文章基于CNKI、Web of Science两大数据库2005—2024年收录的图书馆学习空间研究文献,运用CiteSpace、Bicomb、SPSS软件进行可视化分析。结果显示,国外研究以技术驱动创新为主导,聚焦智能化技术与跨学科应用;而国内研究呈现理论创新与...文章基于CNKI、Web of Science两大数据库2005—2024年收录的图书馆学习空间研究文献,运用CiteSpace、Bicomb、SPSS软件进行可视化分析。结果显示,国外研究以技术驱动创新为主导,聚焦智能化技术与跨学科应用;而国内研究呈现理论创新与实践探索并重,通过大数据、AI等技术形成本土化解决方案。文章提出通过数字技术与人文关怀的平衡发展、国际化视野与本土化创新的有机结合、理论研究与实践应用的深度融合,为我国图书馆学习空间的研究提供借鉴与参考。展开更多
This paper solves the problem of model-free dual-arm space robot maneuvering after non-cooperative target capture under high control quality requirements.The explicit system model is unavailable,and the maneuvering mi...This paper solves the problem of model-free dual-arm space robot maneuvering after non-cooperative target capture under high control quality requirements.The explicit system model is unavailable,and the maneuvering mission is disturbed by the measurement noise and the target adversarial behavior.To address these problems,a model-free Combined Adaptive-length Datadriven Predictive Controller(CADPC)is proposed.It consists of a separated subsystem identification method and a combined predictive control strategy.The subsystem identification method is composed of an adaptive data length,thereby reducing sensitivity to undetermined measurement noises and disturbances.Based on the subsystem identification,the combined predictive controller is established,reducing calculating resource.The stability of the CADPC is rigorously proven using the Input-to-State Stable(ISS)theorem and the small-gain theorem.Simulations demonstrate that CADPC effectively handles the model-free space robot post operation in the presence of significant disturbances,state measurement noise,and control input errors.It achieves improved steady-state accuracy,reduced steady-state control consumption,and minimized control input chattering.展开更多
In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and...In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and G(z)=∑^(N)_(i)=1 A_(−i)z^(i),A_(i)ae culants.展开更多
In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale in...In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale inequalities of mixed quasi-martingale Hardy spaces.Moreover,we furnish sufficient conditions for the boundedness ofσ-sublinear operators in these spaces.These findings extend the existing conclusions regarding mixed quasi-martingale Hardy spaces defined with the help of the mixed L_(p)-norm.展开更多
Space exploration is significant for scientific innovation,resource utilization,and planetary security.Space exploration involves several systems including satellites,space suits,communication systems,and robotics,whi...Space exploration is significant for scientific innovation,resource utilization,and planetary security.Space exploration involves several systems including satellites,space suits,communication systems,and robotics,which have to function under harsh space conditions such as extreme temperatures(−270 to 1650℃),microgravity(10^(-6)g),unhealthy humidity(<20%RH or>60%RH),high atmospheric pressure(~1450 psi),and radiation(4000–5000 mSv).Conventional energy-harvesting technologies(solar cells,fuel cells,and nuclear energy),that are normally used to power these space systems have certain limitations(e.g.,sunlight dependence,weight,degradation,big size,high cost,low capacity,radioactivity,complexity,and low efficiency).The constraints in conventional energy resources have made it imperative to look for non-conventional yet efficient alternatives.A great potential for enhancing efficiency,sustainability,and mission duration in space exploration can be offered by integrating triboelectric nanogenerators(TENGs)with existing energy sources.Recently,the potential of TENG including energy harvesting(from vibrations/movements in satellites and spacecraft),self-powered sensing,and microgravity,for multiple applications in different space missions has been discussed.This review comprehensively covers the use of TENGs for various space applications,such as planetary exploration missions(Mars environment monitoring),manned space equipment,In-orbit robotic operations/collision monitoring,spacecraft’s design and structural health monitoring,Aeronautical systems,and conventional energy harvesting(solar and nuclear).This review also discusses the use of self-powered TENG sensors for deep space object perception.At the same time,this review compares TENGs with conventional energy harvesting technologies for space systems.Lastly,this review talks about energy harvesting in satellites,TENG-based satellite communication systems,and future practical implementation challenges(with possible solutions).展开更多
