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1.
V. B. Khazanov 《Journal of Mathematical Sciences》2007,141(6):1690-1700
An approach to solving spectral problems for multiparameter polynomial matrices based on passing to accompanying pencils of
matrices is described. Also reduction of spectral problems for multiparameter pencils of complex matrices to the corresponding
real problems is considered. Bibliography: 6 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2006, pp. 212–231. 相似文献
2.
3.
Sofiya Ostrovska 《Numerical Algorithms》2007,44(1):69-82
Since in the case q > 1, q-Bernstein polynomials are not positive linear operators on C[0,1], the study of their approximation properties is essentially more difficult than that for 0<q<1. Despite the intensive research conducted in the area lately, the problem of describing the class of functions in C[0,1] uniformly approximated by their q-Bernstein polynomials (q > 1) remains open. It is known that the approximation occurs for functions admit ting an analytic continuation into a disc
{z:|z| < R}, R > 1. For functions without such an assumption, no general results on approximation are available. In this paper, it is shown
that the function f(x) = ln (x + a), a > 0, is uniformly approximated by its q-Bernstein polynomials (q > 1) on the interval [0,1] if and only if a ≥ 1.
相似文献
4.
V. N. Kublanovskaya 《Journal of Mathematical Sciences》2006,132(2):214-223
The paper continues the investigation of methods for factorizing q-parameter polynomial matrices and considers their applications
to solving multiparameter problems of algebra. An extension of the AB-algorithm, suggested earlier as a method for solving
spectral problems for matrix pencils of the form A - λB, to the case of q-parameter (q ≥ 1) polynomial matrices of full rank
is proposed. In accordance with the AB-algorithm, a finite sequence of q-parameter polynomial matrices such that every subsequent
matrix provides a basis of the null-space of polynomial solutions of its transposed predecessor is constructed. A certain
rule for selecting specific basis matrices is described. Applications of the AB-algorithm to computing complete polynomials
of a q-parameter polynomial matrix and exhausting them from the regular spectrum of the matrix, to constructing irreducible
factorizations of rational matrices satisfying certain assumptions, and to computing “free” bases of the null-spaces of polynomial
solutions of an arbitrary q-parameter polynomial matrix are considered. Bibliography: 7 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 309, 2004, pp. 127–143. 相似文献
5.
The paper continues the series of papers devoted to surveying and developing methods for solving algebraic problems for two-parameter
polynomial and rational matrices of general form. It considers linearization methods, which allow one to reduce the problem
of solving an equation F(λ, μ)x = 0 with a polynomial two-parameter matrix F(λ, μ) to solving an equation of the form D(λ,
μ)y = 0, where D(λ, μ) = A(μ)-λB(μ) is a pencil of polynomial matrices. Consistent pencils and their application to solving
spectral problems for the matrix F(λ, μ) are discussed. The notion of reducing subspace is generalized to the case of a pencil
of polynomial matrices. An algorithm for transforming a general pencil of polynomial matrices to a quasitriangular pencil
is suggested. For a pencil with multiple eigenvalues, algorithms for computing the Jordan chains of vectors are developed.
Bibliography: 8 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 359, 2008, pp. 166–207. 相似文献
6.
V. N. Kublanovskaya 《Journal of Mathematical Sciences》2010,165(5):562-573
This paper continues the series of publications devoted to surveying and developing methods for solving the following problems
for a two-parameter matrix F (λ, μ) of general form: exhausting points of the mixed regular spectrum of F (λ, μ); performing operations on polynomials in two variables (computing the GCD and LCM of a few polynomials, division of
polynomials, and factorization); computing a minimal basis of the null-space of polynomial solutions of the matrix F (λ, μ) and separation of its regular kernel; inversion and pseudo in version of polynomial and rational matrices in two variables,
and solution of systems of nonlinear algebraic equations in two unknowns. Most of the methods suggested are based on rank
factorizations of a two-parameter polynomial matrix and on the method of hereditary pencils. Bibliography: 8 titles. 相似文献
7.
Thomas P. Wakefield 《Algebras and Representation Theory》2011,14(4):609-623
Let G be a finite group and cd(G) be the set of irreducible character degrees of G. Bertram Huppert conjectured that if H is a finite nonabelian simple group such that cd(G) = cd(H), then G ≅ H×A, where A is an abelian group. In this paper, we verify the conjecture for the twisted Ree groups 2
G
2(q
2) for q
2 = 32m + 1, m ≥ 1. The argument involves verifying five steps outlined by Huppert in his arguments establishing his conjecture for many
of the nonabelian simple groups. 相似文献
8.
