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1.
Summary Statistical topography involves the study of the geometrical properties of the iso-sets (contour lines or surfaces) of a random potential (r). Previous work [1,2] has addressed coastlines on a random relief (x, y) that possess a single characteristic spatial scale with topography belonging to the universality class of the random percolation problem. In the present paper this previous analytical approach is extended to the case of a multiscale random function with a power spectrum of scales,
H
, in a wide range of wavelengths, 0 < <
m
. It is found that the pattern of the coastline differs significantly from that of a monoscale landscape provided that –3/4 <H < 1, with the case –3/4 <H < 0 corresponding to the long-range correlated percolation and 0 <H < 1 to the fractional Brownian relief. The expression for the fractal dimension of an individual coastline is derived,D
h
= (10 – 3H)/7, the maximum value of whichD
h = 7/4, corresponds to the monoscale relief. The distribution functionF(a) of level lines over their sizea is calculated:F(a) a
–4(1-H)/7, for 0 a
m
. A comparison of the theoretical results with geographical data is presented. 相似文献
2.
Thewidth (chain number) of a partial order P, < is the smallest cardinal such that ¦A¦< 1 + whenever A is an antichain (chain) in P. We prove that, if a partial order (P, <) has width and cf()=, then P contains antichains An (n<) such that ¦A
0¦<¦A1¦ <...<={¦An¦: n < < } and either A01 A2< ... or A0>A1 >A2> ... A similar structure result is obtained for partial orders with chain number if cf()=. As an application we solve a problem of van Douwen, Monk and Rubin [1] by showing that if a Boolean algebra has width , thencf() .This work has been partially supported by NATO grant No. 339/84.Presented by Bjarni Jonsson. 相似文献
3.
We study the regularity of the minimizer u
for the functional F
(u,f)=|u|2 + |u–f{2 over all maps uH
1(, S
2). We prove that for some suitable functions f every minimizer u
is smooth in if 0 and for the same functions f, u
has singularities when is large enough.
Résumé On étudie la régularité des minimiseurs u du problème de minimisation minueH 1(,S2)(|u|2 + |u–f{2. On montre que pour certaines fonctions f, u est régulière lorsque 0 et pour les mêmes f, si est assez grand, alors u possède des singularités.相似文献
4.
V. A. Marchenko 《Journal of Mathematical Sciences》1993,63(2):217-232
In the paper one investigates the dependence of Weyl's solution ,)=c(,)+n()s(,) of the Sturm-Liouville equation y+q()y=2y on the spectral parameter . Under the condition that the potential q is bounded from below and q()exp(c0+c[in1 ¦¦), it is proved for {ie217-01} for any positive values and A. If q()>1 and {ie217-02} for all >0, then in the semiplane >0 the Weyl solution (, ) is obtained from the Weyl solution (,x) is obtained from the Weyl solution eix with zero potential, with the aid of a generalization of B. Ya Levin's transformation operators.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 184–206, 1989.I express my sincere gratitude to L. A. Pastur and I. V. Ostrovskii for valuable advice and discussions. 相似文献
5.
Saharon Shelah 《Archive for Mathematical Logic》1991,31(1):25-53
REF is the statement that every stationary subset of a cardinal reflects, unless it fails to do so for a trivial reason. The main theorem, presented in Sect. 0, is that under suitable assumptions it is consistent that REF and there is a which is +n
-supercompact. The main concepts defined in Sect. 1 are PT, which is a certain statement about the existence of transversals, and the bad stationary set. It is shown that supercompactness (and even the failure of PT) implies the existence of non-reflecting stationary sets. E.g., if REF then for many PT(, 1). In Sect. 2 it is shown that Easton-support iteration of suitable Levy collapses yield a universe with REF if for every singular which is a limit of supercompacts the bad stationary set concentrates on the right cofinalities. In Sect. 3 the use of oracle c.c. (and oracle proper—see [Sh-b, Chap. IV] and [Sh 100, Sect. 4]) is adapted to replacing the diamond by the Laver diamond. Using this, a universe as needed in Sect. 2 is forced, where one starts, and ends, with a universe with a proper class of supercompacts. In Sect. 4 bad sets are handled in ZFC. For a regular {<+ : cf<} is good. It is proved in ZFC that if=cf>1 then {<+ : cf<} is the union of sets on which there are squares. 相似文献
6.
