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1.
The degree conjecture for the Selberg class
of L-functions states that the degree d
F
of every F ∈
is an integer. Moreover, it is expected that every F ∈
has polynomial Euler product, and that the degree ∂
F
of such an Euler product coincides with d
F
. In this note we prove that a suitable continuity assumption on the degree d
F
implies that ∂
F
= d
F
for all F ∈
with polynomial Euler product.
相似文献
2.
Sergiy Maksymenko 《Central European Journal of Mathematics》2009,7(2):272-298
Let F be a C
∞ vector field defined near the origin O ∈ ℝ
n
, F(O) = 0, and (F
t
) be its local flow. Denote by
the set of germs of orbit preserving diffeomorphisms h: ℝ
n
→ ℝ
n
at O, and let
, (r ≥ 0), be the identity component of
with respect to the weak Whitney W
r
topology. Then
contains a subset
consisting of maps of the form F
α(x)(x), where α: ℝ
n
→ ℝ runs over the space of all smooth germs at O. It was proved earlier by the author that if F is a linear vector field, then
=
.
In this paper we present a class of examples of vector fields with degenerate singularities at O for which
formally coincides with
, i.e. on the level of ∞-jets at O.
We also establish parameter rigidity of linear vector fields and “reduced” Hamiltonian vector fields of real homogeneous polynomials
in two variables.
相似文献
3.
R. Rimányi V. Schechtman V. Tarasov A. Varchenko 《Functional Analysis and Its Applications》2011,45(4):252-264
We interpret the equivariant cohomology HGLn *H_{GL_n }^* (ℱ
λ
,ℂ) of a partial flag variety ℱ
λ
parametrizing chains of subspaces 0 = F
0 ⊂ F
1 ⊂ … ⊂ F
N
= ℂ
n
, dimF
i
/F
i−1 = λ
i
, as the Bethe algebra of the -weight subspace of a [t]-module . 相似文献
4.
Let (X,d
X
) be an n-point metric space. We show that there exists a distribution over non-contractive embeddings into trees f: X → T such that for every x ∈ X, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs,
including fault-tolerant versions of k-median and facility location. 相似文献
5.
Yu Cheng Li 《数学学报(英文版)》2008,24(10):1737-1750
In this paper, using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space. For f(z) = z^ng(z) (n ≥1), g(z) = b0 + b1z^p1 +b2z^p2 +.. , bk ≠ 0 (k = 0, 1, 2,...), our main result is =A′(Mf) = A′(Mzn)∩A′(Mg) = A′(Mz^s), where s = g.c.d.(n,p1,p2,...). In the last section, we study the relation between strongly irreducible curve and the winding number W(f,f(α)), α ∈ D. 相似文献
6.
Let m and n be fixed, positive integers and P a space composed of real polynomials in m variables. The authors study functions f : R →R which map Gram matrices, based upon n points of R^m, into matrices, which are nonnegative definite with respect to P Among other things, the authors discuss continuity, differentiability, convexity, and convexity in the sense of Jensen, of such functions 相似文献
7.
Han Peters 《Mathematische Annalen》2007,337(1):1-13
Let F be an automorphism of which has an attracting fixed point. It is well known that the basin of attraction is biholomorphically equivalent to . We will show that the basin of attraction of a sequence of automorphisms f
1, f
2, . . . is also biholomorphic to if every f
n
is a small perturbation of the original map F. 相似文献
8.
For an additive subgroup G of a field F of characteristic zero, a Lie algebra B(G) of Block type is defined with basis {Lα,i| α∈G, i∈Z+} and relations [Lα,i, Lβ,j] = (β-α)Lα+β,i+j+(αj-βi)Lα+β,Lα+β,i+j-1.It is proved that an irreducible highest weight B(Z)-module is quasifinite if and only if it is a proper quotient of a Verma module. Furthermore, for a total order λ on G and any ∧∈B(G)0^*(the dual space of B(G)0 = span{L0,i|i∈Z+}), a Verma B(G)-module M(∧,λ) is defined, and the irreducibility of M(A,λ) is completely determined. 相似文献
9.
