An NLMS algorithm for the identification of bilinear forms

AbstractIn the paper we formulate a criterion for the nonsingularity of a bilinear form on a direct sum of finitely many invertible ideals of a domain. We classify these forms up to isometry and, in the case of a Dedekind domain, up to similarity.

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EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY AND LINEAR SUBSPACES OF COMPLETE INTERSECTIONS

Journal of the Institute of Mathematics of Jussieu ◽

10.1017/s147474802100027x ◽

2021 ◽

pp. 1-66

Author(s):

Tom Bachmann ◽

Kirsten Wickelgren

Keyword(s):

Commutative Algebra ◽

Vector Bundles ◽

Euler Class ◽

Complete Intersections ◽

Bilinear Forms ◽

Euler Numbers ◽

Coherent Sheaves ◽

Linear Subspaces ◽

Algebraic Vector

Abstract We equate various Euler classes of algebraic vector bundles, including those of [12] and one suggested by M. J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler class and give formulas for local indices at isolated zeros, both in terms of the six-functors formalism of coherent sheaves and as an explicit recipe in the commutative algebra of Scheja and Storch. As an application, we compute the Euler classes enriched in bilinear forms associated to arithmetic counts of d-planes on complete intersections in $\mathbb P^n$ in terms of topological Euler numbers over $\mathbb {R}$ and $\mathbb {C}$ .

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Bilinear forms on non-homogeneous Sobolev spaces

Forum Mathematicum ◽

10.1515/forum-2019-0311 ◽

2020 ◽

Vol 32 (4) ◽

pp. 995-1026

Author(s):

Carme Cascante ◽

Joaquín M. Ortega

Keyword(s):

Sobolev Spaces ◽

Bilinear Form ◽

Positive Measure ◽

Bilinear Forms ◽

Homogeneous Sobolev Spaces

AbstractIn this paper, we show that if {b\in L^{2}(\mathbb{R}^{n})}, then the bilinear form defined on the product of the non-homogeneous Sobolev spaces {H_{s}^{2}(\mathbb{R}^{n})\times H_{s}^{2}(\mathbb{R}^{n})}, {0<s<1}, by(f,g)\in H_{s}^{2}(\mathbb{R}^{n})\times H_{s}^{2}(\mathbb{R}^{n})\to\int_{% \mathbb{R}^{n}}(\mathrm{Id}-\Delta)^{\frac{s}{2}}(fg)(\mathbf{x})b(\mathbf{x})% \mathop{}\!d\mathbf{x}is continuous if and only if the positive measure {\lvert b(\mathbf{x})\rvert^{2}\mathop{}\!d\mathbf{x}} is a trace measure for {H_{s}^{2}(\mathbb{R}^{n})}.

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Research on digital predistortion technology based on improved NLMS algorithm

International Journal of RF and Microwave Computer-Aided Engineering ◽

10.1002/mmce.22661 ◽

2021 ◽

Author(s):

Xin Wang ◽

Simin Li ◽

Jincai Ye ◽

Xiangsuo Fan ◽

Mimi Qin ◽

...

Keyword(s):

Digital Predistortion ◽

Nlms Algorithm

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Polarization Relations and Dispersion Equations for Anisotropic Moving Media

Zeitschrift für Naturforschung A ◽

10.1515/zna-1979-1001 ◽

1979 ◽

Vol 34 (10) ◽

pp. 1147-1157 ◽

Cited By ~ 2

Author(s):

Helmut Hebenstreit ◽

Kurt Suchy

Keyword(s):

Quadratic Forms ◽

Bilinear Forms ◽

Dispersion Equations ◽

Left And Right ◽

Moving Media ◽

Eigenvectors And Eigenvalues

Abstract For media anisotropic (but not bi-anisotropic) in the comoving frame polarization relations and dispersion equations are derived using bilinear forms and quadratic forms, respectively. Specializations for media electrically anisotropic but magnetically isotropic (or vice versa) are given using (left and right) eigenvectors and eigenvalues of the material tensors.

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Convergence analysis of the NLMS algorithm with M-independent inputs

2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221) ◽

10.1109/icassp.2001.940683 ◽

2002 ◽

Cited By ~ 1

Author(s):

P. Scalart

Keyword(s):

Convergence Analysis ◽

Nlms Algorithm

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Some criteria for nuclearity

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100065956 ◽

1986 ◽

Vol 100 (1) ◽

pp. 151-159 ◽

Cited By ~ 1

Author(s):

M. A. Sofi

Keyword(s):

Sequence Space ◽

Convex Space ◽

Locally Convex Space ◽

Sequence Spaces ◽

Bilinear Forms ◽

Simple Formulation ◽

Normal Topology ◽

Nuclear Spaces ◽

Locally Convex

For a given locally convex space, it is always of interest to find conditions for its nuclearity. Well known results of this kind – by now already familiar – involve the use of tensor products, diametral dimension, bilinear forms, generalized sequence spaces and a host of other devices for the characterization of nuclear spaces (see [9]). However, it turns out, these nuclearity criteria are amenable to a particularly simple formulation in the setting of certain sequence spaces; an elegant example is provided by the so-called Grothendieck–Pietsch (GP, for short) criterion for nuclearity of a sequence space (in its normal topology) in terms of the summability of certain numerical sequences.

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