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81.
Aleksander Simonic 《Transactions of the American Mathematical Society》1996,348(3):975-995
The aim of this work is to generalize Lomonosov's techniques in order to apply them to a wider class of not necessarily compact operators. We start by establishing a connection between the existence of invariant subspaces and density of what we define as the associated Lomonosov space in a certain function space. On a Hilbert space, approximation with Lomonosov functions results in an extended version of Burnside's Theorem. An application of this theorem to the algebra generated by an essentially self-adjoint operator yields the existence of vector states on the space of all polynomials restricted to the essential spectrum of . Finally, the invariant subspace problem for compact perturbations of self-adjoint operators acting on a real Hilbert space is translated into an extreme problem and the solution is obtained upon differentiating certain real-valued functions at their extreme.
82.
Sara C. Billey William Jockusch Richard P. Stanley 《Journal of Algebraic Combinatorics》1993,2(4):345-374
Schubert polynomials were introduced by Bernstein et al. and Demazure, and were extensively developed by Lascoux, Schützenberger, Macdonald, and others. We give an explicit combinatorial interpretation of the Schubert polynomial
in terms of the reduced decompositions of the permutation w. Using this result, a variation of Schensted's correspondence due to Edelman and Greene allows one to associate in a natural way a certain set
of tableaux with w, each tableau contributing a single term to
. This correspondence leads to many problems and conjectures, whose interrelation is investigated. In Section 2 we consider permutations with no decreasing subsequence of length three (or 321-avoiding permutations). We show for such permutations that
is a flag skew Schur function. In Section 3 we use this result to obtain some interesting properties of the rational function
, where
denotes a skew Schur function.Sara C. Billey: Supported by the National Physical Science Consortium. William Jockusch: Supported by an NSF Graduate Fellowship. Richard P. Stanley: Partially supported by NSF grants DMS-8901834 and DMS-9206374 相似文献
83.
具有良好传递性的区组设计的分类问题是组合设计研究的活跃领域.利用置换群的次轨道和典型群的子群结构,研究区传递2-(v,k,1)设计的分类.特别地,讨论了自同构群的基柱为典型单群的区传递,点本原但非旗传递的2-(v,6,1)设计.设D为一个2-(v,6,1)设计,G≤Aut(D)是区传递、点本原但非旗传递的,若v为奇数,则G的基柱Soc(G)不是有限域GF(q)上的典型单群PSpn(q). 相似文献
84.
V. A. Kyrov 《Russian Mathematics (Iz VUZ)》2008,52(6):25-36
In the theory of physical structures the classification of metric functions (both on a single set and on two ones) plays an important role. A metric function represents a two-point invariant of a certain local Lie transformation group. Moreover, one can uniquely restore this group with the help of the invariance condition. According to this theorem, in order to find all metric functions, it suffices to construct the complete classification of local Lie transformation groups. In this paper we classify Lie algebras of simply transitive local Lie groups of local transformations of a four-dimensional space, and then we define metric functions. The obtained results admit application in physics, in particular, in thermodynamics. 相似文献
85.
Dragan Marui
《Journal of Graph Theory》2000,35(2):152-160
An infinite family of cubic edge‐transitive but not vertex‐transitive graphs with edge stabilizer isomorphic to ℤ2 is constructed. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 152–160, 2000 相似文献
86.
Charles Garnet Cox 《代数通讯》2019,47(3):978-989
87.
Josephine Emms 《Discrete Mathematics》2009,309(13):4475-2036
We construct continuum many non-isomorphic countable digraphs which are highly arc transitive, have finite out-valency and infinite in-valency, and whose automorphism groups are primitive. 相似文献
88.
For a complex semisimple Lie group and a real form we define a Poisson structure on the variety of Borel subgroups of with the property that all -orbits in as well as all Bruhat cells (for a suitable choice of a Borel subgroup of ) are Poisson submanifolds. In particular, we show that every non-empty intersection of a -orbit and a Bruhat cell is a regular Poisson manifold, and we compute the dimension of its symplectic leaves.
89.
We present a new family of locally geodesic transitive graphs with arbitrarily large diameter and valencies, containing a particular case to be geodesic transitive. We also prove that it is a unique family in some generalised family of graphs. 相似文献
90.
In this paper, we classify finite permutation groups with a transitive abelian subgroup that are almost simple, quasiprimitive and innately transitive, which extend the results of Li and Praeger that is on finite permutation groups with a transitive cyclic subgroup. 相似文献