Zoltán M. Balogh Alexandre Engulatov Lars Hunziker Outi Elina Maasalo 《Potential Analysis》2012,36(2):317-337
We study the connection between the p-Talagrand inequality and the q-logarithmic Sololev inequality for conjugate exponents p ≥ 2, q ≤ 2 in proper geodesic metric spaces. By means of a general Hamilton–Jacobi semigroup we prove that these are equivalent,
and moreover equivalent to the hypercontractivity of the Hamilton–Jacobi semigroup. Our results generalize those of Lott and
Villani. They can be applied to deduce the p-Talagrand inequality in the sub-Riemannian setting of the Heisenberg group. 相似文献
9.
M. H. M. Rashid 《Ukrainian Mathematical Journal》2012,63(8):1256-1267
If T (or T*) is an algebraically wF(p, r, q) operator with p, r > 0 and q ≥ 1 acting in an infinite-dimensional separable Hilbert space, then we prove that Weyl’s theorem holds for f(T) for any f ∈ Hol(σ(T)), where Hol(σ(T)) is the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T* is a wF(p, r, q) operator with p, r > 0 and q ≥ 1, then the a-Weyl’s theorem holds for f(T). In addition, if T (or T*) is an algebraically wF(p, r, q) operator with p, r > 0 and q ≥ 1, then we establish the spectral mapping theorems for the Weyl spectrum and for the essential approximate point spectrum
of T for any f ∈ Hol(σ(T)), respectively. Finally, we examine the stability of Weyl’s theorem and the a-Weyl’s theorem under commutative perturbations
by finite-rank operators. 相似文献
10.
We study the “q-commutative” power series ring R: = k
q
[[x
1,...,x
n
]], defined by the relations x
i
x
j
= q
ij
x
j
x
i
, for mulitiplicatively antisymmetric scalars q
ij
in a field k. Our results provide a detailed account of prime ideal structure for a class of noncommutative, complete, local, noetherian
domains having arbitrarily high (but finite) Krull, global, and classical Krull dimension. In particular, we prove that the
prime spectrum of R is normally separated and is finitely stratified by commutative noetherian spectra. Combining this normal separation with
results of Chan, Wu, Yekutieli, and Zhang, we are able to conclude that R is catenary. Following the approach of Brown and Goodearl, we also show that links between prime ideals are provided by canonical
automorphisms. Moreover, for sufficiently generic q
ij
, we find that R has only finitely many prime ideals and is a UFD (in the sense of Chatters). 相似文献
11.
Olivier Teulié 《Monatshefte für Mathematik》2002,116(3):313-324
In this paper, we prove that if β1,…, β n are p-adic numbers belonging to an algebraic number field K of degree n + 1 over Q such that 1, β1,…,β n are linearly independent over Z, there exist infinitely many sets of integers (q 0,…, q n ), with q 0 ≠ 0 and
with H = H(q 0,…, q n ). Therefore, these numbers satisfy the p-adic Littlewood conjecture. To obtain this result, we are using, as in the real case by Peck [2], the structure of a group of units of K. The essential argument to obtain the exponent 1/(n-1) (the same as in the real case) is the use of the p-adic logarithm. We also prove that with the same hypothesis, the inequalities
have no integer solution (q 0,…, q n ) with q 0 ≠ 0, if ɛ > 0 is small enough. 相似文献
12.
Methods and algorithms for the solution of spectral problems of singular and regular pencils D(λ, μ)=A(μ)-λB(μ) of polynomial
matrices A(μ) and B(μ) are suggested (the separation of continuous and discrete spectra, the computation of points of a discrete
spectrum with the corresponding, Jordan chains, the computation of minimal indices and a minimal basis of polynomial solutions,
the computation of the determinant of a regular pencil). Bibliography: 13 titles.
Translated by V. N. Kublanovskaya
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 202, 1992, pp. 26–70 相似文献
13.
V. B. Khazanov 《Journal of Mathematical Sciences》2005,127(3):2033-2050
Methods for solving the partial eigenproblem for multiparameter regular pencils of real matrices, which allow one to improve given approximations of an eigenvector and the associated point of the spectrum (both finite and infinite) are suggested. Ways of extending the methods to complex matrices, polynomial matrices, and coupled multiparameter problems are indicated. Bibliography: 10 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 296, 2003, pp. 139–168. 相似文献
14.
Agarwal and Bressoud (Pacific J. Math.
136(2) (1989) 209–228) defined a class of weighted lattice paths and interpreted several q-series combinatorially. Using the same class of lattice paths, Agarwal (Utilitas Math.
