共查询到20条相似文献,搜索用时 15 毫秒
1.
Toshiyasu Arai 《Archive for Mathematical Logic》2000,39(5):353-391
In this paper we introduce a recursive notation system of ordinals. An element of the notation system is called an ordinal diagram following G. Takeuti [25]. The system is designed for proof theoretic study of theories of recursively Mahlo universes. We
show that for each in
KPM proves that the initial segment of determined by is a well ordering. Proof theoretic study for such theories will be reported in [9].
Received: 13 January, 1998 相似文献
2.
Arthur W. Apter 《Archive for Mathematical Logic》2000,39(3):209-211
We give a new proof using iterated Prikry forcing of Magidor's theorem that it is consistent to assume that the least strongly
compact cardinal is the least supercompact cardinal.
Received: 8 December 1997 / Revised version: 12 November 1998 相似文献
3.
Paul Corazza 《Archive for Mathematical Logic》2000,39(3):219-226
The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended language , and that asserts the existence of a nontrivial elementary embedding . The well-known inconsistency proofs are avoided by omitting from the schema all instances of Replacement for j-formulas. We show that the theory ZFC + V = HOD + WA is consistent relative to the existence of an embedding. This answers a question about the existence of Laver sequences for regular classes of set embeddings: Assuming there is an -embedding, there is a transitive model of ZFC +WA + “there is a regular class of embeddings that admits no Laver sequence.”
Received: 7 July 1998 / Revised version: 5 November 1998 相似文献
4.
We shall give a direct proof of the independence result of a Buchholz style-Hydra Game on labeled finite trees. We shall
show that Takeuti-Arai's cut-elimination procedure of and of the iterated inductive definition systems can be directly expressed by the reduction rules of Buchholz's Hydra Game.
As a direct corollary the independence result of the Hydra Game follows.
Received: August 23, 1994 / Revised: July 24, 1995 and May 9, 1996 相似文献
5.
Timothy J. Carlson 《Archive for Mathematical Logic》1999,38(7):449-460
We will introduce a partial ordering on the class of ordinals which will serve as a foundation for an approach to ordinal notations for formal systems of set
theory and second-order arithmetic. In this paper we use to provide a new characterization of the ubiquitous ordinal .
Received: 18 August 1997 相似文献
6.
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
7.
Alexander N. Malyshev 《Numerische Mathematik》1999,83(3):443-454
Summary. We prove that the 2-norm distance from an matrix A to the matrices that have a multiple eigenvalue is equal to where the singular values are ordered nonincreasingly. Therefore, the 2-norm distance from A to the set of matrices with multiple eigenvalues is
Received February 19, 1998 / Revised version received July 15, 1998 / Published online: July 7, 1999 相似文献
8.
Summary.
In an abstract framework we present a formalism which
specifies the notions of consistency and stability of
Petrov-Galerkin
methods used to approximate nonlinear problems which are, in many
practical situations, strongly nonlinear elliptic problems. This
formalism gives rise to a priori and a posteriori error estimates which
can be used for the refinement of the mesh in adaptive finite element
methods applied to elliptic nonlinear problems. This theory is
illustrated with the example: in a two
dimensional domain with Dirichlet boundary conditions.
Received June 10, 1992 / Revised version received February
28, 1994 相似文献
9.
Bilinear estimates in BMO and the Navier-Stokes equations 总被引:1,自引:0,他引:1
We prove that the BMO norm of the velocity and the vorticity controls the blow-up phenomena of smooth solutions to the Navier-Stokes equations.
Our result is applied to the criterion on uniqueness and regularity of weak solutions in the marginal class.
Received February 15, 1999; in final form October 11, 1999 / Published online July 3, 2000 相似文献
10.
Summary. In the fields like Astronomy and Ecology, the need for proper statistical analysis of data that are censored is being increasingly
recognized. Such data occur when, due to noise or other factors, instruments fail to detect low luminosities of celestial
objects, or low concentrations of certain pollutants. For multivariate censored data sets there are very few distribution
free methods available and researchers in the various fields often impose an assumption on the joint distribution, such as
multivariate normality, and carry out parametric inferences. Under censoring, however, such parametric inferences are asymptotically
wrong if the imposed assumption is incorrect. In this paper we propose a class of goodness-of-fit procedures for testing assumptions
about the multivariate distribution under random censoring. The test procedures generalize Pearson's goodness-of-fit test
in the sense that they are based on the concept of observed-minus-expected frequencies. The theory of the test statistic,
however, differs from that for the classical Pearson test due to the accommodation of censored data.
Received: 24 May 1994 / In revised form: 3 March 1996 相似文献
11.
We study the slopes of Frobenius on the rigid cohomology and the rigid cohomology with compact support of an algebraic variety over a perfect field of positive characteristic. We then prove that any unipotent overconvergent F-isocrystal on a smooth variety has a slope filtration whose graded parts are pure. Received: 23 December 1998 / Revised version: 5 July 1999 相似文献
12.
