Abstract:
The background motivation, and some preliminary results, are reported for a recently begun investigation of a potentially important mechanism for electromagnetic radiation from space, Double Layer Radiation (DL-radiation). This type of radiation is proposed to come from DL-associated, spatially localized high frequency (hf) spikes that are driven by the electron beam on the high-potential side of the double layer. It is known, but only qualitatively, from laboratory experiments that double layers radiate in the electromagnetic spectrum. In our experiment the spectrum has high amplitude close to the plasma frequency, several hundred MHz. No clear theoretical model exists today. The quantitative evaluation is complicated because measurements are made in the near field of the radiating structure, and in the vicinity of conducting laboratory hardware that distorts the field. Because the localized electrostatic wavelengths (approximately 1 cm) can be relatively small compared to the emitted electromagnetic wavelengths, the situation is further complicated. We discuss the mutual influence between the ion density profile and hf-spike formation, and propose that some kind of self-organization of the density profile through the ponderomotive force of the hf spike might be operating. First results regarding the electromagnetic radiation are reported: the frequency, the time variation of the amplitude, and the spatial distribution in the discharge vessel.

Abstract:
There has been significant recent work on the theory and application of randomized coordinate descent algorithms, beginning with the work of Nesterov [SIAM J. Optim., 22(2), 2012], who showed that a random-coordinate selection rule achieves the same convergence rate as the Gauss-Southwell selection rule. This result suggests that we should never use the Gauss-Southwell rule, as it is typically much more expensive than random selection. However, the empirical behaviours of these algorithms contradict this theoretical result: in applications where the computational costs of the selection rules are comparable, the Gauss-Southwell selection rule tends to perform substantially better than random coordinate selection. We give a simple analysis of the Gauss-Southwell rule showing that---except in extreme cases---it's convergence rate is faster than choosing random coordinates. Further, in this work we (i) show that exact coordinate optimization improves the convergence rate for certain sparse problems, (ii) propose a Gauss-Southwell-Lipschitz rule that gives an even faster convergence rate given knowledge of the Lipschitz constants of the partial derivatives, (iii) analyze the effect of approximate Gauss-Southwell rules, and (iv) analyze proximal-gradient variants of the Gauss-Southwell rule.

Abstract:
We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length $\omega$ to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite set of ordinal parameters if and only if it is an element of Goedel's constructible universe L. This characterization can be used to prove the generalized continuum hypothesis in L.

Abstract:
A method is presented to calculate UV irradiances on inclined surfaces that additionally takes into account the influence of sky obstructions caused by obstacles such as mountains, houses, trees, or umbrellas. With this method it is thus possible to calculate the impact of UV radiation on biological systems, such as, for instance, the human skin or eye, in any natural or artificial environment. The method, which consists of a combination of radiation models, is explained here and the accuracy of its results is demonstrated. The effect of a natural skyline is shown for an Alpine ski area, where the UV irradiance even on a horizontal surface may increase due to reflection from snow by more than 10 percent. In contrast, in a street canyon the irradiance on a horizontal surface is reduced to 30% in shadow and to about 75% for a position in the sun.

Abstract:
A method is presented to calculate UV irradiances on inclined surfaces that additionally takes into account the influence of sky obstructions caused by obstacles such as mountains, houses, trees, or umbrellas. Thus the method allows calculating the impact of UV radiation on biological systems, such as for instance the human skin or eye, in any natural or artificial environment. The method, a combination of radiation models, is explained and the correctness of its results is demonstrated. The effect of a natural skyline is shown for an Alpine ski area, where the UV irradiance even on a horizontal surface may increase due to reflection at snow by more than 10%. In contrast in a street canyon the irradiance on a horizontal surface is reduced down to 30% in shadow and to about 75% for a position in the sun.

Abstract:
We propose a natural theory SO axiomatizing the class of sets of ordinals in a model of ZFC set theory. Both theories possess equal logical strength. Constructibility theory in SO corresponds to a natural recursion theory on ordinals.

Abstract:
We show using a proof of the Global Square property in Core Models below a measurable of Mitchell order o(kappa)=kappa^++ (a result originally due to Jensen & Zeman) that Foreman and Magidor's Mutual Stationarity property MS(Aleph_n (1

Abstract:
We extend a transitive model V of ZFC + GCH cardinal preservingly to a model N of ZF + "GCH holds below Alef_omega" + "there is a surjection from the power set of Alef_omega onto lambda" where lambda is an arbitrarily high fixed cardinal in V.

Abstract:
We prove that every homogeneously Souslin set is coanalytic provided that either (a) 0^long does not exist or else (b) V=K where K is the core model below a \mu-measurable cardinal.

Abstract:
By Easton's theorem one can force the exponential function on regular cardinals to take rather arbitrary cardinal values provided monotonicity and Koenig's lemma are respected. In models without choice we employ a "surjective" version of the exponential function. We then prove a choiceless Easton's theorem: one can force the surjective exponential function on all infinite cardinals to take arbitrary cardinal values, provided monotonicity and Cantor's theorem are satisfied, irrespective of cofinalities.