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1.
In this communication we deal with the analysis of Hamiltonian Hopf bifurcations in 4-DOF systems defined by perturbed isotropic
oscillators (1-1-1-1 resonance), in the presence of two quadratic symmetries I
1 and I
2. As a perturbation we consider a polynomial function with a parameter. After normalization, the truncated normal form gives
rise to an integrable system which is analyzed using reduction to a one degree of freedom system. The Hamiltonian Hopf bifurcations
are found using the ‘geometric method’ set up by one of the authors.
相似文献
2.
The ordered fieldR(M) consists of the realsR with a transcendentalM adjoined, which is larger than any realr ∈R. Given any semi-infinite matrix (s.i.m.) interpreted as linear inequalities:u
tPi≧c
i, ∀
i
∈I, an arbitrary index set, it is also shown that the following are equivalent. (1) For every finiteJ ⊆I the systemu
tPi≧c
i,i ∈J is consistent, and (2) the s.i.m. has a solutionu ∈R(M)
n. Some consequences for “duality gaps” are also given.
These results were obtained as part of the activities of the Management Science Research Group and School of Urban and Public
Affairs, Carnegie-Mellon University. 相似文献
3.
This paper deals with the analysis of Hamiltonian Hopf as well as saddle-center bifurcations in 4-DOF systems defined by perturbed
isotropic oscillators (1:1:1:1 resonance), in the presence of two quadratic symmetries Ξ and L
1. When we normalize the system with respect to the quadratic part of the energy and carry out a reduction with respect to
a three-torus group we end up with a 1-DOF system with several parameters on the thrice reduced phase space. Then, we focus
our analysis on the evolution of relative equilibria around singular points of this reduced phase space. In particular, dealing
with the Hamiltonian Hopf bifurcation the ‘geometric approach’ is used, following the steps set up by one of the authors in
the context of 3-DOF systems. In order to see the interplay between integrals and physical parameters in the analysis of bifurcations,
we consider as a perturbation a one-parameter family, which in particular includes one of the classical Stark–Zeeman models
(parallel case) in three dimensions. 相似文献
4.
Huan Yin CHEN 《数学学报(英文版)》2007,23(2):357-364
Let R be an exchange ring with primitive factors artinian. We prove that there exists a u∈U(R) such that 1R ± u ∈ U(R), if and only if for any a ∈ R, there exists a u ∈ U(R) such that a ± u∈ U(R). Phrthermore, we prove that, for any A ∈ Mn(R)(n ≥ 2), there exists a U ∈ GLn(R) such that A ± U ∈ GLn(R). 相似文献
5.
E. G. Goluzina 《Journal of Mathematical Sciences》1998,89(1):958-966
Let TR be the class of functions
that are regular and typically real in the disk E={z:⋱z⋱<1}. For this class, the region of values of the system {f(z0), f(r)} for z0 ∈ ℝ, r∈(-1,1) is studied. The sets Dr={f(z0):f∈TR, f(r)=a} for −1≤r≤1 and Δr={(c2, c3): f ∈ TR, −f(−r)=a} for 0<r≤1 are found, where aε(r(1+r)−2, r(1−r)−2) is an arbitrary fixed number. Bibliography: 11 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 69–79. 相似文献
6.
The role that a prescribed holomorphic Hopf (Quadratic) differential A(z) dz dz plays in the construction of a negatively
curved immersed simply connected complete surface ∑0
of prescribed constant mean curvature c ∈ (−1, 1)in the hyperbolic 3-Space
H
3
is investigated in this work. When a holomorphic function A(z), which is the coefficient function of the Hopf differential,
is prescribed on a unit disk |z| < 1,it is shown that the unit disk |z| < 1can be immersed in the hyperbolic 3-Space
H
3
as a negatively curved complete surface of constant mean curvature c ∈ (−1, 1),provided that |A(z)| satisfies a certain growth condition. Moreover, it is shown that the unit disk |z| < 1can be uniquely embedded in
H
3
when the holomorphic function A(z) has a certain admissible structure. 相似文献
7.
