A note on the hyperbolic singular value decomposition without hyperexchange matrices

Shirokov, D. S.

doi:10.1016/j.cam.2021.113450

Cited by 7 publications

(5 citation statements)

References 15 publications

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“…In this paper, we present explicit form of all constant solutions of the Yang-Mills-Dirac equations with SU(2) gauge symmetry in Minkowski space R 1,3 (see Theorems 2, 3, and 5). The solutions are written out with an appropriate choice of the coordinate system and gauge.…”

Section: Discussionmentioning

confidence: 99%

“…We can always choose the matrices P ∈ SO(3) and Q ∈ O(1, 3) such that QAP is in the canonical form (15). We use the following theorem on the hyperbolic singular value decomposition (see also [1,3]).…”

Section: Classification and Explicit Form Of All Constant Solutions O...mentioning

confidence: 99%

“…We can always find the matrices W −1 ∈ SU(2, 2) and S ∈ SU(2) from the special (pseudo-)unitary groups. If the matrix S has the determinant −1, then we can change the sign of one of the columns of the matrix S (which is the eigenvector of the matrix Ψ † ωΨ, see the details in [1]) and at the same time we should change the sign of the corresponding column of the matrix Σ Ψ . If the matrix W −1 has the determinant −1, then we can change the sign of one of the rows of the matrix W −1 (which is the eigenvector or the generalized eigenvector in the case d = 0 of the matrix ωΨΨ † , see the details in [1]) and at the same time we should change the sign of the corresponding row of the matrix Σ Ψ .…”

Section: Theorem 1 ([1]) Assume (1) For An Arbitrary Matrixmentioning

confidence: 99%

“…In this paper, we present explicit form of all constant solutions of the Yang-Mills-Dirac equations with SU(2) gauge symmetry in Minkowski space R 1,3 . We use our previous results on the hyperbolic singular value decomposition [1] and results on constant solutions of the Yang-Mills equations with arbitrary current [2,3]. The presentation is given independently.…”

Section: Introductionmentioning

confidence: 99%

“…It was proposed in 1991 [28,29] and is used in signal and image processing, engineering, and computer science. The new version of the HSVD without the use of hyperexchange matrices is presented in our previous paper [1]. This new version of HSVD naturally incudes the ordinary SVD.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Classification of all constant solutions of the Yang-Mills-Dirac equations

Shirokov¹

2022

Preprint

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We present a complete classification of all constant solutions of the Yang-Mills-Dirac equations with SU(2) gauge symmetry in Minkowski space R 1,3 . The explicit form of all solutions is given. Nonconstant solutions are considered in the form of series of perturbation theory using constant solutions as a zeroth approximation. We use our previous results on the hyperbolic singular value decomposition of real and complex matrices and results on constant solutions of the SU(2) Yang-Mills equations in pseudo-Euclidean spaces.

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Section: Discussionmentioning

confidence: 99%

Section: Classification and Explicit Form Of All Constant Solutions O...mentioning

confidence: 99%

Section: Theorem 1 ([1]) Assume (1) For An Arbitrary Matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Classification of all constant solutions of the Yang-Mills-Dirac equations

Shirokov¹

2022

Preprint

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On SVD and Polar Decomposition in Real and Complexified Clifford Algebras

Shirokov

2024

Adv. Appl. Clifford Algebras

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Informative singular value decomposition and its application in fault detection of planetary gearbox

Shen

Shi

Shen

et al. 2022

Meas. Sci. Technol.

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The faults of rotating machineries are generally characterized by the periodic singular impulses. However, the fault features of planetary gearbox are often complex modulated and submerged by other components, for its vibration signal has the characteristics of multi-source and multi transmission path. An informative singular value decomposition (ISVD) filter based on the modulation performance of singular value component signal (SVCS) is developed to enhance the fault characteristics of planetary gearbox and weaken the interference in this paper. The fault features can be detected by the envelope spectrum analysis (ESA). In this method, a fast SVD is firstly performed to decompose the vibration signal into a series of SVCSs. Secondly, the information detector of negentropy combined with cyclic autocorrelation (CA) is applied to estimate the informativeness of each SVCS. Then the ISVD filtered signal can be obtained by the reconstruction of amplified informative SVCSs. Finally, the fault features can be extracted by ESA from the ISVD filtered signal. The performance of the proposed method is verified by simulation study and experimental data measured from a planetary gearbox. Results show that the proposed ISVD-ESA strategy can enhance and extract the weak features of multi-modulation, and it can accurately extract the faults of tooth tip pitting and misalignment of sun gear of the planetary gearbox.

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A note on the hyperbolic singular value decomposition without hyperexchange matrices

Cited by 7 publications

References 15 publications

Classification of all constant solutions of the Yang-Mills-Dirac equations

Classification of all constant solutions of the Yang-Mills-Dirac equations

On SVD and Polar Decomposition in Real and Complexified Clifford Algebras

Informative singular value decomposition and its application in fault detection of planetary gearbox

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