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1.
In this paper, Melnikov functions which apper in the study of limit cycles of a perturbed planar Hamiltonlan system are studied. There are two main contributions here. The first one is related to the explicit formulae for these functions: a new method is developed to achieve the goal for the second one (Theorem A). the authors also discover a close relation between Melnlkov functions and focal qtmntities (Theorem 13). This relation is useful in both judging when a Melnikov function is identically zero and simplifying the computation of a Melnikov function (see §5). I)espite these results, this paper also includes other related resuEs, e.g. some estimations of the upper bound for the number of limit cycles in a perturbed Hamiltonian system. 相似文献
2.
Nitin Nitsure 《Proceedings Mathematical Sciences》1986,95(1):61-77
The purpose of this paper is to compute the Betti numbers of the moduli space ofparabolic vector bundles on a curve (see Seshadri [7], [8] and Mehta & Seshadri [4]), in the case where every semi-stable parabolic bundle is necessarily
stable. We do this by generalizing the method of Atiyah and Bott [1] in the case of moduli of ordinary vector bundles. Recall
that (see Seshadri [7]) the underlying topological space of the moduli of parabolic vector bundles is the space of equivalence
classes of certain unitary representations of a discrete subgroup Γ which is a lattice in PSL (2,R). (The lattice Γ need not necessarily be co-compact).
While the structure of the proof is essentially the same as that of Atiyah and Bott, there are some difficulties of a technical
nature in the parabolic case. For instance the Harder-Narasimhan stratification has to be further refined in order to get
the connected strata. These connected strata turn out to have different codimensions even when they are part of the same Harder-Narasimhan
strata.
If in addition to ‘stable = semistable’ the rank and degree are coprime, then the moduli space turns out to be torsion-free
in its cohomology.
The arrangement of the paper is as follows. In § 1 we prove the necessary basic results about algebraic families of parabolic
bundles. These are generalizations of the corresponding results proved by Shatz [9]. Following this, in § 2 we generalize
the analytical part of the argument of Atiyah and Bott (§ 14 of [1]). Finally in § 3 we show how to obtain an inductive formula
for the Betti numbers of the moduli space. We illustrate our method by computing explicitly the Betti numbers in the special
case of rank = 2, and one parabolic point. 相似文献
3.
El Hassan Essaky 《随机分析与应用》2013,31(2):277-301
Abstract We study the limit of the solutions of systems of semi-linear partial differential equations (PDEs) of second order of parabolic type, with rapidly oscillating periodic coefficients, a singular drift, and singular coefficients of the zero and second order terms. Our basic tool is the approach given by Pardoux [14]. In particular, we use the weak convergence of an associated backward stochastic differential equation (BSDE). 相似文献
4.
We prove that if f belongs to the Morrey space
, with λ ∊ [0, n−2], and u is the solution of the problem
then Du belongs to the space
, for any
Mathematics Subject Classification (2000) 35J25, 35D10 相似文献
5.
In [1], Bannai presents a fusion condition and uses this to consider central Schur rings (S-rings) over the simple groups PSL(2,q) where q is a prime power. In this paper, we concretely describe all such S-rings in terms of symmetric S-rings over cyclic groups. The final section discusses counting these. 相似文献
6.
W. W. Golubeff 《Annali di Matematica Pura ed Applicata》1930,8(1):29-52
Sommaire § 1. Généralités; les exposants d'un groupe fuchsien. — § 2. Les fonctions fuchsiennes de la 1-re classe; les valeurs des
fonctions fuchsiennes sur la frontière de la région de l'existence. — § 3. Les fonctions automorphes bornées. — § 4. Sur la
représentation analytique des fonctions fuchsiennes de la 1-re classe. — § 5. Sur l'expression analytique des coefficients
d'un groupe donné. 相似文献
7.
Saharon Shelah 《Israel Journal of Mathematics》1990,70(2):129-187
We answer some questions of Monk, and give some information on others concerning cardinal invariants of Boolean algebras under
ultraproducts and products.
The author would like to thank the United States-Israel Binational Science Foundation for partially supporting this research,
and Alice Leonhardt for the beautful typing. Publication no. 345.
§1–4 of this paper are essentially the letters which the author sent in December 1987 to Monk solving problems from his notes
on cardinal invariants of B.A.; §8 and §9 were written for §4; the other sections, §§5, 6 and 7, were completed in March 1988.
