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Monomial Toeplitz operators T z p z ¯ q on the weighted Bergman space of the unit ball in C n are natural extension of the weighted shift operators. In higher dimensions, dim ker ⁡ T z p z ¯ q = ∞ may occur for non-trivial case, thus complex symmetric phenomena will appear. In this paper, we completely characterize when the monomial Toeplitz operator T z p z ¯ q on the weighted Bergman space is J A -symmetric, where J A f ( z ) = f ( A z ‾ ) ‾ with the symmetric unitary n × n matrix A. Moreover, we also determine all possible forms of A such that T z p z ¯ q is J A -symmetric. As an application, we construct the weakly closed unital commutative algebra generated by complex symmetric Toeplitz operators.

In this paper, we give a new characterization for the boundedness of weighted differentiation composition operator from logarithmic Bloch spaces to Bloch-type spaces and calculate its essential norm in terms of the n-th power of induced analytic self-map on the unit disk. From which a sufficient and necessary condition of compactness of this operator follows immediately.

The authors characterize the order boundedness of weighted composition operators acting between Dirichlet type spaces.

We investigate isometric composition operators on the weighted Dirichlet space \({D_\alpha }\) with standard weights \({(1 - {\left| z \right|^2})^\alpha },\alpha > - 1\). The main technique used comes from Martin and Vukotic who completely characterized the isometric composition operators on the classical Dirichlet space D. We solve some of these but not in general. We also investigate the situation when \({D_\alpha }\) is equipped with another equivalent norm.

Silicon nitride whiskers or rod-like crystals have a wide range application due to its excellent mechanical properties and high temperature performance. Two different silicon powders with different size (mesh 200 and mesh 300, respectively) were chosen to prepare rod-like Si3N4 crystals by SHS method and the effects of silicon particle size on the morphology of rod-like Si3N4 crystals were investigated. The results indicate that rod-like Si3N4 crystals could be formed with either kind of silicon powders when no more than 9wt% extra Y2O3 was introduced, which could effectively promote the growth of rod-like Si3N4 crystals. The residual free silicon was detected when using coarse silicon powders, while the silicon could be reacted completely with nitrogen gas when using fine silicon powders. The morphology of samples with coarse Si powders as starting materials is more uniform and regular than that of fine Si powders samples. Fine silicon powders are not ideal candidates for forming uniform and regular rod-like Si3N4 crystals.

We discuss the frequent hypercyclicity and hypercyclicity of multiples of the linear fractional composition operators on A α p and give equivalent conditions of the frequent hypercyclicity and hypercyclicity. We also characterize disjoint hypercyclicity and disjoint mixing behavior of finitely many linear fractional composition operators on the weighted Bergman spaces A α p .

In the present paper, we investigate the disjoint mixing property of finitely many linear fractional composition operators acting on the space of holomorphic functions on the unit ball in C N , and generalize parts of the results obtained by Bes, Martin and Peris in 2011.

In this paper, we investigate when weighted composition operators acting on Dirichlet spaces $\mathcal{D}(\mathbb{B}_{N})$ are complex symmetric with respect to some special conjugations, and provide some characterizations of Hermitian weighted composition operators on $\mathcal{D}(\mathbb{B}_{N})$. Furthermore, we give a sufficient and necessary condition for $J$-symmetric weighted composition operators on Hardy spaces $H^2(\mathbb{B}_{N})$ to be unitary or Hermitian, then some new examples of complex symmetric weighted composition operators on $H^2(\mathbb{B}_{N})$ are obtained. We also discuss the normality of complex symmetric weighted composition operators on $H^2(\mathbb{B}_{N})$., 18 pages

In this article, we give equivalent conditions for the hypercyclicity of bilateral operator-weighted shifts on $L^{2}(\mathcal{K})$ with weight sequence $\{A_{n}\}_{n=-\infty}^{\infty}$ of positive invertible diagonal operators on a separable complex Hilbert space $\mathcal{K}$ , as well as for hereditarily hypercyclicity and supercyclicity.

