BIG HANKEL OPERATORS ON HARDY SPACES OF STRONGLY PSEUDOCONVEX DOMAINS

In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.

PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

SUMS OF DUAL TOEPLITZ PRODUCTS ON THE ORTHOGONAL COMPLEMENTS OF FOCK-SOBOLEV SPACES

We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.

Weighted multilinear p-adic Hardy operators and commutators on p-adic Herz-type spaces

In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.

THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES

Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.

The Dual of the Two-Variable Exponent Amalgam Spaces (Lq(),lp())(Ω)

Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (Lq(),lp())(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.

Motion and Special Relativity in Complex Spaces

A natural extension of the Lorentz transformation to its complex version was constructed together with a parallel extension of the Minkowski M4 model for special relativity (SR) to complex C4 space-time. As the [signed] absolute values of complex coordinates of the underlying motion’s characterization in C4 one obtains a Newtonian-like type of motion whereas as the real parts of the complex motion’s description and of the complex Lorentz transformation, all the SR theory as modeled by M4 real space-time can be recovered. This means all the SR theory is preserved in the real subspace M4 of the space-time C4 while becoming simpler and clearer in the new complex model’s framework. Since velocities in the complex model can be determined geometrically, with no primary use of time, time turns out to be definable within the equivalent theory of the reduced complex C4 model to the C3 “para-space” model. That procedure allows us to separate time from the (para)space and consider all the SR theory as a theory of C3 alone. On the other hand, the complex time defined within the C3 theory is interpreted and modeled by the single separate C1 complex plane. The possibility for application of the C3 model to quantum mechanics is suggested. As such, the model C3 seems to have unifying abilities for application to different physical theories.

Identity of Urban Spaces: Assessment and Evaluation

As a major symbol of civilization,the city was built by man for his security and comfort.It is not only a settlement,but also an urban development which has been identified with the spirit that has been breathed into the community.Urban identity which is also known as collective identity,has gained meaning through the content of objective manifestation and the creation of flashbacks,citizens’memories and mental associations.That is what makes urban dwellers become citizens.Although the identity of the city is a result of civic culture,it still has an influence on the process of citizenship and can also be a reason for developing criteria related to the participation and assessment of its inhabitants.According to the view that identity is a set of traits and characteristics that distinguishes the dignity of a person and a society from other individuals and communities,a city becomes characterized and independent by adhering to these criteria.Despite the importance of identity as one of the richest qualitative aspects of urban life that gives meaning and fulfilment to the human quiddity,this complicated and expanded concept has still not been seriously considered,especially in relation to urban spaces.In fact,identity in architecture and urban spaces has recently diminished,since the main focus lies on building spaces for optimized profit and not for high quality living areas.In this research paper,parameters affecting urban identity are evaluated,and strategies and guidelines to promote these parameters are finally presented.

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.

THREE KINDS OF DENTABILITIES IN BANACH SPACES AND THEIR APPLICATIONS

In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.

Attributes of Domestic Spaces for Contemporary Habitation-A Secondary Publication

The domestic space can be defined as the sphere that articulates the needs for subjective containment and contextual stimuli.In this sense,questions arise about the indispensable attributes that spaces must possess for this articulation to take place adequately.Architecture,as the discipline in charge of satisfying the specific spatial needs of those who inhabit these spaces and,in a broader sense,as a concrete contribution to society,must address this relationship in all its complexity and generate concrete responses that incorporate the appropriate spatial attributes during the design processes.The design processes that shape living spaces confront this dialectic,and the manner in which they do so brings identity and character to them.It is believed that the higher the level of variables that are contemplated and weighted,the greater the adequacy of spaces to the changing dynamics of the people who inhabit them.This article focuses on a thorough analysis of these spatial attributes,in parallel to the definition of each one as a particular condition for design,based on their conceptualization,breakdown,and articulation.Conceptually,the following attributes are addressed:flexibility,adaptability,variability,versatility,multiplicity,plurality,integrality,gradualness,incrementality,progressiveness,independence,connectivity,intimacy,and privacy.Each of these attributes is valued as a contribution to creating adequate habitability in contextual terms,with consideration to possible integrations and combinations.

