Fuzzy Synthetic Evaluation of Wetland Soil Quality Degradation:A Case Study on the Sanjiang Plain,Northeast China

Wetland soil quality degradation caused by large-scale agricultural reclamation on the Sanjiang Plain of Northeast China has been widely reported. A relative soil quality evaluation (RSQE) model and a projection pursuit evaluation (PPE) model based on real-coded accelerating genetic algorithm were introduced to evaluate quality variations in top layers of the main wetland soils on the Sanjiang Plain in 1999 and 2003, respectively. As soil quality degradation boundaries were vague, this study established two fuzzy synthetic evaluation (FSE) models based on the original data and criteria used in the RSQE and PPE models. The outputs of the two FSE models were obtained by choosing two fuzzy composite operators M(∧, ∨) and M(·, ⊕). Statistical analysis showed that the results of the FSE, RSQE, and PPE models were correlated. In particular, outputs of the FSE model using M(·, ⊕) were significantly correlated with those of the RSQE model with r = 0.989 at P < 0.01. Compared with RSQE and PPE models, the FSE model may be more objective in showing soil quality variations and was closer to the natural situation, showing the feasibility and applicability of the FSE model in evaluating soil quality degradation. However, the choice of composite operator was of critical importance. The study of wetland soil quality degradation on the Sanjiang Plain was of scientific and practical significance for protection and management of soils and for sustainable development of agriculture in this area in the future.

THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

Let p 〉 0 and μ be a normal function on [0, 1）, u（r） = （1 - r2）1＋n^pμ（r） for r ∈ [0, 1）. In this article, the bounded or compact weighted composition operator Tφ,ψ from the μ-Bergman space AP（p） to the normal weight Bloch type space β （r）in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator Cφ is compact from A^p（μ） to βv, is given. At the same time, the authors give the briefly sufficient and necessary condition that Cv is compact on βμ, for a 〉 1.

COMPOSITION OPERATOR ON BERS-TYPE SPACES

Necessary and sufficient conditions are established for a composition operator C(phi)f = f o phi to be bounded or compact on the Bers-type space H-alpha(infinity) and the little Bers-type space H-alpha(infinity). The boundedness and compactness of the composition operator C-phi on A(infinity)(phi) are characterized, which generalize the case of C-phi on H-alpha(infinity).

COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON HOLOMORPHIC FUNCTION SPACES IN THE UNIT BALL

We find a lower bound for the essential norm of the difference of two composition operators acting on H 2（BN ） or As2 （BN ） （s 1）. This result plays an important role in proving a necessary and sufficient condition for the difference of linear fractional composition operators to be compact, which answers a question posed by MacCluer and Weir in 2005.

COMPOSITION OPERATORS FROM B^a TO F(p,q,s)

Necessary and sufficient conditions are given for a composition operator Cof = f o o to be bounded and compact from Ba to F(p, q, s).

Weighted Composition Operators between Hardy Spaces on the Unit Ball

We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the operator from H^1 to H^1 is compact if and only if it is weakly compact. Meanwhile, we get the analogue on the Bergman spaces.

ESSENTIAL NORMS OF PRODUCTS OF WEIGHTED COMPOSITION OPERATORS AND DIFFERENTIATION OPERATORS BETWEEN BANACH SPACES OF ANALYTIC FUNCTIONS

We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.

COMPOSITION OPERATORS BETWEEN BLOCH TYPE SPACES IN THE UNIT BALL

In this paper, we obtain some new necessary and sufficient conditions for the boundedness and compactness of composition operators Cφ between Bloch type spaces in the unit ball Bn.

WEIGHTED COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES

We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.

COLLECTIVELY COMPACT COMPOSITION OPERATOR SEQUENCES BETWEEN BERGMAN AND HARDY SPACES

This paper studies the collective compactness of composition operator sequences between the Bergman and Hardy spaces. Some sufficient and necessary conditions involving the generalized Nevanlinna counting functions for composition operator sequences to be collectively compact between weighted Bergman spaces are given

COMPOSITION OPERATORS FROM p-BLOCH SPACES TO LITTLE q-BLOCH SPACES ON THE UNIT BALL OF C^n

For all 0 〈 p, q 〈 ∞, let Cφ denote the composition operator from q-Bloch spaces βp to little p-Bloch spaces β0q on the unit ball of C^n. In this article, necessary and sufficient conditions for Cφ to be a bounded or compact operator are given.

THE BEREZIN TRANSFORM AND ITS APPLICATIONS

We give a survey on the Berezin transform and its applications in operator theory. The focus is on the Bergman space of the unit disk and the Fock space of the complex plane. The Berezin transform is most effective and most successful in the study of Hankel and Toepltiz operators.

Weighted composition operators from F(p,q,s) spaces to Bers-type spaces in the unit ball

This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.

COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL

Let φ be a holomorphic self-map of Bn and ψ ∈ H（Hn）. A composition type operator is defined by Tψ,φ（f） = ψf o φ for f ∈ H（Bn）, which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator Tψ,φ to be bounded or compact from Hardy space HP（Bn） to μ-Bloch space Bμ（Bn）. The conditions are some supremums concerned with ψ,φ, their derivatives and Bergman metric of Bn. At the same time, two corollaries are obtained.

PRODUCTS OF WEIGHTED COMPOSITION AND DIFFERENTIATION OPERATORS INTO WEIGHTED ZYGMUND AND BLOCH SPACES

We characterize boundedness and compactness of products of differentiation op- erators and weighted composition operators between weighted Banach spaces of analytic functions and weighted Zygmund spaces or weighted Bloch spaces with general weights.

Composition Operators Mapping into the E(p,q) Spaces

Composition operators are used to study the E(p,q) spaces. The boundedness of these operators is also considered. The criteria for these operators to be bounded are given in terms of the Carleson measure.

Composition Operators on Compact Riemann Surfaces

In the present paper, the characterization of invertible composition oper-ators on compact Riemann surfaces is obtained, which is very different from that in the case of Hardy or Bergman spaces on a disk of the complex plane C.

Composition Operators Between the Weighted Dirichlet Spaces on Bounded Symmetric Domains of C^n

In this paper, we define the weighted Dirichlet space D p α(Ω) on bounded symmetric domains Ω of C n. Using η-α Carleson measure,we study the boundedness and compactmess of the composition operators between the weighted Dirichlet spaces.

WEIGHTED COMPOSITION OPERATORS ON THE HILBERT SPACE OF DIRICHLET SERIES

In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized, and the spectra of compact and invertible weighted composition operators are also described.

COMPACT COMPOSITION OPERATORS ON GENERALIZED LIPSCHITZ SPACES

In this paper, boundedness and compactness of the composition operator on the generalized Lipschitz spaces Λα （α 〉 1） of holomorphic functions in the unit disk are characterized.