D. F. Miller 《Journal of Optimization Theory and Applications》2007,134(3):413-432
This paper develops boundary integral representation formulas for the second variations of cost functionals for elliptic domain
optimization problems. From the collection of all Lipschitz domains Ω which satisfy a constraint ∫
Ω
g(x) dx=1, a domain is sought which maximizes either
, fixed x
0∈Ω, or ℱ(Ω)=∫
Ω
F(x,u(x)) dx, where u solves the Dirichlet problem Δu(x)=−f(x), x∈Ω, u(x)=0, x∈∂Ω. Necessary and sufficient conditions for local optimality are presented in terms of the first and second variations of the
cost functionals
and ℱ. The second variations are computed with respect to domain variations which preserve the constraint. After first summarizing
known facts about the first variations of u and the cost functionals, a series of formulas relating various second variations of these quantities are derived. Calculating
the second variations depends on finding first variations of solutions u when the data f are permitted to depend on the domain Ω. 相似文献
10.
Ján Jakubík 《Mathematica Slovaca》2008,58(3):289-300
In a previous author’s paper, sequential convergences on an MV-algebra
have been studied; the Urysohn’s axiom was assumed to be valid. The system of all such convergences was denoted by Conv
. In the present paper we investigate analogous questions without supposing the validity of the Urysohn’s axiom; the corresponding
system of convergences is denoted by conv
. Both Conv
and conv
are partially ordered by the set-theoretical inclusion. We deal with the properties of conv 289-6 and the relations between conv
and Conv
. We prove that each interval of conv
is a distributive lattice. The system conv
has the least element, but it does not possess any atom. Hence it is either a singleton set or it is infinite. We consider
also the relations between conv
and conv G, where (G, u) is a unital lattice-ordered group with
= Γ (G, u).
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence — Physics of
Information, Grant 1/2/2005. 相似文献
11.
Cheng Jun Hou 《数学学报(英文版)》2008,24(6):983-996
We introduce two notions of the pressure in operator algebras, one is the pressure Pα(π, T) for an automorphism α of a unital exact C^*-algebra A at a self-adjoint element T in A with respect to a faithful unital *-representation π the other is the pressure Pτ,α(T) for an automorphism α of a hyperfinite von Neumann algebra M at a self-adjoint element T in M with respect to a faithful normal α-invariant state τ. We give some properties of the pressure, show that it is a conjugate invaxiant, and also prove that the pressure of the implementing inner automorphism of a crossed product A×α Z at a self-adjoint operator T in A equals that of α at T. 相似文献
12.
Ján Jakubík 《Mathematica Slovaca》2008,58(2):143-154
For an MV-algebra
let J
0(
) be the system of all closed ideals of
; this system is partially ordered by the set-theoretical inclusion. A radical class X of MV-algebras will be called a K-radical class iff, whenever
∈ X and
is an MV-algebra with J
0(
) ≅ J
0(
), then
∈ X. An analogous notation for lattice ordered groups was introduced and studied by Conrad. In the present paper we show that
there is a one-to-one correspondence between K-radical classes of MV-algebras and K-radical classes of abelian lattice ordered groups. We also prove an analogous result for product radical classes of MV-algebras; product radical classes of lattice ordered groups were studied by Ton.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information,
Grant I/2/2005. 相似文献
13.
Marian Genčev 《Mathematica Slovaca》2009,59(3):365-378
The aim of the paper is the investigation of special infinite series of the form
where (a, b, m
1, m
2, θ, c, P(n)) ∈ ℝ4 × ℂ × {±1} ×
[n] and is a sequence of rational functions. A general summation method for the sum above in the case of the special choice of parameters
a, b and f
n
(n) is included. We find the 2m-tuple of rational numbers α
i
, β
j
(1 ≤ i ≤ m, 1 ≤ j ≤ m) for which
iff
and vice versa.
相似文献
14.
