共查询到20条相似文献,搜索用时 156 毫秒
1.
Pei-Lin Zhang Xin Ma Zhi-Long Peng Wen-Xin Qin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,19(4):823-839
In this paper we investigate the monotonicity in the pendulum type equations with position dependent damping. We show that
the system is strongly monotone under the overdamped condition. In the underdamped case, the Poincaré map PT is strongly monotone in a forward invariant region provided the average of the external force is large enough. Combining
the strong monotonicity with the dissipation property we show that the Poincaré map has in the cylindrical phase space an
invariant circle, on which PT is actually an orientation preserving circle homeomorphism. A series of consequences has then been obtained, including the
existence and uniqueness of the average velocity. Furthermore, we discuss the smoothness of this invariant curve and the ergodicity
of PT on this curve. 相似文献
2.
Employing the monotonicity approach and the theory of orientation preserving circle homeomorphisms, we provide a rigorous
analysis on the IV characteristics of the coupled Josephson junctions including an interference term in a specified parameters region. In particular,
when the system is driven by a dc-current, we show that there exist either globally stable single-wave-form solutions if and
only if the average voltage is nonzero, or equilibria if and only if the average voltage vanishes.
Supported by National Natural Science Foundation of China (10771155, 10571131) and Natural Science Foundation of Jiangsu Province
(BK 2006046). 相似文献
3.
In this paper, we will prove the existence of infinitely many harmonic and subharmonic solutions for the second order differential
equation ẍ + g(x) = f(t, x) using the phase plane analysis methods and Poincaré–Birkhoff Theorem, where the nonlinear restoring field g exhibits superlinear conditions near the infinity and strong singularity at the origin, and f(t, x) = a(t)x
γ + b(t, x) where 0 ≤ γ ≤ 1 and b(t, x) is bounded.
This project was supported by the Program for New Century Excellent Talents of Ministry of Education of China and the National
Natural Science Foundation of China (Grant No. 10671020 and 10301006). 相似文献
4.
GAOYI 《高校应用数学学报(英文版)》1998,13(2):150-158
Some modified Levitin-Polyak projection methods are proposed in this paper for solving monotone linear variational inequality x∈Ω,(x′-x)^T(Hx c)≤0,for any x′∈Ω.It is pointed out that there are similar methods for solving a general linear variational inequality. 相似文献
5.
FENGJINGHAI 《高校应用数学学报(英文版)》1997,12(3):363-370
In this paper, we will discuss the constructiOn problems about the invariant sets and invariant measures of continues maps~ which map complexes into themselves, using simplical approximation and Markov cbeirs. In [7], the author defined a matrix by using r-normal subdivi of the w,dimensional unit cube, considered it a Markov matrix, and constructed the invariantset and invafiant measure, In fact, the matrix he defined is not Markov matrix generally. So wewill give [7] and amendment in the last pert of this paper. We also construct an invariant set thatis the chain-recurrent set of the map by means of a non-negative matrix which only depends on themap. At hst, we will prove the higher dimension?Banach variation formuls that can simplify thetransition matrix. 相似文献
6.
The notion of locally weak monotonicity inequality for weakly harmonic maps is introduced and various results on this class
of maps are obtained. For example, the locally weak monotonicity inequality is nearly equivalent to theε-regularity.
Project supported by the National Natural Science Foundation of China (Grant No. 19571028) and the Guangdong Provincial Natural
Science Foundation of China. 相似文献
7.
~UNQIYU ZHENGYANZHANG 《高校应用数学学报(英文版)》1996,11(2):243-246
Abstract. In this note we construct an example of compactly supported orthonormal wavelets of non-tensor type from a multiresolutlon of 相似文献
8.
In this paper we study surfaces in S4 and their twistor Gauss maps. Some necessary and sufficient conditions that the twistor Gauss map is harmonic are given. We find many examples of nonisotropic harmonic maps from a surface to P
3.Supported by the National Natural Science Foundation of China and the Science Foundation of Zhejiang Province. 相似文献
9.
Miguel Angel Javaloyes Levi Lopes de Lima Paolo Piccione 《Mathematische Zeitschrift》2008,260(2):277-303
Following the lines of Bott in (Commun Pure Appl Math 9:171–206, 1956), we study the Morse index of the iterates of a closed
geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic
Jacobi field. Given one such closed geodesic γ, we prove the existence of a locally constant integer valued map Λγ on the unit circle with the property that the Morse index of the iterated γ
N
is equal, up to a correction term εγ∈{0,1}, to the sum of the values of Λγ at the N-th roots of unity. The discontinuities of Λγ occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincaré map of γ.
We discuss some applications of the theory. 相似文献
10.
Wen Ming WU Li Guang WANG 《数学学报(英文版)》2007,23(3):491-496
11.
In this paper we show that the number of generators of the cotangent cohomology groups T
Y
n
, n≥2, is the same for all rational surface singularities Y of fixed multiplicity. For a large class of rational surface singularities, including quotient singularities, this number
is also the dimension. For them we obtain an explicit formula for the Poincaré series P
Y
(t)=∑dim T
n
Y
·t
n
. In the special case of the cone over the rational normal curve we give the multigraded Poincaré series.
