392 research outputs found
Minimizing the regularity of maximal regular antichains of 2- and 3-sets
Let be a natural number. We study the problem to find the
smallest such that there is a family of 2-subsets and
3-subsets of with the following properties: (1)
is an antichain, i.e. no member of is a subset of
any other member of , (2) is maximal, i.e. for every
there is an with or , and (3) is -regular, i.e. every point
is contained in exactly members of . We prove lower
bounds on , and we describe constructions for regular maximal antichains
with small regularity.Comment: 7 pages, updated reference
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Protection Measures against Product Piracy and Application by the Use of AM
Presently the implications Additive Manufacturing (AM) on intellectual properties are
discussed in public. Here AM is often mentioned as a driver for product piracy as it allows to
produce and to copy objects with any geometries. Imitators need a lot of information to copy
an object accurately. As reverse engineering has been identified as the most important
information source for product imitators, AM can also help to reduce the threat of product
piracy when correctly applied in the product development. Due to the layer wise production
process that allows the manufacturing of very complex shapes and geometries, the reverse-engineering process can be complicated by far. By this, quite contrary to the public opinion,
AM can increase the needed effort of imitators and strongly reduce the economic efficiency of
product piracy. This paper will show different protection measures and a methodological
approach of how to apply these measures to a product. Beside the protective effect some
measures allow a traceability of parts over the product’s lifecycle and thus support the quality
management of AM processes and additively produced parts.Mechanical Engineerin
Explicitly correlated Gaussian functions with shifted-center and projection techniques in pre-Born-Oppenheimer calculations
Numerical projection methods are elaborated for the calculation of
eigenstates of the non-relativistic many-particle Coulomb Hamiltonian with
selected rotational and parity quantum numbers employing shifted explicitly
correlated Gaussian functions, which are, in general, not eigenfunctions of the
total angular momentum and parity operators. The increased computational cost
of numerically projecting the basis functions onto the irreducible
representations of the three dimensional rotation-inversion group is the price
to pay for the increased flexibility of the basis functions. This increased
flexibility allowed us to achieve a substantial improvement for the variational
upper bound to the Pauli-allowed ground-state energy of the
Hpppee molecular ion treated as an explicit
five-particle system. We compare our pre-Born-Oppenheimer result for this
molecular ion with rovibrational results including non-adiabatic corrections.Comment: 29 pages, 3 figures, 4 table
[(CH3)3Si]14Si7O21 - ein neuer cyclischer Kieselsäuretrimethylsilylester
Durch Trimethylsilylierung des Bariumchloridsilicates 2BaO - 3BaCl2 - 2SiO2 wurde ein bisher unbekannter Kieselsäuretrimethylsilylester hergestellt, der mit Hilfe der Kapillargaschromatographie, Massenspektroskopie29Si-NMR-Spektroskopie und Dünnschichtchromatographie charakterisiert wurde. Aus den Untersuchungen folgt für den Ester die Konstitution eines Cycloheptakieselsäuretrimethylsilylesters (Tetradecakistrimethylsiloxicycloheptasiloxan) der Formel [(CH3)3Si]14Si7O21. Die Verwendung des Esters als Standardsubstanz wird diskutiert
Synthese, Aufbau und Eigenschaften käfigartiger vinyl- und allylsilylierter Kieselsäuren
Durch Umsatz des Tetramethylammoniumsilicats [N(CH3)4]8Si8O20 · 69 H2O mit Vinyldimethylchlorsilan (I) bzw. Divinyltetramethyldisiloxan oder Allydimethylchlorsilan wurden der Vinyldimethylsilylkieselsäureester [CH2CHCH2(CH3)2Si]8Si8O20 und Allyldimethylsilyl-kieselsäureester [CH2CHCH2(CH3)2Si]8Si8O20 erhalten. Mit Hilfe der Gaschromatographie, Massenspektroskopie sowie 1H-und 29Si-NMR wurden die Verbindungen charakterisiert und eine käfigartig aufgebaute Doppelvierring (D4R)-Struktur des Kieselsäuregerüsts nachgewiesen, an deren 8 terminalen O-Atomen des Kieselsäuregerüsts nachgewiesen, an deren 8 terminalen O-Atomen des Kieselsäuregerüsts Vinyldimethylsiyl- bzw. Allydimethylsilylgruppen gebunden sind. Durch Silylierung mit I und Trimethylchlorsilan sind in Abhängigkeit vom Mischungsverhältnis Vinyldimethylsilytrimethysily1-D4R-Kieselsäureester mit einer mittleren Anzahl ungesättigter Gruppen < 8 herzustellen
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Ein neues Verfahren für namensbasierte Zufallsstichproben von Migranten
