Search results for "Mathematik"
showing 10 items of 59 documents
A parts-per-billion measurement of the antiproton magnetic moment
2017
The magnetic moment of the antiproton is measured at the parts-per-billion level, improving on previous measurements by a factor of about 350. Comparing the fundamental properties of normal-matter particles with their antimatter counterparts tests charge–parity–time (CPT) invariance, which is an important part of the standard model of particle physics. Many properties have been measured to the parts-per-billion level of uncertainty, but the magnetic moment of the antiproton has not. Christian Smorra and colleagues have now done so, and report that it is −2.7928473441 ± 0.0000000042 in units of the nuclear magneton. This is consistent with the magnetic moment of the proton, 2.792847350 ± 0.0…
Perturbed Bernstein-type operators
2018
The present paper deals with modifications of Bernstein, Kantorovich, Durrmeyer and genuine Bernstein-Durrmeyer operators. Some previous results are improved in this study. Direct estimates for these operators by means of the first and second modulus of continuity are given. Also the asymptotic formulas for the new operators are proved.
Fixpunktmengen von halbeinfachen Automorphismen in halbeinfachen Lie-Algebren
1976
Let g be a semisimple Lie algebra over an algebraically closed field of characteristic 0. The set of fixed points of a semisimple inner automorphism of g is a regular reductive subalgebra of maximal rank [1], so it is defined by a subsystem of the root system Φ of g relative to a suitable Cartan subalgebra. The main theorem of the article characterizes the corresponding subsystems of Φ. The second part of the article shows how to compute the fixed point algebras of semisimple outer automorphisms of g. A complete list of all fixed point algebras is then easily obtainable. The results are applied to bounded symmetric domains. References
Thermodynamic and electrochemical study of tailor-made crown ethers for redox-switchable (pseudo)rotaxanes
2020
Crown ethers are common building blocks in supramolecular chemistry and are frequently applied as cation sensors or as subunits in synthetic molecular machines. Developing switchable and specifically designed crown ethers enables the implementation of function into molecular assemblies. Seven tailor-made redox-active crown ethers incorporating tetrathiafulvalene (TTF) or naphthalene diimide (NDI) as redox-switchable building blocks are described with regard to their potential to form redox-switchable rotaxanes. A combination of isothermal titration calorimetry and voltammetric techniques reveals correlations between the binding energies and redox-switching properties of the corresponding ps…
A sampling method for detecting buried objects using electromagnetic scattering
2005
We consider a simple (but fully three-dimensional) mathematical model for the electromagnetic exploration of buried, perfect electrically conducting objects within the soil underground. Moving an electric device parallel to the ground at constant height in order to generate a magnetic field, we measure the induced magnetic field within the device, and factor the underlying mathematics into a product of three operations which correspond to the primary excitation, some kind of reflection on the surface of the buried object(s) and the corresponding secondary excitation, respectively. Using this factorization we are able to give a justification of the so-called sampling method from inverse scat…
The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study
2021
The classical Heisenberg model in two spatial dimensions constitutes one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still, despite its paradigmatic character and the widely accepted ban of a (continuous) spontaneous symmetry breaking, controversies remain whether the model exhibits a phase transition at finite temperature. Importantly, the model can be interpreted as a lattice discretization of the $O(3)$ non-linear sigma model in $1+1$ dimensions, one of the simplest quantum field theories encompassing crucial features of celebrated higher-dimensional ones (like quantum chromodynamics in $3+1$ dimensio…
Graphical representation of some duality relations in stochastic population models
2007
We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. http://www.ams.org/mathscinet-getitem?mr=MR2123250) and for the self-duality of Feller's branching diffusion with logistic growth (cf. math/0509612). The two dual processes are approximated by particle processes which are forward and backward processes in a graphical representation. We identify duality relations between the basic building blocks of the particle processes which lead to the two dualities mentioned above.
Dual-stimuli pseudorotaxane switches under kinetic control
2021
A series of dumbbell-shaped sec-ammonium salts with bulky (pseudo)stoppers (‘speed bumps’) were tested for their ability to form pseudorotaxanes with a redox-switchable, tetrathiafulvalene (TTF)-decorated [24]crown-8 ether. Depending on the size of the pseudostoppers, fast (less than ten minutes), slow (hours to days) and very slow (no pseudorotaxanes observed) threading has been observed. NMR spectroscopy as well as tandem mass spectrometry indicate the formation of non-threaded face-to-face complexes prior to pseudorotaxanes formation. Both isomers can be distinguished by their substantially different stability in collision-induced dissociation (CID) experiments. Two external stimuli affe…
Protein dynamics observed by tunable mid-IR quantum cascade lasers across the time range from 10 ns to 1 s
2017
We have developed a spectrometer based on tunable quantum cascade lasers (QCLs) for recording time-resolved absorption spectra of proteins in the mid-infrared range. We illustrate its performance by recording time-resolved difference spectra of bacteriorhodopsin in the carboxylic range (1800–1700 cm− 1) and on the CO rebinding reaction of myoglobin (1960–1840 cm− 1), at a spectral resolution of 1 cm− 1. The spectrometric setup covers the time range from 4 ns to nearly a second with a response time of 10–15 ns. Absorption changes as low as 1 × 10− 4 are detected in single-shot experiments at t > 1 μs, and of 5 × 10− 6 in kinetics obtained after averaging 100 shots. While previous time-res…
Localized potentials in electrical impedance tomography
2008
In this work we study localized electric potentials that have an arbitrarily high energy on some given subset of a domain and low energy on another. We show that such potentials exist for general L ∞ -conductivities in almost arbitrarily shaped subregions of a domain, as long as these regions are connected to the boundary and a unique continuation principle is satisfied. From this we deduce a simple, but new, theoretical identifiability result for the famous Calderon problem with partial data. We also show how to con- struct such potentials numerically and use a connection with the factorization method to derive a new non-iterative algorithm for the detection of inclusions in electrical imp…