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Jiongmin Yong - One of the best experts on this subject based on the ideXlab platform.
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Optimal Control Problems of Forward-Backward Stochastic Volterra Integral Equations
arXiv: Optimization and Control, 2014Co-Authors: Yufeng Shi, Tianxiao Wang, Jiongmin YongAbstract:Optimal control problems of forward-backward stochastic Volterra integral equations (FBSVIEs in short) are formulated and studied. A general Duality Principle is established for linear backward stochastic integral equation and linear stochastic Fredholm-Volterra integral equation with mean-field. With the help of such a Duality Principle, together with some other new delicate and subtle skills, Pontryagin type maximum Principles are proved for two optimal control problems of FBSVIEs.
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BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS AND SOME RELATED PROBLEMS
Stochastic Processes and their Applications, 2006Co-Authors: Jiongmin YongAbstract:AbstractBackward stochastic Volterra integral equations (BSVIEs, for short) are introduced. The existence and uniqueness of adapted solutions are established. A Duality Principle between linear BSVIEs and (forward) stochastic Volterra integral equations is obtained. As applications of the Duality Principle, a comparison theorem is proved for the adapted solutions of BSVIEs, and a Pontryagin type maximum Principle is established for an optimal control of stochastic integral equations
Thomas Vaupel - One of the best experts on this subject based on the ideXlab platform.
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a mfie efie fast multipole volume surface integral equation approach for substrate integrated waveguide structures and leaky wave slot antennas using the Duality Principle
International Conference on Electromagnetics in Advanced Applications, 2019Co-Authors: Thomas VaupelAbstract:Substrate Integrated Waveguide (SIW) components and antennas have the advantage of being characterized and fabricated as quasi-planar structures thus they can be integrated easily together with other microstrip/coplanar components. SIWs with slots in the upper groundplane are very attractive building blocks for the design of e.g. leaky-wave antennas with transverse slots or resonant slot arrays with longitudinal slots. For the characterization of the slots, magnetic surface currents are introduced within an integral equation approach using the Duality Principle whereas the SIW is modeled by two rows of vias modeled by volume current basis functions within a parallel-plate medium described by extended Green's functions. The integral equation is solved with a fast multipole approach utilizing branch cut contributions and especially the pole contributions of the parallel-plate waves. Furthermore the volume basis functions are used as field monitors to extract amplitudes and propagation constants of the waves within the SIW for S-parameter determination and leaky-wave characterization.
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A MFIE/EFIE Fast Multipole Volume/Surface Integral Equation Approach for Substrate Integrated Waveguide Structures and Leaky-Wave/Slot Antennas Using the Duality Principle
2019 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2019Co-Authors: Thomas VaupelAbstract:Substrate Integrated Waveguide (SIW) components and antennas have the advantage of being characterized and fabricated as quasi-planar structures thus they can be integrated easily together with other microstrip/coplanar components. SIWs with slots in the upper groundplane are very attractive building blocks for the design of e.g. leaky-wave antennas with transverse slots or resonant slot arrays with longitudinal slots. For the characterization of the slots, magnetic surface currents are introduced within an integral equation approach using the Duality Principle whereas the SIW is modeled by two rows of vias modeled by volume current basis functions within a parallel-plate medium described by extended Green's functions. The integral equation is solved with a fast multipole approach utilizing branch cut contributions and especially the pole contributions of the parallel-plate waves. Furthermore the volume basis functions are used as field monitors to extract amplitudes and propagation constants of the waves within the SIW for S-parameter determination and leaky-wave characterization.
Fabio Gavarini - One of the best experts on this subject based on the ideXlab platform.
