scholarly journals Affine twisted length function

2021 ◽  
Vol 359 (7) ◽  
pp. 873-879
Author(s):  
Nathan Chapelier-Laget
Keyword(s):  
Length Function

Parallel Residues

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Distance Function ◽  
Length Function ◽  
Coxeter System ◽  
Vertex Set ◽  
Ordered Pairs

This chapter considers the notion of parallel residues in a building. It begins with the assumption that Δ‎ is a building of type Π‎, which is arbitrary except in a few places where it is explicitly assumed to be spherical. Δ‎ is not assumed to be thick. The chapter then elaborates on a hypothesis which states that S is the vertex set of Π‎, (W, S) is the corresponding Coxeter system, d is the W-distance function on the set of ordered pairs of chambers of Δ‎, and ℓ is the length function on (W, S). It also presents a notation in which the type of a residue R is denoted by Typ(R) and concludes with the condition that residues R and T of a building will be called parallel if R = projR(T) and T = projT(R).

The length function and matrix algebras

2013 ◽  
Vol 193 (5) ◽  
pp. 687-768 ◽  
Author(s):  
O. V. Markova
Keyword(s):  
Length Function ◽  
Matrix Algebras

scholarly journals Embedding construction based on amalgamations of group relators

2016 ◽  
Vol 08 (01) ◽  
pp. 1-24 ◽  
Author(s):  
A. Yu. Olshanskii
Keyword(s):  
Length Function ◽  
Tits Alternative

An embedding construction [Formula: see text] for groups [Formula: see text] with length function was introduced by the author earlier. Here we obtain new properties of this embedding, answering some questions raised by M. V. Sapir. In particular, an analog of Tits’ alternative holds for the subgroups of [Formula: see text].

Prediction of compressible turbulent boundary layer via a symmetry-based length model

2018 ◽  
Vol 857 ◽  
pp. 449-468 ◽  
Author(s):  
Zhen-Su She ◽  
Hong-Yue Zou ◽  
Meng-Juan Xiao ◽  
Xi Chen ◽  
Fazle Hussain
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Layer Structure ◽  
Analytic Form ◽  
Algebraic Model ◽  
Length Function ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Reynolds Analogy ◽  
The Mean

A recently developed symmetry-based theory is extended to derive an algebraic model for compressible turbulent boundary layers (CTBL) – predicting mean profiles of velocity, temperature and density – valid from incompressible to hypersonic flow regimes, thus achieving a Mach number ($Ma$) invariant description. The theory leads to a multi-layer analytic form of a stress length function which yields a closure of the mean momentum equation. A generalized Reynolds analogy is then employed to predict the turbulent heat transfer. The mean profiles and the friction coefficient are compared with direct numerical simulations of CTBL for a range of$Ma$from 0 (e.g. incompressible) to 6.0 (e.g. hypersonic), with an accuracy notably superior to popular current models such as Baldwin–Lomax and Spalart–Allmaras models. Further analysis shows that the modification is due to an improved eddy viscosity function compared to competing models. The results confirm the validity of our$Ma$-invariant stress length function and suggest the path for developing turbulent boundary layer models which incorporate the multi-layer structure.

scholarly journals Nilpotent Group C*-algebras as Compact Quantum Metric Spaces

2017 ◽  
Vol 60 (1) ◽  
pp. 77-94 ◽  
Author(s):  
Michael Christ ◽  
Marc A. Rieòel
Keyword(s):  
Finite Groups ◽  
Word Length ◽  
Polynomial Growth ◽  
Metric Spaces ◽  
Length Function ◽  
C Algebra ◽  
Pointwise Multiplication ◽  
C Algebras ◽  
Definition Of ◽  
Compact Quantum Metric Space

AbstractLet be a length function on a group G, and let M denote the operator of pointwise multiplication by on l2(G). Following Connes, M𝕃 can be used as a “Dirac” operator for the reduced group C*-algebra (G). It deûnes a Lipschitz seminorm on (G), which defines a metric on the state space of (G). We show that for any length function satisfying a strong form of polynomial growth on a discrete group, the topology from this metric coincides with the weak-* topology (a key property for the definition of a “compact quantum metric space”). In particular, this holds for all word-length functions on ûnitely generated nilpotent-by-finite groups.

An Example of an Integer-Valued Length Function on a Group

1977 ◽  
Vol s2-16 (1) ◽  
pp. 67-75 ◽  
Author(s):  
I. M. Chiswell
Keyword(s):  
Length Function

Term Algebras with Length Function and Bounded Quantifier Alternation

2004 ◽  
pp. 321-336 ◽  
Author(s):  
Ting Zhang ◽  
Henny B. Sipma ◽  
Zohar Manna
Keyword(s):  
Length Function ◽  
Quantifier Alternation

On the geodesic distance and group actions on trees

1991 ◽  
Vol 110 (1) ◽  
pp. 67-70
Author(s):  
Marco Pavone
Keyword(s):  
Distance Function ◽  
Geodesic Distance ◽  
Group Actions ◽  
Length Function ◽  
Definite Function ◽  
Negative Definite Function ◽  
Negative Type

The natural distance function on the vertices of a tree is a kernel of negative type. As a corollary, for any group G acting on a tree X, the length function |g| = d(υ, gυ) is a negative definite function on G for any given vertex υ of X.

INVERSIONS IN CLASSICAL WEYL GROUPS

2007 ◽  
Vol 09 (01) ◽  
pp. 1-20
Author(s):  
KEQUAN DING ◽  
SIYE WU
Keyword(s):  
Finite Group ◽  
Weyl Group ◽  
Root Systems ◽  
Flag Manifold ◽  
Length Function ◽  
Weyl Groups ◽  
Flag Manifolds ◽  
A Finite Group

We introduce inversions for classical Weyl group elements and relate them, by counting, to the length function, root systems and Schubert cells in flag manifolds. Special inversions are those that only change signs in the Weyl groups of types Bn, Cnand Dn. Their counting is related to the (only) generator of the Weyl group that changes signs, to the corresponding roots, and to a special subvariety in the flag manifold fixed by a finite group.

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