scholarly journals Quantum-classical duality for Gaudin magnets with boundary

2020 ◽  
Vol 952 ◽  
pp. 114931 ◽  
Author(s):  
M. Vasilyev ◽  
A. Zabrodin ◽  
A. Zotov
Keyword(s):  
Classical Duality

scholarly journals Duality of Complex Systems Built from Higher-Order Elements

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Dalibor Biolek ◽  
Zdeněk Biolek ◽  
Viera Biolková
Keyword(s):  
Nonlinear Systems ◽  
Complex Systems ◽  
Higher Order ◽  
Duality Principle ◽  
Shift Type ◽  
Hardware Emulation ◽  
Classical Duality ◽  
Memristive Circuits ◽  
Circuit Elements

The duality of nonlinear systems built from higher-order two-terminal Chua’s elements and independent voltage and current sources is analyzed. Two different approaches are now being generalized for circuits with higher-order elements: the classical duality principle, hitherto restricted to circuits built from R-C-L elements, and Chua’s duality of memristive circuits. The so-called storeyed structure of fundamental elements is used as an integrating platform of both approaches. It is shown that the combination of associated flip-type and shift-type transformations of the circuit elements can generate dual networks with interesting features. The regularities of the duality can be used for modeling, hardware emulation, or synthesis of systems built from elements that are not commonly available, such as memristors, via classical dual elements.

scholarly journals Duality for finite abelian hypergroups over splitting fields

1979 ◽  
Vol 20 (1) ◽  
pp. 57-70 ◽  
Author(s):  
J.R. McMullen ◽  
J.F. Price
Keyword(s):  
Finite Group ◽  
Duality Theory ◽  
Abelian Groups ◽  
Conjugacy Classes ◽  
Finite Abelian Groups ◽  
Precise Sense ◽  
Classical Duality ◽  
A Finite Group

A duality theory for finite abelian hypergroups over fairly general fields is presented, which extends the classical duality for finite abelian groups. In this precise sense the set of conjugacy classes and the set of characters of a finite group are dual as hypergroups.

Characterization of stochastic equilibrium controls by the Malliavin calculus

2021 ◽  
pp. 2150054
Author(s):  
Jiang Yu Nguwi ◽  
Nicolas Privault
Keyword(s):  
Malliavin Calculus ◽  
Linear Quadratic ◽  
Merton Problem ◽  
Classical Duality ◽  
The Mean ◽  
Time Inconsistent ◽  
Necessary And Sufficient ◽  
Mean Variance ◽  
Quadratic Case

We derive a characterization of equilibrium controls in continuous-time, time-inconsistent control (TIC) problems using the Malliavin calculus. For this, the classical duality analysis of adjoint BSDEs is replaced with the Malliavin integration by parts. This results into a necessary and sufficient maximum principle which is applied to a linear-quadratic TIC problem, recovering previous results obtained by duality analysis in the mean-variance case, and extending them to the linear-quadratic setting. We also show that our results apply beyond the linear-quadratic case by treating the generalized Merton problem.

Quantal–Classical Duality and the Semiclassical Trace Formula

1998 ◽  
Vol 264 (2) ◽  
pp. 108-170 ◽  
Author(s):  
Doron Cohen ◽  
Harel Primack ◽  
Uzy Smilansky
Keyword(s):  
Trace Formula ◽  
Classical Duality

scholarly journals The Fourier Algebra for Locally Compact Groupoids

2004 ◽  
Vol 56 (6) ◽  
pp. 1259-1289 ◽  
Author(s):  
Alan L. T. Paterson
Keyword(s):  
Duality Theorem ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Fourier Algebra ◽  
Hilbert Modules ◽  
Locally Compact ◽  
Classical Duality ◽  
Special Case

AbstractWe introduce and investigate using Hilbert modules the properties of the Fourier algebra A(G) for a locally compact groupoid G. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This includes as a special case the classical duality theorem for locally compact groups proved by P. Eymard.

scholarly journals Additive functionals and excursions of Kuznetsov processes

2005 ◽  
Vol 2005 (13) ◽  
pp. 2031-2040
Author(s):  
Hacène Boutabia
Keyword(s):  
Additive Functional ◽  
Standard Process ◽  
Additive Functionals ◽  
Isolated Points ◽  
Classical Duality

LetBbe a continuous additive functional for a standard process(Xt)t∈ℝ+and let(Yt)t∈ℝbe a stationary Kuznetsov process with the same semigroup of transition. In this paper, we give the excursion laws of(Xt)t∈ℝ+conditioned on the strict past and future without duality hypothesis. We study excursions of a general regenerative system and of a regenerative system consisting of the closure of the set of times the regular points ofBare visited. In both cases, those conditioned excursion laws depend only on two pointsXg−andXd, where]g,d[is an excursion interval of the regenerative setM. We use the(FDt)-predictable exit system to bring together the isolated points ofMand its perfect part and replace the classical optional exit system. This has been a subject in literature before (e.g., Kaspi (1988)) under the classical duality hypothesis. We define an “additive functional” for(Yt)t∈ℝwithB, we generalize the laws cited before to(Yt)t∈ℝ, and we express laws of pairs of excursions.

SCALAR CONSERVATION LAWS ON A HALF-LINE: A PARABOLIC APPROACH

2010 ◽  
Vol 07 (01) ◽  
pp. 165-189 ◽  
Author(s):  
MIRIAM BANK ◽  
MATANIA BEN-ARTZI
Keyword(s):  
Boundary Value Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Scalar Conservation Laws ◽  
Duality Method ◽  
Scalar Conservation Law ◽  
Classical Duality ◽  
Scalar Conservation ◽  
Initial Boundary Value ◽  
Unique Limit

The initial-boundary value problem for the (viscous) nonlinear scalar conservation law is considered, [Formula: see text] The flux f(ξ) ∈ C2(ℝ) is assumed to be convex (but not strictly convex, i.e. f″(ξ)≥ 0). It is shown that a unique limit u = lim ∊ → 0 u∊ exists. The classical duality method is used to prove uniqueness. To this end parabolic estimates for both the direct and dual solutions are obtained. In particular, no use is made of the Kružkov entropy considerations.

scholarly journals NONCOMMUTATIVE GRAVITY, A "NO STRINGS ATTACHED" QUANTUM–CLASSICAL DUALITY, AND THE COSMOLOGICAL CONSTANT PUZZLE

2008 ◽  
Vol 17 (13n14) ◽  
pp. 2593-2598
Author(s):  
T. P. SINGH
Keyword(s):  
Differential Geometry ◽  
Quantum Mechanics ◽  
Cosmological Constant ◽  
Relativistic Particle ◽  
Space Time ◽  
Planck Mass ◽  
Classical Space ◽  
Classical Duality ◽  
Noncommutative Gravity ◽  
The Masses

There ought to exist a reformulation of quantum mechanics which does not refer to an external classical space–time manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which follows is that the "weakly quantum, strongly gravitational" dynamics of a relativistic particle whose mass is much greater than the Planck mass is dual to the "strongly quantum, weakly gravitational" dynamics of another particle whose mass is much less than the Planck mass. The masses of the two particles are inversely related to each other, and the product of their masses is equal to the square of the Planck mass. This duality explains the observed value of the cosmological constant, and also why this value is nonzero but extremely small in Planck units.

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