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1.
Let K be a positive integer and α be a real number, and for let if the fractional part of is , and if it is . The pseudorandom properties of the sequence are studied. As measures of pseudorandomness, the regularity of the distribution relative to arithmetic progressions and
the correlation are used. In a previous paper the authors studied the special cases and , while here the case is considered.
(Received 5 November 1997; in revised form 7 March 2000) 相似文献
2.
Gerhard Larcher Reinhard Wolf Jürgen Eichenauer‐Herrmann 《Monatshefte für Mathematik》1999,127(2):141-154
In the present paper we give an upper and a lower bound for the average value of the discrepancy of non-overlapping s-tuples of successive elements of a first order congruential pseudo-random-number generator (with prime modulus and maximal
period). The estimates are – up to logarithmic factors – sharp also for short parts of the period.
Received 30 January 1997; in revised form 2 May 1997 相似文献
3.
For every compact generalized polygon whose point space has finite dimension, we show that the automorphism group has finite
dimension as well. This opens the field for the application of Lie theoretic methods.
Received 12 November 1997; in revised form 10 March 1998 相似文献
4.
Denote by the family of all real valued functions on a metric space which satisfy a Lipschitz condition on the compact (bounded) subsets of X. We prove that every homomorphism on is the evaluation at some point of X if and only if X is realcompact (every closed bounded subset of X is compact).
(Received 4 November 1998; in revised form 31 May 1999) 相似文献
5.
Let M be a complete metric space. If admits an isometric shift, then M is separable.
(Received 2 February 2001; in revised form 9 April 2001) 相似文献
6.
A characterization is given for the K?the matrices B such that the K?the sequence space , with , contains all K?the sequence spaces of order p as subspaces. It follows that the class of K?the sequence spaces of order p has a universal element which is quasinormable. In particular, there is a quasinormable space (respectively, which contains every nuclear Fréchet space with basis (respectively, every countably normed Fréchet Schwartz space). Only
Fréchet spaces with continuous norm are considered in this note.
Received 15 January 1997; in final form 9 June 1997 相似文献
7.
On the stability of the incomplete LU-factorizations
and characterizations of H-matrices 总被引:2,自引:0,他引:2
A. Messaoudi 《Numerische Mathematik》1995,69(3):321-331
Summary.
Meijerink and van der Vorst [8] have
shown that the incomplete LU-factorizations are numerically stable for M-matrices. Varga, Saff and
Mehrmann [16] gave some characterizations of the H-matrices by using the
incomplete LU-factorizations of them. The purpose of this paper is to show that
the incomplete LU-factorizations of an H-matrix are at least as stable as the
complete LU-factorizations of its comparison matrix. We give also some new
characterizations of the H-matrices in connection with their incomplete
LU-factorizations.
Received
November 12, 1993 / Revised version received May 27, 1994 相似文献
8.
9.
A. Heppes 《Monatshefte für Mathematik》2001,134(1):51-66
In a recent paper of G. Fejes Tóth, G. Kuperberg and W. Kuperberg [1] a conjecture has been published concerning the greatest
lower bound of the density of a 2-saturated packing of unit discs in the plane. (A packing of unit discs is said to be 2-saturated
if none of the discs could be replaced by two other ones of the same size to generate a new packing. A packing of the unit
disc is a lattice packing if the centers form a point lattice.) In the present note we study this problem for lattice packings,
however, in a more general form in which the removed unit disc is replaced by two discs of radius r. A corollary of our results supports the above conjecture proving that a lattice packing cannot be 2-saturated except if its density is larger than the conjectured bound.
(Received 6 December 2000; in revised form March 29, 2001) 相似文献
10.
M. I. Gil’ 《Monatshefte für Mathematik》2000,129(1):15-24
Matrix integral operators are considered. Bounds for the spectrum are established. In particular, they give the invertibility
conditions and estimates for the spectral radius.
(Received 16 December 1998; in revised form 30 May 1999) 相似文献
11.
H. Mäurer 《Monatshefte für Mathematik》1999,128(1):7-21
A bijection of the compact convex set with is called a reflection of K, if σ maps convex subsets of K into convex subsets. Conditions are stated unter which the existence of few reflections imply that is an ellipse.
Received 4 March, 1998 相似文献
12.
