General Relativity, the Cosmological Constant and Modular Forms

Strong field (exact) solutions of the gravitational field equations of General Relativity in the presence of a Cosmological Constant are investigated. In particular, a full exact solution is derived within the inhomogeneous Szekeres-Szafron family of space-time line element with a nonzero Cosmological Constant. The resulting solution connects, in an intrinsic way, General Relativity with the theory of modular forms and elliptic curves. The homogeneous FLRW limit of the above space-time elements is recovered and we solve exactly the resulting Friedmann Robertson field equation with the appropriate matter density for generic values of the Cosmological Constant %Lambda and curvature constant K. A formal expression for the Hubble constant is derived. The cosmological implications of the resulting non-linear solutions are systematically investigated. Two particularly interesting solutions i) the case of a flat universe K=0, Lambda not= 0 and ii) a case with all three cosmological parameters non-zero, are described by elliptic curves with the property of complex multiplication and absolute modular invariant j=0 and 1728, respectively. The possibility that all non-linear solutions of General Relativity are expressed in terms of theta functions associated with Riemann-surfaces is discussed.Comment: LaTeX file, 34 pages plus 9 EPS figures, Accepted for Publication in Classical and Quantum Gravit

Quasi-uniformity of Minimal Weighted Energy Points on Compact Metric Spaces

For a closed subset $K$ of a compact metric space $A$ possessing an $\alpha$-regular measure $\mu$ with $\mu(K)>0$, we prove that whenever $s>\alpha$, any sequence of weighted minimal Riesz $s$-energy configurations $\omega_N=\{x_{i,N}^{(s)}\}_{i=1}^N$ on $K$ (for `nice' weights) is quasi-uniform in the sense that the ratios of its mesh norm to separation distance remain bounded as $N$ grows large. Furthermore, if $K$ is an $\alpha$-rectifiable compact subset of Euclidean space ($\alpha$ an integer) with positive and finite $\alpha$-dimensional Hausdorff measure, it is possible to generate such a quasi-uniform sequence of configurations that also has (as $N\to \infty$) a prescribed positive continuous limit distribution with respect to $\alpha$-dimensional Hausdorff measure. As a consequence of our energy related results for the unweighted case, we deduce that if $A$ is a compact $C^1$ manifold without boundary, then there exists a sequence of $N$-point best-packing configurations on $A$ whose mesh-separation ratios have limit superior (as $N\to \infty$) at most 2

Finanzjournalismus im Spannungsfeld von Fachwissen, Stories und Finanzliteralität

Fachwissen, Stories und Finanzliteralität – Wie hängen sie zusammen und was bedeuten sie für Gesellschaft und Finanzjournalisten? Für die vorliegende Studie wurden Finanzjournalisten auf dem Platz Zürich dazu befragt. Die Ergebnisse liefern einerseits den Verantwortlichen von Fachmedien Anhaltspunkte für mögliche Reflexion, Strategien und Massnahmen in der Praxis. Die Resultate zeigen Bildungsinstitutionen anderseits, was es noch braucht, damit eine breite Leserschaft die Sprache der Zahlen versteht

Interactions between KSHV ORF57 and the novel human TREX proteins, CHTOP and CIP29

The coupling of mRNA processing steps is essential for precise and efficient gene expression. The human transcription/export (hTREX) complex is a highly conserved multi-protein complex responsible for eukaryotic mRNA stability and nuclear export. We have previously shown that the Kaposi's sarcoma-associated ORF57 protein orchestrates the recruitment of the hTREX complex onto viral intronless mRNA forming a stable and export competent viral ribonucleoprotein particle (vRNP). Recently, additional cellular proteins, namely CHTOP, CIP29 and POLDIP3 have been proposed as novel hTREX components. Herein we extend our previous research and provide evidence that ORF57 interacts with CHTOP and CIP29, in contrast to POLDIP3. Moreover, depletion studies show both CHTOP and CIP29 effect ORF57-mediated viral mRNA processing. As such, these results suggest both CHTOP and CIP29 are hTREX components and are recruited to an ORF57-mediated vRNP