Research on the Spatio-Temporal Evolution and Driving Forces of Green Spaces in the Central Urban Area of Zunyi City

Green space,as a medium for carrying out urban functions and guiding urban development,is becoming a scarce resource along with the urbanization process and the intensification of environmental problems.In the face of the spatial mismatch between high demand and low supply,it is of great significance to clarify the evolution mechanism of green space to undertake national spatial planning,protect the natural strategic resources in the urban fringe area,and promote the sustainable development of the“three living spaces.”The study focuses on the Zunyi City Center,selecting the 20 years of rapid development following its establishment as a city as the study period.It explores the dynamic evolution of green space and the main driving forces during different periods using remote-sensing image data.The study shows that from 2003 to 2023,the total scale of green space has an obvious decreasing trend along with the expansion of the urban built-up area.A large amount of arable land is being converted to construction land,resulting in a sudden decrease in arable land area.In the past 10 years,the comprehensive land use dynamics have accelerated.Still,the spatial difference has gradually narrowed,indicating that the overall development intensity of Zunyi City’s central urban area has increased.There is a gradual spread of the trend to the hilly areas.The limiting effect of the mountainous natural environment on the city’s development has gradually diminished under the superposition of external factors,such as economic development,industrial technological upgrading,and policy orientation so the importance of the effective protection and rational utilization of urban green space has become more prominent.

Interactive Media Visual Interpretation of Traditional Chinese Graphics in Urban Public Spaces

This paper focuses on the application of interactive media technology in the visual interpretation of traditional graphic urban public spaces in China.Case studies and practical exploration show that interactive media technologies such as projection mapping,interactive devices,virtual reality technology,etc.,have realized the diversity of traditional graphics display forms in urban public space.The rich interactive experience design enhances the sense of participation and experience of urban citizens and tourists and promotes the visual culture transmission of traditional Chinese graphics.The future urban public space exhibition is destined to continue to deepen the integration of technology and graphics,promote the visual communication of traditional Chinese graphics visual interpretation in urban public space,and promote sustainable innovation in cultural output in urban public space exhibitions around the world.

数据空间建设的实践进展与运营模式分析——基于Data Spaces Radar的案例

数据空间建设为数据要素的价值实现提供了可资借鉴的实践经验,全面解析其实践进展与运营模式,有助于破解数据流通的现实堵点、拓展数据利用的发展思路。文章首先将结构主义分析方法中的案例研究法作为主要研究方法,综合运用文献调研、比较分析等方法,以Data Spaces Radar为案例来源,从实践进展、运营模式、核心要素等维度提炼数据空间建设特征。其次,在制度与技术的双轮驱动下,数据空间建设秉持制度规范统一性、技术设计整体性和治理模式协同性的架构原则,并按照产业思维、底线思维、信任思维、链式思维、集约思维的底层逻辑,形成较为完整的运营体系。未来应着力探索和解决数据空间视域下的数据资源价值化开发路径,针对数据流通堵点、利用痛点及信任难点问题,从体制机制、政策框架与技术应用等角度为推进我国的数据要素流通利用提供有益参考。

3D MERGE与3D SPACE STIR序列在腰椎间盘突出症检查中的应用比较

目的:对比三维多回波恢复梯度回波(3D MERGE)、三维可变反转角快速自旋回波(3D SPACE STIR)序列在腰椎间盘突出症(LDH)检查中的应用效果。方法:选择2020年1月~2022年11月收治的135例LDH患者,回顾性分析患者临床和磁共振成像(MRI)资料,所有患者均接受常规MRI扫描及3D MERGE、3D SPACE STIR序列扫描,对比3D MERGE、3D SPACE STIR序列测量神经根直径的一致性,评价两种序列的图像质量参数[信噪比(SNR)、对比噪声比(CNR)]、图像清晰度评分。结果:3D MERGE和3D SPACE STIR序列测量的L3~S1神经根直径比较差异无统计学意义(P>0.05),且两组序列测量的L3、L4、L5和S1直径均显示出较高相关性(r=0.957,0.986,0.975,0.972,P<0.05);3D MERGE序列的SNR及CNR均高于3D SPACE STIR序列,神经根显示分级、图像清晰度评分优于3D SPACE STIR序列,差异有统计学意义(P<0.05)。结论:3D MERGE、3D SPACE STIR序列在LDH神经根直径测量中具有极高一致性,3D MERGE序列较3D SPACE STIR序列能够更清晰显示神经跟的解剖形态,图像质量更好。