Oblatum: 18-XI-1998 & 25-III-1999 / Published online: 6 July 1999 相似文献
12.
In this paper we characterize the Liouvillian integrable orthogonal separable Hamiltonian systems on T
2 for a given metric, and prove that the Hamiltonian flow on any compact level hypersurface has zero topological entropy. Furthermore,
by examples we show that the integrable Hamiltonian systems on T
2 can have complicated dynamical phenomena. For instance they can have several families of invariant tori, each family is bounded
by the homoclinic-loop-like cylinders and heteroclinic-loop-like cylinders. As we know, it is the first concrete example to
present the families of invariant tori at the same time appearing in such a complicated way.
This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 10671123, 10231020), “Dawn”
Program of Shanghai Education Comission of China (Grant No. 03SG10) and Program for New Century Excellent Tatents in University
of China (Grant No. 050391) 相似文献
13.
V. V. Kozlov 《Mathematical Notes》1995,58(3):938-947
Conditions are found for the existence of integral invariants of Hamiltonian systems. For two-degrees-of-freedom systems these
conditions are intimately related to the existence of nontrivial symmetry fields and multivalued integrals. Any integral invariant
of a geodesic flow on an analytic surface of genus greater than 1 is shown to be a constant multiple of the Poincaré-Cartan
invariant. Poincaré's conjecture that there are no additional integral invariants in the restricted three-body problem is
proved.
Translated fromMatematicheskie Zametki, Vol. 58, No. 3, pp. 379–393, September, 1995.
The work was financially supported by the Russian Foundation for Basic Research (grant No. 242 93-013-16244), International
Science Foundation (grant No. MCY 000), and INTAS (grant No. 93-339). 相似文献
14.
A numerical isomorphism invariant,joining-rank, was introduced in [1] as a quantitative generalization of Rudolph’s property of minimal selfjoinings. Therein, a structure
theory was developed for those transformationsT whose joining-rank, jr (T), is finite. Here, we sharpen the theorem and show it to be canonical: If jr (T)<∞ then there is a unique triple 〈e, p, S〉 wheree andp are natural numbers andS is a map with minimal self-joinings, such thatT is ane-point extension ofS
P. Furthermore, the producte·p equals the joining-rank ofT.
This theorem applies to any finite-rank mixing map, since for such maps the rank dominates the joining-rank. Another corollary
is that any rank-1 transformation which is partial-mixing has minimal self-joinings. This partially answers a question of
[3].
Partially supported by a National Science Foundation Postdoctoral Research Fellowship. 相似文献
15.
In this paper, we establish a theoretical framework of path-following interior point algorithms for the linear complementarity
problems over symmetric cones (SCLCP) with the Cartesian P
*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-,
semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh
to the Cartesian P
*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10671010, 70841008) 相似文献
16.
Bifurcations of a degenerate homoclinic orbit with orbit flip in high dimensional system are studied. By establishing a local
coordinate system and a Poincaré map near the homoclinic orbit, the existence and uniqueness of 1–homoclinic orbit and 1–periodic
orbit are given. Also considered is the existence of 2–homoclinic orbit and 2–periodic orbit. In additon, the corresponding
bifurcation surfaces are given.
Project supported by the National Natural Science Foundation of China (No: 10171044), the Natural Science Foundation of Jiangsu
Province (No: BK2001024), the Foundation for University Key Teachers of the Ministry of Education of China 相似文献
17.
We develop the theory of analytically controlled Poincaré complexes over C
*-algebras. We associate a signature in C
*-algebra K-theory to such a complex, and we show that it is invariant under bordism and homotopy.
The authors were supported in part by NSF Grant DMS-0100464. 相似文献
18.
LetM be an open Riemann surface with a finite set of punctures, a complete Poincaré-like metric is introduced near the punctures
and the equivalence between the stability of an indecomposable parabolic Higgs bundle, and the existence of a Hermitian-Einstein
metric on the bundle is established.
Project surpported partially by the National Natural Science Foundation of China (Grant No. 19701034). 相似文献
19.
Zaihong Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(4):592-608
In this paper, we study the existence of periodic solutions of Rayleigh equation
where f, g are continuous functions and p is a continuous and 2π-periodic function. We prove that the given equation has at least one 2π-periodic solution provided that f(x) is sublinear and the time map of equation x′′ + g(x) = 0 satisfies some nonresonant conditions. We also prove that this equation has at least one 2π-periodic solution provided that g(x) satisfies
and f(x) satisfies sgn(x)(f(x) − p(t)) ≥ c, for t ∈R, |x| ≥ d with c, d being positive constants.Received: July 1, 2002; revised: February 19, 2003Research supported by the National Natural Science Foundation of China, No.10001025 and No.10471099, Natural Science Foundation of Beijing, No. 1022003 and by a postdoctoral Grant of University of Torino, Italy. 相似文献
20.
Yong-ping Liu Gui-qiao XuDepartment of Mathematics Beijing Normal University Beijing China Department of Mathematics Tianjin Normal Univesity Tianjin . China 《应用数学学报(英文版)》2002,18(4):663-674
The classes of the multivariate functions with bounded moduli on Rd and Td are given and their average σ-widths and non-linear n-widths are discussed. The weak asymptotic behaviors are established for the corresponding quantities. 相似文献