共查询到20条相似文献,搜索用时 15 毫秒
1.
Binyamin Schwarz 《Israel Journal of Mathematics》1993,84(1-2):119-128
LetH be the domain inC
2 defined byH={Z=(z
1,z
2):║Z║1=│z║1│+│z║2│<1}. LetC
H(z,w) be the Carathéodory distance ofH,z,w∈H. The Carathéodory ballB
C(zC,α;H) with centerz
C,zC∈H, and radius α, 0<α<1, is defined byB
c(zC,α;H)={z∶CH(z,zC)<arc tanh α}. The norm ballB
N(zN,r) with centerz
N,zN∈H, and radiusr, 0<r<1-‖z
N‖1, is defined byB
N(zN,r)={z∶ ‖z−zN‖1<r}.
Theorem:The only Carathéodory balls of H which are also norm balls are those with their center at the origin. 相似文献
2.
Qiao Hua Yang 《数学学报(英文版)》2010,26(8):1575-1590
Let G be a simple Lie group of real rank one and N be in the Iwasawa decomposition of G. Under the assumption of some symmetries, we obtain an existent result for the nonlinear equation △NU + (1 + ∈K(x, z))u2*-1 = 0 on N, which generalizes the result of Malchiodi and Uguzzoni to the Kohn's subelliptic context on N in presence of symmetry. 相似文献
3.
Zeng Jian LOU Shou Zhi YANG Dao Jin SONG 《数学学报(英文版)》2005,21(4):949-954
We give a decomposition of the Hardy space Hz^1(Ω) into "div-curl" quantities for Lipschitz domains in R^n. We also prove a decomposition of Hz^1(Ω) into Jacobians det Du, u ∈ W0^1,2 (Ω,R^2) for Ω in R^2. This partially answers a well-known open problem. 相似文献
4.
In recent years, the spin parity effect in magnetic macroscopic quantum tunneling has attracted extensive attention. Using
the spin coherent-state path-integral method it is shown that if the HamiltonianH of a single-spin system hasM - fold rotational symmetry around z-axis, the tunneling amplitude 〈−S|e
Ht
|S〉 vanishes when S, the quantum number of spin, is not an integer multiple ofM/2, where |m〉 (m=-S, -S +1, ⋯, S) are the eigenstates of Sz. Not only is a pure quantum mechanical approach adopted to the above result, but also is extended to more general cases where
the quantum system consists ofN spins, the quantum numbers of which can take any values, including the single-spin system, ferromagnetic particle and antiferromagnetic
particle as particular instances, and where the states involved are not limited to the extreme ones. The extended spin parity
effect is that if the Hamiltonian ℋ of the system ofN spins also has the above symmetry, then 〈m′N⋯m′2
m′1|e−H
t
|m
1
m
2⋯m
N vanishes when ∑
i=1
N
(m
i−m′1) not an integer multiple ofM, where |m
1
m
2⋯m
N〉=∏
α=1
N
|m
a
〉 are the eigenstates of S
a
z
. In addition, it is argued that for large spin the above result, the so-called spin parity effect, does not mean the quenching
of spin tunneling from the direction of ⊕-z to that of ±z.
Project supported by the National Natural Science Foundation of China (Grant Nos. 19674002, 19677101). 相似文献
5.
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
6.
A. M. Vershik 《Journal of Mathematical Sciences》2011,176(1):1-6
The paper studies the region of values of the system {c
2, c
3, f(z
1), f′(z
1)},where z
1 is an arbitrary fixed point of the disk |z| < 1; f ∈ T,and the class T consists of all the functions f(z) = z + c
2
z
2 + c
3z3 + ⋯ regular in the disk |z| < 1 that satisfy the condition Im z · Im f(z) > 0 for Im z ≠ 0. The region of values of f′(z
1) in the subclass of functions f ∈ T with prescribed values c
2, c
3, and f(z
1) is determined. Bibliography: 10 titles. 相似文献
7.