Flower-like and roughly spherical ZnO nanocrystalline have been successfully synthesized through mild wet chemical method. The photocatalytic activities of the prepared photocatalysts were evaluated by degradation of rhodamine B (RhB) and phenol under UV light irradiation. Remarkably, the roughly spherical ZnO powder via homogeneous precipitation method exhibited superior photocatalytic performance and better photo-stability than that of flower-like ZnO substrate by hydrothermal synthesis way. The enhanced photocatalytic properties could be attributed to more active catalytic sites and superior charges separation efficiency.

Resistance to benzimidazole fungicides in many phytopathogenic fungi is caused by specific point mutations in the β-tubulin gene (β-tubulin). However, the mutated locus and genotype of β-tubulin differ among phytopathogenic fungi. To validate the point mutation in Fusarium asiaticum β

For an analytic self-map of the unit disk in the complex plane and a nonnegative integer , the composition operator followed by differentiation on is defined byfor and . In this paper, we study the boundedness and compactness of from or spaces to Bloch-type spaces or little Bloch-type spaces.

We characterize the supercyclic behavior of sequences of operators in a $C_0$-semigroup whose index set is a sector $\Delta$ in the complex plane $\mathbb{C}$.

Let u be a holomorphic function and φ a holomorphic self-map of the open unit disk $$\mathbb{D}$$ in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators uC φ from Zygmund type spaces to Bloch type spaces in $$\mathbb{D}$$ in terms of u, φ, their derivatives, and φ n , the n-th power of φ. Moreover, we obtain some similar estimates for the essential norms of the operators uC φ , from which sufficient and necessary conditions of compactness of uC φ follows immediately.

In this paper we show that the property of disjoint supercyclic operators T1, ⋯, TN satisfying d-supercyclicity criterion on the same Hilbert space is equivalent to disjointness in supercyclicity of the corresponding left multiplication operators induced by T1, ⋯, TN in the strong operator topology. Besides, by the similar discussion, we also obtain that d-hypercyclicity criterion for any T1, ⋯, TN on the same Hilbert space is equivalent to d-hypercyclicity of the corresponding left multiplication operators induced by T1, ⋯, TN in the ‖.‖2 topology.

In this paper, analogues of the Berkson–Porta formula for the infinitesimal generators of one-parameter semigroup of holomorphic self-maps on the polydisk are obtained. We give a necessary and sufficient condition for a holomorphic vector field to be an infinitesimal generator which improves the theorem given by Contreras, de Fabritiis and Diaz-Madrigal.

We characterize the difference of derivative weighted composition operators on the Bergman space in the unit disk and determine when linear-fractional derivative weighted composition operators belong to the same component of the space of derivative weighted composition operators on the Bergman space under the operator norm topology.

A bounded linear operator $T$ on a Banach space $X$ is called subspace-hypercyclic for a nonzero subspace $M$ if $orb\left( {T,x} \right) \cap M$ is dense in $M$ for a vector $x \in X$, where $orb (T,x)=\{T^nx: n=0,1,2,\cdots\}$. Similarly, the bounded linear operator $T$ on a Banach space $X$ is called subspace-supercyclic for a nonzero subspace $M$ if there exists a vector whose projective orbit intersects the subspace $M$ in a relatively dense set. In this paper we provide a Subspace-Supercyclicity Criterion and offer two equivalent conditions of this criterion. At the same time, we also characterize other properties of subspace-supercyclic operators.

We give some new characterizations for compactness of weighted composition operators uCφ acting on Bloch-type spaces in terms of the power of the components of φ where φ is a holomorphic self-map of the polydisk 𝔻n, thus generalizing the results obtained by Hyvärinen and Lindström in 2012.

Let be the class of all holomorphic functions on the unit ball in . For with and an analytic self-map of , the generalized composition operator is defined byIn this paper, we give estimates for the essential norms of the generalized composition operators between Bloch-type spaces in terms of the powers of the components of . We also give new characterizations for the boundedness and compactness of between Bloch-type spaces.

In this paper, we give a sufficient condition for the existence of a common universal subspace for various countable families of universal sequences of linear operators. Besides, we show that if σ p ( T ⁎ ) = ∅ , the unitary orbit of the supercyclic operator T contains a path of operators whose closure contains the entire unitary orbit with the strong operator topology, and yet every nonzero vector in the linear span of the orbit of a given supercyclic vector is a common supercyclic vector for the entire path.