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A Global Quantum Duality Principle for Subgroups and Homogeneous Spaces
arXiv: Quantum Algebra, 2014Co-Authors: N. Ciccoli, Fabio GavariniAbstract:For a complex or real algebraic group G, with g := Lie(G), quantizations of global type are suitable Hopf algebras Fq(G) or Uq(g) over Cq,q −1 � . Any such quantization yields a structure of Poisson group on G, and one of Lie bialgebra on g: correspondingly, one has dual Poisson groups G ∗ and a dual Lie bialgebra g ∗ . In this context, we introduce suitable notions of quantum subgroup and, correspondingly, of quantum homogeneous space, in three versions: weak, proper and strict (also called flat in the literature). The last two notions only apply to those subgroups which are coisotropic, and those homogeneous spaces which are Poisson quotients; the first one instead has no restrictions whatsoever. The global quantum Duality Principle (GQDP), as developed in (F. Gavarini, The global quantum Duality Principle, Journ. fur die Reine Angew. Math. 612 (2007), 17-33.), associates with any global quan- tization of G, or of g, a global quantization of g ∗ , or of G ∗ . In this paper we present a similar GQDP for quantum subgroups or quan- tum homogeneous spaces. Roughly speaking, this associates with ev- ery quantum subgroup, resp. quantum homogeneous space, of G, a quantum homogeneous space, resp. a quantum subgroup, of G ∗ . The construction is tailored after four parallel paths — according to the different ways one has to algebraically describe a subgroup or a ho- mogeneous space — and is "functorial", in a natural sense. Remarkably enough, the output of the constructions are always quan- tizations of proper type. More precisely, the output is related to the input as follows: the former is the coisotropic dual of the coisotropic interior of the latter — a fact that extends the occurrence of Poisson Duality in the original GQDP for quantum groups. Finally, when the
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Quantum Duality Principle for Quantum Grassmannians
Quantum Groups and Noncommutative Spaces, 2011Co-Authors: Rita Fioresi, Fabio GavariniAbstract:The quantum Duality Principle (QDP) for homogeneous spaces gives four recipes to\ud obtain, from a quantum homogeneous space, a dual one, in the sense of Poisson Duality.\ud One of these recipes fails (for lack of the initial ingredient) when the homogeneous space wevstart from is not a quasi-a ne variety. In this work we solve this problem for the quantum Grassmannian, a key example of quantum projective homogeneous space, providing a suitable analogue of the QDP recipe
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Quantization of Projective Homogeneous Spaces and Duality Principle
arXiv: Quantum Algebra, 2008Co-Authors: N. Ciccoli, Rita Fioresi, Fabio GavariniAbstract:We introduce a general recipe to construct quantum projective homogeneous spaces, with a particular interest for the examples of the quantum Grassmannians and the quantum generalized flag varieties. Using this construction, we extend the quantum Duality Principle to quantum projective homogeneous spaces.
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The global quantum Duality Principle
Journal für die reine und angewandte Mathematik (Crelles Journal), 2007Co-Authors: Fabio GavariniAbstract:Let R be an integral domain, let h in R be anon-zero element such that k := R/hR is a field, and let \HA be the category of torsionless (or flat) Hopf algebras over R. We call an object H in \HA a "quantized function algebra" (in short, a QFA), resp. "quantized restricted universal enveloping algebra" (in short, a QrUEA), at h if — roughly speaking — the quotient H/hH is the function algebra of a connected Poisson group, resp. the (restricted, if R/hR has positive characteristic) universal enveloping algebra of a (restricted) Lie bialgebra. Extending a result of Drinfeld, we establish an "inner" Galois' correspondence on \HA, via two endofunctors, ( )^\vee and ( )', of \HA such that H^\vee is a QrUEA and H' is a QFA (for all H in \HA). In addition: (a) the image of ( )^\vee, resp. of ( )', is the full subcategory of all QrUEAs, resp. of all QFAs; (b) if p := Char(k) = 0, the restrictions of ( )^\vee to QFAs and of ( )' to QrUEA yield equivalences inverse to each other; (c) if p=0, starting from a QFA over a Poisson group G, resp. from a QrUEA over a Lie bialgebra g, the functor ( )^\vee, resp. ( )', gives a QrUEA, resp. a QFA, over the dual Lie bialgebra, resp. the dual Poisson group. Several, far-reaching applications are developed in detail in [Ga2]–[Ga4].
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THE GLOBAL QUANTUM Duality Principle: THEORY, EXAMPLES, AND APPLICATIONS
arXiv: Quantum Algebra, 2006Co-Authors: Fabio GavariniAbstract:Let R be an integral domain, h non-zero in R such that R/hR is a field, and HA the category of torsionless (or flat) Hopf algebras over R. We call any H in HA "quantized function algebra" (=QFA), resp. "quantized (restricted) universal enveloping algebra" (=QrUEA), at h if H/hH is the function algebra of a connected Poisson group, resp. the (restricted, if R/hR has positive characteristic) universal enveloping algebra of a (restricted) Lie bialgebra. We establish an "inner" Galois' correspondence on HA, via the definition of two endofunctors, ( )^\vee and ( )', of HA such that: (a) the image of ( )^\vee, resp. of ( )', is the full subcategory of all QrUEAs, resp. all QFAs, at h; (b) if R/hR has zero characteristic, the restriction of ( )^\vee to QFAs and of ( )' to QrUEAs yield equivalences inverse to each other; (c) if R/hR has zero characteristic, starting from a QFA over a Poisson group, resp. from a QrUEA over a (restricted) Lie bialgebra, the functor ( )^\vee, resp. ( )', gives a QrUEA, resp. a QFA, over the dual Lie bialgebra, resp. the dual Poisson group. In particular, (a) yields a recipe to produce quantum groups of both types (QFAs or QrUEAs), (b) gives a characterization of them within HA, and (c) gives a "global" version of the "quantum Duality Principle" after Drinfeld. We then apply our result to Hopf algebras defined over a field k and extended to the polynomial ring k[h]: this yields quantum groups, hence "classical" geometrical symmetries of Poisson type (via specialization) associated to the "generalized symmetry" encoded by the original Hopf algebra over k. Both the main result and the above mentioned application are illustrated via several examples of many different kinds, which are studied in full detail. WARNING: this paper is *NOT meant for publication*! The results presented here are (or will be) published in separate articles; therefore, any reader willing to quote anything from the present paper is kindly invited to ask the author for the precise reference(s).
