On n-algebraic structures in the Calogero model

2020 ◽  
Vol 35 (23) ◽  
pp. 2050137 ◽  
Author(s):  
Chun-Hong Zhang ◽  
Rui Wang
Keyword(s):  
Matrix Model ◽  
Closed Formula ◽  
Algebraic Structures ◽  
Model Based ◽  
Calogero Model

We construct two realizations of the [Formula: see text] algebra in the classical Calogero model based on the [Formula: see text] constraints for the Hermitian one-matrix model. We also discuss the quantum Calogero model and construct the new operators which yield the closed [Formula: see text][Formula: see text]-algebra. The super [Formula: see text][Formula: see text]-algebra is derived for the supersymmetric quantum Calogero model.

Research on Combinational Reasoning of Directional Relations Based on Double Projections Model in Three-Dimensional Space

2011 ◽  
Vol 186 ◽  
pp. 61-65
Author(s):  
Yong Shan Liu ◽  
Wei Jie Gu
Keyword(s):  
Matrix Model ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Model Based ◽  
Computational Performance ◽  
Minimum Bounding Rectangle ◽  
Directional Relations ◽  
Three Dimensional Space

The xoy and xoz planes are divided into nine areas in three-dimensional space respectively by the MBR (Minimum Bounding Rectangle), which are produced by the reference objects’ projection to their planes. The intersecting situations between the projection of target objects and the two of reference objects are expressed by two 3×3 matrices. Then, a directional relations matrix model based on double projections is put forward. A combinational reasoning method is proposed by using the computational performance of matrices based on this model. Moreover, a combinational reasoning experiment is given and the result matches the reality.

scholarly journals "The Matrix": A Model of Community Music Therapy Processes

2006 ◽  
Vol 6 (3) ◽  
Author(s):  
Stuart Wood
Keyword(s):  
Music Therapy ◽  
Matrix Model ◽  
Theoretical Background ◽  
Research Data ◽  
Ongoing Study ◽  
Theoretical Modelling ◽  
Community Music ◽  
Model Based ◽  
The Matrix

This article arises out of my research in a number of consecutive community music therapy projects,[1] and presents the model that resulted from these research periods. It is part of an ongoing study in which I track the development of my own community music therapy projects and explore a theoretical modelling to underpin it. The article proposes a model based on a matrix formation. It begins with a description of the 'matrix model' and goes on to set out the theoretical background, then survey the music therapy research data that led to its formulation. The article concludes with a discussion of how this model contributes to the evaluation of community music therapy practice.

Research of the Assembly Model Based on Parts Attribute Semantic

2014 ◽  
Vol 509 ◽  
pp. 147-151
Author(s):  
Ya Jun Yang ◽  
Hong Gen Fang ◽  
Hao Luan ◽  
Tian Guo Jin
Keyword(s):  
Competitive Advantage ◽  
Matrix Model ◽  
Assembly Sequence Planning ◽  
Two Dimensional ◽  
Assembly Model ◽  
Assembly Sequence ◽  
Sequence Planning ◽  
Model Based ◽  
Dimensional Matrix ◽  
Precedence Relations

Aiming at the problems in the modeling of assembly sequence planning, this paper proposes a assembly model based on the semantic and two-dimensional matrix which is easy to calculate and expression. The paper complement the parts attribute semantic and it is used to make the assembly model .So the parts about the attributes of parts assembly can be used in the ASP. Assembly relations including Assembly Precedence Relations (APRs), Contact semantic, Connection and Transmission semantic are transformed into a matrix model. Finally shaft structure is used as a example to represent a competitive advantage of this model.

scholarly journals Flavon VEV scales in U(3)×U(3)′ model

2017 ◽  
Vol 32 (15) ◽  
pp. 1750085 ◽  
Author(s):  
Yoshio Koide ◽  
Hiroyuki Nishiura
Keyword(s):  
Matrix Model ◽  
Charged Lepton ◽  
Mass Matrix ◽  
Family Symmetry ◽  
Parameter Fitting ◽  
Model Based ◽  
Final Goal ◽  
Input Parameters ◽  
Unified Description

We have recently proposed a quark and lepton mass matrix model based on U(3)[Formula: see text]×[Formula: see text]U(3)[Formula: see text] family symmetry as the so-called Yukawaon model, in which the U(3) symmetry is broken by VEVs of flavons [Formula: see text] which are [Formula: see text] of U(3)[Formula: see text]×[Formula: see text]U(3)[Formula: see text]. The model has successfully provided the unified description of quark and lepton masses and mixings by using the observed charged lepton masses as only family-number dependent input parameters. However, our final goal is not only to give well-satisfied fitting of quark and lepton masses and mixings, but also to investigate physics behind such a successful parameter fitting. Therefore, our next concern is scales of VEVs of the flavons because we have not paid attention to scales of flavons in the previous study. In order to give consistency among the scales, the previous flavon model is drastically changed together with economizing number of the flavons, but with keeping previous phenomenological success. We estimate that VEVs of flavons with [Formula: see text], [Formula: see text] and [Formula: see text] are of the orders of 10 TeV, 104 TeV and 107 TeV, respectively.

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