In this paper we give a Carleson measure characterization for the compact composition operators between Dirichlet type spaces. We use this characterization to show that every compact composition operator on Dirichlet type spaces is compact on the Bloch space.

In this paper, we completely determine the commutativity of two Toeplitz operators on the harmonic Bergman space with integrable quasihomogeneous symbols, one of which is of the form $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}e^{ik\theta }r^{\, {m}}$. As an application, the problem of when their product is again a Toeplitz operator is solved. In particular, Toeplitz operators with bounded symbols on the harmonic Bergman space commute with $T_{e^{ik\theta }r^{\, {m}}}$ only in trivial cases, which appears quite different from results on analytic Bergman space in Čučković and Rao [‘Mellin transform, monomial symbols, and commuting Toeplitz operators’, J. Funct. Anal.154 (1998), 195–214].

The benign interaction of teaching and scientific research is analyzed in the teaching-oriented local university. It clarifies that the benign interaction of teaching and scientific research can enhance the overall university level. The article proposes the opinions of constructing a benign interaction of scientific research and teaching, such as formation of teaching and research team effect, design scientific research and teaching experimental items, development characteristic scientific research by relying on the geographical advantages, improvement the integrative evaluation system of scientific research and teaching, and establishment coordinated incentive mechanism of scientific research and teaching.

We characterize disjoint mixing and disjoint hypercyclicity of finite many composition operators acting on the Hardy space on the unit ball.

【In this paper we first characterize the hereditarily hypercyclicity of the unilateral (or bilateral) weighted shifts on the spaces $L^2(\mathbb{N},\mathcal{K})$ (or $L^2(\mathbb{Z},\mathcal{K})$ ) with weight sequence { $A_n$ } of positive invertible diagonal operators on a separable complex Hilbert space $\mathcal{K}$ . Then we give the necessary and sufficient conditions for the supercyclicity of those weighted shifts, which extends some previous results of H. Salas. At last, we give some conditions for the supercyclicity of three different weighted shifts.】

In this paper, we give some new and simple characterizations for the boundedness and compactness of the integral-type composition operators acting on Bloch-type spaces, and obtain corresponding estimates for their essential norms in terms of the sequence . From which the sufficient and necessary conditions of compactness of the integral-type composition operators follows immediately.

We discuss the boundedness and compactness of some integral-type operators acting from spaces to mixed-norm spaces on the unit ball of .

We study the compact intertwining relations for compositionoperators, whose intertwining operators are Volterra type operators fromthe weighted Bergman spaces to the weighted Bloch spaces in the unitdisk. As consequences, we find a new connection between the weightedBergman spaces and little weighted Bloch spaces through this relations. 1. IntroductionIf X and Y are two Banach spaces, the symbol B(X,Y ) denotes the col-lection of all bounded linear operators from X to Y . Let K(X,Y ) be thecollection of all compact elements of B(X,Y ), and Q(X,Y) be the quotientset B(X,Y )/K(X,Y ).For linear operators A ∈ B(X,X), B ∈ B(Y,Y ) and T ∈ B(X,Y ), thephrase “T intertwines A and B in Q(X,Y)” (or “T intertwines A and B com-pactly”) means that(1.1) TA = BT mod K(X,Y ) with T 6= 0 .Notation A ∝ K B (T) represents the relation in equation (1.1). In fact, if T isan invertible operator on X, then the relation ∝ K is symmetric.We denote the class of all holomorphic functions on the complex unit disk Dby H(D), and the collection of all the holomorphic self mappings of Dby S(D).Let α > −1, 0 0. These settingsof α,β,γ and p are valid in the following context unless specifications.

This paper concerns affine infinitesimal generators of continuous semigroups of holomorphic functions on the polydisk. An easy-to-check necessary and sufficiently condition for an affine vector field to be an infinitesimal generator is given.

The same scene, the infrared image and visible image fusion can concurrently take advantage of the original image information can overcome the limitations and differences of a single sensor image in terms of geometric, spectral and spatial resolution, to improve the quality of the image , which help to locate, identify and explain the physical phenomena and events. Put forward a kind of image fusion method based on wavelet transform. And for the wavelet decomposition of the frequency domain, respectively, discussed the principles of select high-frequency coefficients and low frequency coefficients, highlight the contours of parts and the weakening of the details section, fusion, image fusion has the characteristics of two or multiple images, more people or the visual characteristics of the machine, the image for further analysis and understanding, detection and identification or tracking of the target image.

