Pointwise universal trigonometric series

A series $S_a=\sum\limits_{n=-\infty}^\infty a_nz^n$ is called a {\it pointwise universal trigonometric series} if for any $f\in C(\T)$, there exists a strictly increasing sequence $\{n_k\}_{k\in\N}$ of positive integers such that $\sum\limits_{j=-n_k}^{n_k} a_jz^j$ converges to $f(z)$ pointwise on $\T$. We find growth conditions on coefficients allowing and forbidding the existence of a pointwise universal trigonometric series. For instance, if $|a_n|=O(\e^{\,|n|\ln^{-1-\epsilon}\!|n|})$ as $|n|\to\infty$ for some $\epsilon>0$, then the series $S_a$ can not be pointwise universal. On the other hand, there exists a pointwise universal trigonometric series $S_a$ with $|a_n|=O(\e^{\,|n|\ln^{-1}\!|n|})$ as $|n|\to\infty$.

Scaling of Superdomain Bands in Ferroelectric Dots

Bundles of 90° stripe domains have been observed to form into distinct groups, or bands, in mesoscale BaTiO3 single crystal dots. Vector piezoresponse force microscopy (PFM) shows that each band region, when considered as a single entity, possesses a resolved polarization that lies approximately along the pseudocubic direction; antiparallel alignment of this resultant polarization in adjacent bands means that these regions can be considered as 180° “superdomains.” For dots with sidewall dimensions below ~2 microns, Landau–Kittel like scaling in the width of these superdomains was observed, strongly suggesting that they form in response to lateral depolarizing fields. In larger dot structures, scaling laws break down. We have rationalized these observations by considering changes in the driving force for the adoption of equilibrium superdomain periodicities implied by Landau–Kittel-free energy models; we conclude that the formation of ordered bands of superdomains is a uniquely meso/nanoscale phenomenon. We also note that the superdomain bands found by PFM imaging in air contrast with the quadrant arrangements seen previously by Schilling et al. (Nano Lett., 9, 3359 (2009)) through transmission electron microscopy imaging in vacuum. The importance of the exact nature of the boundary conditions in determining the domain patterns that spontaneously form in nanostructures is therefore clearly implied.

'The Arbitrarium' and 'The Universal Key' (short stories)

Short stories

Computational Verification of Two Universal Relations for Simple Ionic Liquids. Kinetic Properties of a Model 2:1 Molten Salt

Two semianalytical relations [Nature, 1996, 381, 137 and Phys. Rev. Lett. 2001, 87, 245901] predicting dynamical coefficients of simple liquids on the basis of structural properties have been tested by extensive molecular dynamics simulations for an idealized 2:1 model molten salt. In agreement with previous simulation studies, our results support the validity of the relation expressing the self-diffusion coefficient as a Function of the radial distribution functions for all thermodynamic conditions such that the system is in the ionic (ie., fully dissociated) liquid state. Deviations are apparent for high-density samples in the amorphous state and in the low-density, low-temperature range, when ions condense into AB(2) molecules. A similar relation predicting the ionic conductivity is only partially validated by our data. The simulation results, covering 210 distinct thermodynamic states, represent an extended database to tune and validate semianalytical theories of dynamical properties and provide a baseline for the interpretation of properties of more complex systems such as the room-temperature ionic liquids.

Structural similarity of directed universal hierarchical graphs: A low computational complexity approach

In the present paper we mainly introduce an efficient approach to measure the structural similarity of so called directed universal hierarchical graphs. We want to underline that directed universal hierarchical graphs can be obtained from generalized trees which are already introduced. In order to classify these graphs, we state our novel graph similarity method. As a main result we notice that our novel algorithm has low computational complexity. (c) 2007 Elsevier Inc. All rights reserved.

Europe’s Information Society project and Digital Inclusion: universal service obligations or social solidarity?

The importance of digital inclusion to Europe is obvious: as we move towards an ever more internet-communicating society the lack of access to basic digital infrastructures for a significant segment of the population is both problematic for those individuals without access and also problematic for those providing services which should be efficient and fully utilised. The EU’s ‘Information Society’ project has been the central plank of the European attempt to build a European digital marketplace, a concept which necessitates digital inclusion of the population at large. It is a project which prefers universal service obligations to achieve inclusion. If that is to be the preferred solution I suggest that we must consider exclusion from the banking system, given that the Information Society is at root an economic community.

However, universal service obligations are not the only method whereby digital inclusion can be encouraged and I posit we may need to reconsider the role of the state as supplier of services through the concept of ‘social solidarity’.

GAIN SCALING RELATIONSHIPS FOR NE-LIKE GE SLAB TARGETS

The gain coefficient of the strongest 3p --> 3s, J = 2 --> 1 lasing transition at 23.6 nm in the Ne-like Ge collisional excitation scheme has been measured, using the fundamental wavelength from a Nd:glass laser (1.06-mu-m), for a range of incident intensities on massive stripe targets up to 2.2 cm in length. From a threshold incident laser intensity of approximately 6 x 10(12) W/cm2, the gain coefficient rises to approximately 4.5 cm-1 for an irradiation intensity of approximately 2.5 x 10(13) W/cm2, tending towards still higher gain coefficients at higher incident intensities. For targets of maximum length, a gain-length product gL almost-equal-to 10 was reached with a resultant output power at 23.6 nm estimated to be at the approximately kW level. The beam divergence decreased with length to a minimum of approximately 7 mrad but no significant trend in beam pointing with plasma length was observed. From the trend in the gain coefficient, it appears that for a fixed energy laser irradiating a approximately 100-mu-m wide slab targets, an incident intensity of I(i) approximately 1.2 x 10(13) W/cm2 represents an optimum working level, assuming that plasma length is not limited by refractive effects. In addition to the usual valence electron excited 3p --> 3s transitions, the gain coefficient for the core excited 1s(2)2s2p(6)3d --> 1s(2)2s2p(6)3p transition at 19.9 nm has been measured to be approximately 1.5 cm-1 for an incident irradiance of approximately 2.5 x 10(13) W/cm2.

Measurements of fast electron scaling generated by petawatt laser systems

Fast electron energy spectra have been measured for a range of intensities between 10(18) and 10(21) W cm(-2) and for different target materials using electron spectrometers. Several experimental campaigns were conducted on petawatt laser facilities at the Rutherford Appleton Laboratory and Osaka University, where the pulse duration was varied from 0.5 to 5 ps relevant to upcoming fast ignition integral experiments. The incident angle was also changed from normal incidence to 40 degrees in p-polarized. The results confirm a reduction from the ponderomotive potential energy on fast electrons at the higher intensities under the wide range of different irradiation conditions.

Scaling of proton acceleration driven by petawatt-laser-plasma interactions

The possibility of using high-power lasers to generate high-quality beams of energetic ions is attracting large global interest. The prospect of using laser-accelerated protons in medicine attracts particular interest, as these schemes may lead to compact and relatively low-cost sources. Among the challenges remaining before these sources can be used in medicine is to increase the numbers and energies of the ions accelerated. Here, we extend the energy and intensity range over which proton scaling is experimentally investigated, up to 400 J and 6 x 10(20) W cm(-2) respectively, and find a slower proton scaling than previously predicted. With the aid of plasma-expansion simulation tools, our results suggest the importance of time-dependent and multidimensional effects in predicting the maximum proton energy in this ultrahigh-intensity regime. The implications of our new understanding of proton scaling for potential medical applications are discussed.