scholarly journals Quantum groups and functional relations for arbitrary rank

2021 ◽  
pp. 115517
Author(s):  
Alexander V. Razumov
Keyword(s):  
Quantum Groups ◽  
Arbitrary Rank ◽  
Functional Relations

scholarly journals Quantum groups and functional relations for higher rank

2014 ◽  
Vol 47 (27) ◽  
pp. 275201 ◽  
Author(s):  
Hermann Boos ◽  
Frank Göhmann ◽  
Andreas Klümper ◽  
Khazret S Nirov ◽  
Alexander V Razumov
Keyword(s):  
Quantum Groups ◽  
Functional Relations ◽  
Higher Rank

scholarly journals Universal R-matrix and functional relations

2014 ◽  
Vol 26 (06) ◽  
pp. 1430005 ◽  
Author(s):  
Herman Boos ◽  
Frank Göhmann ◽  
Andreas Klümper ◽  
Khazret S. Nirov ◽  
Alexander V. Razumov
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Integrable Systems ◽  
Vertex Model ◽  
Quantum Space ◽  
R Matrix ◽  
Functional Relations

We collect and systematize general definitions and facts on the application of quantum groups to the construction of functional relations in the theory of integrable systems. As an example, we reconsider the case of the quantum group [Formula: see text] related to the six-vertex model. We prove the full set of the functional relations in the form independent of the representation of the quantum group in the quantum space and specialize them to the case of the six-vertex model.

Case Formulation and Design of Behavioral Treatment Programs

2003 ◽  
Vol 19 (3) ◽  
pp. 164-174 ◽  
Author(s):  
Stephen N. Haynes ◽  
Andrew E. Williams
Keyword(s):  
Functional Analysis ◽  
Behavior Problems ◽  
Behavioral Treatment ◽  
Clinical Case ◽  
Relative Magnitude ◽  
Mechanisms Of Action ◽  
Treatment Programs ◽  
Case Formulation ◽  
Functional Relations ◽  
Causal Variables

Summary: We review the rationale for behavioral clinical case formulations and emphasize the role of the functional analysis in the design of individualized treatments. Standardized treatments may not be optimally effective for clients who have multiple behavior problems. These problems can affect each other in complex ways and each behavior problem can be influenced by multiple, interacting causal variables. The mechanisms of action of standardized treatments may not always address the most important causal variables for a client's behavior problems. The functional analysis integrates judgments about the client's behavior problems, important causal variables, and functional relations among variables. The functional analysis aids treatment decisions by helping the clinician estimate the relative magnitude of effect of each causal variable on the client's behavior problems, so that the most effective treatments can be selected. The parameters of, and issues associated with, a functional analysis and Functional Analytic Clinical Case Models (FACCM) are illustrated with a clinical case. The task of selecting the best treatment for a client is complicated because treatments differ in their level of specificity and have unequally weighted mechanisms of action. Further, a treatment's mechanism of action is often unknown.

Diagnostics of perfusion-functional relations in lacrimal gland pathology

Reflection ◽  
2018 ◽  
Vol 6 (1) ◽  
pp. 188-193
Author(s):  
Y. V. Falina ◽  
◽  
V. A. Obodov ◽  
V. V. Pankin ◽  
A. A. Smirnov ◽  
...  
Keyword(s):  
Lacrimal Gland ◽  
Functional Relations

scholarly journals Curved Rickard complexes and link homologies

2020 ◽  
Vol 2020 (769) ◽  
pp. 87-119
Author(s):  
Sabin Cautis ◽  
Aaron D. Lauda ◽  
Joshua Sussan
Keyword(s):  
Spectral Sequence ◽  
Quantum Groups ◽  
Braid Group ◽  
Derived Categories ◽  
Duke Math ◽  
Khovanov Homology ◽  
Hilbert Schemes ◽  
Coherent Sheaves ◽  
Knot Homology ◽  
Original Motivation

AbstractRickard complexes in the context of categorified quantum groups can be used to construct braid group actions. We define and study certain natural deformations of these complexes which we call curved Rickard complexes. One application is to obtain deformations of link homologies which generalize those of Batson–Seed [3] [J. Batson and C. Seed, A link-splitting spectral sequence in Khovanov homology, Duke Math. J. 164 2015, 5, 801–841] and Gorsky–Hogancamp [E. Gorsky and M. Hogancamp, Hilbert schemes and y-ification of Khovanov–Rozansky homology, preprint 2017] to arbitrary representations/partitions. Another is to relate the deformed homology defined algebro-geometrically in [S. Cautis and J. Kamnitzer, Knot homology via derived categories of coherent sheaves IV, colored links, Quantum Topol. 8 2017, 2, 381–411] to categorified quantum groups (this was the original motivation for this paper).

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