53 (1998) 71–80; ARS Combinatoria
76 (2005) 151–160) provided combinatorial interpretations for several more q-series. In this paper, a new class of weighted lattice paths, which we call associated lattice paths is introduced. It is
shown that these new lattice paths can also be used for giving combinatorial meaning to certain q-series. However, the main advantage of our associated lattice paths is that they provide a graphical representation for partitions
with n + t copies of n introduced and studied by Agarwal (Partitions with n copies of n, Lecture Notes in Math., No. 1234 (Berlin/New York: Springer-Verlag) (1985) 1–4) and Agarwal and Andrews (J. Combin. Theory
A45(1) (1987) 40–49). 相似文献
15.
Peter A. Lesky 《Monatshefte für Mathematik》2001,132(2):123-140
The explicit form and the three term recurrance relation for all the polynomial solutions in x and q
−x
from q-operator equations of second order are given. The known 17 q-orthogonal polynomial systems are special cases of 7 comprehensive q-systems.
(Eingegangen 27. M?rz 2000; in revidierter Fassung 2. November 2000) 相似文献
16.
A classical Rayleigh-quotient iterative algorithm (known as “broken iteration”) for finding eigenvalues and eigenvectors is
applied to semisimple regular matrix pencils A − λB. It is proved that cubic convergence is attained for eigenvalues and superlinear convergence of order three for eigenvectors.
Also, each eigenvalue has a local basin of attraction. A closely related Newton algorithm is examined. Numerical examples
are included.
Dedicated to the memory of Gene H. Golub. 相似文献
17.
Thomas P. Wakefield 《Algebras and Representation Theory》2012,15(3):427-448
Let G denote a finite group and cd (G) the set of irreducible character degrees of G. Bertram Huppert conjectured that if H is a finite nonabelian simple group such that cd (G) = cd (H), then G ≅ H × A, where A is an abelian group. Huppert verified the conjecture for PSp4(q) when q = 3, 4, 5, or 7. In this paper, we extend Huppert’s results and verify the conjecture for PSp4(q) for all q. This demonstrates progress toward the goal of verifying the conjecture for all nonabelian simple groups of Lie type of rank
two. 相似文献
18.
Gérard Meurant 《Numerical Algorithms》2012,60(2):193-204
We describe algorithms to compute isotropic vectors for matrices with real or complex entries. These are unit vectors b satisfying b
*
Ab = 0. For real matrices the algorithm uses only the eigenvectors of the symmetric part corresponding to the extreme eigenvalues.
For complex matrices, we first use the eigenvalues and eigenvectors of the Hermitian matrix K = (A − A
*)/2i. This works in many cases. In case of failure we use the Hermitian part H or a combination of eigenvectors of H and K. We give some numerical experiments comparing our algorithms with those proposed by R. Carden and C. Chorianopoulos, P. Psarrakos
and F. Uhlig. 相似文献
19.
G. A. Tolstikhina 《Journal of Mathematical Sciences》2011,177(4):623-632
In this paper, we present the main results of the study of multidimensional three-websW(p, q, r) obtained by the method of external forms and moving Cartan frame. The method was developed by the Russian mathematicians
S. P. Finikov, G. F. Laptev, and A. M. Vasiliev, while fundamentals of differential-geometric (p, q, r)-webs theory were described by M. A. Akivis and V. V. Goldberg. Investigation of (p, q, r)-webs, including algebraic and geometric theory aspects, has been continued in our papers, in particular, we found the structure
equations of a three-web W(p, q, r), where p = λl, q = λm, and r = λ(l + m − 1). For such webs, we define the notion of a generalized Reidemeister configuration and proved that a three-web W(λl, λm, λ(l + m − 1)), on which all sufficiently small generalized Reidemeister configurations are closed, is generated by a λ-dimensional Lie group G. The structure equations of the web are connected with the Maurer–Cartan equations of the group G. We define generalized Reidemeister and Bol configurations for three-webs W(p, q, q). It is proved that a web W(p, q, q) on which generalized Reidemeister or Bol configurations are closed is generated, respectively, by the action of a local
smooth q-parametric Lie group or a Bol quasigroup on a smooth p-dimensional manifold. For such webs, the structure equations are found and their differential-geometric properties are studied. 相似文献
20.
The two-level local projection stabilization is considered as a one-level approach in which the enrichments on each element
are piecewise polynomial functions. The dimension of the enrichment space can be significantly reduced without losing the
convergence order. On triangular meshes, for example, using continuous piecewise polynomials of degree r ≥ 1, only 2r − 1 functions per macro-cell are needed for the enrichment compared to r
2 in the two-level approach. In case of the Stokes problem r − 1 functions per macro-cell are already sufficient to guarantee stability and to preserve convergence order. On quadrilateral
meshes the corresponding reduction rates are even higher. We give examples of “reduced” two-level approaches and study how
the constant in the local inf-sup condition for the one-level and different two-level approaches, respectively, depends on
the polynomial degree r. 相似文献