product $A\times B$ is vertex-transitive if and only if both $A$ and $B$ are vertex-transitive. But this is not necessarily true if one of $A$ or $B$ is bipartite, and until now there has been no characterization of such vertex-transitive direct products. We prove that if $A$ and $B$ are both bipartite, or both non-bipartite, then $A\times B$ is vertex-transitive if and only if both $A$ and $B$ are vertex-transitive. Also, if $A$ has an odd cycle and $B$ is bipartite, then $A\times B$ is vertex-transitive if and only if both $A\times K_2$ and $B$ are vertex-transitive.

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