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Non-commutative Hodge structures

Claude Sabbah (2011)

Annales de l’institut Fourier

This article gives a survey of recent results on a generalization of the notion of a Hodge structure. The main example is related to the Fourier-Laplace transform of a variation of polarizable Hodge structure on the punctured affine line, like the Gauss-Manin systems of a proper or tame algebraic function on a smooth quasi-projective variety. Variations of non-commutative Hodge structures often occur on the tangent bundle of Frobenius manifolds, giving rise to a tt* geometry.

Noncompact perturbation of nonconvex noncompact sweeping process with delay

Mohammed S. Abdo, Ahmed G. Ibrahim, Satish K. Panchal (2020)

Commentationes Mathematicae Universitatis Carolinae

We prove an existence theorem of solutions for a nonconvex sweeping process with nonconvex noncompact perturbation in Hilbert space. We do not assume that the values of the orient field are compact.

Nonconventional limit theorems in averaging

Yuri Kifer (2014)

Annales de l'I.H.P. Probabilités et statistiques

We consider “nonconventional” averaging setup in the form d X ε ( t ) d t = ε B ( X ε ( t ) , 𝛯 ( q 1 ( t ) ) , 𝛯 ( q 2 ( t ) ) , ... , 𝛯 ( q ( t ) ) ) where 𝛯 ( t ) , t 0 is either a stochastic process or a dynamical system with sufficiently fast mixing while q j ( t ) = α j t , α 1 l t ; α 2 l t ; l t ; α k and q j , j = k + 1 , ... , grow faster than linearly. We show that the properly normalized error term in the “nonconventional” averaging principle is asymptotically Gaussian.

Nondegenerate linearizable centre of complex planar quadratic and symmetric cubic systems in C2.

Colin Christopher, Christiane Rousseau (2001)

Publicacions Matemàtiques

In this paper we consider complex differential systems in the plane, which are linearizable in the neighborhood of a nondegenerate centre. We find necessary and sufficient conditions for linearizability for the class of complex quadratic systems and for the class of complex cubic systems symmetric with respect to a centre. The sufficiency of these conditions is shown by exhibiting explicitly a linearizing change of coordinates, either of Darboux type or a generalization of it.

Nonhermitian systems and pseudospectra

Lloyd N. Trefethen (2005/2006)

Séminaire Équations aux dérivées partielles

Four applications are outlined of pseudospectra of highly nonnormal linear operators.

Non-Leibniz algebras with logarithms do not have the trigonometric identity

D. Przeworska-Rolewicz (2000)

Banach Center Publications

Let X be a Leibniz algebra with unit e, i.e. an algebra with a right invertible linear operator D satisfying the Leibniz condition: D(xy) = xDy + (Dx)y for x,y belonging to the domain of D. If logarithmic mappings exist in X, then cosine and sine elements C(x) and S(x) defined by means of antilogarithmic mappings satisfy the Trigonometric Identity, i.e. [ C ( x ) ] 2 + [ S ( x ) ] 2 = e whenever x belongs to the domain of these mappings. The following question arises: Do there exist non-Leibniz algebras with logarithms such that...

Currently displaying 4281 – 4300 of 9351