Root Group Labelings

2020 ◽  
pp. 117-130
Keyword(s):  
Root Group

Indices for the Exceptional Bruhat-Tits Buildings

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Division Algebra ◽  
Capital Letter ◽  
Coxeter Diagram ◽  
Root Group ◽  
Relative Type ◽  
Quaternion Division Algebra

This chapter considers the affine Tits indices for exceptional Bruhat-Tits buildings. It begins with a few small observations and some notations dealing with the relative type of the affine Tits indices, the canonical correspondence between the circles in a Tits index and the vertices of its relative Coxeter diagram, and Moufang sets. It then presents a proposition about an involutory set, a quaternion division algebra, a root group sequence, and standard involution. It also describes Θ‎-orbits in S which are disjoint from A and which correspond to the vertices of the Coxeter diagram of Ξ‎ and hence to the types of the panels of Ξ‎. Finally, it shows how it is possible in many cases to determine properties of the Moufang set and the Tits index for all exceptional Bruhat-Tits buildings of type other than Latin Capital Letter G with Tilde₂.

scholarly journals Long term clinical result of implant induced injury on the adjacent tooth

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yang-Jin Yi ◽  
In-Woo Park ◽  
Jeong-Kui Ku ◽  
Deuk-Won Jo ◽  
Jung-Suk Han ◽  
...  
Keyword(s):  
Retrospective Study ◽  
Root Surface ◽  
Chi Square ◽  
Group Iii ◽  
Direct Invasion ◽  
Adjacent Tooth ◽  
Group I ◽  
Long Term Result ◽  
Root Group

AbstractThe purpose of the retrospective study was to investigate the long-term result of implant-induced injury on the adjacent tooth. The subjects of this retrospective study were patients who had received implants and had tooth injury; direct invasion of root (group I), root surface contact (group II), or < 1 mm distance of the implant from the root (group III). Clinical and pathological changes were periodically examined using radiographs and intra-oral examinations. Paired t-tests and chi-square tests were used to evaluate the implant stability quotient (ISQ) of implant and tooth complications, respectively (α = 0.05). A total of 32 implants and teeth in 28 patients were observed for average 122.7 (± 31.7, minimum 86) months. Seven teeth, three of which were subsequently extracted, needed root canal treatment. Finally, 90.6% of the injured teeth remained functional. Complications were significant and varied according to the group, with group I showing higher events than the others. The ISQs increased significantly. One implant in group I resulted in osseointegration failure. The implant survival rate was 96.9%. In conclusion, it was found even when a tooth is injured by an implant, immediate extraction is unnecessary, and the osseointegration of the invading implant is also predictable.

scholarly journals Этимологическое гнездо *ber- в праславянском языке: Реконструкция, словообразование, семантика

2021 ◽  
Vol 56 ◽  
Author(s):  
Наталия [Nataliia] Вячеславовна [Viacheslavovna] Пятаева [Piataeva]
Keyword(s):  
General Practice ◽  
Word Formation ◽  
Slavic Language ◽  
Semantic Description ◽  
European Origin ◽  
Slavic Languages ◽  
Semantic Development ◽  
History Of ◽  
Root Group ◽  
Roman Alphabet

