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1.
Joan C. Artés Jaume Llibre Nicolae Vulpe 《Rendiconti del Circolo Matematico di Palermo》2007,56(3):417-444
A quadratic polynomial differential system can be identified with a single point of through the coefficients. Using the algebraic invariant theory we classify all the quadratic polynomial differential systems
of having a rational first integral of degree 2. We show that there are only 24 topologically different phase portraits in the
Poincaré disc associated to this family of quadratic systems up to a reversal of the sense of their orbits, and we provide
a unique representative of every class modulo an affine change of variables and a rescalling of the time variable. Moreover,
each one of these 24 representatives is determined by a set of invariant conditions and each respective first integral is
given in invariant form directly in
The authors are partially supported by a MEC/FEDER grant MTM2005-06098-C02-01, and a CONACIT grant number 2005SGR-00550.
Partially supported by CRDF-MRDA CERIM-1006-06 相似文献
2.
Ivan Č. Jovanović Eberhard Malkowsky Vladimir Rakočević 《Rendiconti del Circolo Matematico di Palermo》2003,52(2):308-314
LetF be aBK space withAK and
denote the set of all formal power series
with
such that
ε F for the sequence of coefficients of
. We give a necessary and sufficient condition for a point to be a bounded point evaluation on
, and for a polynomial to be cyclic in
. As special cases, we obtain the results for the space ℓ
p
(β) in [7].
Research of the authors supported under the research project #1232 of the Serbian Ministry of Sciences and Tecnology and,
in the case of the second author, also by the DAAD foundation (German Academic Exchange Service), grant 911 103 102 8. 相似文献
3.
B. Yousefi 《Rendiconti del Circolo Matematico di Palermo》2000,49(1):115-120
Let
be a sequence of positive numbers and 1 ≤p < ∞. We consider the spacel
P(β) of all power series
such that
. We give a necessary and sufficient condition for a polynomial to be cyclic inl
P(β) and a point to be bounded point evaluation onl
P(β). 相似文献
4.
Manuel Falconi Ernesto A. Lacomba Jaume Llibre 《Rendiconti del Circolo Matematico di Palermo》2004,53(2):153-164
We consider the topological classification of cubic surfaces which are obtained as intersection of the sphere
with the algebraic variety defined by the zeroes of a homogeneous cubic polynomial in Arnold’s normal form. This classification
is based on the parameters appearing in this normal form, obtaining a correspondence between the parameters of the surface
and its topological type. General classifications of cubic surfaces are made in the projective space ℙ3(ℝ), but our method, based on a very simple combinatorial procedure is easier to implement in
. We split the cubic surfaces parameter space into ten equivalence classes. 相似文献
5.
M. Taghavi 《Rendiconti del Circolo Matematico di Palermo》1999,48(2):237-242
The quotient of
divided by
, whereP is a self-inversive and unimodular polynomial of any degree, dominates an absolute constantK>1. A 1989 paper gaveK=1.0252 on which its authors conjetured that the best constant is
. We supply counter examples to their claim and provide a partial result for whenever theL
q norm is replaced by some “discrete” type norm.
Research supported by the Shiraz University Grant 72-SC-784-432. 相似文献
6.
Let
denote the class of ergodic probability preserving transformations which are disjoint from every weakly mixing system. Let
be the class of multipliers for
, i.e. ergodic transformations whose all ergodic joinings with any element of
are also in
. Fix an ergodic rotationT, a mildly mixing actionS of a locally compact second countable groupG and an ergodic cocycle ϕ forT with values inG. The main result of the paper is a sufficient (and also necessary by [LeP] whenG is countable Abelian andS is Bernoullian) condition for the skew product build fromT, ϕ andS to be an element of
. Moreover, the self-joinings of such extensions ofT are described with an application to study semisimple extensions of rotations.
Dedicated to Hillel Furstenberg on the occasion of his retirement
The first-named author was supported in part by CRDF, grant UM1-2546-KH-03.
The second-named author was supported in part by KBN grant 1P03A 03826. 相似文献
7.