The set of best methods for sampling mi- grant populations includes name-based sampling. So far this is done using either ad-hoc lists or onomastic dictionaries for the classi cation of names. This paper pro- poses a new name-based procedure, which uses a Bayes-classi er for the n-grams of the name. The new procedure is fault-tol- erant of alternate spellings, and also allows the classi cation of names that are not found in dictionaries. It was tested using the names of about 1.600 foreigners in the PASS panel. Finally, a CATI survey based on the new method in Hesse is described
Sequential decoupling of negative-energy states in Douglas-Kroll-Hess theory
Here, we review the historical development, current status, and prospects of
Douglas--Kroll--Hess theory as a quantum chemical relativistic electrons-only
theory.Comment: 15 page
Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules
We present a new class of tensor network states that are specifically
designed to capture the electron correlation of a molecule of arbitrary
structure. In this ansatz, the electronic wave function is represented by a
Complete-Graph Tensor Network (CGTN) ansatz which implements an efficient
reduction of the number of variational parameters by breaking down the
complexity of the high-dimensional coefficient tensor of a
full-configuration-interaction (FCI) wave function. We demonstrate that CGTN
states approximate ground states of molecules accurately by comparison of the
CGTN and FCI expansion coefficients. The CGTN parametrization is not biased
towards any reference configuration in contrast to many standard quantum
chemical methods. This feature allows one to obtain accurate relative energies
between CGTN states which is central to molecular physics and chemistry. We
discuss the implications for quantum chemistry and focus on the spin-state
problem. Our CGTN approach is applied to the energy splitting of states of
different spin for methylene and the strongly correlated ozone molecule at a
transition state structure. The parameters of the tensor network ansatz are
variationally optimized by means of a parallel-tempering Monte Carlo algorithm
Block-Diagonalization of Operators with Gaps, with Applications to Dirac Operators
We present new results on the block-diagonalization of Dirac operators on
three-dimensional Euclidean space with unbounded potentials. Classes of
admissible potentials include electromagnetic potentials with strong Coulomb
singularities and more general matrix-valued potentials, even non-self-adjoint
ones. For the Coulomb potential, we achieve an exact diagonalization up to
nuclear charge Z=124 and prove the convergence of the Douglas-Kroll-He\ss\
approximation up to Z=62, thus improving the upper bounds Z=93 and Z=51,
respectively, by H.\ Siedentop and E.\ Stockmeyer considerably. These results
follow from abstract theorems on perturbations of spectral subspaces of
operators with gaps, which are based on a method of H.\ Langer and C.\ Tretter
and are also of independent interest
Reliable estimation of prediction uncertainty for physico-chemical property models
The predictions of parameteric property models and their uncertainties are
sensitive to systematic errors such as inconsistent reference data, parametric
model assumptions, or inadequate computational methods. Here, we discuss the
calibration of property models in the light of bootstrapping, a sampling method
akin to Bayesian inference that can be employed for identifying systematic
errors and for reliable estimation of the prediction uncertainty. We apply
bootstrapping to assess a linear property model linking the 57Fe Moessbauer
isomer shift to the contact electron density at the iron nucleus for a diverse
set of 44 molecular iron compounds. The contact electron density is calculated
with twelve density functionals across Jacob's ladder (PWLDA, BP86, BLYP, PW91,
PBE, M06-L, TPSS, B3LYP, B3PW91, PBE0, M06, TPSSh). We provide systematic-error
diagnostics and reliable, locally resolved uncertainties for isomer-shift
predictions. Pure and hybrid density functionals yield average prediction
uncertainties of 0.06-0.08 mm/s and 0.04-0.05 mm/s, respectively, the latter
being close to the average experimental uncertainty of 0.02 mm/s. Furthermore,
we show that both model parameters and prediction uncertainty depend
significantly on the composition and number of reference data points.
Accordingly, we suggest that rankings of density functionals based on
performance measures (e.g., the coefficient of correlation, r2, or the
root-mean-square error, RMSE) should not be inferred from a single data set.
This study presents the first statistically rigorous calibration analysis for
theoretical Moessbauer spectroscopy, which is of general applicability for
physico-chemical property models and not restricted to isomer-shift
predictions. We provide the statistically meaningful reference data set MIS39
and a new calibration of the isomer shift based on the PBE0 functional.Comment: 49 pages, 9 figures, 7 table
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