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1.
Wolfgang Müller 《Monatshefte für Mathematik》1999,128(4):315-330
Denote by the number of points of the lattice in the “blown up” domain , where is a convex body in () whose boundary is smooth and has nonzero curvature throughout. It is proved that for every fixed
where for and . This improves a classic result of E. Hlawka [8] and its refinements due to E. Kr?tzel and W. G. Nowak ([14], [15]). The proof uses a multidimensional variant of the method of van der Corput for the estimation of exponential
sums.
Received 28 August 1998 相似文献
2.
Yuk-Kam Lau 《Monatshefte für Mathematik》1999,110(3):111-129
Based on the method in Meurman [5], we study the mean square formula of the error term for a class of Arithmetical functions whose Dirichlet series satisfies a functional equation with multiple gamma factors. We obtain improvements on some results of Chandrasekharan and Narasimhan [1]. 相似文献
3.
Klaus Schmidt 《Monatshefte für Mathematik》2000,129(1):37-61
Let α be an expansive automorphisms of compact connected abelian group X whose dual group is cyclic w.r.t. α (i.e. is generated by for some ). Then there exists a canonical group homomorphism ξ from the space of all bounded two-sided sequences of integers onto X such that , where σ is the shift on . We prove that there exists a sofic subshift such that the restriction of ξ to V is surjective and almost one-to-one. In the special case where α is a hyperbolic toral automorphism with a single eigenvalue
and all other eigenvalues of absolute value we show that, under certain technical and possibly unnecessary conditions, the restriction of ξ to the two-sided beta-shift
is surjective and almost one-to-one.
The proofs are based on the study of homoclinic points and an associated algebraic construction of symbolic representations
in [13] and [7]. Earlier results in this direction were obtained by Vershik ([24]–[26]), Kenyon and Vershik ([10]), and Sidorov and Vershik ([20]–[21]).
(Received 27 October 1998; in revised form 17 May 1999) 相似文献
4.
On the Nilpotent Ranks of the Principal Factors of Order-preserving Transformation Semigroups 总被引:1,自引:0,他引:1
Xiuliang Yang 《Semigroup Forum》1998,57(3):331-340
On
of order-preserving selfmaps on X
n
= {1,2,..., n} were studied by gomes and Howie [2], Garba [1]. In this paper we study the nilpotent ranks of the principal factors of
the semigroup O
n
. 相似文献
5.
Changyu Xia 《Monatshefte für Mathematik》1999,128(2):165-171
Let M be an n-dimensional simply connected Hadamard manifold with Ricci curvature satisfying and be a bounded domain having smooth boundary. In this paper, we prove that the first n nonzero Neumann eigenvalues of the Laplacian on Ω satisfy , where is a computable constant depending only on and , Ω being the volume of Ω. This result generalizes the corresponding estimate for bounded domains in a Euclidean space obtained
recently by M. S. Ashbaugh and R. D. Benguria.
(Received 19 May 1998; in revised form 21 September 1998) 相似文献
6.
Zhenlin Gao 《Semigroup Forum》1998,56(3):323-333
n on po-semigroups. We study the least property of (ordered) semilattice congruences, and prove:
1. N is the least ordered semilattice congruence on pr-semigroups (cf.[1]).
2. n is the least semilattice congruence on po-semigroups.
3. N is not the least semilattice congruence on po-semigroups in general.
Thus, we give a complete solution to the problem posed by N. Kehayopulu in [1]. 相似文献
7.
Ioannis K. Argyros 《Monatshefte für Mathematik》1990,109(3):175-193
We study the Newton-Kantorovich method under mild differentiability conditions. Using Zabrejko-Nguen assumptions we extend the results obtained byZabrejko andNguen in [11]. We also derive Ptâk error estimates which compare favorably with the ones obtained previously byKeller [4],Rokne [7], andArgyros in [1]. 相似文献
8.