The Etymological Nest *ber- in the Proto-Slavic Language: Reconstruction, Word-Formation, SemanticsThe article presents a multidimensional (phonetic, etymological, derivational, morphological and semantic) description of the etymological nest (EN) *ber- ‘take’, reconstructed for the Proto-Slavic period in the history of the Russian and other Slavic languages. The root *ber-, around which the EN was formed, belongs to ancient Slavic roots and has Indo-European origin, which led to the natural phonetic variants reflecting the Proto-Slavic and Indo-European alternations: *ber- // *bor- // *bьr- // *bir-.At the Proto-Slavic level, 137 units with the root *ber- are reconstructed, organized in the EN in accordance with the relations of word-formation pro­ductivity and semantic motivation of lexemes as part of word-formation pairs, chains and paradigms: (1) the nucleus of the nest is the etymon *bherəmņ // *bherəmen ‘carry, burden’, reconstructed for the Proto-Indo-European lan­guage, which served as the basis for three Proto-Slavic innovations *bermę ‘burden; armful, bundle; fetus; *berdja ‘pregnant; foal (about animals)’; *bьrati *berǫ ‘take, take away, grab, pluck; receive, borrow, accept; enter into a mar­riage union’; (2) in accordance with a general practice adopted in etymological dictionaries, reconstructed lexemes are marked with an asterisk (*) and are represented in the Roman alphabet for the Proto-Indo-European and Proto- Slavic preliterate periods, and in Cyrillic for the period between the eleventh and the seventeenth centuries; (3) at the first stage of derivation, derivatives are arranged in the following order: verbs, verbal names, participles, prefixed verbs, composites; within these groups, words are arranged alphabetically; (4) the phonetic variants of a lexeme are separated with a double slash (//); (5) meanings are given in single quotation marks. The reconstruction of the EN *ber- and the semantic development of its main lexemes are given in two diagrams at the end of the article.A review of the material indicates that (1) the old Indo-European mean­ing ‘carry, load’ moved to the periphery of the EN *ber-, continuing to exist exclusively in the formations associated with the stem *bermę, and partly with *berdja; (2) a new meaning ‘take’ (*bьrati) became the most relevant for the semantic development of the EN *ber- in Late Slavic; its connection with the original ‘carry’ is seen in the fact that they correlate with adjacent sequen­tial actions aimed at the attached object: ‘take’ what? – ‘object to be attached’ → ‘carry’ what? – ‘attached object’; (3) the new Proto-Slavic meaning ‘take’ (*bьrati), inherent in EN *ber-, determined the synonymy of this root group with the EN *em- (*jęti, *jьmati ‘take’). Gniazdo etymologiczne *ber- w języku prasłowiańskim. Rekonstrukcja, słowotwórstwo, semantyka W artykule przedstawiono wielowymiarowy opis gniazda etymologicz­nego *ber- ‘brać’ (w aspekcie fonetycznym, etymologicznym, derywacyjnym, morfologicznym i semantycznym), zrekonstruowanego dla okresu prasłowiań­skiego w historii języka rosyjskiego i innych języków słowiańskich. Rdzeń *ber-, wokół którego powstało gniazdo etymologiczne, należy do pierwotnych rdzeni słowiańskich i ma pochodzenie indoeuropejskie, co oznaczało rozwój naturalnych wariantów fonetycznych, odzwierciedlających oboczności pra­słowiańskie i indoeuropejskie: *ber- // *bor- // *bьr- // *bir-.Na poziomie prasłowiańskim zrekonstruowano 137 jednostek z rdzeniem *ber-, które zorganizowano w ramach gniazda zgodnie z relacjami produktywno­ści słowotwórczej i motywacji semantycznej leksemów w ramach par, łańcuchów i paradygmatów słowotwórczych: 1) jądrem gniazda jest zrekonstruowany dla języka praindoeuropejskiego etymon *bherəmņ // *bherəmen ‘nieść, brzemię’, który posłużył za podstawę dla trzech prasłowiańskich innowacji *bermę ‘brzemię; naręcze, tobołek; płód’; *berdja ‘brzemienna (o zwierzętach); źrebię’; *bьrati *berǫ ‘brać, zabrać, chwycić, wyrwać; otrzymać, pożyczyć, przyjąć; zawrzeć małżeństwo’; 2) zgodnie z powszechną praktyką przyjętą w słowni­kach etymologicznych zrekonstruowane leksemy są oznaczone gwiazdką (*) i zapisane w alfabecie łacińskim dla praindoeuropejskich i prasłowiańskich okresów przedpiśmiennych oraz cyrylicą dla okresu od XI do XVII wieku; 3) na pierwszym etapie derywacji derywaty są ułożone w następującej kolejności: czasowniki, rzeczowniki odczasownikowe, imiesłowy, czasowniki przedrost­kowe, złożenia; w tych grupach słowa są ułożone alfabetycznie; 4) warianty fonetyczne leksemu są oddzielone podwójnym ukośnikiem (//); 5) znaczenia podano w pojedynczych cudzysłowach. Rekonstrukcję gniazda etymologicz­nego *ber- i rozwój semantyczny jego głównych leksemów przedstawiono na dwóch wykresach na końcu artykułu.Przegląd materiału wskazuje, że 1) dawne indoeuropejskie znaczenie ‘nieść, brzemię’ przeszło na obrzeża gniazda etymologicznego *ber- i utrzymało się nadal wyłącznie w formacjach związanych z rdzeniem *bermę i częściowo *berdja; 2) nowe znaczenie: ‘brać’ (*bьrati) stało się najbardziej istotne dla semantycznego rozwoju gniazda *ber- w okresie późnosłowiańskim; związek tego znaczenia z pierwotnym ‘nieść’ przejawia się w fakcie korelacji pomiędzy nimi w sekwencji działań na umocowany obiekt: ‘brać’ co? – ‘obiekt do umo­cowania’ → ‘nieść’ co? – ‘umocowany obiekt’; 3) nowe prasłowiańskie znaczenie ‘brać’ (*bьrati), nieodłącznie związane z gniazdem *ber-, określiło synonimię tej grupy rdzeniowej z gniazdem *em- (*jęti, *jьmati ‘brać’).

scholarly journals On the action of the Hua subgroups in special Moufang sets

2008 ◽  
Vol 144 (1) ◽  
pp. 77-84 ◽  
Author(s):  
YOAV SEGEV ◽  
RICHARD M. WEISS
Keyword(s):  
Invariant Subgroup ◽  
Cartan Subgroup ◽  
Root Group

AbstractWe show that in a special Moufang set, either the root groups are elementary abelian 2-groups, or the Hua subgroup H (= the Cartan subgroup) acts “irreducibly” on U, i.e. the only non-trivial H-invariant subgroup of a root group normalized by H is the whole root group.

