scholarly journals FUSION RULES FOR THE q-VERTEX OPERATORS OF ${\rm U}_q (\widehat{{\rm sl} (2)})$

1992 ◽  
Vol 07 (24) ◽  
pp. 2235-2243
Author(s):  
HIDETOSHI AWATA ◽  
YASUHIKO YAMADA
Keyword(s):  
Existence Condition ◽  
Null Vector ◽  
Vertex Operators ◽  
Fusion Rules

We analyze the properties of the q-vertex operators [Formula: see text] introduced by Frenkel and Reshetikhin. As the condition for the null vector decoupling, we derive the existence condition of the q-vertex operators (the fusion rules).

FUSION RULES FOR THE FRACTIONAL LEVEL $\widehat{{\rm sl}(2)}$ ALGEBRA

1992 ◽  
Vol 07 (13) ◽  
pp. 1185-1195 ◽  
Author(s):  
HIDETOSHI AWATA ◽  
YASUHIKO YAMADA
Keyword(s):  
Null Vector ◽  
Primary Field ◽  
Fusion Rules ◽  
Weyl Transformation ◽  
Interesting Structure

We derive, as the condition for the null vector decoupling, the fusion rules for the [Formula: see text] algebra with fractional level, which have an interesting structure related to affine Weyl transformation. It is shown that, to get non-trivial fusion rules, we must include the primary field which belongs to neither the highest nor the lowest weight representations.

Vertex operators and fusion rules in the free field realizations of WZNW models

1991 ◽  
Vol 258 (1-2) ◽  
pp. 127-133 ◽  
Author(s):  
Peter Bouwknecht ◽  
Jim McCarthy ◽  
Dennis Nemeschansky ◽  
Krzysztof Pilch
Keyword(s):  
Free Field ◽  
Vertex Operators ◽  
Fusion Rules

Coercion and the Nature of Law

2020 ◽  
Author(s):  
Kenneth Einar Himma
Keyword(s):  
Conceptual Analysis ◽  
Existence Condition ◽  
Necessary Condition ◽  
First Order ◽  
Normative System ◽  
Motivating Reasons

COERCION AND THE NATURE OF LAW argues that it is a conceptually necessary condition for something to count as a system of law according to our conceptual practices that it authorizes the imposition of coercive sanctions for violations of some mandatory norms governing non-official behavior (the Coercion Thesis). The book begins with an explication of the modest approach to conceptual analysis that is deployed throughout. The remainder of the book is concerned to show that an institutional normative system is not reasonably contrived to do anything that law must be able to do for us to make sense of why we adopt systems of law to regulate non-official behavior unless we assume that mandatory norms governing that behavior are backed by the threat of a sovereign; an institutional normative system that satisfies every other plausible existence condition for law is not reasonably contrived to give rise to either objective or subjective first-order motivating reasons to comply with mandatory norms governing non-official behavior unless they are backed by the threat of a coercive sanction. Law’s presumed conceptual normativity can be explained only by the Coercion Thesis.

scholarly journals Polynomial ring representations of endomorphisms of exterior powers

2021 ◽  
Author(s):  
Ommolbanin Behzad ◽  
André Contiero ◽  
Letterio Gatto ◽  
Renato Vidal Martins
Keyword(s):  
Lie Algebra ◽  
Polynomial Ring ◽  
Vertex Operators ◽  
Exterior Power ◽  
Infinite Dimensional ◽  
Symmetric Structure ◽  
Rational Polynomials ◽  
Exterior Powers ◽  
Vertex Representation ◽  
Countably Infinite

AbstractAn explicit description of the ring of the rational polynomials in r indeterminates as a representation of the Lie algebra of the endomorphisms of the k-th exterior power of a countably infinite-dimensional vector space is given. Our description is based on results by Laksov and Throup concerning the symmetric structure of the exterior power of a polynomial ring. Our results are based on approximate versions of the vertex operators occurring in the celebrated bosonic vertex representation, due to Date, Jimbo, Kashiwara and Miwa, of the Lie algebra of all matrices of infinite size, whose entries are all zero but finitely many.

scholarly journals Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Nattawut Khansai ◽  
Akapak Charoenloedmongkhon
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Control ◽  
Positive Periodic Solution ◽  
Existence Condition ◽  
Predator Prey ◽  
Type Iv ◽  
Prey System ◽  
Existence And Stability ◽  
Predator Behavior

AbstractIn the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

scholarly journals Relating the b ghost and the vertex operators of the pure spinor superstring

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Osvaldo Chandia ◽  
Brenno Carlini Vallilo
Keyword(s):  
Vertex Operator ◽  
Bosonic String ◽  
Vertex Operators ◽  
Pure Spinor ◽  
Double Pole ◽  
Lorenz Gauge

Abstract The OPE between the composite b ghost and the unintegrated vertex operator for massless states of the pure spinor superstring is computed and shown to reproduce the structure of the bosonic string result. The double pole vanishes in the Lorenz gauge and the single pole is shown to be equal to the corresponding integrated vertex operator.

scholarly journals Discrete-Time Constrained Average Stochastic Games with Independent State Processes

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1089
Author(s):  
Wenzhao Zhang
Keyword(s):  
Discrete Time ◽  
Stochastic Games ◽  
Transition Probability ◽  
Existence Condition ◽  
Linear Program ◽  
Global Minimizer ◽  
Independent State ◽  
Occupation Measures ◽  
Best Response ◽  
Mathematic Program

In this paper, we consider the discrete-time constrained average stochastic games with independent state processes. The state space of each player is denumerable and one-stage cost functions can be unbounded. In these game models, each player chooses an action each time which influences the transition probability of a Markov chain controlled only by this player. Moreover, each player needs to pay some costs which depend on the actions of all the players. First, we give an existence condition of stationary constrained Nash equilibria based on the technique of average occupation measures and the best response linear program. Then, combining the best response linear program and duality program, we present a non-convex mathematic program and prove that each stationary Nash equilibrium is a global minimizer of this mathematic program. Finally, a controlled wireless network is presented to illustrate our main results.

scholarly journals Quantum dimensions and fusion rules of the VOA VLC×Dτ

2016 ◽  
Vol 459 ◽  
pp. 309-349 ◽  
Author(s):  
Hsian-Yang Chen ◽  
Ching Hung Lam
Keyword(s):  
Fusion Rules ◽  
Quantum Dimensions
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