Search results for "rex"
showing 10 items of 701 documents
A counterexample to Feit's Problem VIII on decomposition numbers
2016
We find a counterexample to Feit's Problem VIII on the bound of decomposition numbers. This also answers a question raised by T. Holm and W. Willems.
Poincaré Week in Göttingen, 22–28 April 1909
2018
When Paul Wolfskehl died in 1906, his will established a prize for the first mathematician who could supply a proof of Fermat’s Last Theorem, or give a counterexample refuting it. The interest from this prize money was later used to bring world-renowned mathematicians to Gottingen to deliver a series of lectures. Hilbert was apparently very pleased with this arrangement, and once jested that the only thing that kept him from proving Fermat’s famous conjecture was the thought of killing the goose that laid these golden eggs.
Counterexamples to the Kneser conjecture in dimension four.
1995
We construct a connected closed orientable smooth four-manifold whose fundamental group is the free product of two non-trivial groups such that it is not homotopy equivalent toM 0#M 1 unlessM 0 orM 1 is homeomorphic toS 4. LetN be the nucleus of the minimal elliptic Enrique surfaceV 1(2, 2) and putM=N∪ ∂NN. The fundamental group ofM splits as ℤ/2 * ℤ/2. We prove thatM#k(S 2×S2) is diffeomorphic toM 0#M 1 for non-simply connected closed smooth four-manifoldsM 0 andM 1 if and only ifk≥8. On the other hand we show thatM is homeomorphic toM 0#M 1 for closed topological four-manifoldsM 0 andM 1 withπ 1(Mi)=ℤ/2.
Historical Notes on Star Geometry in Mathematics, Art and Nature
2018
Gamma: “I can. Look at this Counterexample 3: a star-polyhedron I shall call it urchin. This consists of 12 star-pentagons. It has 12 vertices, 30 edges, and 12 pentagonal faces-you may check it if you like by counting. Thus the Descartes-Euler thesis is not true at all, since for this polyhedron \(V - E + F = - 6\)”. Delta: “Why do you think that your ‘urchin’ is a polyhedron?” Gamma: “Do you not see? This is a polyhedron, whose faces are the twelve star-pentagons”. Delta: “But then you do not even know what a polygon is! A star-pentagon is certainly not a polygon!”
Fronteras por definir, descontento creciente, alianzas inestables y amenazas externas: la Unión Europea y su tormenta perfecta
2018
espanolLa Union Europea se halla en una crisis existencial tan evidente que incluso politicos y analistas con antecedentes ideologicos diametralmente opues-tos han acabado coincidiendo en su diagnostico, y en la necesidad urgente de una terapia de choque que detenga lo que parece una carrera hacia la destruccion del proyecto europeo. El proposito del presente ensayo es pasar revista —aun al precio de tener que ser extraordinariamente sintetico en su abordaje— a los problemas que han sumido a la Union Europea en la mas grave crisis de su ya larga historia. Problemas que en todo caso son susceptibles de agruparse en cuatro grandes rubros: los que han ralentizado y hasta invertido el proceso d…
Defect-Induced Orbital Polarization and Collapse of Orbital Order in Doped Vanadium Perovskites
2018
We explore mechanisms of orbital order decay in doped Mott insulators $R_{1-x}$(Sr,Ca)$_x$VO$_3$ ($R=\,$Pr,Y,La) caused by charged (Sr,Ca) defects. Our unrestricted Hartree-Fock analysis focuses on the combined effect of random, charged impurities and associated doped holes up to $x=0.5$. The study is based on a generalized multi-band Hubbard model for the relevant vanadium $t_{2g}$ electrons, and includes the long-range (i) Coulomb potentials of defects and (ii) electron-electron interactions. We show that the rotation of occupied $t_{2g}$ orbitals, induced by the electric field of defects, is a very efficient perturbation that largely controls the suppression of orbital order in these com…
Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
2007
Quantum mechanical superexchange interactions form the basis of quantum magnetism in strongly correlated electronic media. We report on the direct measurement of superexchange interactions with ultracold atoms in optical lattices. After preparing a spin-mixture of ultracold atoms in an antiferromagnetically ordered state, we measure a coherent superexchange-mediated spin dynamics with coupling energies from 5 Hz up to 1 kHz. By dynamically modifying the potential bias between neighboring lattice sites, the magnitude and sign of the superexchange interaction can be controlled, thus allowing the system to be switched between antiferromagnetic or ferromagnetic spin interactions. We compare our…
Mais qui est Boris Johnson ?
2019
International audience
From soft to hard Brexit: UKIP's not so invisible influence on the Eurosceptic radicalisation of the Conservative Party since 2015
2018
International audience
Inducible Genetic Code Expansion in Eukaryotes
2020
Abstract Genetic code expansion (GCE) is a versatile tool to site‐specifically incorporate a noncanonical amino acid (ncAA) into a protein, for example, to perform fluorescent labeling inside living cells. To this end, an orthogonal aminoacyl‐tRNA‐synthetase/tRNA (RS/tRNA) pair is used to insert the ncAA in response to an amber stop codon in the protein of interest. One of the drawbacks of this system is that, in order to achieve maximum efficiency, high levels of the orthogonal tRNA are required, and this could interfere with host cell functionality. To minimize the adverse effects on the host, we have developed an inducible GCE system that enables us to switch on tRNA or RS expression whe…