Concerning §§5–9, for further results see Abstracts of AMS and subsequent papers. §10 was written during the Arcata meeting,
summer 1985, and §11 in January 1986, after questions of Todorcevic. 相似文献
8.
Saharon Shelah 《Israel Journal of Mathematics》1994,85(1-3):351-390
We show in §1 that the Ax-Kochen isomorphism theorem [AK] requires the continuum hypothesis. Most of the applications of this
theorem are insensitive to set theoretic considerations. (A probable exception is the work of Moloney [Mo].) In §2 we give
an unrelated result on cuts in models of Peano arithmetic which answers a question on the ideal structure of countable ultraproducts
of ℤ posed in [LLS]. In §1 we also answer a question of Keisler regarding Scott complete ultrapowers of ℝ (see 1.18).
相似文献
9.
A. M. Bedarida 《Annali di Matematica Pura ed Applicata》1926,3(1):189-238
Sommario Introduzione — Parte I.Forme definite ed indefinite di Hermite - § 1. Equivalenza delle sostituzioni aritmetiche a modulo indecomponibile - § 2. Il sistema completo normale di sostituzioni
applicato alle forme di Hermite - § 3. Continuazione - § 4. Osservazione fondamentale — Parte II.Forme definite di Hermite - § 5. Le forme definite di Hermite nello spazio non euclideo - § 6. I gruppi automorfi aritmetici delle forme definite di
Hermite — Parte III.Relazioni sopra il numero delle classi di forme definite di Hermite - § 7. I valori del numeron per le forme definite di Hermite - § 8. Forme definite di Hermite primitive di prima specie - § 9. Forme definite di Hermite
primitive di seconda specie. 相似文献
10.
Marlies Gerber 《Israel Journal of Mathematics》1987,57(1):28-48
In §§1–5, we classifyn-point extensions of ergodic automorphisms up to factor orbit-equivalence (which is the natural analogue of factor isomorphism).
This classification is in terms of conjugacy classes of subgroups of the symmetric group onn points, and parallels D. Rudolph’s classification ofn-point extensions of Bernoulli shifts up to factor isomorphism. In §6, we give another proof of A. Fieldsteel’s theorem on
factor orbit-equivalence of compact group extensions. 相似文献
11.
Correct proofs are given for Theorem 3 and the Propositions of §§5, 6 of [4]. For the latter, we must modify the principle
(S)″ in a technical way. We prove a weaker version of Theorem 2, where □ is replaced by the stronger hypothesis PΓN
1
b.
Partially supported by NSF grant MCS 8301042. 相似文献
12.
Beniamino Segre 《Annali di Matematica Pura ed Applicata》1957,43(1):1-23
Sunto § 1:Introduzione. — Parte prima:Alcune proprietà di dilatazioni e contrazioni, nonché dei loro prodotti. § 2:Generalità sugli elementi irregolari delle corrispondenze birazionali. § 3:Influenza delle dilatazioni sopra la base per le varietà algebriche contenute in una data. § 4:Alcune proprietà delle transformazioni birazionali fra superficie. § 5:Estensioni alle varietà superiori. — Parte seconda:Topologia di varietà algebriche tagliate, ed applicazioni alle corrispondenze birazionali. § 6:Premesse. § 7:Proprietà omologiche d’immersione di una varietà algebrica in un’ altra. § 8:Alcune applicazioni alle trasformazioni birazionali. 相似文献
13.
In this article we construct a new type of solutions for the Gierer and Meinhardt system
with boundary conditions u
x
(0) = u
x
(L) = 0 and v
x
(0) = v
x
(L) = 0. As ε approaches zero, we construct a family of positive solution (u
ε
, v
ε
) such that the activator u
ε
oscillates c
0/ε times, with c
0 in an appropriate range, while the inhibitor remains close to a limiting profile, which is a strictly decreasing function. 相似文献
14.
In §2, we prove that if a 2-group G and all its nonabelian maximal sub-groups are two-generator, then G is either metacyclic or minimal non-abelian. In §3, we consider a similar question for p > 2. In §4 the 2-groups all of whose minimal nonabelian subgroups have order 16 and a cyclic subgroup of index 2, are classified.
It is proved, in §5, that if G is a nonmetacyclic two-generator 2-group and A, B, C are all its maximal subgroups with d(A) ≤ d(B) ≤ d(C), then d(C) = 3 and either d(A) = d(B) = 3 (this occurs if and only if G/G′ has no cyclic subgroup of index 2) or else d(A) = d(B) = 2. Some information on the last case is obtained in Theorem 5.3. 相似文献
15.
