Let E be an elliptic curve over Q and A another elliptic curve over a real quadratic number field. We construct a Q-motive of rank 8, together with a distinguished class in the associated Bloch–Kato Selmer group, using Hirzebruch–Zagier cycles, that is, graphs of Hirzebruch–Zagier morphisms. We show that, under certain assumptions on E and A, the non-vanishing of the central critical value of t...

In this paper we show that the existence of algebro-geometrical analogs of the higher Morava K-theories satisfying some basic properties would imply the Bloch-Kato conjecture with Z/2-coefficients for fields which admit resolution of singularities (see [2] for a precise formulation of this condition). Our approach is inspired by two different ideas. The first is the use of algebraic K-theory an...

Suppose / is a holomorphic function on the open unit ball Bn of Cn. For 1 < p < oo and to > 0 an integer, we show that / is in Lp(Bn,dV) (with dV the volume measure) iff all the functions dmf/dza (\a\ = to) are in Lp(Bn,dV). We also prove that / is in the Bloch space of Bn iff all the functions dmf/dza (\a\ = m) are bounded on Bn. The corresponding result for the little Bloch space of Bn is est...

This paper presents a novel impedance-based approach for out-of-step (OOS) protection of a synchronous generator. The most popular and commonly used approaches for detecting OOS conditions are based on the measurement of positive sequence impedance at relay location. However, FACTS devices change the measured impedance value and thus disrupt the performance of impedance-based relay function. In...

This paper demontrates that the conditions for the existence of a dissipation-induced heteroclinic orbit between the inverted and noninverted states of a tippe top are determined by a complex version of the equations for a simple harmonic oscillator: the modified Maxwell– Bloch equations. A standard linear analysis reveals that the modified Maxwell–Bloch equations describe the spectral instabil...

We generalise our previous results of universal linear manipulations [Phys. Rev. A 63, 032304 (2001)] to investigate three types of nonlinear qubit transformations using measurement and quantum based schemes. Firstly, nonlinear rotations are studied. We rotate different parts of a Bloch sphere in opposite directions about the z-axis. The second transformation is a map which sends a qubit to its...

To enhance the optimization ability of quantumbehaved particle swarm optimization algorithm, some improvement measures are proposed. First, we propose a encoding approach based on qubits described on Bloch sphere. This approach makes each particle contain three groups of Bloch coordinates of qubits, and all three groups of coordinates are regarded as approximate solutions describing optimizatio...

As an important electron transportation phenomenon, Bloch oscillations have been extensively studied in condensed matter. Due to the similarity in wave properties between electrons and other quantum particles, Bloch oscillations have been observed in atom lattices, photonic lattices, and so on. One of the many distinct advantages for choosing these systems over the regular electronic systems is...

We have derived a new set of semiclassical equations for electrons in magnetic Bloch bands. The velocity and energy of magnetic Bloch electrons are found to be modified by the Berry phase and magnetization. This semiclassical approach is used to study general electron transport in a DC or AC electric field. We also find a close connection between the cyclotron orbits in magnetic Bloch bands and...

We investigate the dynamics of the cascade, lambda and vee type of three-level configurations which in the SU(3) basis precisely qualify as the qutrit system. The Bloch equation formulation is used to solve the systems exactly while taking the energy levels placed in a definite order. This scheme differs from the proposal put forward by Eberly and Hioe [Phys Rev A25 2168 (1982)], where the posi...