GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF C^(N)

In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.

JOHN-NIRENBERG-Q SPACES VIA CONGRUENT CUBES

To shed some light on the John-Nirenberg space,the authors of this article introduce the John-Nirenberg-Q space via congruent cubes,JNQp,qα(Rn),which,when p=∞and q=2,coincides with the space Qα(Rn)introduced by Essen,Janson,Peng and Xiao in[Indiana Univ Math J,2000,49(2):575-615].Moreover,the authors show that,for some particular indices,JNQp,qα(Rn)coincides with the congruent John-Nirenberg space,or that the(fractional)Sobolev space is continuously embedded into JNQp,qα(Rn).Furthermore,the authors characterize JNQp,qα(Rn)via mean oscillations,and then use this characterization to study the dyadic counterparts.Also,the authors obtain some properties of composition operators on such spaces.The main novelties of this article are twofold:establishing a general equivalence principle for a kind of’almost increasing’set function that is here introduced,and using the fine geometrical properties of dyadic cubes to properly classify any collection of cubes with pairwise disjoint interiors and equal edge length.

AN INTEGRAL ESTIMATE AND THE EQUIVALENT NORMS ON F(p, q, s, k) SPACES IN THE UNIT BALL

In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.

CARLESON MEASURES,RIEMANN-STIELTJES OPERATORS AND MULTIPLIERS ON F(p,q,s)SPACES IN THE UNIT BALL OF C^n

This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, BMOA and Q8 spaces. The boundedness and compactness of these operators on F（p, q, s） spaces are characterized by means of an embedding theorem, i.e., F（p,q, s） spaces boundedly embedded into the tent-type spaces Tp,s^∞（μ）

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-integral Type Operators from F（p, q, s） Spaces to Bloch-type Spaces

This paper deals with the boundedness and compactness of the compositionintegral type operators T g, from F (p, q, s) spaces to(little) Bloch-type spaces in the unit ball of C n , where Tg,φf(z) =∫01fφ(tz)Rg(tz)(dt)/t , z ∈ B, g ∈ H(B) and φ∈H(B, B).

ON F(p,q,s)SPACES

The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and have connections with many other areas of mathematics.In this survey we present some basic properties and recent results on F(p,q,s)spaces.

q–differ-integral operator on p–valent functions associated with operator on Hilbert space

Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated.

On Some Novel Fixed Point Results for Generalized F-Contractions in b-Metric-Like Spaces with Application

The focusofourwork is on themost recent results infixedpoint theoryrelated tocontractivemappings.Wedescribe variants of(s,q,φ,F)-contractions that expand,supplement and unify an important work widely discussed in the literature,based on existing classes of interpolative and F-contractions.In particular,a large class of contractions in terms of s,q,φand F for both linear and nonlinear contractions are defined in the framework of b-metric-like spaces.The main result in our paper is that(s,q,φ,F)-g-weak contractions have a fixed point in b-metric-like spaces if function F or the specified contraction is continuous.As an application of our results,we have shown the existence and uniqueness of solutions of some classes of nonlinear integral equations.

CRITERIA FOR AN ANALYTIC FUNCTION BELONGING TO THE Q_K SPACES

The author gives a mild integral condition in a nondecreasing function K : [0, ∞) → [0, ∞), which is sufficient and the best possible to ensure that f is a Bloch function if and only if f belongs to QK, a Mbius-invariant space of functions analytic in the unit disk. Their contributions are slight improvements of known results, and the proofs presented here are independently developed. The corresponding results for meromorphic case are also given.

Toeplitz and Translation Operators on the q-Fock Spaces

In this work, we introduce a class of Hilbert spaces Fq of entire functions on the disk , , with reproducing kernel given by the q-exponential function eq(z);and we prove some properties concerning Toeplitz operators on this space. The definition and properties of the space extend naturally those of the well-known classical Fock space. Next, we study the multiplication operator Dq by and the q-Derivative operator on the Fock space Fq;and we prove that these operators are adjoint-operators and continuous from this space into itself. Lastly, we study a generalized translation operators and a Weyl commutation relations on Fq .