On the convergence of line iterative methods for cyclically
reduced non-symmetrizable linear systems
Summary. We derive analytic bounds on the convergence factors associated
with block relaxation methods for solving the discrete
two-dimensional convection-diffusion equation. The analysis
applies to the reduced systems derived when one step of block
Gaussian elimination is performed on red-black ordered
two-cyclic discretizations. We consider the case where centered
finite difference discretization is used and one cell Reynolds
number is less than one in absolute value and the other is
greater than one. It is shown that line ordered relaxation
exhibits very fast rates of convergence.
Received March 3, 1992/Revised version received July 2, 1993 相似文献
13.
On Patterns in Sequences of Random Events 总被引:1,自引:0,他引:1
This paper considers patterns of particular events in sequences of trials, some independent and others Markovian. Matrix recursions are found for the number of sequences of
length n avoiding a specific pattern, and the associated probability of this event is evaluated. A Markov chain method for the study
of such problems is outlined, and is illustrated in various cases. Finally, configurations of length 3 in Bernoulli trials
are examined as an example.
Received 12 January 1998 in revised form 26 June 1998 相似文献
14.
Yuichi Kanjin 《Monatshefte für Mathematik》1999,127(4):311-319
For the real Hardy spaces , we shall show the Hardy type integral inequalities, and applying the inequalities we shall establish the Hardy’s inequalities
with respect to Hankel transforms.
Received 21 October 1997; in revised form 19 October 1998 相似文献
15.
Summary.
Hybrid methods for the solution of systems of linear equations
consist of a first phase where some information about the associated
coefficient matrix is acquired, and a second phase in which a
polynomial iteration designed with respect to this information is
used. Most of the hybrid algorithms proposed recently for the
solution of nonsymmetric systems rely on the direct use of
eigenvalue estimates constructed by the Arnoldi process in Phase I.
We will show the limitations of this approach and propose an
alternative, also based on the Arnoldi process, which approximates
the field of values of the coefficient matrix and of its inverse in
the Krylov subspace. We also report on numerical experiments
comparing the resulting new method with other hybrid algorithms.
Received May 27, 1993 / Revised version received
November 14, 1994 相似文献
16.
We study composition of power series and polynomials over algebraically closed fields of arbitrary characteristic. The so-called
Boettcher function of a power series is introduced and investigated. It is the principal aim of this paper to prove some results
going back to J. F. Ritt in this general setting. In particular, we determine the pairs of permutable polynomials and characterize
polynomials which satisfy a certain rational functional equation and polynomials which have a common iterate.
Received 12 February 1998; in revised form 20 April 1998 相似文献
17.
Josef Šlapal 《Monatshefte für Mathematik》2000,131(4):335-341
Limit ?-net spaces are defined as convergence spaces whose convergence is expressed by using generalized nets, the so-called
?-nets (where ? is a construct). For limit ?-net spaces we study compactifications, especially those ones that are analogous
to the Alexandrov and Čech-Stone compactifications known for topological spaces.
(Received 24 February 2000) 相似文献
18.
A metric space (X,d) has the Haver property if for each sequence ?1,?2,… of positive numbers there exist disjoint open collections V1,V2,… of open subsets of X, with diameters of members of Vi less than ?i and covering X, and the Menger property is a classical covering counterpart to σ-compactness. We show that, under Martin's Axiom MA, the metric square (X,d)×(X,d) of a separable metric space with the Haver property can fail this property, even if X2 is a Menger space, and that there is a separable normed linear Menger space M such that (M,d) has the Haver property for every translation invariant metric d generating the topology of M, but not for every metric generating the topology. These results answer some questions by L. Babinkostova [L. Babinkostova, When does the Haver property imply selective screenability? Topology Appl. 154 (2007) 1971-1979; L. Babinkostova, Selective screenability in topological groups, Topology Appl. 156 (1) (2008) 2-9]. 相似文献
19.
20.
Let S be a symmetric operator with defect index (1,1) in a Pontryagin space ℋ. The Krein formula establishes a bijective correspondence
between the generalized resolvents of S and the set of Nevanlinna functions as parameters. We give an analogue of the Krein formula in the case that ℋ is a degenerated
inner product space. The set of parameters is determined by a kernel condition. These results are applied to some classical
interpolation problems with singular data.
Received 3 February 1997; in revised form 9 June 1997 相似文献