Recently, automatic face recognition method has become one of the key issues in the field of pattern recognition and artificial intelligence. Typically, the face recognition process can be divided into three parts: the detection and recognition of human face, facial feature extraction and face recognition, and among which the facial feature extraction is the key to face recognition technology. In this paper, an extraction algorithm of face recognition feature, which is based on face recognition feature, is proposed. The experimental results based on the ORL face database demonstrate that this algorithm works well.

In this article, we characterize the differences of the products of integral type and composition operators acting from the space of bounded functions to the Bloch space in the disc. Corresponding necessary and sufficient conditions are also given for the differences to be bounded and compact.

In this paper, we study the boundness and compactness of differences of weighted composition operators from the Bloch space B to the space H ∞ of bounded analytic functions on the open unit ball of C n . Moreover, we estimate the norm and the essential norm of differences of composition operators from B to H ∞ .

In this paper, we give a new characterization for the boundedness of the product of differentiation and composition operators \({C_\varphi D^m}\) acting on Bloch-type spaces and obtain an estimate for its essential norm in terms of the sequence \({\{z^n\}^{\infty}_{n=1}}\), from which the sufficient and necessary condition of compactness of the operator \({C_\varphi D^m}\) follows immediately.

Let $\varphi,\psi$ be the analytic self-maps of the unit ball ${\mathbb B}$, we characterize the Hilbert-Schmidt differences of two composition operator $C_\varphi$ and $C_\psi$ on weighted Bergman space $A_\alpha^2$, and give some conclusions about the topological structure of $\mathcal{C}(A_\alpha^2)$, the space of all bounded composition operators on $A_\alpha^2$ endowed with operator norm.

In 2010, Ruhan Zhao obtained the essential norms of composition operators between Bloch type spaces in the disk by the nth power of the induced analytic function. This paper will generalize Zhao’s results to the polydisk. Unlike the case of the composition operators on the unit disk, the essential norms are different for the cases \({p \in (0,1)}\) and p ≥ 1.

Some sufficient conditions under which the tuple of the adjoint of weighted composition operators $(C_{\omega_1,\varphi_1}^* , C_{\omega_2,\varphi_2}^*)$ on the Hilbert space $\mathcal{H}$ of analytic functions is disk-cyclic (or codisk-cyclic) were investigated.

In this paper, we characterize the boundedness and compactness of the weighted composition operators from the weighted Bergman space to the standard mixed-norm space or the mixed-norm space with normal weight on the unit ball and estimate the essential norms of the weighted composition operators.

In this paper, we limit our analysis to the difference of the weighted composition operators acting from the Hardy space to weighted-type space in the unit ball of ℂN, and give some necessary and sufficient conditions for their boundedness or compactness. The results generalize the corresponding results on the single weighted composition operators and on the differences of composition operators, for example, M. Lindstrom and E. Wolf: Essential norm of the difference of weighted composition operators. Monatsh. Math. 153 (2008), 133–143.

Preparation of single-phase and high purity nanophase TiO2 powders with small crystallite size were investigated by microwave hydrothermal method. By varying starting materials and reaction condition, four titania powders were prepared. Single-phase and high purity nanocrystalline anatase was obtained by hydrolysis of Ti(C4H9O)4 at 120oC for 3 h, which exhibited granulous and uniformly dispersed, with the average crystallite size of 10 nm. Well crystallized and single-phase rutile was obtained by hydrolysis of TiCl4 first at 120oC for 1.5 h and then at 180oC for 1 h, which exhibited shuttle-like and well-dispersed TiO2, with average diameter of 10 nm, by means of XRD and TEM.

In this paper, we obtain a symmetry number for the commutator of quasi- homogeneous Toeplitz operators on the harmonic Bergman space. Then we use it to characterize the commuting Toeplitz operators with quasihomogeneous symbols. Also, we show that a Toeplitz operator with an analytic or co-analytic monomial symbol commutes with another Toeplitz operator only in the trivial case.