Vladica Andrejic - One of the best experts on this subject based on the ideXlab platform.
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On quasi-Clifford Osserman curvature tensors
Filomat, 2019Co-Authors: Vladica Andrejic, Katarina LukicAbstract:We consider pseudo-Riemannian generalizations of Osserman, Clifford, and the Duality Principle properties for algebraic curvature tensors and investigate relations between them. We introduce quasi- Clifford curvature tensors using a generalized Clifford family and show that they are Osserman. This allows us to discover an Osserman curvature tensor that does not satisfy the Duality Principle. We give some necessary and some sufficient conditions for the total Duality Principle.
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Quasi-special Osserman manifolds
Filomat, 2014Co-Authors: Vladica AndrejicAbstract:In this paper we deal with a pseudo-Riemannian Osserman curvature tensor whose reduced Jacobi operator is diagonalizable with exactly two distinct eigenvalues. The main result gives new insight into the theory of the Duality Principle for pseudo-Riemannian Osserman manifolds. We concern with special Osserman curvature tensor and propose new ways to exclude some additional Duality Principle conditions from its definition.
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Duality Principle and special osserman manifolds
Publications De L'institut Mathematique, 2013Co-Authors: Vladica AndrejicAbstract:We investigate the connection between the Duality Principle and the Osserman condition in a pseudo-Riemannian setting. We prove that a connected pointwise two-leaves Osserman manifold of dimension n > 5 is globally Osserman and investigate the relation between the special Osserman condition and the two-leaves Osserman one. [Projekat Ministarstva nauke Republike Srbije, br. 174012]
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Duality Principle and special Osserman manifolds
Publications de l'Institut Math?matique (Belgrade), 2013Co-Authors: Vladica AndrejicAbstract:We investigate the connection between the Duality Principle and the Osserman condition in a pseudo-Riemannian setting. We prove that a connected pointwise two-leaves Osserman manifold of dimension n > 5 is globally Osserman and investigate the relation between the special Osserman condition and the two-leaves Osserman one.
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on the Duality Principle in pseudo riemannian osserman manifolds
Journal of Geometry and Physics, 2007Co-Authors: Vladica Andrejic, Z RakicAbstract:Abstract Here we give a natural extension of the Duality Principle for the curvature tensor of pointwise pseudo-Riemannian Osserman manifolds. We proved that this extended Duality Principle holds under certain additional assumptions. Also, it is proved that Duality Principle holds for every four-dimensional Osserman manifold.
Terrence W. Mak - One of the best experts on this subject based on the ideXlab platform.
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Consistencies for Ultra-Weak Solutions in Minimax Weighted CSPs Using the Duality Principle
2012Co-Authors: Arnaud Lallouet, Jimmy H.m. Lee, Terrence W. MakAbstract:MinimaxWeighted Constraint Satisfaction Problems (formerly called QWCSPs) are a framework for modeling soft constrained problems with adversarial conditions. In this paper, we describe novel definitions and implementations of node, arc and full directional arc consistency notions to help reduce search space on top of the basic tree search with alpha-beta pruning for solving ultraweak solutions. In particular, these consistencies approximate the lower and upper bounds of the cost of a problem by exploiting the semantics of the quantifiers and reusing techniques from both Weighted and Quantified CSPs. Lower bound computation employs standard estimation of costs in the sub-problems used in alpha-beta search. In estimating upper bounds, we propose two approaches based on the Duality Principle: Duality of quantifiers and Duality of constraints. The first Duality amounts to changing quantifiers from min to max, while the second Duality re-uses the lower bound approximation functions on dual constraints to generate upper bounds. Experiments on three benchmarks comparing basic alpha-beta pruning and the six consistencies from the two dualities are performed to confirm the feasibility and efficiency of our proposal.
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CP - Consistencies for ultra-weak solutions in minimax weighted CSPs using the Duality Principle
Lecture Notes in Computer Science, 2012Co-Authors: Arnaud Lallouet, Jimmy H.m. Lee, Terrence W. MakAbstract:Minimax Weighted Constraint Satisfaction Problems (formerly called Quantified Weighted CSPs) are a framework for modeling soft constrained problems with adversarial conditions. In this paper, we describe novel definitions and implementations of node, arc and full directional arc consistency notions to help reduce search space on top of the basic tree search with alpha-beta pruning for solving ultra-weak solutions. In particular, these consistencies approximate the lower and upper bounds of the cost of a problem by exploiting the semantics of the quantifiers and reusing techniques from both Weighted and Quantified CSPs. Lower bound computation employs standard estimation of costs in the sub-problems used in alpha-beta search. In estimating upper bounds, we propose two approaches based on the Duality Principle: Duality of quantifiers and Duality of constraints. The first Duality amounts to changing quantifiers from min to max , while the second Duality re-uses the lower bound approximation functions on dual constraints to generate upper bounds. Experiments on three benchmarks comparing basic alpha-beta pruning and the six consistencies from the two dualities are performed to confirm the feasibility and efficiency of our proposal.