H. J. Veldman 《Graphs and Combinatorics》1995,11(4):379-388
Letk and be positive integers, andG a 2-connected graph of ordern with minimum degree and independence number. A cycleC ofG is called aD
-cycle if every component ofG – V(C) has order smaller than. The graphG isk-cyclable if anyk vertices ofG lie on a common cycle. A previous result of the author is that if k 2, G isk-connected and every connected subgraphH ofG of order has at leastn +k
2 + 1/k + 1 – vertices outsideH adjacent to at least one vertex ofH, thenG contains aD
-cycle. Here it is conjectured that k-connected can be replaced by k-cyclable, and this is proved fork = 3. As a consequence it is shown that ifn 4 – 6, or ifG is triangle-free andn 8 – 10, thenG contains aD
3-cycle orG , where denotes a well-known class of nonhamiltonian graphs of connectivity 2. As an analogue of a result of Nash-Williams it follows that ifn 4 – 6 and – 1, thenG is hamiltonian orG . The results are all best possible and compare favorably with recent results on hamiltonicity of graphs which are close to claw-free. 相似文献
7.
In many problems the local zero-pole structure (i.e. locations of zeros and poles together with their orders) of a scalar rational functionw is a key piece of structure. Knowledge of the order of the pole or zero of the rational functionw at the point is equivalent to knowledge of the
-module
(where
is the space of rational functions analytic at ). For the more intricate case of a rationalp×m matrix functionW, we consider the structure of the module
as the appropriate analogue of zero-pole structure (location of zeros and poles together with directional information), where
is the set of column vectors of heightm with entries equal to rational functions which are analytic at . Modules of the form
in turn can be explicitly parametrized in terms of a collection of matrices (C
,A
,B
,B
,
) together with a certain row-reduced(p–m)×m matrix polynomialP(z) (which is independent of ) which satisfy certain normalization and consistency conditions. We therefore define the collection (C
,A
,Z
,B
,
,P(z)) to be the local spectral data set of the rational matrix functionW at . We discuss the direct problem of how to compute the local spectral data explicitly from a realizationW(z)=D+C(z–A)
–1
B forW and solve the inverse problem of classifying which collections (C
,A
,Z
,B
,
,P(z)) satisfying the local consistency and normalization conditions arise as the local spectral data sets of some rational matrix functionW. Earlier work in the literature handles the case whereW is square with nonzero determinant. 相似文献
8.
Paolo Lipparini 《Archive for Mathematical Logic》1996,35(2):63-87
We develop a method for extending results about ultrafilters into a more general setting. In this paper we shall be mainly concerned with applications to cardinality logics. For example, assumingV=L, Gödel's Axiom of Constructibility, we prove that if > then the logic with the quantifier there exist many is (,)-compact if and only if either is weakly compact or is singular of cofinality<. As a corollary, for every infinite cardinals and , there exists a (,)-compact non-(,)-compact logic if and only if either < orcf<cf or < is weakly compact.Counterexamples are given showing that the above statements may fail, ifV=L is not assumed.However, without special assumptions, analogous results are obtained for the stronger notion of [,]-compactness. 相似文献
9.
Milan Kučera 《Czechoslovak Mathematical Journal》1999,49(3):449-474
Variational inequalities
are studied, where K is a closed convex cone in
, 3, B
is a × matrix, G is a small perturbation, a real parameter. The assumptions guaranteeing a Hopf bifurcation at some 0 for the corresponding equation are considered and it is proved that then, in some situations, also a bifurcation of periodic solutions to our inequality occurs at some I 0. Bifurcating solutions are obtained by the limiting process along branches of solutions to penalty problems starting at 0 constructed on the basis of the Alexander-Yorke theorem as global bifurcation branches of a certain enlarged system. 相似文献
10.
We study (s, k, 1, 2)-translation divisible designs with 10 in the singular and semi-regular case. Precisely, we describe singular (s, k, 1, 2)-TDD's by quasi-partitions of suitable quotient groups or subgroups of their translation groups. For semi-regular (s, k, 1, 2)-TDD's (and, more general, for the case 2>1) we prove that their translation groups are either Frobenius groups or p-groups of exponent p. Some examples are given for the singular, semi-regular and regular case. 相似文献
11.
There is a symmetric nonnegative matrix A, subordinate to a given bipartite graph G on n vertices, with eigenvalues 12
n
if and only if, 1 +
n
0, 2 +
n-10,...,
m
+
n - m + 10,
m + 10,...,
n - m
0, in which m is the matching numberof G. Other observations are also made about the symmetric nonnegative inverse eigenvalue problem with respect to a graph 相似文献
12.
Reverse Functional Inequalities and Their Applications to Nonlinear Elliptic Boundary Value Problems
We establish some reverse inequalities. We give applications to nonlinear elliptic boundary value problems containing a parameter which have two branches of solutions u
(0) and U
(>0) of which the first is continuous at the origin and the second increases indefinitely as 0. 相似文献
13.
