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Stabilization in non-abelian Iwasawa theory

Andrea Bandini, Fabio Caldarola (2015)

Acta Arithmetica

Let K/k be a ℤₚ-extension of a number field k, and denote by kₙ its layers. We prove some stabilization properties for the orders and the p-ranks of the higher Iwasawa modules arising from the lower central series of the Galois group of the maximal unramified pro-p-extension of K (resp. of the kₙ).

Stabilization of the wave equation by on-off and positive-negative feedbacks

Patrick Martinez, Judith Vancostenoble (2002)

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by several works on the stabilization of the oscillator by on-off feedbacks, we study the related problem for the one-dimensional wave equation, damped by an on-off feedback a ( t ) u t . We obtain results that are radically different from those known in the case of the oscillator. We consider periodic functions a : typically a is equal to 1 on ( 0 , T ) , equal to 0 on ( T , q T ) and is q T -periodic. We study the boundary case and next the locally distributed case, and we give optimal results of stability. In both cases,...

Stabilization of the wave equation by on-off and positive-negative feedbacks

Patrick Martinez, Judith Vancostenoble (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by several works on the stabilization of the oscillator by on-off feedbacks, we study the related problem for the one-dimensional wave equation, damped by an on-off feedback a ( t ) u t . We obtain results that are radically different from those known in the case of the oscillator. We consider periodic functions a: typically a is equal to 1 on (0,T), equal to 0 on (T, qT) and is qT-periodic. We study the boundary case and next the locally distributed case, and we give optimal results of stability....

Stable reduction of three point covers

Stefan Wewers (2005)

Journal de Théorie des Nombres de Bordeaux

This note gives a survey of some recent results on the stable reduction of covers of the projective line branched at three points.

Standard Models of Abstract Intersection Theory for Operators in Hilbert Space

Grzegorz Banaszak, Yoichi Uetake (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

For an operator in a possibly infinite-dimensional Hilbert space of a certain class, we set down axioms of an abstract intersection theory, from which the Riemann hypothesis regarding the spectrum of that operator follows. In our previous paper (2011) we constructed a GNS (Gelfand-Naimark-Segal) model of abstract intersection theory. In this paper we propose another model, which we call a standard model of abstract intersection theory. We show that there is a standard model of abstract intersection...

Stark's conjecture in multi-quadratic extensions, revisited

David S. Dummit, Jonathan W. Sands, Brett Tangedal (2003)

Journal de théorie des nombres de Bordeaux

Stark’s conjectures connect special units in number fields with special values of L -functions attached to these fields. We consider the fundamental equality of Stark’s refined conjecture for the case of an abelian Galois group, and prove it when this group has exponent 2 . For biquadratic extensions and most others, we prove more, establishing the conjecture in full.

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