C [0,1], α > 0 in (0,1) and α(1), we consider the second order differential operator on C[0,1] defined by Au: = αu″ + βu′, where D(A) may include Wentzell boundary conditions. Under integrability conditions involving √α and β/√α, we prove the
analyticity of the semigroup generated by (A,D(A)) on Co[0,1], Cπ[0,1] and on C[0,1], where Co[0,1]: {u∈ C[0,1]|u (1)} and Cπ[0,1]: = {u∈ C[0,1]| u (0) = u (1)}. We also prove different characterizations of D(A) related to some results in [1], where β≡ 0, exhibiting peculiarities
of Wentzell boundary conditions. Applications can be derived for the case αx = x
k (1 - x )kγ(x )(k≥j/2, x∈ [0,1], γ∈ C{0,1}). 相似文献
9.
Paul M. Voutier 《Monatshefte für Mathematik》1995,119(1-2):125-139
In this paper, we establish new upper bounds on the number ofS-integral solutions to hyper- and super-elliptic equations under the conditions ofLeVeque [3]. Our method is based upon that ofEvertse andSilverman [1]. 相似文献
10.
This paper deals with the class of spaces which are countable unions of zero-dimensional sets and with the larger class of
Haver’s C-spaces. All spaces are assumed to be separable and metrizable. We are concerned with various aspects of universality
of these classes when they are combined with the covering analogue for σ-compactness defined by Menger and the rational dimension
introduced by Menger and N?beling. A solution of a problem of S. D. Iliadis [16] concerning universal spaces for rational dimension will result.
Received 11 September 1998; in revised form 12 January 1999 相似文献
11.
Dr. H. Sies 《Monatshefte für Mathematik》1982,94(2):155-162
In [5]Ky Fan derived several theorems on real square matrices from well-known covering theorems on simplexes given byE. Sperner [13] andB. Knaster-C. Kuratowski-S. Mazurkiewicz [9]. In this note some theorems on monotone matrices and nonsingularM-matrices are presented which extend some ofFan's results. The proofs will be based on certain topological theorems on simplexes which were recently established by the author in [12] and which include the mentioned covering theorems. 相似文献
12.
Ignace I. Kolodner 《Annali di Matematica Pura ed Applicata》1963,63(1):11-32
Summary
T. Carleman [1] showed that a certain 2 x 2 hyperbolic, semilinear system of partial differential equations has many features in common
with the integro-differential equation ofBoltzmann. We produce here a global existence theory for theCauchy problem for this system and its generalizations. The main result is derived by exploiting the fact that the solution of a
certainRiccati equation depends isotonically (with respect to a suitable partial order) on the forcing term and the initial data.
Research supported by the National Science Foundation, Grant NSF G-21053. 相似文献
13.
Tangent measure distributions were introduced byBandt [2] andGraf [8] as a means to describe the local geometry of self-similar sets generated by iteration of contractive similitudes. In this paper we study the tangent measure distributions of hyperbolic Cantor sets generated by certain contractive mappings, which are not necessarily similitudes. We show that the tangent measure distributions of these sets equipped with either Hausdorff- or Gibbs measure are unique almost everywhere and give an explicit formula describing them as probability distributions on the set of limit models ofBedford andFisher [5]. 相似文献
14.
Summary The paper is concerned with the assignment of input probabilities to achieve the maximum rate of transmission when the transition matrix is prespecified. Unlike the standard reference [Muroga, 1953], in whichLagrange multipliers are used in conventional form, mathematical programming approach has been proposed.
Vorgel. v.:J. Nitsche 相似文献
Zusammenfassung Die Zuordnung von Eingabe-Wahrscheinlichkeiten zur Erzielung einer maximalen Übertragungsrate bei vorgegebenen Übergangswahrscheinlichkeiten wird untersucht. Entgegen der Behandlung unter Verwendung vonLagrangeschen Multiplikatoren [Muroga, 1953] wird hier der Zugang mit Hilfe konvexer Programmierung betrachtet.
