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1.
Joshua Maglione 《Journal of Pure and Applied Algebra》2021,225(3):106528
Like the lower central series of a nilpotent group, filters generalize the connection between nilpotent groups and graded Lie rings. However, unlike the case with the lower central series, the associated graded Lie ring may share few features with the original group: e.g. the associated Lie ring can be trivial or arbitrarily large. We determine properties of filters such that every isomorphism between groups is induced by an isomorphism between graded Lie rings. 相似文献
2.
3.
Tomasz Przebinda 《Journal of Functional Analysis》2018,274(5):1284-1305
We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range. 相似文献
4.
5.
G. Panina 《Central European Journal of Mathematics》2003,1(2):157-168
All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible
with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples
of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual
polytope. 相似文献
6.
7.
We investigate congruence classes and direct congruence classes of m-tuples in the complex projective space ℂP
n
. For direct congruence one allows only isometries which are induced by linear (instead of semilinear) mappings. We establish
a canonical bijection between the set of direct congruence classes of m-tuples of points in ℂP
n
and the set of equivalence classes of positive semidefinite Hermitean m×m-matrices of rank at most n+1 with 1's on the diagonal. As a corollary we get that the direct congruence class of an m-tuple is uniquely determined by the direct congruence classes of all of its triangles, provided that no pair of points of
the m-tuple has distance π/2. Examples show that the situation changes drastically if one replaces direct congruence classes by
congruence classes or if distances π/2 are allowed. Finally we do the same
kind of investigation also for the complex hyperbolic space ℂH
n
. Most of the results are completely analogous, however, there are also some interesting differences.
Received: 15 January 1996 相似文献
8.
Summary. Let be a square matrix dependent on parameters and , of which we choose as the eigenvalue parameter. Many computational problems are equivalent to finding a point such that has a multiple eigenvalue at . An incomplete decomposition of a matrix dependent on several parameters is proposed. Based on the developed theory two new algorithms are
presented for computing multiple eigenvalues of with geometric multiplicity . A third algorithm is designed for the computation of multiple eigenvalues with geometric multiplicity but which also appears to have local quadratic convergence to semi-simple eigenvalues. Convergence analyses of these methods
are given. Several numerical examples are presented which illustrate the behaviour and applications of our methods.
Received December 19, 1994 / Revised version received January 18, 1996 相似文献
9.
10.
For z1,z2,z3∈Zn, the tristance d3(z1,z2,z3) is a generalization of the L1-distance on Zn to a quantity that reflects the relative dispersion of three points rather than two. A tristance anticodeAd of diameter d is a subset of Zn with the property that d3(z1,z2,z3)?d for all z1,z2,z3∈Ad. An anticode is optimal if it has the largest possible cardinality for its diameter d. We determine the cardinality and completely classify the optimal tristance anticodes in Z2 for all diameters d?1. We then generalize this result to two related distance models: a different distance structure on Z2 where d(z1,z2)=1 if z1,z2 are adjacent either horizontally, vertically, or diagonally, and the distance structure obtained when Z2 is replaced by the hexagonal lattice A2. We also investigate optimal tristance anticodes in Z3 and optimal quadristance anticodes in Z2, and provide bounds on their cardinality. We conclude with a brief discussion of the applications of our results to multi-dimensional interleaving schemes and to connectivity loci in the game of Go. 相似文献