共查询到20条相似文献,搜索用时 31 毫秒
1.
Let X be a homogeneous polynomial vector field of degree 2 on $
\mathbb{S}^2
$
\mathbb{S}^2
. We show that if X has at least a non-hyperbolic singularity, then it has no limit cycles. We give necessary and sufficient conditions for determining
if a singularity of X on $
\mathbb{S}^2
$
\mathbb{S}^2
is a center and we characterize the global phase portrait of X modulo limit cycles. We also study the Hopf bifurcation of X and we reduce the 16
th
Hilbert’s problem restricted to this class of polynomial vector fields to the study of two particular families. Moreover,
we present two criteria for studying the nonexistence of periodic orbits for homogeneous polynomial vector fields on $
\mathbb{S}^2
$
\mathbb{S}^2
of degree n. 相似文献
2.
In this note we construct a function φ in L2(Bn,dμ) which is unbounded on any neighborhood of each boundary point of Bn such that Tφ is a trace class operator on weighted Bergman space Lα2(Bn,dμ) for several complex variables. 相似文献
3.
B. Wróbel 《Acta Mathematica Hungarica》2009,124(4):333-351
Imaginary powers associated to the Laguerre differential operator $
L_\alpha = - \Delta + |x|^2 + \sum _{i = 1}^d \frac{1}
{{x_i^2 }}(\alpha _i^2 - 1/4)
$
L_\alpha = - \Delta + |x|^2 + \sum _{i = 1}^d \frac{1}
{{x_i^2 }}(\alpha _i^2 - 1/4)
are investigated. It is proved that for every multi-index α = (α1,...α
d
) such that α
i
≧ −1/2, α
i
∉ (−1/2, 1/2), the imaginary powers $
\mathcal{L}_\alpha ^{ - i\gamma } ,\gamma \in \mathbb{R}
$
\mathcal{L}_\alpha ^{ - i\gamma } ,\gamma \in \mathbb{R}
, of a self-adjoint extension of L
α, are Calderón-Zygmund operators. Consequently, mapping properties of $
\mathcal{L}_\alpha ^{ - i\gamma }
$
\mathcal{L}_\alpha ^{ - i\gamma }
follow by the general theory. 相似文献
4.
Stevo Stević 《Siberian Mathematical Journal》2009,50(6):1098-1105
Let $
\mathbb{B}
$
\mathbb{B}
be the unit ball in ℂ
n
and let H($
\mathbb{B}
$
\mathbb{B}
) be the space of all holomorphic functions on $
\mathbb{B}
$
\mathbb{B}
. We introduce the following integral-type operator on H($
\mathbb{B}
$
\mathbb{B}
):
$
I_\phi ^g (f)(z) = \int\limits_0^1 {\operatorname{Re} f(\phi (tz))g(tz)\frac{{dt}}
{t}} ,z \in \mathbb{B},
$
I_\phi ^g (f)(z) = \int\limits_0^1 {\operatorname{Re} f(\phi (tz))g(tz)\frac{{dt}}
{t}} ,z \in \mathbb{B},
相似文献
5.
Let X and Y be two smooth Deligne-Mumford stacks and consider a pair of functions f: X → $
\mathbb{A}^1
$
\mathbb{A}^1
, g:Y → $
\mathbb{A}^1
$
\mathbb{A}^1
. Assuming that there exists a complex of sheaves on X × $
\mathbb{A}^1
$
\mathbb{A}^1
Y which induces an equivalence of D
b
(X) and D
b
(Y), we show that there is also an equivalence of the singular derived categories of the fibers f
−1(0) and g
−1(0). We apply this statement in the setting of McKay correspondence, and generalize a theorem of Orlov on the derived category
of a Calabi-Yau hypersurface in a weighted projective space, to products of Calabi-Yau hypersurfaces in simplicial toric varieties
with nef anticanonical class. 相似文献
6.
Mei-Chu Chang 《Combinatorica》2009,29(6):629-635
In this note, we use ‘classical’ methods to obtain sum-product theorems for subsets A⊂$
\mathbb{F}
$
\mathbb{F}
p
. 相似文献
7.
We obtain characterizations (and prove the corresponding equivalence of norms) of function spaces B
pq
sm
($
\mathbb{I}
$
\mathbb{I}
k
) and L
pq
sm
($
\mathbb{I}
$
\mathbb{I}
k
) of Nikol’skii-Besov and Lizorkin-Triebel types, respectively, in terms of representations of functions in these spaces by
Fourier series with respect to a multiple system $
\mathcal{W}_m^\mathbb{I}
$
\mathcal{W}_m^\mathbb{I}
of Meyer wavelets and in terms of sequences of the Fourier coefficients with respect to this system. We establish order-sharp
estimates for the approximation of functions in B
pq
sm
($
\mathbb{I}
$
\mathbb{I}
) and L
pq
sm
($
\mathbb{I}
$
\mathbb{I}
k
) by special partial sums of these series in the metric of L
r
($
\mathbb{I}
$
\mathbb{I}
k
) for a number of relations between the parameters s, p, q, r, and m (s = (s
1, ..., s
n
) ∈ ℝ+
n
, 1 ≤ p, q, r ≤ ∞, m = (m
1, ..., m
n
) ∈ ℕ
n
, k = m
1 +... + m
n
, and $
\mathbb{I}
$
\mathbb{I}
= ℝ or $
\mathbb{T}
$
\mathbb{T}
). In the periodic case, we study the Fourier widths of these function classes. 相似文献
8.