基于Conceptual Play Spaces理论的初中语文教育游戏设计

在真实的情境中教学可以促进学生的理解,对于初中生来说,他们需要一些具体形象的支撑,3D体验游戏可以将抽象的事物具体化,让学生感受到真实的世界。本文以Conceptual Play Spaces理论为基础,根据初中生的学习特征,设计教育游戏桃花源记,激发学习者的学习兴趣,使学生沉浸在教育游戏情境中,提高学习者核心素养。

THE WELL-POSEDNESS OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN COMPLEX BANACH SPACES

Let X be a complex Banach space and let B and C be two closed linear operators on X satisfying the condition D(B)?D(C),and let d∈L^(1)(R_(+))and 0≤β<α≤2.We characterize the well-posedness of the fractional integro-differential equations D^(α)u(t)+CD^(β)u(t)=Bu(t)+∫_(-∞)td(t-s)Bu(s)ds+f(t),(0≤t≤2π)on periodic Lebesgue-Bochner spaces L^(p)(T;X)and periodic Besov spaces B_(p,q)^(s)(T;X).

BANACH SPACES AND INEQUALITIES ASSOCIATED WITH NEW GENERALIZATION OF CESàRO MATRIX

Let the triangle matrix A^(ru)be a generalization of the Cesàro matrix and U∈{c_(0),c,l_(∞)}.In this study,we essentially deal with the space U(A^(ru))defined by the domain of A^(ru)in the space U and give the bases,and determine the Kothe-Toeplitz,generalized K?theToeplitz and bounded-duals of the space U(A^(ru)).We characterize the classes(l_(∞)(A^(ru)):l_(∞)),(l_(∞)(A^(ru)):c),(c(A^(ru)):c),and(U:V(A^(ru)))of infinite matrices,where V denotes any given sequence space.Additionally,we also present a Steinhaus type theorem.As an another result of this study,we investigate the l_(p)-norm of the matrix A^(ru)and as a result obtaining a generalized version of Hardy's inequality,and some inclusion relations.Moreover,we compute the norm of well-known operators on the matrix domain l_(p)(A^(ru)).

基于Cite Space对螺旋藻藻蓝蛋白的研究进展与热点分析

螺旋藻(Spirulina)藻蓝蛋白具有独特的理化特性及生理功能,是药物、食品和化妆品的天然原料,具有较大的开发潜力。为探讨螺旋藻藻蓝蛋白的研究现状与发展前景,对中国知网和Web of Science数据库中1990—2023年发表的文献进行检索并筛选,使用Cite Space软件对文章发文量、研究团队及研究热点进行图谱分析。综合分析可知,国内年发文量偏少,呈平稳趋势;国外年发文量持续上升,尤其近几年发文量迅速增长,且发文量超过了100篇;国外研究热点集中于藻蓝蛋白在食品、医药行业的应用方面,而国内研究热点集中在提取纯化、稳定性、功能活性的研究与应用,下一步应结合研究现状开发适合规模化生产的提取纯化工艺,进一步加强藻蓝蛋白研究的广度与深度;国内外研究群体主要是高校的相关生物技术学院或研究机构等,总体来讲,学者间存在较为密切的合作,但研究机构间尚未形成紧密的合作关系,在地域上比较分散,各大高校和研究机构应突破地区或机构间的各种限制,促进该研究领域的深度融合和快速发展,深入挖掘藻蓝蛋白在各个领域的潜在应用。