We give a characterization of lacunary series in the Bloch space of the unit ball in C in terms of Taylor coefficients. We also characterize Bloch functions whose Taylor coefficients are nonnegative. The corresponding problems for BMOA are discussed as well.

The conjectures of Deligne, Bĕılinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebrogeometric objects and the special values of their L-functions. We make a numerical study for symmetric power L-functions of elliptic curves, obtaining data about the validity of their functional equations, frequency of vanishing of central values, and divisibility of Bloc...

studies show that any complications including hemorrhage, lack of blood supply, lack of oxygen supply, and death of cells in a tissue, will have a clear effect on electrical properties of that tissue. thus, by measuring impedance of a set of tissues, potential problems of the damaged tissue may be found. since electrical impedance is closely related to the measuring frequency, obviously, every ...

We present a systematic numerical approach to compute the eigenmodes and the related eigenfrequencies of a disordered photonic crystal, characterized by small fluctuations of the otherwise periodic dielectric profile. The field eigenmodes are expanded on the basis of Bloch modes of the corresponding periodic structure, and the resulting eigenvalue problem is diagonalized on a truncated basis in...

Let N be a complete, orientable, finite-volume, one-cusped hyperbolic 3-manifold with an ideal triangulation. Using combinatorics of the ideal triangulation of N we construct a plane curve in C×C which contains the squares of eigenvalues of PSL(2,C) representations of the meridian and longitude. We show that the defining polynomial of this curve is related to the PSL(2,C) A-polynomial and has p...

The Bloch equation provides the fundamental description of nuclear magnetic resonance(NMR) and relaxation(T1 andT2). This equation is the basis for both NMR spectroscopy andmagnetic resonance imaging (MRI). The fractional-order Bloch equation is a generalizationof the integer-order equation that interrelates the precession of the x, y and z componentsof magnetization wit...

Buckling analyses of heavily corrugated cylindrical shells based on detailed full finite element models are usually computationally expensive. To address this issue, we have proposed an efficient computational method of predicting the onset of buckling for corrugated cylindrical shells which builds on the Bloch wave method for infinitely periodic structures. We modified the traditional Bloch wa...

Using the Bloch representation of anN -dimensional quantum system and immediate results from quantum stochastic calculus, we establish a closed formula for the Bloch vector, hence also for the density operator, of a quantum system following a Lindblad evolution with selfadjoint Lindblad operators.

The conjectures of Deligne, Bĕılinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebrogeometric objects and the special values of their L-functions. We make a numerical study for symmetric power L-functions of elliptic curves, obtaining data about the validity of their functional equations, frequency of vanishing of central values, and divisibility of Bloc...

It was established that at low temperatures, quantum oscillations of a pair of interacting nanoscale structural inhomogeneities (vertical Bloch lines) occur in a domain wall of stripe domain in uniaxial ferromagnetic film. The effective mass of vertical Bloch line and conditions for this effect were determined. The effect can be used in the hybrid storage devices bit + q-bit.