BASUDEB DHARA 《Proceedings Mathematical Sciences》2012,122(1):121-128
Let R be a prime ring with its Utumi ring of quotient U, H and G be two generalized derivations of R and L a noncentral Lie ideal of R. Suppose that there exists 0 ≠ a ∈ R such that a(H(u)u − uG(u))
n
= 0 for all u ∈ L, where n ≥ 1 is a fixed integer. Then there exist b′,c′ ∈ U such that H(x) = b′x + xc′, G(x) = c′x for all x ∈ R with ab′ = 0, unless R satisfies s
4, the standard identity in four variables. 相似文献
8.
A. V. Romanov 《Mathematical Notes》2000,68(3):378-385
An example of a dissipative semilinear parabolic equation in a Hilbert space without smooth inertial manifolds is constructed.
Moreover, the attractor of this equation can be embedded in no finite-dimensionalC
1 invariant submanifold of the phase space. The class of scalar reaction-diffusion equations in bounded domains Ω ⊂ ℝm without inertial manifolds
with the property of absolute normal hyperbolicity on the setE of stationary points of the phase semiflow is described. Such equations may have inertial manifolds with the weaker property
of normal hyperbolicity onE. Three-dimensional reaction-diffusion systems without inertial manifolds normally hyperbolic at stationary points are found.
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 439–447, September, 2000. 相似文献
9.
Let G
m,n be the class of strategic games with n players, where each player has m≥2 pure strategies. We are interested in the structure of the set of correlated equilibria of games in G
m,n when n→∞. As the number of equilibrium constraints grows slower than the number of pure strategy profiles, it might be conjectured
that the set of correlated equilibria becomes large. In this paper, we show that (1) the average relative measure of the set
of correlated equilibria is smaller than 2−n; and (2) for each 1<c<m, the solution set contains c
n correlated equilibria having disjoint supports with a probability going to 1 as n grows large. The proof of the second result hinges on the following inequality: Let c
1, …, c
l be independent and symmetric random vectors in R
k, l≥k. Then the probability that the convex hull of c
1, …, c
l intersects R
k
+ is greater than or equal to .
Received: December 1998/Final version: March 2000 相似文献
10.
Dorin Bucur Ioan R. Ionescu 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(6):1042-1056
We consider an eigenvalue problem associated to the antiplane shearing on a system of collinear faults under a slip-dependent
friction law. Firstly we consider a periodic system of faults in the whole plane. We prove that the first eigenvalues/eigenfunctions
of different physical periodicity are all equal and that the other eigenvalues converge to this first common eigenvalue as
their physical period becomes indefinitely large. Secondly we consider a large scale fault system composed on a small scale
collinear faults periodically disposed. If β0* is the first eigenvalue of the periodic problem in the whole plane, we prove that the first eigenvalue of the microscopic
problem behaves as β0*/∈ when ∈→ 0 regardless the geometry of the domain (here ∈ is the scale quotient). The geophysical implications of this result
is that the macroscopic critical slip Dc scales with Dc∈/∈ (here Dc∈ is the small scale critical slip). 相似文献
11.
A graph is called a proper refinement of a star graph if it is a refinement of a star graph, but it is neither a star graph
nor a complete graph. For a refinement of a star graph G with center c, let G
c
* be the subgraph of G induced on the vertex set V (G)\ {c or end vertices adjacent to c}. In this paper, we study the isomorphic classification of some finite commutative local rings R by investigating their zero-divisor graphs G = Γ(R), which is a proper refinement of a star graph with exactly one center c. We determine all finite commutative local rings R such that G
c
* has at least two connected components. We prove that the diameter of the induced graph G
c
* is two if Z(R)2 ≠ {0}, Z(R)3 = {0} and G
c
* is connected. We determine the structure of R which has two distinct nonadjacent vertices α, β ∈ Z(R)* \ {c} such that the ideal [N(α) ∩ N(β)]∪ {0} is generated by only one element of Z(R)*\{c}. We also completely determine the correspondence between commutative rings and finite complete graphs K
n
with some end vertices adjacent to a single vertex of K
n
. 相似文献
12.