G. I. Shishkin L. P. Shishkina 《Computational Mathematics and Mathematical Physics》2010,50(12):2003-2022
For the one-dimensional singularly perturbed parabolic reaction-diffusion equation with a perturbation parameter ɛ, where
ɛ ∈ (0, 1], the grid approximation of the Dirichlet problem on a rectangular domain in the (x, t)-plane is examined. For small ɛ, a parabolic boundary layer emerges in a neighborhood of the lateral part of the boundary
of this domain. A new approach to the construction of ɛ-uniformly converging difference schemes of higher accuracy is developed
for initial boundary value problems. The asymptotic construction technique is used to design the base decomposition scheme
within which the regular and singular components of the grid solution are solutions to grid subproblems defined on uniform
grids. The base scheme converges ɛ-uniformly in the maximum norm at the rate of O(N
−2ln2
N + N
0−1), where N + 1 and N
0 + 1 are the numbers of nodes in the space and time meshes, respectively. An application of the Richardson extrapolation technique
to the base scheme yields a higher order scheme called the Richardson decomposition scheme. This higher order scheme convergesɛ-uniformly
at the rate of O(N
−4ln4
N + N
0−2). For fixed values of the parameter, the convergence rate is O(N
−4 + N
0−2). 相似文献
8.
For a backward shift invariant subspace N in H^2(Г^2), the operators Sz and Sw on N are defined by Sz = PNTz|N and Sw, = PNTw|N, where PN is the orthogonal projection from L^2(Г^2) onto N. We give a characterization of N satisfying rank [Sz, Sw^*] = 1. 相似文献
9.
E. G. Goluzina 《Journal of Mathematical Sciences》2006,137(3):4774-4779
The paper studies the region of values Dm,1(T) of the system {ƒ(z1), ƒ(z2), …, ƒ(zm), ƒ(r)}, m e 1, where zj (j = 1, 2, …,m) are arbitrary fixed points of the disk U = {z: |z| < 1} with Im zj ≠ 0 (j = 1, 2, …,m), and r, 0 < r < 1, is fixed, in the class T of functions ƒ(z) = z+a2z2+ ⋯ regular in the disk U and satisfying in the latter the condition Im ƒ(z) Imz > 0 for Im z ≠ 0. An algebraic characterization of the set Dm,1(T) in terms of nonnegative-definite Hermitian forms is given, and all the boundary functions are described. As an implication,
the region of values of ƒ(zm) in the subclass of functions from the class T with prescribed values ƒ(zk) (k = 1, 2, …,m − 1) and ƒ(r) is determined. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 24–33. Original article submitted June 13, 2005. 相似文献
10.
Let Λℝ denote the linear space over ℝ spanned by z
k
, k∈ℤ. Define the real inner product 〈⋅,⋅〉
L
:Λℝ×Λℝ→ℝ,
, N∈ℕ, where V satisfies: (i) V is real analytic on ℝ∖{0}; (ii) lim
|
x
|→∞(V(x)/ln (x
2+1))=+∞; and (iii) lim
|
x
|→0(V(x)/ln (x
−2+1))=+∞. Orthogonalisation of the (ordered) base
with respect to 〈⋅,⋅〉
L
yields the even degree and odd degree orthonormal Laurent polynomials (OLPs)
: φ
2n
(z)=∑
k=−n
n
ξ
k
(2n)
z
k
, ξ
n
(2n)>0, and φ
2n+1(z)=∑
k=−n−1
n
ξ
k
(2n+1)
z
k
, ξ
−n−1(2n+1)>0. Associated with the even degree and odd degree OLPs are the following two pairs of recurrence relations: z
φ
2n
(z)=c
2n
♯
φ
2n−2(z)+b
2n
♯
φ
2n−1(z)+a
2n
♯
φ
2n
(z)+b
2n+1
♯
φ
2n+1(z)+c
2n+2
♯
φ
2n+2(z) and z
φ
2n+1(z)=b
2n+1
♯
φ
2n
(z)+a
2n+1
♯
φ
2n+1(z)+b
2n+2
♯
φ
2n+2(z), where c
0
♯
=b
0
♯
=0, and c
2k
♯
>0, k∈ℕ, and z
−1
φ
2n+1(z)=γ
2n+1
♯
φ
2n−1(z)+β
2n+1
♯
φ
2n
(z)+α
2n+1
♯
φ
2n+1(z)+β
2n+2
♯
φ
2n+2(z)+γ
2n+3
♯
φ
2n+3(z) and z
−1
φ
2n
(z)=β
2n
♯
φ
2n−1(z)+α
2n
♯
φ
2n
(z)+β
2n+1
♯
φ
2n+1(z), where β
0
♯
=γ
1
♯
=0, β
1
♯
>0, and γ
2l+1
♯
>0, l∈ℕ. Asymptotics in the double-scaling limit N,n→∞ such that N/n=1+o(1) of the coefficients of these two pairs of recurrence relations, Hankel determinant ratios associated with the real-valued,
bi-infinite strong moment sequence
, and the products of the (real) roots of the OLPs are obtained by formulating the even degree and odd degree OLP problems
as matrix Riemann-Hilbert problems on ℝ, and then extracting the large-n behaviours by applying the non-linear steepest-descent method introduced in (Ann. Math. 137(2):295–368, [1993]) and further developed in (Commun. Pure Appl. Math. 48(3):277–337, [1995]) and (Int. Math. Res. Not. 6:285–299, [1997]).
