A FAMILY OF FACE MODELS RELATED TO ZN-SYMMETRIC VERTEX MODEL OF BELAVIN

2004 ◽  
Vol 19 (supp02) ◽  
pp. 478-509
Author(s):  
Y. YAMADA
Keyword(s):  
Baxter Equation ◽  
Vertex Model ◽  
Face Type ◽  
The Face ◽  
Elliptic Solutions ◽  
Intertwining Relation

We present face-type elliptic solutions to the Yang-Baxter equation. They have 2N-2 real parameters. When specializing them to definite values, we recover the various models so far known. The intertwining relation between the face models above and the ZN-symmetric vertex model of Belavin is also given.

Solutions of Yang–Baxter equation in the vertex model and the face model for octet representation

1991 ◽  
Vol 32 (8) ◽  
pp. 2210-2218 ◽  
Author(s):  
Bo‐Yu Hou ◽  
Bo‐Yuan Hou ◽  
Zhong‐Qi Ma ◽  
Yu‐Dong Yin
Keyword(s):  
Baxter Equation ◽  
Vertex Model ◽  
Face Model ◽  
The Face

scholarly journals On the Yang–Baxter equation for the six-vertex model

2014 ◽  
Vol 882 ◽  
pp. 70-96 ◽  
Author(s):  
Vladimir V. Mangazeev
Keyword(s):  
Baxter Equation ◽  
Vertex Model

scholarly journals Retracted: Morphometric study of cephalo-facial indices among Bini children in southern Nigeria

2019 ◽  
Vol 8 (2) ◽  
pp. 1552-1557
Author(s):  
D.R. Omotoso ◽  
A.J. Olanrewaju ◽  
U.C. Okwuonu ◽  
O Adagboyin ◽  
E.O. Bienonwu
Keyword(s):  
Morphological Study ◽  
Human Head ◽  
Morphometric Study ◽  
Anatomical Landmarks ◽  
Common Phenomenon ◽  
Cephalic Index ◽  
Face Type ◽  
The Face ◽  
Important Branch ◽  
Head Type

This article has been retracted by the Editor.Cephalometry is an important branch of anthropometry which involves the morphological study of structures present in the human head or scientific measurement of the dimensions of the head. Some of the most important cephalometric parameters include the length/height and breadth/width of the head, the face and the nose as well as their respective indices. These cephalometric parameters are vital in the description of variation which is a common phenomenon that characterizes human physiognomy. They are also useful in the description of human inter-racial and intra-racial similarities both within and across gender. This study involved 450 Bini children (235 males and 215 females) between ages 5-12 years. The length and width of the head and face of each subject was measured between the appropriate anatomical landmarks using spreading and sliding calipers. The measurements were used to calculate the cephalic and facial indices for each subject. The result showed sexual variation in both cephalic and facial indices among the Bini children with the males having higher values than the females. Also, the result of this study showed that prevalence of brachycephalic head type among both male (51.1%) and female (49.8%) Bini children. The mesoproscopic face type was the most prevalent face type among both male (62.6%) and female (47.4%) Bini children. The cephalo-facial indices are vital in demonstrating similarity and variation in physical morphologies of individuals or group of people of different ethnicity, races, gender and geographical locations.Keywords: Cephalometry, Cephalic index, facial index, Bini children, Nigeria

scholarly journals Littlewood–Richardson coefficients for Grothendieck polynomials from integrability

2019 ◽  
Vol 2019 (757) ◽  
pp. 159-195 ◽  
Author(s):  
Michael Wheeler ◽  
Paul Zinn-Justin
Keyword(s):  
Baxter Equation ◽  
Partition Functions ◽  
Vertex Model ◽  
Structure Constants ◽  
Product Rules ◽  
Grothendieck Polynomials

AbstractWe study the Littlewood–Richardson coefficients of double Grothendieck polynomials indexed by Grassmannian permutations. Geometrically, these are the structure constants of the equivariant K-theory ring of Grassmannians. Representing the double Grothendieck polynomials as partition functions of an integrable vertex model, we use its Yang–Baxter equation to derive a series of product rules for the former polynomials and their duals. The Littlewood–Richardson coefficients that arise can all be expressed in terms of puzzles without gashes, which generalize previous puzzles obtained by Knutson–Tao and Vakil.

GENERALIZED SKLYANIN ALGEBRA

1991 ◽  
Vol 06 (39) ◽  
pp. 3635-3640 ◽  
Author(s):  
YAS-HIRO QUANO ◽  
AKIRA FUJII
Keyword(s):  
Lie Algebra ◽  
Universal Enveloping Algebra ◽  
Baxter Equation ◽  
Enveloping Algebra ◽  
Elliptic Solutions ◽  
Sklyanin Algebra

We propose a [Formula: see text]-Sklyanin algebra to shed new light on elliptic solutions of the Yang–Baxter equation. This object gives a quadratic generalization of the universal enveloping algebra of the Lie algebra [Formula: see text]. We also clarify the meaning of the parameters contained in it.

scholarly journals Integrable probability: stochastic vertex models and symmetric functions

2018 ◽  
Author(s):  
Alexei Borodin ◽  
Leonid Petrov
Keyword(s):  
Symmetric Functions ◽  
Height Function ◽  
Rational Functions ◽  
Universality Class ◽  
Integral Representations ◽  
Baxter Equation ◽  
Partition Functions ◽  
Vertex Model ◽  
Schur Polynomials ◽  
Higher Spin

This chapter presents the study of a homogeneous stochastic higher spin six-vertex model in a quadrant. For this model concise integral representations for multipoint q-moments of the height function and for the q-correlation functions are derived. At least in the case of the step initial condition, these formulas degenerate in appropriate limits to many known formulas of such type for integrable probabilistic systems in the (1+1)d KPZ universality class, including the stochastic six-vertex model, ASEP, various q-TASEPs, and associated zero-range processes. The arguments are largely based on properties of a family of symmetric rational functions that can be defined as partition functions of the higher spin six-vertex model for suitable domains; they generalize classical Hall–Littlewood and Schur polynomials. A key role is played by Cauchy-like summation identities for these functions, which are obtained as a direct corollary of the Yang–Baxter equation for the higher spin six-vertex model.

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