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 $|n|\to\infty$.

'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.

Measuring workforce segregation: religious composition of private-sector employees at individual sites in Northern Ireland

In this paper I examine the scope of publicly available information on the religious composition of employees in private-sector companies in Northern Ireland. I highlight the unavailability of certain types of monitoring data and the impact of data aggregation at company as opposed to site level. Both oversights lead to underestimates of the extent of workplace segregation in Northern Ireland. The ability to provide more-coherent data on workplace segregation, by religion, in Northern Ireland is crucial in terms of advancing equality and other social-justice agendas. I argue that a more-accurate monitoring of religious composition of workplaces is part of an overall need to develop a spatial approach in which the importance of ethnically territorialised spaces in the reproduction of ethnosectarian disputation is understood.

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.