相似文献
11.
S Ponnusamy 《Proceedings Mathematical Sciences》1994,104(2):397-411
Denote byS
* (⌕), (0≤⌕<1), the family consisting of functionsf(z)=z+a
2z2+...+anzn+... that are analytic and starlike of order ⌕, in the unit disc ⋎z⋎<1. In the present article among other things, with very
simple conditions on μ, ⌕ andh(z) we prove the f’(z) (f(z)/z)μ−1<h(z) implies f∈S*(⌕). Our results in this direction then admit new applications in the study of univalent functions. In many cases these results
considerably extend the earlier works of Miller and Mocanu [6] and others. 相似文献
12.
For given analytic functions ϕ(z) = z + Σ
n=2∞ λ
n
z
n
, Ψ(z) = z + Σ
n=2∞ μ with λ
n
≥ 0, μ
n
≥ 0, and λ
n
≥ μ
n
and for α, β (0≤α<1, 0<β≤1), let E(φ,ψ; α, β) be of analytic functions ƒ(z) = z + Σ
n=2∞
a
n
z
n
in U such that f(z)*ψ(z)≠0 and
for z∈U; here, * denotes the Hadamard product. Let T be the class of functions ƒ(z) = z - Σ
n=2∞|a
n
| that are analytic and univalent in U, and let E
T
(φ,ψ;α,β)=E(φ,ψ;α,β)∩T. Coefficient estimates, extreme points, distortion properties, etc. are determined for the class E
T
(φ,ψ;α,β) in the case where the second coefficient is fixed. The results thus obtained, for particular choices of φ(z) and ψ(z), not only generalize various known results but also give rise to several new results.
University of Bahrain, Isa Town, Bahrain. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 9, pp. 1162–1170,
September, 1997. 相似文献
13.
Summary For P∈ F2[z] with P(0)=1 and deg(P)≧ 1, let A =A(P) be the unique subset of N (cf. [9]) such that Σn≧0 p(A,n)zn ≡ P(z) mod 2, where p(A,n) is the number of partitions of n with parts in A. To determine the elements of the set A, it is important to consider the sequence σ(A,n) = Σ d|n, d∈A d, namely, the periodicity of the sequences (σ(A,2kn) mod 2k+1)n≧1 for all k ≧ 0 which was proved in [3]. In this paper, the values of such sequences will be given in terms of orbits. Moreover, a formula
to σ(A,2kn) mod 2k+1 will be established, from which it will be shown that the weight σ(A1,2kzi) mod 2k+1 on the orbit <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>z_i$
is moved on some other orbit zj when A1 is replaced by A2 with A1= A(P1) and A2= A(P2) P1 and P2 being irreducible in F2[z] of the same odd order. 相似文献
14.
Let N be a compact simply connected smooth Riemannian manifold and, for p ∈ {2,3,...}, W
1,p
(R
p+1, N) be the Sobolev space of measurable maps from R
p+1 into N whose gradients are in L
p
. The restriction of u to almost every p-dimensional sphere S in R
p+1 is in W
1,p
(S, N) and defines an homotopy class in π
p
(N) (White 1988). Evaluating a fixed element z of Hom(π
p
(N), R) on this homotopy class thus gives a real number Φ
z,u
(S). The main result of the paper is that any W
1,p
-weakly convergent limit u of a sequence of smooth maps in C
∞(R
p+1, N), Φ
z,u
has a rectifiable Poincaré dual
. Here Γ is a a countable union of C
1 curves in R
p+1 with Hausdorff -measurable orientation and density function θ: Γ→R. The intersection number between and S evaluates Φ
z,u
(S), for almost every p-sphere S. Moreover, we exhibit a non-negative integer n
z
, depending only on homotopy operation z, such that even though the mass may be infinite. We also provide cases of N, p and z for which this rational power p/(p + n
z
) is optimal. The construction of this Poincaré dual is based on 1-dimensional “bubbling” described by the notion of “scans”
which was introduced in Hardt and Rivière (2003). We also describe how to generalize these results to R
m
for any m ⩾ p + 1, in which case the bubbling is described by an (m–p)-rectifiable set with orientation and density function determined by restrictions of the mappings to almost every oriented
Euclidean p-sphere. 相似文献
15.