M. Kappert 《Numerische Mathematik》1996,74(4):397-417
Summary. Let denote the -th partial sum of the exponential function. Carpenter et al. (1991) [1] studied the exact rate of convergence of the zeros
of the normalized partial sums to the so-called Szeg?-curve Here we apply parts of the results found by Carpenter et al. to the zeros of the normalized partial sums of and .
Received August 11, 1995 相似文献
13.
Summary. We study here in detail the location of the real and complex zeros of the partial sums of and , which extends results of Szeg? (1924) and Kappert (1996). Received November 9, 2000 / Published online August 17, 2001 相似文献
14.
Summary.
With denoting the -th partial
sum of ${\rm e}^{z}$, the exact rate of convergence of the zeros of the
normalized partial sums, , to the Szeg\"o curve
was
recently studied by Carpenter et al. (1991), where
is defined by
Here, the above results are generalized to the convergence of
the zeros and poles of certain sequences of normalized Pad\'{e}
approximants
to , where is the associated Pad\'{e} rational approximation to .
Received February 2, 1994 相似文献
15.
A fully discrete finite element method is used to approximate the electric field equation derived from time-dependent Maxwell's equations in three dimensional polyhedral domains. Optimal energy-norm error estimates are achieved for general Lipschitz polyhedral domains. Optimal -norm error estimates are obtained for convex polyhedral domains. Received February 3, 1997 / Revised version received February 27, 1998 相似文献
16.
C. He 《Numerische Mathematik》1997,76(4):463-477
Summary. According to the methodology of [6], many measures of distance arising in problems in numerical linear algebra and control
can be bounded by a factor times the reciprocal of an appropriate condition number, where the distance is thought of as the
distance between a given problem to the nearest ill-posed problem. In this paper, four major problems in numerical linear
algebra and control are further considered: the computation of system Hessenberg form, the solution of the algebraic Riccati
equation, the pole assignment problem and the matrix exponential. The distances considered here are the distance to uncontrollability
and the distance to instability.
Received November 4, 1995 / Revised version received March 4, 1996 相似文献
17.
Summary.
It is well known that the zeros of a polynomial are equal to
the
eigenvalues of the associated companion matrix . In this paper
we take a
geometric view of the conditioning of these two problems and of the stability of
algorithms for polynomial zerofinding. The
is the set of zeros of all polynomials obtained by
coefficientwise perturbations of of size ;
this is a subset of the
complex plane considered earlier by Mosier, and is bounded by a
certain generalized lemniscate. The
is another subset of
defined as the set of eigenvalues of matrices
with ; it is bounded by a
level curve of the resolvent
of $A$. We find that if $A$ is first balanced in the usual EISPACK sense, then
and
are usually quite close to one another. It follows that the Matlab
ROOTS algorithm of balancing the companion matrix, then computing its eigenvalues, is a stable
algorithm for polynomial zerofinding. Experimental comparisons with the
Jenkins-Traub (IMSL) and
Madsen-Reid (Harwell) Fortran codes confirm that these three algorithms have roughly
similar stability properties.
Received June 15, 1993 相似文献
18.
Ji-guang Sun 《Numerische Mathematik》1996,73(2):235-263
Summary.
Perturbation expansions for singular subspaces of a matrix
and for deflating subspaces of a regular matrix pair are derived
by using a technique previously described by the author. The
perturbation expansions are then used to derive Fr\'echet derivatives,
condition numbers, and
th-order
perturbation bounds for the subspaces.
Vaccaro's result on second-order perturbation expansions for a special
class of singular subspaces can be obtained from a general result of this
paper. Besides, new perturbation bounds for singular subspaces
and deflating subspaces are derived
by applying a general theorem on solution of a system of nonlinear
equations. The results of this paper reveal an important fact: Each singular
subspace and each deflating subspace have individual perturbation bounds
and individual condition numbers.
Received July 26, 1994 相似文献
19.
Summary. Systems of integer linear (Diophantine) equations arise from various applications. In this paper we present an approach,
based upon the ABS methods, to solve a general system of linear Diophantine equations. This approach determines if the system
has a solution, generalizing the classical fundamental theorem of the single linear Diophantine equation. If so, a solution
is found along with an integer Abaffian (rank deficient) matrix such that the integer combinations of its rows span the integer
null space of the cofficient matrix, implying that every integer solution is obtained by the sum of a single solution and
an integer combination of the rows of the Abaffian. We show by a counterexample that, in general, it is not true that any
set of linearly independent rows of the Abaffian forms an integer basis for the null space, contrary to a statement by Egervary.
Finally we show how to compute the Hermite normal form for an integer matrix in the ABS framework.
Received July 9, 1999 / Revised version received May 8, 2000 / Published online May 4, 2001 相似文献
20.
The subject of this paper is a characterization of the -definable set functions of Kripke-Platek set theory with infinity and a uniform version of axiom of choice: . This class of functions is shown to coincide with the collection of set functionals of type 1 primitive recursive in a
given choice functional and . This goal is achieved by a G?del Dialectica-style functional interpretation of and a computability proof for the involved functionals.
Received October 9, 1996 相似文献