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131.
We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg
then the state complexity of
is equal to the Wolf bound. For deg
, we use Clifford's theorem to give a simple lower bound on the state complexity of
. We then derive two further lower bounds on the state space dimensions of
in terms of the gonality sequence of
. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of
and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes. 相似文献
132.
This paper shows that for unitary Hessenberg matrices the algorithm, with (an exceptional initial-value modification of) the Wilkinson shift, gives global convergence; moreover, the asymptotic rate of convergence is at least cubic, higher than that which can be shown to be quadratic only for Hermitian tridiagonal matrices, under no further assumption. A general mixed shift strategy with global convergence and cubic rates is also presented.
133.
Kh. D. Ikramov 《Mathematical Notes》2002,71(3-4):500-504
Solvability conditions are examined for the matrix equation
, which cannot be found in the well-known reference books on matrix theory. Methods for constructing solutions to this equation are indicated. 相似文献
134.
The semi-infinite Toda lattice is the system of differential equations d
n
(t)/dt =
n
(t)(b
n+1(t) – b
n
(t)), db
n
(t)/dt = 2(
n
2(t) –
n–1
2(t)), n = 1, 2, ..., t > 0. The solution of this system (if it exists) is a pair of real sequences
n
(t), b
n
(t) which satisfy the conditions
n
(0) =
n
,, b
n
(0) = b
n
, where
n
> 0 and b
n
are given sequences of real numbers. It is well known that the system has a unique solution provided that both sequences
n
and b
n
are bounded. When at least one of the known sequences
n
and b
n
is unbounded, many difficulties arise and, to the best of our knowledge, there are few results concerning the solution of the system. In this letter we find a class of unbounded sequences
n
and b
n
such that the system has a unique solution. The results are illustrated with a typical example where the sequences
i
(t), b
i
(t), i = 1, 2, ... can be exactly determined. The connection of the Toda lattice with the semi-infinite differential-difference equation d2/dt
2 log h
n
= h
n+1 + h
n–1 – 2h
n
, n = 1, 2, ... is also discussed and the above results are translated to analogous results for the last equation. 相似文献
135.
For the unitary ensembles of N×N Hermitian matrices associated with a weight function w there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For the orthogonal and symplectic ensembles of Hermitian matrices there are 2×2 matrix kernels, usually constructed using skew-orthogonal polynomials, which play an analogous role. These matrix kernels are determined by their upper left-hand entries. We derive formulas expressing these entries in terms of the scalar kernel for the corresponding unitary ensembles. We also show that whenever w/w is a rational function the entries are equal to the scalar kernel plus some extra terms whose number equals the order of w/w. General formulas are obtained for these extra terms. We do not use skew-orthogonal polynomials in the derivations 相似文献
136.
We give a closed formula for topological K-theory of the homogeneous space N/, where is the standard integer lattice in the simply connected Heisenberg Lie group N of dimension 2n+1, n
. The main tools in our calculations are obtained by computing diagonal forms for certain incidence matrices that arise naturally in combinatorics. 相似文献
137.
广义对角占优阵的一个等价条件 总被引:2,自引:0,他引:2
郑秉文 《纯粹数学与应用数学》1999,15(2):37-41
给出了实方阵为广义对角占优阵的充要条件,同时给出了判断广义对角占优阵可靠,可行,较简单方法。 相似文献
138.
TZEKIS P.; KARAMPETAKIS N. P.; VARDULAKIS A. I. 《IMA Journal of Mathematical Control and Information》1999,16(4):391-401
The main purpose of this paper is to determine two new algorithmsfor the division of the polynomial matrix B(s) R[s]pxq by A(s) R[s]pxp (a) based on the Laurent matrix expansion at s = =of the inverse of A(s), i.e. A(s)1, and (b) in a waysimilar to the one presented by Gantmacher (1959). 相似文献
139.
Irregular sampling, Toeplitz matrices, and the approximation of entire functions of exponential type
In many applications one seeks to recover an entire function of exponential type from its non-uniformly spaced samples. Whereas the mathematical theory usually addresses the question of when such a function in can be recovered, numerical methods operate with a finite-dimensional model. The numerical reconstruction or approximation of the original function amounts to the solution of a large linear system. We show that the solutions of a particularly efficient discrete model in which the data are fit by trigonometric polynomials converge to the solution of the original infinite-dimensional reconstruction problem. This legitimatizes the numerical computations and explains why the algorithms employed produce reasonable results. The main mathematical result is a new type of approximation theorem for entire functions of exponential type from a finite number of values. From another point of view our approach provides a new method for proving sampling theorems.
140.
Klaus Bö hmer Willy Govaerts Vladimí r Janovský . 《Mathematics of Computation》1999,68(227):1097-1108
A numerical tool for the detection of degenerated symmetry breaking bifurcation points is presented. The degeneracies are classified and numerically processed on -D restrictions of the bifurcation equation. The test functions that characterise each of the equivalence classes are constructed by means of an equivariant numerical version of the Liapunov-Schmidt reduction. The classification supplies limited qualitative information concerning the imperfect bifurcation diagrams of the detected bifurcation points.