Assume that no cardinal κ < 2
ω
is quasi-measurable (κ is quasi-measurable if there exists a κ-additive ideal
$
\mathbb{I}
$
\mathbb{I}
of X contains uncountably many pairwise disjoint subfamilies
$
\mathbb{I}
$
\mathbb{I}
-Bernstein unions ∪
$
\mathbb{I}
$
\mathbb{I}
-Bernstein if A and X \ A meet each Borel $
\mathbb{I}
$
\mathbb{I}
-positive subset B ⊆ X). This result is a generalization of the Four Poles Theorem (see [1]) and results from [2] and [4]. 相似文献
9.
V. G. Puzarenko 《Siberian Advances in Mathematics》2010,20(2):128-154
We study some properties of a $
\mathfrak{c}
$
\mathfrak{c}
-universal semilattice $
\mathfrak{A}
$
\mathfrak{A}
with the cardinality of the continuum, i.e., of an upper semilattice of m-degrees. In particular, it is shown that the quotient semilattice of such a semilattice modulo any countable ideal will be
also $
\mathfrak{c}
$
\mathfrak{c}
-universal. In addition, there exists an isomorphism
$
\mathfrak{A}
$
\mathfrak{A}
such that $
{\mathfrak{A} \mathord{\left/
{\vphantom {\mathfrak{A} {\iota \left( \mathfrak{A} \right)}}} \right.
\kern-\nulldelimiterspace} {\iota \left( \mathfrak{A} \right)}}
$
{\mathfrak{A} \mathord{\left/
{\vphantom {\mathfrak{A} {\iota \left( \mathfrak{A} \right)}}} \right.
\kern-\nulldelimiterspace} {\iota \left( \mathfrak{A} \right)}}
will be also $
\mathfrak{c}
$
\mathfrak{c}
-universal. Furthermore, a property of the group of its automorphisms is obtained. To study properties of this semilattice,
the technique and methods of admissible sets are used. More exactly, it is shown that the semilattice of mΣ-degrees $
L_{m\Sigma }^{\mathbb{H}\mathbb{F}\left( S \right)}
$
L_{m\Sigma }^{\mathbb{H}\mathbb{F}\left( S \right)}
on the hereditarily finite superstructure $
\mathbb{H}\mathbb{F}
$
\mathbb{H}\mathbb{F}
(S) over a countable set S will be a $
\mathfrak{c}
$
\mathfrak{c}
-universal semilattice with the cardinality of the continuum. 相似文献
10.
A. V. Stolyarov 《Russian Mathematics (Iz VUZ)》2010,54(11):56-65
In this paper, the following results are obtained: 1) It is proved that, in the fourth order differential neighborhood, a
regular hypersurface V
n−1 embedded into a projective-metric space K
n
, n ≥ 3, intrinsically induces a dual projective-metric space $
\bar K_n
$
\bar K_n
. 2) An invariant analytical condition is established under which a normalization of a hypersurface V
n−1 ⊂ K
n
(a tangential hypersurface $
\bar V_{n - 1}
$
\bar V_{n - 1}
⊂ $
\bar K_n
$
\bar K_n
) by quasitensor fields H
n
i
, H
i
($
\bar H_n^i
$
\bar H_n^i
, $
\bar H_i
$
\bar H_i
) induces a Riemannian space of constant curvature. If the two conditions are fulfilled simultaneously, the spaces R
n−1 and $
\bar R_{n - 1}
$
\bar R_{n - 1}
are spaces of the same constant curvature $
K = - \tfrac{1}
{c}
$
K = - \tfrac{1}
{c}
. 3) Geometric interpretations of the obtained analytical conditions are given. 相似文献
11.
The set of all m × n Boolean matrices is denoted by $
\mathbb{M}
$
\mathbb{M}
m,n
. We call a matrix A ∈ $
\mathbb{M}
$
\mathbb{M}
m,n
regular if there is a matrix G ∈ $
\mathbb{M}
$
\mathbb{M}
n,m
such that AGA = A. In this paper, we study the problem of characterizing linear operators on $
\mathbb{M}
$
\mathbb{M}
m,n
that strongly preserve regular matrices. Consequently, we obtain that if min{m, n} ⩽ 2, then all operators on $
\mathbb{M}
$
\mathbb{M}
m,n
strongly preserve regular matrices, and if min{m, n} ⩾ 3, then an operator T on $
\mathbb{M}
$
\mathbb{M}
m,n
strongly preserves regular matrices if and only if there are invertible matrices U and V such that T(X) = UXV for all X ε $
\mathbb{M}
$
\mathbb{M}
m,n
, or m = n and T(X) = UX
T
V for all X ∈ $
\mathbb{M}
$
\mathbb{M}
n
. 相似文献
12.
A. I. Stukachev 《Siberian Mathematical Journal》2010,51(3):515-524
We show that each c-simple theory with an additional discreteness condition has an uncountable model Σ-definable in ℍ$
\mathbb{H}
$
\mathbb{H}
($
\mathbb{L}
$
\mathbb{L}
), where $
\mathbb{L}
$
\mathbb{L}
is a dense linear order. From this we establish the same for all c-simple theories of finite signature that are submodel complete. 相似文献
13.
It is proved that for any two subsets A and B of an arbitrary finite field $
\mathbb{F}_q
$
\mathbb{F}_q
such that |A||B| > q, the identity 10AB = $
\mathbb{F}_q
$
\mathbb{F}_q
holds. Under the assumption |A||B| ⩾2q, this improves to 8AB = $
\mathbb{F}_q
$
\mathbb{F}_q
. 相似文献
14.
Szymon Gła̧b 《Central European Journal of Mathematics》2009,7(4):732-740
Let $
\mathcal{K}
$
\mathcal{K}
(ℝ) stand for the hyperspace of all nonempty compact sets on the real line and let d
±(x;E) denote the (right- or left-hand) Lebesgue density of a measurable set E ⊂ ℝ at a point x∈ ℝ. In [3] it was proved that
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