The Low Energy Limit of String Theory and its Compactifications with Background Fluxes

String theory is consistently defined in ten dimensions. In order to extract any information about four-dimensional physics, we need to understand the properties of the six-dimensional compact manifold orthogonal to our four-dimensional universe. A possibility that is being very much explored lately is to look at manifolds on which background fluxes are turned on. In this article, we present an introduction to string theory, focusing on its massless sector. We then review traditional compactifications to four–dimensions, and finally motivate and describe the so-called flux compactifications. We interpret the allowed six-dimensional manifolds from the point of view of generalized complex geometry.     

Dimensional Properties of Fractional Brownian Motion

Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion.     

Estimation of the aggregation number and core radius of microemulsions

Summary A simple working method for the estimation of the aggregation numbers and core radii from weight measurements of sodium bis-2-ethylhexylsulphosuccinate (aerosol-OT orAOT)/decane/water microemulsions of several compositions is proposed.Starting out from the hypotheses that (i) the density of the water inside the droplets is the same as that of free water, (ii) all the surfactant is localized as interface, and (iii) the penetration of the organic phase into the interface is negligible, values for the aggregation number and core radii comparable to those determined using more sophisticated methods were obtained.The results/methodological simplicity ratio may be of great advantage in kinetic work on reaction mechanisms in microemulsions.

---

Abschätzung von Aggregationszahl und Radius von Mikroemulsionen

Zusammenfassung Es wird eine einfache Methode zur Abschätzung von Aggregationszahl und Core-Radius von Mikroemulsionen aus Gewichtsmessungen von Natriumbis-2-ethylhexylsulphosuccinat (aerosol-OT oderAOT)/Decan/Wasser-Mikroemulsionen verschiedener Zusammensetzung vorgeschlagen. Unter den Annahmen, daß (i) die Dichte von Wasser innerhalb der Aggregationen die gleiche als bei freiem Wasser ist, (ii) das ganze Emulsionsmittel in der Grenzfläche vorliegt und (iii) das Eindringen der organischen Phase in die Grenzfläche vernachlässigbar ist, können Werte für Aggregationszahlen und Core-Radien erhalten werden, die durchaus mit entsprechenden Werten aus aufwendigeren Methoden vergleichbar sind. Das Leistungsverhältnis (Ergebnisse/geringer Aufwand) ist sehr vorteilhaft und macht die Methode für kinetische Arbeiten zur Bestimmung von Reaktionsmechanismen in Mikroemulsionen interessant.

     

The binding of manganese(II) and zinc(II) to the synthetic oligonucleotide d(C-G-C-G-A-A-T-T-C-G-C-G)2. A 1H NMR study

The interaction of the synthetic oligonucleotide d(C-G-C-G-A-A-T-T-C-G-C-G)2 with two different transition-metal ions has been investigated in aqueous solution by means of 1H NMR spectroscopy. The effects on the DNA due to the presence of manganese(II) or zinc(II) have been monitored by observing the paramagnetic broadening and diamagnetic shifts of the non-exchangeable proton resonance lines, respectively. The 1H NMR spectra acquired during the course of the manganese(II) titration show very distinct broadening effects on certain DNA resonance lines. Primarily, the H8 resonance of G4 is affected, but also the H5 and H6 resonances of C3 are clearly affected by the metal. The results imply that the binding of manganese(II) to DNA is sequence specific. The 1H spectra obtained during the zinc(II) titration reveal diamagnetic shift effects which largely conform with the paramagnetic broadening effects due to the presence of manganese(II), although this picture is somewhat more complex. The H8 resonance of G4 displays a clearly visible high-field shift, while for the other guanosine H8 protons this effect is absent. The H1' and H2' protons of C3 show an effect of similar strength, although in the opposite direction, while H5 and H6 of C3 are only slightly affected. Local differences in the structure of the DNA and the basicities of potential binding sites on different base steps in the sequence might account for the observed sequence selectivity.     

trans-Bis(azido-κN)bis(pyridine-2-carboxamide-κ2N1,O2)nickel(II)

In the title compound, [Ni(N₃)₂(C₆H₆N₂O)₂], the Ni^II atom lies on an inversion centre. The distorted octahedral nickel(II) coordination environment contains two planar trans-related N,O-chelating picolinamide ligands in one plane and two monodentate azide ligands perpendicular to this plane. Molecules are linked into a three-dimensional framework by N—H...N hydrogen bonds.     

Multiparameter Polynomial Adaptive Stabilizers

In 1983 Morse proved, for unknown scalar one-dimensional linearsystems, the nonexistence of rational or polynomial universalstabilizers (UAS). In 1983, Nussbaum gave an example of an analyticUAS. In our paper, it is shown that there exist time-invariantpolynomial UAS's with multidimensional gain adaptation. Thedesign procedure is developed for linear, minimum-phase systemsof relative degree one. Convergence of the closed-loop systemis proved. Some numerical simulations are provided.     

Cyclic trihydroxamic acid derivatives

In the crystal structures of two cyclic trihydroxamic acid derivatives containing the same substructure unit, viz. 1,3,5‐trihydroxy‐1,3,5‐triazinane‐2,4,6‐trione dihydrate, C₃H₃N₃O₆·2H₂O, (I), and 1,3,5‐benz­yloxy‐1,3,5‐triazinane‐2,4,6‐trione, C₂₄H₂₁N₃O₆, (II), there is no significant difference in the geometric parameters. In (I), there are 11 hydrogen bonds of the O—H⋯O type inter­connecting the mol­ecules in a three‐dimensional network, while in (II) there are only two weak C—H⋯O hydrogen bonds. The results of IR spectroscopic analysis are in good agreement with the crystallographic study.     

Gradient- and Sensitivity-Enhanced TOCSY Experiments

A pulsed field gradient version of the sensitivity-enhanced 2D TOCSY experiment is proposed which yields high-quality spectra with improved sensitivity and a minimum of two scans pert₁increment. For rapid acquisition of 1D TOCSY spectra, the 1D DPFGSE–TOCSY experiment was modified to include phase-encoded multiple-selective excitation followed by a simple spectral editing. Combination of these two building blocks is used in a sensitivity-enhanced 2D analog of the 3D TOCSY–TOCSY experiment which provides an efficient tool for resolving severely overlapped signals of oligomers in short experimental time.