The Experts below are selected from a list of 153 Experts worldwide ranked by ideXlab platform
Wim Michiels - One of the best experts on this subject based on the ideXlab platform.
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InvariancepropertiesintheRootsensitivityoftime-delay systemswithdoubleImaginaryRoots
2020Co-Authors: Elias Jarlebring, Wim MichielsAbstract:If i!2 iR is an eigenvalue of a time-delay system for the delay 0 then i! is also an eigenvalue for the delays k := 0 +k2=! , for anyk2 Z. We investigate the sensitivity, periodicity and invariance properties of the Rooti! for the case thati! is a double eigenvalue for some k. It turns out that under natural conditions (the condition that the Root exhibits the completely regular splitting property if the delay is perturbed), the presence of a double Imaginary Root i! for some delay 0 implies that i! is a simple Root for the other delays k, k6 0. Moreover, we show how to characterize the Root locus around i!. The entire local Root locus picture can be completely determined from the square Root splitting of the double Root. We separate the general picture into two cases depending on the sign of a single scalar constant; the Imaginary part of the rst coecient in the square Root expansion of the double eigenvalue.
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technical communique invariance properties in the Root sensitivity of time delay systems with double Imaginary Roots
Automatica, 2010Co-Authors: Elias Jarlebring, Wim MichielsAbstract:If i@w@?iR is an eigenvalue of a time-delay system for the delay @t"0 then i@w is also an eigenvalue for the delays @t"k@?@t"0+k2@p/@w, for any k@?Z. We investigate the sensitivity, periodicity and invariance properties of the Root i@w for the case that i@w is a double eigenvalue for some @t"k. It turns out that under natural conditions (the condition that the Root exhibits the completely regular splitting property if the delay is perturbed), the presence of a double Imaginary Root i@w for some delay @t"0 implies that i@w is a simple Root for the other delays @t"k, k 0. Moreover, we show how to characterize the Root locus around i@w. The entire local Root locus picture can be completely determined from the square Root splitting of the double Root. We separate the general picture into two cases depending on the sign of a single scalar constant; the Imaginary part of the first coefficient in the square Root expansion of the double eigenvalue.
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invariance properties in the Root sensitivity of time delay systems with double Imaginary Roots
IFAC Proceedings Volumes, 2009Co-Authors: Elias Jarlebring, Wim MichielsAbstract:Abstract If iω ∈ iℝ is an eigenvalue of a time-delay system for the delay τ0 then iω is also an eigenvalue for the delays, for any k ∈ ℤ. We investigate the sensitivity and other properties of the Root iω for the case that iω is a double eigenvalue for some τk. It turns out that under natural conditions, the presence of a double Imaginary Root iω for some delay τ0 implies that iω is a simple Root for the other delays τk k ≠ 0. Moreover, we show how to characterize the Root locus around iω. The entire local Root locus picture can be determined from the square Root splitting of the double Root. We separate the general picture into two cases depending on the sign of a single scalar constant; the Imaginary part of the first coefficient in the square Root expansion of the double eigenvalue.
Walter Freyn - One of the best experts on this subject based on the ideXlab platform.
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dimensions of Imaginary Root spaces of hyperbolic kac moody algebras
arXiv: Representation Theory, 2013Co-Authors: Lisa Carbone, Walter FreynAbstract:We discuss the known results and methods for determining Root multiplicities for hyperbolic Kac-Moody algebras.
Jonathan Beck - One of the best experts on this subject based on the ideXlab platform.
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Crystal Structure of Level Zero Extremal Weight Modules
Letters in Mathematical Physics, 2002Co-Authors: Jonathan BeckAbstract:We consider the crystal structure of the level zero extremal weight modules V(λ) using the crystal base of the quantum affine algebra constructed in Duke Math. J.99 (1999), 455–487. This approach yields an explicit form for extremal weight vectors in the U− part of each connected component of the crystal, which are given as Schur functions in the Imaginary Root vectors. We show the map \(\Phi _\lambda\) induces a correspondence between the global crystal base of V(λ) and elements \(s_{c_0 } \left( {z^{ - 1} } \right)G\left( b \right),b \in B_0 \left( {U_q \left[ {{z_{i,k}}^{{ \pm 1}} } \right]u\prime } \right)\).
