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31.
S. Ya. Grinshpon 《代数通讯》2013,41(11):4273-4282
We study primary groups containing proper fully invariant subgroups isomorphie to the group. The admissable sequence of Ulm–Kaplansky invariants for primary groups is introduced. Using these sequences, If-groups are described in the classes of seperable and periodically complete groups. 相似文献
32.
Link-homotopy and self Δ-equivalence are equivalence relations on links. It was shown by J. Milnor (resp. the last author) that Milnor invariants determine whether or not a link is link-homotopic (resp. self Δ-equivalent) to a trivial link. We study link-homotopy and self Δ-equivalence on a certain component of a link with fixing the other components, in other words, homotopy and Δ-equivalence of knots in the complement of a certain link. We show that Milnor invariants determine whether a knot in the complement of a trivial link is null-homotopic, and give a sufficient condition for such a knot to be Δ-equivalent to the trivial knot. We also give a sufficient condition for knots in the complements of the trivial knot to be equivalent up to Δ-equivalence and concordance. 相似文献
33.
A woven fabric can be described as a surface made of two families of fibers: in this work we study how the geometry of the
weave pattern affects the symmetry properties of the elastic energy of the surface. Four basic symmetry classes of weave patterns
are possible, depending on the angle between the fibers and their material properties. The properties of the pattern determine
the material symmetry group of the network, under which the elastic energy is invariant. We derive representations for the
energy of a woven fabric that are invariant under the symmetry group of the network, and discuss the relation of these invariants
with the curvature and twist of the fibers.
相似文献
34.
In this article, we begin a systematic study of conformal properties of codimension-1 foliations. We first define and study
local conformal invariants. A case of particular interest is that of harmonic foliations of the plane. Then we study existence
of totally umbilical and “Dupin” foliations on compact 3-manifolds of constant curvature.
相似文献
35.
Jack M. Shapiro 《代数通讯》2013,41(6):1879-1898
For a field F with trivial involution we have the Karoubi L-groups ±1Ln(F). For 0≤n≤2 these groups are intimately related to subgroups of the classical Witt ring of quadratic forms. -1L 2(F) also has a presentation by symbols due to Matsumoto. In terms of this data we make explicit calculations for two cup product maps that appear in the L-theory of fields. 相似文献
36.
J. Carlos Díaz-Ramos Eduardo García-Río Luis Hervella 《Annali di Matematica Pura ed Applicata》2005,184(1):115-130
Total scalar curvatures of geodesic spheres obtained by integrating the second-order scalar invariants of the curvature tensor are investigated. The first terms in their power-series expansions are derived and these results are used to characterize the two-point homogeneous spaces among Riemannian manifolds with adapted holonomy. Dedicated to Professor L. VanheckeMathematics Subject Classification (2000) 53C25, 53C30 相似文献
37.
38.
Spyros Alexakis 《Advances in Mathematics》2010,225(2):515-597
This is the fourth in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of “global conformal invariants”; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed as a linear combination of a local conformal invariant, a divergence and of the Chern-Gauss-Bonnet integrand.The present paper lays out the second half of this entire work: The second half proves certain purely algebraic statements regarding local Riemannian invariants; these were used extensively in the first two papers in this series, see Alexakis (2007, 2009) [2] and [3]. These results may be of independent interest, applicable to related problems. 相似文献
39.
Maxim Kontsevich 《Compositio Mathematica》1999,115(1):115-127
We show that recently constructed invariants of 3-dimensional manifolds and of hyperkähler manifolds (L. Rozansky and E. witten) come from characteristic classes of foliations and from Gelfand-fuks cohomology. 相似文献
40.
Héctor Moya-Cessa Francisco Soto-Eguibar José M. Vargas-Martínez Raúl Juárez-Amaro Arturo Zúñiga-Segundo 《Physics Reports》2012
Trapped ions are considered one of the best candidates to perform quantum information processing. By interacting them with laser beams they are, somehow, easy to manipulate, which makes them an excellent choice for the production of nonclassical states of their vibrational motion, the reconstruction of quasiprobability distribution functions, the production of quantum gates, etc. However, most of these effects have been produced in the so-called low intensity regime, this is, when the Rabi frequency (laser intensity) is much smaller than the trap frequency. Because of the possibility to produce faster quantum gates in other regimes it is of importance to study this system in a more complete manner, which is the motivation for this contribution. We start by studying the way ions are trapped in Paul traps and review the basic mechanisms of trapping. Then we show how the problem may be completely solved for trapping states; i.e., we find (exact) eigenstates of the full Hamiltonian. We show how, in the low intensity regime, Jaynes–Cummings and anti-Jaynes–Cummings interactions may be obtained, without using the rotating wave approximation and analyze the medium and high intensity regimes where dispersive Hamiltonians are produced. The traditional approach (low intensity regime) is also studied and used for the generation of non-classical states of the vibrational wavefunction. In particular, we show how to add and subtract vibrational quanta to an initial state, how to produce specific superpositions of number states and how to generate NOON states for the two-dimensional vibration of the ion. It is also shown how squeezing may be measured. The time dependent problem is studied by using Lewis–Ermakov methods. We give a solution to the problem when the time dependence of the trap is considered and also analyze a specific (artificial) time dependence that produces squeezing of the initial vibrational wave function. A way to mimic the ion–laser interaction via classical optics is also introduced. 相似文献