Resolvability of spaces having small spread or extent

In a recent paper O. Pavlov proved the following two interesting resolvability results: (1) If a space $X$ satisfies \Delta(X) > \ps(X) then $X$ is maximally resolvable. (2) If a $T_3$-space $X$ satisfies \Delta(X) > \pe(X) then $X$ is $\omega$-resolvable. Here \ps(X) (\pe(X)) denotes the smallest successor cardinal such that $X$ has no discrete (closed discrete) subset of that size and $\Delta(X)$ is the smallest cardinality of a non-empty open set in $X$. In this note we improve (1) by showing that $\Delta(X) >$ \ps(X) can be relaxed to $\Delta(X) \ge$ \ps(X). In particular, if $X$ is a space of countable spread with $\Delta(X) > \omega$ then $X$ is maximally resolvable. The question if an analogous improvement of (2) is valid remains open, but we present a proof of (2) that is simpler than Pavlov's

D-forced spaces: a new approach to resolvability

We introduce a ZFC method that enables us to build spaces (in fact special dense subspaces of certain Cantor cubes) in which we have "full control" over all dense subsets. Using this method we are able to construct, in ZFC, for each uncountable regular cardinal $\lambda$ a 0-dimensional $T_2$, hence Tychonov, space which is $\mu$-resolvable for all $\mu < \lambda$ but not $\lambda$-resolvable. This yields the final (negative) solution of a celebrated problem of Ceder and Pearson raised in 1967: Are $\omega$-resolvable spaces maximally resolvable? This method enables us to solve several other open problems concerning resolvability as well

New simple method for the assessment of masonry arch bridges

The paper presents an approximation method for the assessment of the load carrying capacity of masonry arch railway bridges. The method is a simple semi-empirical tool for the initial level assessment that is considered to serve as a first sieve and provides conservative values for the load-carrying capacity and permissible axle load of single-span arches. The proposed method is based on results obtained by the RING 2.0 masonry arch bridge analysis software. The method uses a closed mathematical formula to calculate the carrying capacity and its input parameters can easily be determined by simple site inspections or using data from bridge files

Experimental and Numerical Characterization of a Radio-Frequency Plasma Source with a DC-grounded Electrode Configuration Using a Quarter-Wavelength Filter

We present a combined experimental and numerical investigation of the plasma properties in an asymmetric capacitively coupled radio frequency plasma source using argon discharge. Besides driving the system in the conventional way, which results in a high negative self-bias voltage due to the asymmetric configuration, we also connect a `quarter-wavelength filter` to the powered electrode, which lifts its DC potential to zero. At the powered side of the plasma, we employ electrodes with conducting and insulating surfaces, as well as electrodes combining both in different proportions (`hybrid electrodes`). Measurements are carried out for the plasma potential, the electron density and temperature in the bulk plasma, as well as for the flux-energy distribution of the ions at the grounded surface of the system. The nature of the surface of the powered electrode as well as the presence of the quarter-wavelength filter are found to highly influence the plasma potential, . For the electrode with a conducting surface 20 V and $sim$150 V are found in the absence and the presence of the filter, respectively. For the electrode with an insulating surface, the self-bias voltage builds up directly at the plasma interface, thus the filter has no effect and a plasma potential of $sim$20 V is found. For the electrodes with different conducting/insulating proportions of their surface, ranges between the above values. Particle-in-Cell/Monte Carlo Collisions calculations for identical conditions with hybrid electrodes predict double-peaked ion energy distribution at the powered electrode with peaks corresponding to and along with a lowering of the plasma potential (whencompared to wholly conducting electrode), a trend that is observed experimentally. These studies are of great importance for the application of similar plasma sources with in-situ cleaning of mirrors in fusion devices and the results can be extended to a variety of plasma processing applications