Vorgel. v.:J. Nitsche 相似文献
15.
Prof. H. Reiter 《Monatshefte für Mathematik》1978,86(1):13-62
It is shown that the theorem ofWeil-Cartier ([10, Th. 5], [4, Th. 3]) is connected with a homomorphism of groups of unitary operators. The existence proof for this homomorphism is based on simple results in harmonic analysis and on an extension property of the Schwartz-Bruhat functions. Some applications are given, including a result ofIgusa's [6, Th. 3] and the reciprocity formula ofKrazer-Siegel [9, Th. 2]. An outline of the proof has been given in [8]. 相似文献
16.
Professor Ivo Marek 《Numerische Mathematik》1969,13(3):207-216
Summary The well known row sum criterion (in German Zeilensummen-kriterium) is reformulated for transformations on Banach spaces with cones, and some sufficient conditions guaranteeing the convergence ofJacobi, Gauss-Seidel and successive over-relaxation iterations are derived, similar to those given byWalter [12] andKulisch [3] for linear algebraic systems. 相似文献
17.
Summary The stability of a viscous flow between two co-axial circular cylinders, produced by the simultaneous effect of rotation of the interior cylinder and by a constant pressure gradient in peripherical direction, has been examined. (The two single problems had been studied first byTaylor [1] resp.Dean [2].) The perturbations investigated are vortices of the Taylor-Görtler-type and are assumed to be small. It therefore becomes possible to operate on the basis of the linear differential equations for perturbations.The present stability problem had been treated under the same assumptions byDiPrima [5] for small gap-distances by using the series method ofTaylor. In this paper, however, arbitrary gap-distances are admitted, and the integral equation method ofGörtler [3] andHämmerlin [4] has been applied. The calculated dependences of the critical Reynolds number upon the pressure gradient are in good qualitative agreement with the results ofDiPrima. However, our computations performed by more exact methods yielded somewhat different results with regard to the dependence of the critical vortex number upon the pressure gradient. 相似文献
18.
George G. Roussas 《Probability Theory and Related Fields》1965,4(1):69-73
Summary In this note the proof of the consistency of a maximum likelihood estimate (MLE) obtained by Wald in [7] in the case of independent and identically distributed random variables is extended to the case of Markov processes.There is an extensive literature about the existence of a MLE and its consistency, most of which includes the assumption of the existence of derivatives of the densities with respect to the parameter involved. (See, for example, [2] and other references cited there.) Even under the rather strong assumption of pointwise differentiability of densities, and other additional regularity conditions, the problem of existence and consistency of a MLE has not been solved satisfactorily. (See, for example, [1], [2], [4], [6].) On the other hand, there have appeared papers like [3], where the consistency of a MLE is proved for processes with dependent random variables, and without the usual differentiability assumptions. The conditions used in the present paper are, however, of a different nature from those imposed in [3], and also are slightly different from Wald's assumptions in [7]. To our knowledge, a proof of consistency of a MLE under conditions similar to the ones used here has not appeared in the literature.I would like to take this opportunity to thank Professor L. LeCam for a number of remarks in connection with this paper.Prepared with the partial support of the National Science Foundation, Grant GP-10. 相似文献
19.
Attila Nagy 《Semigroup Forum》1998,57(1):92-100
S is called a δ-semigroup if the lattice of all congruences of S is a chain with respect to inclusion. In the literature there are lots of papers which investigate the δ-semigroups in special
classes of semigroups ([1], [3], [5], [6], [10], [11], [12], [14],). In this paper we describe the RGC
n
-commutative δ-semigroups. 相似文献
20.
Hong Shaofang 《Semigroup Forum》1998,56(2):158-186
n , if n≥ 8, then 2
n-1
-k, where k = 1,3, are gaps. This also implies that Konieczny's conjecture [2] is not true. 相似文献