ZHANG Zhenyue & DU Keqin Department of Mathematics Zhejiang University Hangzhou China. 《中国科学A辑(英文版)》2006,49(7):971-986
We present a successive projection method for solving the unbalanced Procrustes problem: given matrix A∈Rn×n and B∈Rn×k, n>k, minimize the residual‖AQ-B‖F with the orthonormal constraint QTQ = Ik on the variant Q∈Rn×k. The presented algorithm consists of solving k least squares problems with quadratic constraints and an expanded balance problem at each sweep. We give a detailed convergence analysis. Numerical experiments reported in this paper show that our new algorithm is superior to other existing methods. 相似文献
13.
IBN rings and orderings on grothendieck groups 总被引:2,自引:0,他引:2
Tong Wenting 《数学学报(英文版)》1994,10(3):225-230
LetR be a ring with an identity element.R∈IBN means thatR
m⋟Rn impliesm=n, R∈IBN
1 means thatR
m⋟Rn⊕K impliesm≥n, andR∈IBN
2 means thatR
m⋟Rm⊕K impliesK=0. In this paper we give some characteristic properties ofIBN
1 andIBN
2, with orderings on the Grothendieck groups. In addition, we obtain the following results: (1) IfR∈IBN
1 and all finitely generated projective leftR-modules are stably free, then the Grothendieck groupK
0(R) is a totally ordered abelian group. (2) If the pre-ordering of the Grothendieck groupK
0(R) of a ringR is a partial ordering, thenR∈IBN
1 orK
0(R)=0.
Supported by National Nature Science Foundation of China. 相似文献
14.
We obtain a generalization of the complete Perron effect whereby the characteristic exponents of all solutions change their
sign from negative for the linear approximation system to positive for a nonlinear system with perturbations of higher-order
smallness [Differ. Uravn., 2010, vol. 46, no. 10, pp. 1388–1402]. Namely, for arbitrary parameters λ
1 ≤ λ
2 < 0 and m > 1 and for arbitrary intervals [b
i
, d
i
) ⊂ [λ
i
,+∞), i = 1, 2, with boundaries d
1 ≤ b
2, we prove the existence of (i) a two-dimensional linear differential system with bounded coefficient matrix A(t) infinitely differentiable on the half-line t ≥ 1 and with characteristic exponents λ
1(A) = λ
1 ≤ λ
2(A) = λ
2 < 0; (ii) a perturbation f(t, y) of smallness order m > 1 infinitely differentiable with respect to time t > 1 and continuously differentiable with respect to y
1 and y
2, y = (y
1, y
2) ∈ R
2 such that all nontrivial solutions y(t, c), c ∈ R
2, of the nonlinear system .y = A(t)y + f(t, y), y ∈ R
2, t ≥ 1, are infinitely extendible to the right and have characteristic exponents λ[y] ∈ [b
1, d
1) for c
2 = 0 and λ[y] ∈ [b
2, d
2) for c
2 ≠ 0. 相似文献
15.
Liang Zongxia 《数学学报(英文版)》1998,14(4):495-506
LetM={M
z, z ∈ R
+
2
} be a continuous square integrable martingale andA={A
z, z ∈ R
+
2
be a continuous adapted increasing process. Consider the following stochastic partial differential equations in the plane:dX
z=α(z, Xz)dMz+β(z, Xz)dAz, z∈R
+
2
, Xz=Zz, z∈∂R
+
2
, whereR
+
2
=[0, +∞)×[0,+∞) and ∂R
+
2
is its boundary,Z is a continuous stochastic process on ∂R
+
2
. We establish a new theorem on the pathwise uniqueness of solutions for the equation under a weaker condition than the Lipschitz
one. The result concerning the one-parameter analogue of the problem we consider here is immediate (see [1, Theorem 3.2]).