确定性筛选设计在Purcise Q膜纯化抗体的应用

目的:通过确定性筛选设计(DSD)方法建立单抗的Purcise Q膜阴离子交换工艺,进一步降低残留宿主细胞蛋白(HCP)含量。方法:将亲和层析洗脱过滤液作为样品,进行Purcise Q膜层析,选取上样pH、上样电导、载量、流速、峰收集条件5个因子为输入因子,以回收率、HCP去除率、多聚体含量为输出响应值,使用确定性筛选设计DOE模型进行实验。结果:在实验参数范围内,多聚体含量没有明显的变化,HCP含量显著降低。上样电导和载量显著影响HCP去除率,而载量、流速和峰收集条件则显著影响层析回收率。利用JMP的模拟实验功能获得了稳健工艺参数组合(上样电导3 ms/cm、载量300 g/L、流速25 MV/min、峰收集50 mAU/mm),进一步利用决策树机器学习方法自动获得设计空间(上样电导3.0~3.6 ms/cm、载量300~460 g/L、流速5~25 MV/min、峰收集50~180 mAU/mm)。结论:确定性筛选设计实验方法适用于膜层析的工艺开发,能够一段式快速获得稳健工艺参数组合和设计空间,对于工艺放大、工艺转移和降低生产风险极具指导意义。

PREDUAL SPACES FOR Q SPACES

To find the predual spaces Pα（R^n） of Qα（R^n） is an important motivation in the study of Q spaces. In this article, wavelet methods are used to solve this problem in a constructive way. First, an wavelet tent atomic characterization of Pα（Rn） is given, then its usual atomic characterization and Poisson extension characterization are given. Finally, the continuity on Pα of Calderon-Zygmund operators is studied, and the result can be also applied to give the Morrey characterization of Pα（Rn）.

Quantum Dynamics via a Hidden Liouville Space

The traditional simulations may occasionally turn out to be challenging for the quantum dynamics, particularly those governed by the nonlinear Hamiltonians. In this work, we introduce a nonstandard iterative technique where the Liouville space is briefly expanded with an additional (virtual) space only within ultrashort subintervals. This tremendously reduces the cost of time-consuming calculations. We implement our technique for an example of a charged particle in both harmonic and anharmonic potentials. The temporal evolutions of the probability for the particle being in the ground state are obtained numerically and compared to the analytical solutions. We further discuss the physics insight of this technique based on a thought-experiment. Successive processes intrinsically “hitchhiking” via virtual space in discrete ultrashort time duration, are the hallmark of our technique. We believe that this technique has potential for solving numerous problems which often pose a challenge when using the traditional approach based on time-ordered exponentials.

<i>Q_K</i>Type Spaces and Bloch Type Spaces on the Unit Ball

Different function spaces have certain inclusion or equivalence relations. In this paper, the author introduces a class of M&#246;bius-invariant Banach spaces QK,0 (p,q) of analytic function on the unit ball of Cn, where K:(0,∞)→[0,∞) are non-decreasing functions and 0P∞, p/2-n-1q∞, studies the inclusion relations between QK,0 (p,q) and a class of B0α spaces which was known before, and concludes that QK,0 (p,q) is a subspace of B0(q+n+1)/p, and the sufficient and necessary condition on kernel function K(r) such that QK,0 (p,q)= B0(q+n+1)/p.

Fock Spaces for the q-Dunkl Kernel

In this work, we introduce a class of Hilbert spaces of entire functions on the disk , 0<q<1 , with reproducing kernel given by the q-Dunkl kernel . The definition and properties of the space extend naturally those of the well-known classical Fock space. Next, we study the multiplication operator Q by z and the q-Dunkl operator on the Fock space;and we prove that these operators are adjoint-operators and continuous from this space into itself.

Multiplication and Translation Operators on the Fock Spaces for the q-Modified Bessel Function

We study the multiplication operator M by z2 and the q-Bessel operator Δq,αon a Hilbert spaces Fq,α of entire functions on the disk D( o, ) , 0qq,α into itself. Next, we study a generalized translation operators on Fq,α .

基于DDQN改进方法的“斗地主”策略

基于当前一些已有方法在牌类博弈中训练时间长、动作空间大、胜率低等问题,提出了针对DDQN算法网络架构、编码方式的改进方法。采用二进制对手牌特征进行编码,采用手牌拆分的方法把神经网络分为主牌神经网络和副牌神经网络,并且增加GRU神经网络处理序列动作。经实验表明,该算法训练时间比传统DQN算法缩短了13%,在“地主”和“农民”位置上的平均胜率为70%和75%,高于DQN算法的28%和60%,证明了改进算法在上述部分指标方面的优势。

On Converse Theorem of Best Approximation by Polynomials in Bergman Spaces H_q^p(p>0,q>1)

A Bernstein type theorem and a converse theorem of best approximation by polynomials in Bergman spaces Hq^p(p>0,q>1) are proved.Some proofs and results in [1] are in proved.

CRITERIA FOR AN ANALYTIC FUNCTION BELONGING TO THE Q_K SPACES

The author gives a mild integral condition in a nondecreasing function K : [0, ∞) → [0, ∞), which is sufficient and the best possible to ensure that f is a Bloch function if and only if f belongs to QK, a Mbius-invariant space of functions analytic in the unit disk. Their contributions are slight improvements of known results, and the proofs presented here are independently developed. The corresponding results for meromorphic case are also given.