Strictly Semi-linear Automorphisms

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Fixed Points ◽  
Division Algebra ◽  
Quadratic Space ◽  
Spherical Building ◽  
Linear Automorphism ◽  
Coxeter Diagram ◽  
Non Linear ◽  
Root Group

This chapter considers the action of a strictly semi-linear automorphism fixing a root on the corresponding root group. It begins with the hypothesis whereby Δ‎ is a Moufang spherical building and Π‎ is the Coxeter diagram of Δ‎; here the chapter fixes an apartment Σ‎ of Δ‎ and a root α‎ of Σ‎. The discussion then turns to a number of assumptions about an isomorphism of Moufang sets, anisotropic quadratic space, and root group sequence, followed by a lemma where E is an octonion division algebra with center F and norm N and D is a quaternion subalgebra of E. The chapter concludes with three versions of what is really one result about fixed points of non-linear automorphisms of the Moufang sets.

Linear Automorphisms

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Quadratic Space ◽  
Spherical Building ◽  
Parameter System ◽  
Linear Automorphism ◽  
Coxeter Diagram ◽  
Root Group

This chapter considers the notion of a linear automorphism of an arbitrary spherical building satisfying the Moufang property. It begins with the notation whereby Ω‎ = (U₊, U₁, ..., Uₙ) is the root group sequence and x₁, ... , xₙ the isomorphisms obtained by applying the recipe in [60, 16.x] for x = 1, 2, 3, ... or 9 to a parameter system Λ‎ of the suitable type (and for suitable n) and Δ‎ is the corresponding Moufang n-gon. The chapter proceeds by looking at cases where Λ‎ is a proper anisotropic pseudo-quadratic space defined over an involutory set or a quadratic space of type E⁶, E₇ or E₈. It also describes a notation dealing with the Moufang spherical building with Coxeter diagram Λ‎, an apartment of Δ‎, and a chamber of Σ‎.

Quadrangles of Type F4

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Quadratic Space ◽  
Root Group ◽  
Tits Building ◽  
Moufang Quadrangle

This chapter deals with the case that the building at infinity Λ‎ of the Bruhat-Tits building Ξ‎ is a Moufang quadrangle of type F₄. It begins with the hypothesis stating that Λ‎ = (K, L, q) is a quadratic space of type F₄, K is complete with respect to a discrete valuation ν‎ and F is closed with respect to ν‎, Λ‎ is the Moufang quadrangle corresponding to a root group sequence, and R₀ and R₁ as the two residues of Ξ‎. The chapter also considers the theorem supposing that Λ‎ is of type F₄ and that R₀ and R₁ are not both indifferent, and claims that both cases really occur. Finally, it presents the proposition that R₀ and R₁ are both indifferent if and only if q is totally wild.

Residues

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Euclidean Plane ◽  
Complete System ◽  
Quadratic Space ◽  
Affine Building ◽  
Root Group ◽  
Tits Building ◽  
Moufang Quadrangle

This chapter deals with the residues of a Bruhat-Tits building whose building at infinity is an exceptional quadrangle. It begins with the remark that if Λ‎ is an arbitrary quadratic space of type Eℓ for ℓ = 6, 7 or 8 or of typeF₄ over a field K that is complete with respect to a discrete valuation, and if in the F4-case the subfield F is closed with respect to this valuation and if Δ‎ is the corresponding Moufang quadrangle of type Eℓ or F₄, then there always exists a unique affine building Ξ‎ such that Δ‎ is the building at infinity of Ξ‎ with respect to its complete system of apartments. The chapter also considers the standard embedding of the apartment A in the Euclidean plane which takes the intersection of A and R to the set of eight triangles containing the origin. Finally, it describes a Moufang polygon with two root group sequences.

A retrospective evaluation of 51 cases of peripheral nerve sheath tumors in the dog

1995 ◽  
Vol 31 (4) ◽  
pp. 349-359 ◽  
Author(s):  
DM Brehm ◽  
CH Vite ◽  
HS Steinberg ◽  
J Haviland ◽  
T van Winkle
Keyword(s):  
Peripheral Nerve ◽  
Clinical Signs ◽  
Diagnostic Procedures ◽  
Lumbosacral Plexus ◽  
Survival Times ◽  
Nerve Sheath Tumors ◽  
Peripheral Nerve Sheath Tumors ◽  
Nerve Sheath ◽  
Significant Difference ◽  
Root Group

Fifty-one cases of canine peripheral nerve sheath tumors were reviewed. Signalment, presenting clinical signs, duration of clinical signs, physical and neurological examination findings, results of diagnostic procedures, type of surgery performed, tumor location, relapse-free intervals and survival times, and causes of death were evaluated. Tumors were divided into three anatomical groups: tumors involving nerves distal to the brachial or lumbosacral plexus (Peripheral Group), tumors involving nerves of the brachial or lumbosacral plexus (Plexus Group), and tumors involving the vertebral canal (Root Group). The most common clinical findings were unilateral forelimb lameness and muscle atrophy. The most useful diagnostic tests were myelography and electromyography. Although there was no significant difference, dogs in the Root Group tended to have shorter relapse-free intervals and survival times than dogs in the Plexus Group. The overall prognosis for surgical management of peripheral nerve sheath tumors is guarded to poor.

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