Unfortunately, the situation is much more complicated for two-parameter process and we believe that our result is the first
one of its kind and is interesting in itself. We have proved the existence theorem for the equation in [2].
Supported by the National Science Foundation and the Postdoctoral Science Foundation of China 相似文献
16.
LetR be a ring and σ an automorphism ofR. We prove the following results: (i)J(R
σ[x])={Σiri
x
i:r0∈I∩J(R]),
r
i∈I for alliε 1} whereI↪ {r∈R:rx ∈J(R
Σ[x])|s= (ii)J(R
σ<x>)=(J(R
σ<x>)∩R)σ<x>. As an application of the second result we prove that ifG is a solvable group such thatG andR, + have disjoint torsions thenJ(R)=0 impliesJ(R(G))=0. 相似文献
17.
The notions of a cleft extension and a cross product with a Hopf algebroid are introduced and studied. In particular it is
shown that an extension (with a Hopf algebroid ℋ = (ℋ
L
, ℋ
R
)) is cleft if and only if it is ℋ
R
-Galois and has a normal basis property relative to the base ring L of ℋ
L
. Cleft extensions are identified as crossed products with invertible cocycles. The relationship between the equivalence classes
of crossed products and gauge transformations is established. Strong connections in cleft extensions are classified and sufficient
conditions are derived for the Chern–Galois characters to be independent on the choice of strong connections. The results
concerning cleft extensions and crossed product are then extended to the case of weak cleft extensions of Hopf algebroids hereby defined.
Dedicated to Stef Caenepeel on the occasion of his 50th birthday. 相似文献
18.
A subsetK ofc
0 is coordinatewise star-shaped (c.s.s.) if there exists a center pointx ∈K such that fory ∈K andz ∈c
0, ifz is coordinatewise betweenx andy thenz ∈K. We prove that a weakly compact c.s.s. subset ofc
0 has the fixed point property for nonexpansive mappings and that a fixed point for such a mapping can be obtained in a constructive
manner.
Research of the first two authors was partially supported by NSF Grant MCS78-01344 and of the last author by MCS78-01501. 相似文献
19.
Günter Heimbeck 《Geometriae Dedicata》1987,22(2):235-245
Let K be any commutative field and V:=K
4. A collection
of ruled quadrics in V is called a flock of ruled quadrics if the following holds true. (1) ⋃ℱ∈
G
ℱ = V; (2) There is a line S⊂V such that ℱ1⋂ℱ2= S for all distinct ℱ1, ℱ2∈
. The group ΓL(V) decomposes the set of all those flocks into equivalence classes. Besides that, we consider any cone R in V, say R:= {x∈V|x
1
x
3 - x
2
2
= 0}. Let R denote the set of all regular points of R. Plane sections of R which do not contain the singular point of ℜ are called regular sections. We consider decompositions of R
* by regular sections and their equivalence classes with respect to the symmetry group ΓL(V)R of the cone ℜ. The main result is as follows. There is a (natural) bijection between the classes of equivalent flocks of
rules quadrics and the classes of equivalent decompositions of R
* by regular sections. A brief discussion of those flocks of ruled quadrics on which the construction of the so-called Betten-Walker
planes is based ends the paper. Provided that char K≠3, these planes exist if and only if x∈K→x
3∈K is bijective.
相似文献
20.
Vincenzo De Filippis 《Proceedings Mathematical Sciences》2010,120(3):285-297
Let R be a prime ring, U the Utumi quotient ring of R, C = Z(U) the extended centroid of R, L a non-central Lie ideal of R, H and G non-zero generalized derivations of R. Suppose that there exists an integer n ≥ 1 such that (H(u)u − uG(u))
n
= 0, for all u ∈ L, then one of the following holds: (1) there exists c ∈ U such that H(x) = xc, G(x) = cx; (2) R satisfies the standard identity s
4 and char (R) = 2; (3) R satisfies s
4 and there exist a, b, c ∈ U, such that H(x) = ax+xc, G(x) = cx+xb and (a − b)
n
= 0. 相似文献