16.
The first part of this paper is devoted to the study of FN{\Phi_N} the orthogonal polynomials on the circle, with respect to a weight of type f = (1 − cos θ)
α
c where c is a sufficiently smooth function and ${\alpha > -\frac{1}{2}}${\alpha > -\frac{1}{2}}. We obtain an asymptotic expansion of the coefficients F*(p)N(1){\Phi^{*(p)}_{N}(1)} for all integer p where F*N{\Phi^*_N} is defined by
F*N (z) = zN [`(F)]N(\frac1z) (z 1 0){\Phi^*_N (z) = z^N \bar \Phi_N(\frac{1}{z})\ (z \not=0)}. These results allow us to obtain an asymptotic expansion of the associated Christofel–Darboux kernel, and to compute the
distribution of the eigenvalues of a family of random unitary matrices. The proof of the results related to the orthogonal
polynomials are essentially based on the inversion of the Toeplitz matrix associated to the symbol f. 相似文献
17.
The aim of this paper is to prove some stability result for nonlinear elliptic systems of the form
where Δp denotes the p-Laplacian operator defined by Δpz = div(|∇ z|p-2∇ z); p > 2, Ω is a bounded domain in RN (N > 1) with smooth boundary where with h = 1 when α = 1, λ is a positive parameter and f,g are C2 functin on [0,∞) × [0,∞). We prove stability and instability results of positive stationary solutions under various choices
of f and g. 相似文献
18.
Dejan Kolarič 《Journal of Geometric Analysis》2009,19(4):847-863
Let A?? N be an algebraic variety with dim?A≤N?2. Given discrete sequences {a j },{b j }?? N \ A with slow growth ( $\sum_{j}{1\over|a_{j}|^{2}}<\infty,\sum_{j}{1\over |b_{j}|^{2}}<\inftyLet A⊂ℂ
N
be an algebraic variety with dim A≤N−2. Given discrete sequences {a
j
},{b
j
}⊂ℂ
N
\
A with slow growth (
?j[1/(|aj|2)] < ¥,?j[1/(|bj|2)] < ¥\sum_{j}{1\over|a_{j}|^{2}}<\infty,\sum_{j}{1\over |b_{j}|^{2}}<\infty
) we construct a holomorphic automorphism F with F(z)=z for all z∈A and F(a
j
)=b
j
for all j∈ℕ. Additional approximation of a given automorphism on a compact polynomially convex set, fixing A, is also possible. Given unbounded analytic variety A there is a tame set E such that F(E)≠{(j,0
N−1):j∈ℕ} for all automorphisms F with F|
A
=id. As an application we obtain an embedding of a Stein manifold into the complement of an algebraic variety in ℂ
N
with interpolation on a given discrete set. 相似文献
19.
James R. Holub 《Israel Journal of Mathematics》1985,52(3):231-238
LetW(D) denote the set of functionsf(z)=Σ
n=0
∞
A
n
Z
n
a
nzn for which Σn=0
∞|a
n
|<+∞. Given any finite set lcub;f
i
(z)rcub;
i=1
n
inW(D) the following are equivalent: (i) The generalized shift sequence lcub;f
1(z)z
kn
,f
2(z)z
kn+1, …,f
n
(z)z
(k+1)n−1rcub;
k=0
∞
is a basis forW(D) which is equivalent to the basis lcub;z
m
rcub;
m=0
∞
. (ii) The generalized shift sequence is complete inW(D), (iii) The function
has no zero in |z|≦1, wherew=e
2πiti
/n. 相似文献
20.
For α satisfying 0 < α < π, suppose that C
1 and C
2 are rays from the origin, C
1: z = re
i(π−α) and C
2: z = re
i(π+α), r ≥ 0, and that D = {z: | arg z − π| < α}. Let u be a nonconstant subharmonic function in the plane and define B(r, u) = sup|z|=r
u(z) and A
D
(r, u) = $
\inf _{z \in \bar D_r }
$
\inf _{z \in \bar D_r }
u(z), where D
r
= {z: z ∈ D and |z| = r}. If u(z) = (1 + o(1))B(|z|, u) as z → ∞ on C
1 ∪ C
2 and A
D
(r, u) = o(B(r, u)) as r → ∞, then the lower order of u is at least π/(2α). 相似文献