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1.
In this paper, we introduce the subfamilies H m ($ \mathcal{R}_{IV} $ \mathcal{R}_{IV} (n)) of holomorphic mappings defined on the Lie ball $ \mathcal{R}_{IV} $ \mathcal{R}_{IV} (n) which reduce to the family of holomorphic mappings and the family of locally biholomorphic mappings when m = 1 and m → +∞, respectively. Various distortion theorems for holomophic mappings H m ($ \mathcal{R}_{IV} $ \mathcal{R}_{IV} (n)) are established. The distortion theorems coincide with Liu and Minda’s as the special case of the unit disk. When m = 1 and m → +∞, the distortion theorems reduce to the results obtained by Gong for $ \mathcal{R}_{IV} $ \mathcal{R}_{IV} (n), respectively. Moreover, our method is different. As an application, the bounds for Bloch constants of H m ($ \mathcal{R}_{IV} $ \mathcal{R}_{IV} (n)) are given.  相似文献   

2.
We characterize and discuss the properties of $ \mathcal{I}R $ \mathcal{I}R -closed sets and $ A_{\mathcal{I}R} $ A_{\mathcal{I}R} -sets. Also, we give characterizations of weakly $ \mathcal{I} $ \mathcal{I} -locally closed sets and $ \mathcal{I} $ \mathcal{I} -submaximal spaces. A characterization of codense ideals in terms of $ \mathcal{I}R $ \mathcal{I}R -closed sets is also given.  相似文献   

3.
4.
$ \mathcal{I}_g $ \mathcal{I}_g -normal and $ \mathcal{I}_g $ \mathcal{I}_g -regular spaces are introduced and various characterizations and properties are given. Characterizations of normal, mildly normal, g-normal, regular and almost regular spaces are also given.  相似文献   

5.
We first propose a generalization of the notion of Mathieu subspaces of associative algebras $ \mathcal{A} $ \mathcal{A} , which was introduced recently in [Zhao W., Generalizations of the image conjecture and the Mathieu conjecture, J. Pure Appl. Algebra, 2010, 214(7), 1200–1216] and [Zhao W., Mathieu subspaces of associative algebras], to $ \mathcal{A} $ \mathcal{A} -modules $ \mathcal{M} $ \mathcal{M} . The newly introduced notion in a certain sense also generalizes the notion of submodules. Related with this new notion, we also introduce the sets σ(N) and τ(N) of stable elements and quasi-stable elements, respectively, for all R-subspaces N of $ \mathcal{A} $ \mathcal{A} -modules $ \mathcal{M} $ \mathcal{M} , where R is the base ring of $ \mathcal{A} $ \mathcal{A} . We then prove some general properties of the sets σ(N) and τ(N). Furthermore, examples from certain modules of the quasi-stable algebras [Zhao W., Mathieu subspaces of associative algebras], matrix algebras over fields and polynomial algebras are also studied.  相似文献   

6.
We develop a Wold decomposition for the shift semigroup on the Hardy space $ \mathcal{H}^2 $ \mathcal{H}^2 of square summable Dirichlet series convergent in the half-plane $ \Re (s) > 1/2 $ \Re (s) > 1/2 . As an application we have that a shift invariant subspace of $ \mathcal{H}^2 $ \mathcal{H}^2 is unitarily equivalent to $ \mathcal{H}^2 $ \mathcal{H}^2 if and only if it has the form $ \phi \mathcal{H}^2 $ \phi \mathcal{H}^2 for some $ \mathcal{H}^2 $ \mathcal{H}^2 -inner function φ.  相似文献   

7.
Let M be a smooth manifold with a regular foliation $ \mathcal{F} $ \mathcal{F} and a 2-form ω which induces closed forms on the leaves of $ \mathcal{F} $ \mathcal{F} in the leaf topology. A smooth map f: (M, $ \mathcal{F} $ \mathcal{F} ) → (N, σ) in a symplectic manifold (N, σ) is called a foliated symplectic immersion if f restricts to an immersion on each leaf of the foliation and further, the restriction of f*σ is the same as the restriction of ω on each leaf of the foliation. If f is a foliated symplectic immersion then the derivative map Df gives rise to a bundle morphism F: TMT N which restricts to a monomorphism on T $ \mathcal{F} $ \mathcal{F} ⊆ T M and satisfies the condition F*σ = ω on T $ \mathcal{F} $ \mathcal{F} . A natural question is whether the existence of such a bundle map F ensures the existence of a foliated symplectic immersion f. As we shall see in this paper, the obstruction to the existence of such an f is only topological in nature. The result is proved using the h-principle theory of Gromov.  相似文献   

8.
Lin and Su classified A$ \mathcal{T} $ \mathcal{T} -algebras of real rank zero. This class includes all A$ \mathbb{T} $ \mathbb{T} -algebras of real rank zero as well as many C*-algebras which are not stably finite. An A$ \mathcal{T} $ \mathcal{T} -algebra often becomes an extension of an A$ \mathbb{T} $ \mathbb{T} -algebra by an AF-algebra. In this paper, we show that there is an essential extension of an A$ \mathbb{T} $ \mathbb{T} -algebra by an AF-algebra which is not an A$ \mathcal{T} $ \mathcal{T} -algebra. We describe a characterization of an extension E of an A$ \mathbb{T} $ \mathbb{T} -algebra by an AF-algebra if E is an A$ \mathcal{T} $ \mathcal{T} -algebra.  相似文献   

9.
We consider a Dedekind σ-complete Banach lattice E whose dual is weakly sequentially complete. Suppose that E has a positive element u and a family of positive operators $ \mathcal{G} $ \mathcal{G} such that
(i)  each T′, T ∈ $ \mathcal{G} $ \mathcal{G} , is a lattice homomorphism  相似文献   

