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81.
82.
Linus Kramer 《Advances in Mathematics》2005,193(1):142-173
Let G be a connected semisimple Lie group with at least one absolutely simple factor S such that and let Γ be a uniform lattice in G.
- (a)
- If CH holds, then Γ has a unique asymptotic cone up to homeomorphism.
- (b)
- If CH fails, then Γ has 22ω asymptotic cones up to homeomorphism.
83.
F. Mach P. Lederle A. Suchier W. R. Austin C. Ahrens W. E. Tischtschenko M. M. Raines K. Scharrer N. v. Bittera L. Dwořak Th. Dunkel N. Blome A. Travers Bauer K. Bamberg J. D'Ans F. Pohle W. Schuppe R. Dubrisay C. C. Howes C. B. Jacob F. Scheffer 《Analytical and bioanalytical chemistry》1935,102(5-6):222-235
84.
Theorem A:If ℬ is an infinite Moufang polygon of finite Morley rank, then ℬ is either the projective plane, the symplectic quadrangle,
or the split Cayley hexagon over some algebraically closed field. In particular, ℬ is an algebraic polygon.
It follows that any infinite simple group of finite Morley rank with a spherical MoufangBN-pair of Tits rank 2 is eitherPSL
3(K),PSp
4(K) orG
2(K) for some algebraically closed fieldK.
Spherical irreducible buildings of Tits rank ≥ 3 are uniquely determined by their rank 2 residues (i.e. polygons). Using Theorem
A we show
Theorem B:If G is an infinite simple group of finite Morley rank with a spherical Moufang BN-pair of Tits rank ≥ 2, then G is (interpretably)
isomorphic to a simple algebraic group over an algebraically closed field.
Theorem C:Let K be an infinite field, and let G(K) denote the group of K-rational points of an isotropic adjoint absolutely simple K-algebraic
group G of K-rank ≥ 2. Then G(K) has finite Morley rank if and only if the field K is algebraically closed.
We also obtain a result aboutBN-pairs in splitK-algebraic groups: such aBN-pair always contains the root groups. Furthermore, we give a proof that the sets of points, lines and flags of any ℵ1-categorical polygon have Morley degree 1.
Partially sponsored by the Edmund Landau Center for Research in Mathematical Analysis, supported by the Minerva Foundation
(Germany).
Supported by the Minerva Foundation (Germany).
Research Director at the Fund for Scientific Research-Flanders (Belgium). 相似文献
85.
Elias J. Corey Guanglin Luo Linus Shouzhong Lin 《Angewandte Chemie (International ed. in English)》1998,37(8):1126-1128
Coupling between a sulfone and an acylsilane fragment (see below) constitutes the first step in the exceptionally short total syntheses of two chiral hexacyclic hydrocarbons isolated from Eocene Messel shale (Germany). Like the first step, subsequent steps also employ a powerful synthetic tactic: polycyclization of a specially constructed chiral, multiply unsaturated oxirane. TBS=tBuMe2Si. 相似文献
86.
87.
88.
We prove a decomposition result for a group G acting strongly transitively on the Tits boundary of a Euclidean building. As an application we provide a local to global result for discrete Euclidean buildings, which generalizes results in the locally compact case by Caprace–Ciobotaru and Burger–Mozes. Let X be a Euclidean building without cone factors. If a group G of automorphisms of X acts strongly transitively on the spherical building at infinity ?X, then the G-stabilizer of every affine apartment in X contains all reflections along thick walls. In particular G acts strongly transitively on X if X is simplicial and thick. 相似文献
89.
Linus Scholz Johannes Tölle Johannes Neugebauer 《International journal of quantum chemistry》2020,120(21):e26213
We analyze the ability of subsystem time-dependent density-functional theory (sTDDFT) to describe environmental response effects. To this end, we utilize the recently proposed “exact” version of sTDDFT relying on projection-based embedding (PbE), which so far was applied only for the special case of two subsystems. We confirm that PbE-sTDDFT in combination with supersystem bases yields results equivalent to those of supermolecular TDDFT calculations for systems solvated by many solvent molecules, using the previously studied system of methylene-cyclopropene⋯(H2O)17 as an example. By means of this exact reference embedding framework, we are able to disentangle solvent effects introduced in terms of the embedding potential from those caused by solvent response couplings, both for the PbE variant and for sTDDFT with approximate non-additive kinetic energy functionals. Furthermore, we show that the use of a monomer basis introduces significant errors for the environmental response contribution. Employing a virtual-orbital localization strategy on top of PbE-sTDDFT, we can also directly assess the impact of inter-subsystem charge-transfer excitations on the entire solvent effect, which turn out to play a significant role for the environmental response. Finally, we analyze the response effects introduced by the individual solvent molecules and their interdependence, and show that a simple, pair-wise additive correction for solvent response yields excellent results in the present example. 相似文献
90.
Ping Liu Thomas J. Lanza Jr.James P. Jewell Carrie P. JonesWilliam K. Hagmann Linus S. Lin 《Tetrahedron letters》2003,44(49):8869-8871
A highly active catalyst system for the heteroarylation of acetone has been identified. The coupling between the in situ generated tributyltin enolate of acetone and a variety of heteroaromatic bromides, chlorides, and triflates in the presence of this catalyst system provided arylacetones in good yields. 相似文献