Let F be a subfield of a commutative field extending ℝ. Let
We say thatf :
preserves distanced ≥ 0 if for eachx,y ∈ ℝ ∣x- y∣= d implies ϕ2(f(x),f(y)) = d2
. We prove that each unit-distance preserving mappingf :
has a formI o (ρ,ρ), where
is a field homomorphism and
is an affine mapping with orthogonal linear part. 相似文献
8.
Ivan Ginchev Angelo Guerraggio Matteo Rocca 《Rendiconti del Circolo Matematico di Palermo》2007,56(1):137-156
In this paper the constrained vector optimization problem mic
C
f(x), g(x) ∃ − K, is considered, where and are locally Lipschitz functions and and are closed convex cones. Several solution concepts are recalled, among them the concept of a properly efficient point (p-minimizer) and an isolated minimizer (i-minimizer). On the base of certain first-order optimalitty conditions it is shown that there is a close relation between
the solutions of the constrained problem and some unconstrained problem. This consideration allows to “double” the solution
concepts of the given constrained problem, calling sense II optimality concepts for the constrained problem the respective
solutions of the related unconstrained problem, retaining the name of sense I concepts for the originally defined optimality
solutions. The paper investigates the stability properties of thep-minimizers andi-minimizers. It is shown, that thep-minimizers are stable under perturbations of the cones, while thei-minimizers are stable under perturbations both of the cones and the functions in the data set. Further, it is shown, that
sense I concepts are stable under perturbations of the objective data, while sense II concepts are stable under perturbations
both of the objective and the constraints. Finally, the so called structural stability is discused. 相似文献
9.
In this paper we extend the Darboux theory of integrability in ℝ
n
to the regular algebraic hypersurfaces. Then we apply the extended theory first to the 3-dimensional generalized cylinders
×ℝ3−r
of ℝ4 forr=0, 1, 2, 3; and after to then-dimensional sphere
of ℝ
n+1. 相似文献
10.
11.
Michael Christ 《Journal of Geometric Analysis》1991,1(3):193-230
For a large class of subharmonicφ, the equation
is studied in
. Pointwise upper bounds are derived for the distribution kernels of the canonical solution operator and of the orthogonal
projection onto the space of entire functions inH. Existence theorems inL
p norms are derived as a corollary. A class of counterexamples, related to the failure of
to be analytic-hypoelliptic on certain CR manifolds, is discussed.
Communicated by Steven Krantz 相似文献
12.
A. G. Babenko 《Mathematical Notes》1996,60(3):248-263
In this paper we prove the Jackson-Stechkin inequalityE
n−1(f)<ω
n
(f, 2τ
n
,λ),n≥1,m≥5,r≥1, f ∈L2(
),f ≢ const, which is sharp for eachn=2, 3, ...; hereE
n−1
(f) is the best approximation of a functionf by spherical polynomials of degree ≤n−1, ω
n
(f, τ) is theτth modulus of continuity off based on the translations
,t ∈ ℝ,x ∈
,
,
is the measure of the unit Euclidean sphere
,
, andτ
n
,λ is the first positive zero of the Gegenbauer cosine polynomial
(cost).
Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 333–355, September, 1996.
The present paper was discussed at Ural State University in a seminar headed by Professor Arestov. The author is grateful
to Professor Arestov and Associate Professor Popov for useful conversations.
This research was supported by the State Commission for Higher Education of the Russian Federation under grant No. 2-16-5-31
and by the Russian Foundation for Basic Research under grant No. 93-011-196. 相似文献
13.
In this paper we consider special elements of the Fock space #x2131;
n
. That is the space of entire functionsf:ℂ:
n
→ℂ, such that the followingL
2- condition is satisfied:
. Here we show that there exists an entire functiong:ℂ
n
→ℂ such that for every one-dimensional subspace Π⊂ℂ
n
and for all 0<∈<2 we have
, but in the limit case ∈=0 we have
. This result is analogue to a result from [1]. There holomorphic functions on the unit-ball are investigated. Furthermore
the proof — as the one in [1] — uses a theorem from [2]. Therefore we give another application of the results from [2] — namely
for spaces of entire functions. 相似文献
14.