V. B. Semenyuk 《Ukrainian Mathematical Journal》1994,46(9):1345-1355
For unbounded domains with external power-type peaks, we propose a method for the approximation of functionsf(x)
w
p
r
() by polynomial splines in the metricw
p
r
(), 1pq, and present the corresponding estimates.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 9, pp. 1224–1233, September, 1994. 相似文献
14.
S. R. Treil' 《Journal of Mathematical Sciences》1989,44(6):868-869
It is proved that for every sequence of points n from the unit circle, n1, and for an arbitrary sequence of positive numbers An, An, there exists a continuous real function u, such that for the Toeplitz operator T (acting in the Hardy space H2) with the symbol =e
iu
we have the estimates (T–nI)–1>An, n.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, AN SSSR, Vol. 157, pp. 175–177, 1987. 相似文献
15.
Benny N. Cheng 《Geometriae Dedicata》1992,44(2):139-145
In 1955, Arne Pleijel proposed the following problem which remains unsolved to this day: Given a closed plane convex curve C and a point x() at a fixed distance above the plane, as the point x() varies, characterize the point for which the conical surface with vertex x() and base C attains its minimum, and determine the limits as 0 and of this minimum point. The purpose of this paper is to solve the cases where approach its extremities and in the course of the solution, we obtain an interesting characterization of the limit points, which we shall call the Pleijel points of C. A consequence is that the inner Pleijel point provides an upper bound for the isoperimetric defect of C. We also generalize the problem to higher dimensional spaces, and obtain the corresponding characterizations of the limiting points for convex surfaces. 相似文献
16.
Difference Sets with n = 2pm 总被引:1,自引:0,他引:1
Mikhail Muzychuk 《Journal of Algebraic Combinatorics》1998,7(1):77-89
Let D be a (v,k,) difference set over an abelian group G with even n = k - . Assume that t N satisfies the congruences t q
i
fi
(mod exp(G)) for each prime divisor qi of n/2 and some integer fi. In [4] it was shown that t is a multiplier of D provided that n > , (n/2, ) = 1 and (n/2, v) = 1. In this paper we show that the condition n > may be removed. As a corollary we obtain that in the case of n= 2pa when p is a prime, p should be a multiplier of D. This answers an open question mentioned in [2]. 相似文献
17.
Alvaro Rovella 《Bulletin of the Brazilian Mathematical Society》1993,24(2):233-259
We show here that by modifying the eigenvalues 2 < 3 < 0 < 1 of the geometric Lorenz attractor, replacing the usualexpanding condition 3+1 > 0 by acontracting condition 3+1 < 0, we can obtain vector fields exhibiting transitive non-hyperbolic attractors which are persistent in the following measure theoretical sense: They correspond to a positive Lebesgue measure set in a twoparameter space. Actually, there is a codimension-two submanifold in the space of all vector fields, whose elements are full density points for the set of vector fields that exhibit a contracting Lorenz-like attractor in generic two parameter families through them. On the other hand, for an open and dense set of perturbations, the attractor breaks into one or at most two attracting periodic orbits, the singularity, a hyperbolic set and a set of wandering orbits linking these objects. 相似文献
19.
We characterize the relationship between the space L1() and the dual L1() of the space L1(), where (, ) is a dual pair of vector measures with associated spaces of integrable functions L1() and L1() respectively. Since the result is rather restrictive, we introduce the notion of range duality in order to obtain factorizations of operators from Banach function spaces that are dominated by the integration map associated to the vector measure . We obtain in this way a generalization of the Grothendieck-Pietsch Theorem for p-summing operators.*The research was partially supported by MCYT DGI project BFM 2001-2670.**The research was partially supported by MCYT DGI project BFM 2000-1111. 相似文献
20.
Dr. Krishna Balasundaram Athreya 《Probability Theory and Related Fields》1969,12(4):320-332
Summary Let X(t)=(X
1
(t), X
2
(t), , X
t
(t)) be a k-type (2k<) continuous time, supercritical, nonsingular, positively regular Markov branching process. Let M(t)=((m
ij
(t))) be the mean matrix where m
ij
(t)=E(X
j
(t)¦X
r
(0)=
ir
for r=1, 2, , k) and write M(t)=exp(At). Let be an eigenvector of A corresponding to an eigenvalue . Assuming second moments this paper studies the limit behavior as t of the stochastic process
. It is shown that i) if 2 Re >1, then · X(t)e{–t¦ converges a.s. and in mean square to a random variable. ii) if 2 Re 1 then [ · X(t)] f(v · X(t)) converges in law to a normal distribution where f(x)=(x)
–1
if 2 Re <1 and f(x)=(x log x)–1 if 2 Re =1, 1 the largest real eigenvalue of A and v the corresponding right eigenvector.Research supported in part under contracts N0014-67-A-0112-0015 and NIH USPHS 10452 at Stanford University. 相似文献