We investigate classes of the so-called ring Q-homeomorphisms including, in particular, Q-homeomorphisms, various classes of homeomorphisms with finite length distortion, Sobolev’s classes etc. In terms of the majorant
Q(x), we give a series of criteria for normality based on estimates of the distortion of the spherical distance under ring Q-homeomorphisms. In particular, it is shown that the class of all ring Q-homeomorphisms f of a domain D ⊂ ℝ
n
into
, n ≥ 2, with
, forms a normal family, if Q(x) has finite mean oscillation in D. We also prove normality of , for instance, if Q(x) has singularities of logarithmic type whose degrees are not greater than n − 1 at every point x ∈ D. The results are applicable, in particular, to mappings with finite length distortion and Sobolev’s classes. 相似文献
15.
P. Quittner W. Reichel 《Calculus of Variations and Partial Differential Equations》2008,32(4):429-452
Consider the equation −Δu = 0 in a bounded smooth domain , complemented by the nonlinear Neumann boundary condition ∂ν
u = f(x, u) − u on ∂Ω. We show that any very weak solution of this problem belongs to L
∞(Ω) provided f satisfies the growth condition |f(x, s)| ≤ C(1 + |s|
p
) for some p ∈ (1, p*), where . If, in addition, f(x, s) ≥ −C + λs for some λ > 1, then all positive very weak solutions are uniformly a priori bounded. We also show by means of examples that
p* is a sharp critical exponent. In particular, using variational methods we prove the following multiplicity result: if N ∈ {3, 4} and f(x, s) = s
p
then there exists a domain Ω and such that our problem possesses at least two positive, unbounded, very weak solutions blowing up at a prescribed point of
∂Ω provided . Our regularity results and a priori bounds for positive very weak solutions remain true if the right-hand side in the differential
equation is of the form h(x, u) with h satisfying suitable growth conditions. 相似文献
16.
Edoardo Ballico 《Central European Journal of Mathematics》2009,7(1):54-58
Here we study the deformation theory of some maps f: X → ℙ
r
, r = 1, 2, where X is a nodal curve and f|T is not constant for every irreducible component T of X. For r = 1 we show that the “stratification by gonality” for any subset of
with fixed topological type behaves like the stratification by gonality of M
g.
相似文献
17.
De Xu Zhou 《数学学报(英文版)》2009,25(9):1567-1582
Assume that S is an almost excellent extension of R. Using functors HomR(S,-) and -×R S, we establish some connections between classes of modules lR and lS, cotorsion pairs (AR, BR) and (AS, BS). If lS is a T-extension or (and) H-extension of lR, we show that lS is a (resp., monomorphic, epimorphic, special) preenveloping class if and only if so is lR. If (AS, BS) is a TH- extension of (AR, BR), we obtain that (AS, BS) is complete (resp., of finite type, of cofinite type, hereditary, perfect, n-tilting) if and only if so is (AR, BR). 相似文献
18.
This paper studies the asymptotic behavior near the boundary for large solutions of the semilinear equation Δu + au = b(x)f(u) in a smooth bounded domain Ω of ℝN with N ≥ 2, where a is a real parameter and b is a nonnegative smooth function on
. We assume that f(u) behaves like u(ln u)α as u → ∞, for some α > 2. It turns out that this case is more difficult to handle than those where f(u) grows like u
p (p > 1) or faster at infinity. Under suitable conditions on the weight function b(x), which may vanish on ∂Ω, we obtain the first order expansion of the large solutions near the boundary. We also obtain some
uniqueness results.
Research of both authors supported by the Australian Research Council. 相似文献
19.
Let (, d, μ) be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we consider the behavior on × ⋯ × for the m-linear singular integral operators with nonsmooth kernels which were first introduced by Duong, Grafakos and Yan. 相似文献
20.
Ján Jakubík 《Czechoslovak Mathematical Journal》2008,58(4):1129-1143
The notion of bounded commutative residuated ℓ-monoid (BCR ℓ-monoid, in short) generalizes both the notions of MV-algebra and of BL-algebra. Let
be a BCR ℓ-monoid; we denote by ℓ(
) the underlying lattice of
. In the present paper we show that each direct product decomposition of ℓ(
) determines a direct product decomposition of
. This yields that any two direct product decompositions of
have isomorphic refinements. We consider also the relations between direct product decompositions of
and states on
.
This work was supported by Slovak Research and Development Agency under the contract No APVV-0071-06.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information
(grant I/2/2005). 相似文献