M. Nowak 《Rendiconti del Circolo Matematico di Palermo》1998,47(3):363-374
In 1986 S. Axler [3] proved that forf∈L
a
2
the Hankel operator
is compact if and only iff is in the little Bloch space {itB}{in0}. In this note we show that the same is true for
, 1<p<∞. Moreover we prove that
is ⋆-compact if and only if
as |z|→1−. 相似文献
15.
Summary Quaternion generalized fiber bundles
are studied, both isomorphic to global tensorial product
ordinary quaternion fiber bundles right and left respectively) and quite general ones. A cohomology class
is considered which represents the obstruction in order the fiber bundle be a tensorial product. Several properties and a
splitting principle are proved for bundles
. On this ground and founding on a convenient bundle BE → X associated to jaz (that we call Bonan's bundle and for which ɛ(
=ɛ(BE)) relations are stated among Stiefel-Whitney classes of
, BE and the class ɛ.
Entrata in Redazione il 14 agosto 1974.
Lavoro eseguito con contributo del C.N.R., nell'ambito del Gruppo Nazionale per le Strutture Algebriche e Geometriche e loro Applicazioni. 相似文献
Entrata in Redazione il 14 agosto 1974.
Lavoro eseguito con contributo del C.N.R., nell'ambito del Gruppo Nazionale per le Strutture Algebriche e Geometriche e loro Applicazioni. 相似文献
16.
Let
be the unit disk of the complex plane. A conformai map of
into itself is called hyperbolically convex if the non-Euclidean segment between any two points of
also belongs to
. In this paper we prove several inequalities that are analogous to inequalities about (Euclidean) convex univalent functions.
We show that if ƒ (0) = 0, then Re zf′/f > 1/2. This inequality is the key for the results of this paper. In particular we
deduce a three-variable inequality corresponding to that of Ruscheweyh and Sheil-Small. The sharp bound for the Schwarzian
derivative remains open. 相似文献
17.
Given ∈, we construct a sequence
, … of Borel sub-sigma-algebras on the unit interval with the following property. Suppose the identity functionf(x)=x is transformed by successive conditioning on
, then
, then
, Then the lim sup, with respect ton, will exceed (pointwise almost-everywhere) 1−∈ and its lim inf will be less than ∈.
The sequence of functions also will fail to converge in the
. This contrasts with the long-open conjecture that if all the
come from a finite set of sigma-algebras, then the resulting sequence of functions must converge in
.
J. L. King was partially supported by NSF grant DMS-9112595. 相似文献
18.
B. Yousefi 《Rendiconti del Circolo Matematico di Palermo》2002,51(3):403-410
Let
be a sequence of positive numbers and 1≤p<∞. We consider the spaceH
p(β) of all power series
such that Σ|
(n)|p β(n
p<∞. We investigate regions on which our formal power series represent bounded analytic functions.
Research partially supported by the Shiraz University Research Council Grant No. 79-SC-1311-675. 相似文献
19.
In this paper we investigate a class of Lie group actions on
, the so-calledpolar actions, that naturally generalize the standard
actions. For a domain invariant under such an action (i.e., a generalized Reinhardt domain) we characterize the invariant
plurisubharmonic functions and determine the envelope of holomorphy in geometric terms. For a generalized Reinhardt domain
containing the origin of
we also compute its automorphism group.
Supported in part by NSF Grant 8602020 相似文献
20.
Yasunori Fujikoshi Yoshimichi Ochi 《Annals of the Institute of Statistical Mathematics》1984,36(1):119-128
Summary In this paper we obtain an asymptotic expansion of the distribution of the maximum likelihood estimate (MLE)
based onT observations from the first order Gaussian process up to the term of orderT
−1. The expansion is used to compare
with a generalized estimate
including the least square estimate (LSE)
, based on the asymptotic probabilities around the true value of the estimates up to the terms of orderT
−1. It is shown that
(or the modified MLE
) is better than
(or the modified estimate
). Further, we note that
does not attain the bound for third order asymptotic median unbiased estimates. 相似文献