S. Shelah 《Israel Journal of Mathematics》1990,69(1):94-116
In those notes we prove in ZFC: (a) that the monadic theory of linear order (syntactically) interprets and has the same Lowenheim
number as second order logic (the interpretation is semantical but not in the “classical” way), (b) a parallel (weaker) result
for the monadic logic for completely metrizable spaces. The main results are in §§5, 6.
The author would like to thank the United States-Israel Binational Science Foundation for partially supporting this research,
and Alice Leonhardt for the beautiful typing. Publication No. 284b. 相似文献
16.
Hong Oh Kim Rae Young Kim Yeon Ju Lee Jungho Yoon 《Advances in Computational Mathematics》2010,33(3):255-283
We present a new family of compactly supported and symmetric biorthogonal wavelet systems. Each refinement mask in this family
has tension parameter ω. When ω = 0, it becomes the minimal length biorthogonal Coifman wavelet system (Wei et al., IEEE Trans Image Proc 7:1000–1013, 1998). Choosing ω away from zero, we can get better smoothness of the refinable functions at the expense of slightly larger support. Though
the construction of the new biorthogonal wavelet systems, in fact, starts from a new class of quasi-interpolatory subdivision
schemes, we find that the refinement masks accidently coincide with the ones by Cohen et al. (Comm Pure Appl Math 45:485–560,
1992, §6.C) (or Daubechies 1992, §8.3.5), which are designed for the purpose of generating biorthogonal wavelets close to orthonormal cases. However, the
corresponding mathematical analysis is yet to be provided. In this study, we highlight the connection between the quasi-interpolatory
subdivision schemes and the masks by Cohen, Daubechies and Feauveau, and then we study the fundamental properties of the new
biorthogonal wavelet systems such as regularity, stability, linear independence and accuracy. 相似文献
17.
The two-dimensional striation model consists of a nonlinear system of PDE's which arises in the modeling of the ionospheric plasma. The local-in-time existence of strong solutions is first proved using Banach's fixed point theorem. Then, under physically relevant assumptions, the system is shown to be nonlinearly unstable as soon as it is linearly unstable. Moreover, the instability occurs before the possible blow-up time of the solution. The proof relies on an earlier work of Hwang and Guo (2003). The first step of the proof is to investigate under which conditions the linearized system is unstable and to prove that its spectrum is bounded, by means of a variational formulation. The second one consists in constructing a family of solutions depending on the parameter δ measuring the smallness of the perturbation to the steady-state. Thanks to the boundedness of the linearized spectrum, this family of solutions is shown to be unstable by means of a power series expansion in δ. 相似文献
18.
《代数通讯》2013,41(6):3037-3043
ABSTRACT In his recent work, [1] and [2], on the pure semisimplicity conjecture Simson raised two problems about the structure of the direct sum decomposition of the direct product modulo the direct sum of indecomposable preinjective modules over right pure semisimple hereditary rings. The main goal of this paper is the proof of a theorem that resolves one of these problems and provides a partial answer to the other. 相似文献
19.
Saharon Shelah 《Archive for Mathematical Logic》2002,41(3):207-213
Here we deal with some problems posed by Matet. The first section deals with the existence of stationary subsets of [λ]<κ with no unbounded subsets which are not stationary, where, of course, κ is regular uncountable ≤λ. In the second section
we deal with the existence of such clubs. The proofs are easy but the result seems to be very surprising. Theorem 1.2 was
proved some time ago by Baumgartner (see Theorem 2.3 of [Jo88]) and is presented here for the sake of completeness.
Received: 10 December 1998 / Revised version: 2 February 1999 / Published online: 27 March 2002
RID="★"
ID="★" Publication number 698 in author's list. Partially supported by the Israel Science Foundation. 相似文献
20.
Xu XU 《数学学报(英文版)》2007,23(4):711-714
Risler & Trotman in 1997 proved that the multiplicity of an analytic function germ is left-right lipschitz invariant, which provided a partial answer to Zariski conjecture. In this note, based on the recent work of Comte, Milman & Trotman, we generalize the work of them to prove that the multiplicity of a C^∞ differentiable function germ is also left-right lipschitz invariant. 相似文献