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Crystal structure of level zero extremal weight modules
arXiv: Quantum Algebra, 2002Co-Authors: Jonathan BeckAbstract:We consider the crystal structure of the level zero extremal weight modules $V(\lambda)$ using the crystal base of the quantum affine algebra constructed by Beck, Chari and Pressley. This approach yields an explicit form for the U^- extremal weight vectors in each connected component of the crystal of $V(\lambda)$, which are given as Schur functions in the Imaginary Root vectors. We use this fact to demonstrate Kashiwara's conjectures regarding the crystal structure of $V(\lambda)$.
Elias Jarlebring - One of the best experts on this subject based on the ideXlab platform.
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InvariancepropertiesintheRootsensitivityoftime-delay systemswithdoubleImaginaryRoots
2020Co-Authors: Elias Jarlebring, Wim MichielsAbstract:If i!2 iR is an eigenvalue of a time-delay system for the delay 0 then i! is also an eigenvalue for the delays k := 0 +k2=! , for anyk2 Z. We investigate the sensitivity, periodicity and invariance properties of the Rooti! for the case thati! is a double eigenvalue for some k. It turns out that under natural conditions (the condition that the Root exhibits the completely regular splitting property if the delay is perturbed), the presence of a double Imaginary Root i! for some delay 0 implies that i! is a simple Root for the other delays k, k6 0. Moreover, we show how to characterize the Root locus around i!. The entire local Root locus picture can be completely determined from the square Root splitting of the double Root. We separate the general picture into two cases depending on the sign of a single scalar constant; the Imaginary part of the rst coecient in the square Root expansion of the double eigenvalue.
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technical communique invariance properties in the Root sensitivity of time delay systems with double Imaginary Roots
Automatica, 2010Co-Authors: Elias Jarlebring, Wim MichielsAbstract:If i@w@?iR is an eigenvalue of a time-delay system for the delay @t"0 then i@w is also an eigenvalue for the delays @t"k@?@t"0+k2@p/@w, for any k@?Z. We investigate the sensitivity, periodicity and invariance properties of the Root i@w for the case that i@w is a double eigenvalue for some @t"k. It turns out that under natural conditions (the condition that the Root exhibits the completely regular splitting property if the delay is perturbed), the presence of a double Imaginary Root i@w for some delay @t"0 implies that i@w is a simple Root for the other delays @t"k, k 0. Moreover, we show how to characterize the Root locus around i@w. The entire local Root locus picture can be completely determined from the square Root splitting of the double Root. We separate the general picture into two cases depending on the sign of a single scalar constant; the Imaginary part of the first coefficient in the square Root expansion of the double eigenvalue.
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invariance properties in the Root sensitivity of time delay systems with double Imaginary Roots
IFAC Proceedings Volumes, 2009Co-Authors: Elias Jarlebring, Wim MichielsAbstract:Abstract If iω ∈ iℝ is an eigenvalue of a time-delay system for the delay τ0 then iω is also an eigenvalue for the delays, for any k ∈ ℤ. We investigate the sensitivity and other properties of the Root iω for the case that iω is a double eigenvalue for some τk. It turns out that under natural conditions, the presence of a double Imaginary Root iω for some delay τ0 implies that iω is a simple Root for the other delays τk k ≠ 0. Moreover, we show how to characterize the Root locus around iω. The entire local Root locus picture can be determined from the square Root splitting of the double Root. We separate the general picture into two cases depending on the sign of a single scalar constant; the Imaginary part of the first coefficient in the square Root expansion of the double eigenvalue.
Lisa Carbone - One of the best experts on this subject based on the ideXlab platform.
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dimensions of Imaginary Root spaces of hyperbolic kac moody algebras
arXiv: Representation Theory, 2013Co-Authors: Lisa Carbone, Walter FreynAbstract:We discuss the known results and methods for determining Root multiplicities for hyperbolic Kac-Moody algebras.