10.
Consider a class of M-estimators indexed by a criterion function ψ. When the function ψ is taken to be in a class of functions $ \mathcal{F} $ \mathcal{F} , a family of processes indexed by the class $ \mathcal{F} $ \mathcal{F} is obtained and called M-processes. Pooling the M-estimators in such class may be used to define new kind of estimators. In order to get the asymptotic properties of these pooled estimators, the convergence in probability of the corresponding M-process is studied uniformly on $ \mathcal{F} $ \mathcal{F} together with their weak convergence towards a Gaussian process. An application to location estimation is presented and discussed.  相似文献   

11.
We find simple explicit closed-form formulas for the Fermi-Dirac function $ \mathcal{F}_{ - n} (z) $ \mathcal{F}_{ - n} (z) and Bose-Einstein function $ \mathcal{B}_{ - n} (z) $ \mathcal{B}_{ - n} (z) for arbitrary n ε ℕ. The obtained formulas involve the higher tangent numbers defined by Carlitz and Scoville. We present some examples and direct consequences of applying the main results.  相似文献   

12.
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   

13.
Let X be a complex space of dimension n, not necessarily reduced, whose cohomology groups H 1(X, $ \mathcal{O} $ \mathcal{O} ), ...,H n−1(X, $ \mathcal{O} $ \mathcal{O} ) are of finite dimension (as complex vector spaces). We show that X is Stein (resp., 1-convex) if, and only if, X is holomorphically spreadable (resp., X is holomorphically spreadable at infinity).  相似文献   

14.
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   

15.
We apply the results on the integral approximation of the characteristic function of an interval by the subspace $ \mathcal{T}_{n - 1} $ \mathcal{T}_{n - 1} of trigonometric polynomials of order at most n − 1, which were obtained by the authors earlier, to investigate the Jackson inequality between the best uniform approximation of a continuous periodic function by the subspace $ \mathcal{T}_{n - 1} $ \mathcal{T}_{n - 1} and its modulus of continuity of the second order. The corresponding method of the uniform approximation of continuous periodic functions by trigonometric polynomials is constructed.  相似文献   

16.
The bipartite density of a graph G is max {|E(H)|/|E(G)|: H is a bipartite subgraph of G}. It is NP-hard to determine the bipartite density of any triangle-free cubic graph. A biased maximum bipartite subgraph of a graph G is a bipartite subgraph of G with the maximum number of edges such that one of its partite sets is independent in G. Let $ \mathcal{H} $ \mathcal{H} denote the collection of all connected cubic graphs which have bipartite density $ \tfrac{4} {5} $ \tfrac{4} {5} and contain biased maximum bipartite subgraphs. Bollobás and Scott asked which cubic graphs belong to $ \mathcal{H} $ \mathcal{H} . This same problem was also proposed by Malle in 1982. We show that any graph in $ \mathcal{H} $ \mathcal{H} can be reduced, through a sequence of three types of operations, to a member of a well characterized class. As a consequence, we give an algorithm that decides whether a given graph G belongs to $ \mathcal{H} $ \mathcal{H} . Our algorithm runs in polynomial time, provided that G has a constant number of triangles that are not blocks of G and do not share edges with any other triangles in G.  相似文献   

17.
We consider the =2 supersymmetric massive Yang-Mills field theory formulated in the =2 harmonic superspace. We present various gauge-invariant forms of writing the mass term in the action (in particular, using the Stueckelberg superfield), which result in dual formulations of the theory. We develop a gaugeinvariant and explicitly supersymmetric scheme of the loop expansion of the superfield effective action beyond the mass shell. In the framework of this scheme, we calculate gauge-invariant and explicitly =2 supersymmetric one-loop counterterms including new counterterms depending on the Stueckelberg superfield. We analyze the component structure of one of these counterterms. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 22–40, October, 2008.  相似文献   

18.
Characterizations and properties of $ \mathcal{I}_g $ \mathcal{I}_g -closed sets and $ \mathcal{I}_g $ \mathcal{I}_g -open sets are given. A characterization of normal spaces is given in terms of $ \mathcal{I}_g $ \mathcal{I}_g -open sets. Also, it is established that an $ \mathcal{I}_g $ \mathcal{I}_g -closed subset of an $ \mathcal{I} $ \mathcal{I} -compact space is $ \mathcal{I} $ \mathcal{I} -compact.  相似文献   

19.
A direct and unifying scheme for explicitly constructing quasiperiodic wave solutions (multiperiodic wave solutions) of supersymmetric KdV equation in a superspace is proposed. The scheme is based on the concept of super Hirota forms and on the use of super Riemann theta functions. In contrast to ordinary KdV equation with purely bosonic field, some new phenomena on super quasiperiodic waves occur in the supersymmetric KdV equation with the fermionic field. For instance, it is shown that the supersymmetric KdV equation does not possess an N ‐periodic wave solution for N≥ 2 for arbitrary parameters. It is further observed that there is an influencing band occurred among the quasiperiodic waves under the presence of the Grassmann variable. The quasiperiodic waves are symmetric about the band but collapse along with the band. In addition, the relations between the quasiperiodic wave solutions and soliton solutions are rigorously established. It is shown that quasiperiodic wave solution convergence to the soliton solutions under certain conditions and small amplitude limit.  相似文献   

20.
We classify deformations of the standard embedding of the Lie superalgebra $ \mathcal{K} $ \mathcal{K} (2) of contact vector fields on the (1, 2)-dimensional supercircle into the Lie superalgebra SΨD(S 1|2 ) of pseudodifferential operators on the supercircle S 1|2 . The proposed approach leads to the deformations of the central charge induced on $ \mathcal{K} $ \mathcal{K} (2) by the canonical central extension of SΨD(S 1|2 ).  相似文献   

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