It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and t...It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.展开更多
At 11:00 p.m. on January 13, 2026, floodlights illuminated the launch pad at the Hainan Commercial Space Launch Site in Wenchang,south China’s Hainan Province. A Long March-8A (CZ-8A) carrier rocket lifted off with a...At 11:00 p.m. on January 13, 2026, floodlights illuminated the launch pad at the Hainan Commercial Space Launch Site in Wenchang,south China’s Hainan Province. A Long March-8A (CZ-8A) carrier rocket lifted off with a steady roar, its exhaust lighting up the night sky as it delivered a satellite into its designated orbit.The development of China’s first commercial space launch site has been striking. Since its inaugural launch in2024, it has completed 11 missions in less than 14 months—each a success.展开更多
Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted...Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).展开更多
In recent years,the rapid development of mega-constellations has significantly exacerbated the deterioration of the space debris environment,posing substantial and escalating threats to the safety of spacecraft.This s...In recent years,the rapid development of mega-constellations has significantly exacerbated the deterioration of the space debris environment,posing substantial and escalating threats to the safety of spacecraft.This study aims to explore the complex evolution of the space debris environment and assess the collision risks associated with spacecraft.First,a space debris environment topological network model is proposed,which incorporates interdisciplinary methods from topological networks,fluid mechanics,and spacecraft dynamics.This model enables a structured representation of the relationships among space objects and provides rapid predictions of the space debris environment.Then,a collision probability algorithm based on the topological network model is introduced.This algorithm inherits the efficiency advantages of the topological network model and has been validated for reliability through comparison with the classical ESA’s DRAMA software.Finally,based on the above models,the collision risks of constellation satellites in Low Earth Orbit(LEO)are analyzed,including both operational and deorbit processes.The study reveals that constellation satellites face a much higher risk of internal collisions with satellites from the same constellation during operations than that with other space objects.Additionally,during the satellite deorbit process,the collision risk peaks when satellites traverse the operational region of Starlink satellites.展开更多
The Pantone Color of the Year 2026,PANTONE 11-4201 Cloud Dancer,has been introduced as a soft,lofty white symbolizing calm and clarity in an increasingly noisy world.This gentle shade invites a sense of peace and spac...The Pantone Color of the Year 2026,PANTONE 11-4201 Cloud Dancer,has been introduced as a soft,lofty white symbolizing calm and clarity in an increasingly noisy world.This gentle shade invites a sense of peace and spaciousness,encouraging focus and creating room for creativity and reflection.Cloud Dancer embodies a desire for simplicity and renewal-a blank canvas that allows our minds to wander and new ideas to take shape.Its expansive presence fosters environments where tranquility meets inspiration,offering visual calm that supports wellbeing and mental lightness.展开更多
In this paper,we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball BX of a complex Banach space X into ℂ.As applications,we will establish refined Bohr...In this paper,we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball BX of a complex Banach space X into ℂ.As applications,we will establish refined Bohr inequalities of functional type or of norm type for holomorphic mappings with lacunary series on the unit ball BX with values in higher dimensional spaces.Next,we obtain the Bohr-Rogosinski inequality for the class of holomorphic functions on BX.In addition,we establish an improved version of the Bohr inequality for holomorphic functions on BX.All the results are proved to be sharp.展开更多
The neutral surface of a concave thin mirror is too close to the mirror surface,which makes it difficult to effectively mount the flexible structure and increases the mirror surface shape error.To address this problem...The neutral surface of a concave thin mirror is too close to the mirror surface,which makes it difficult to effectively mount the flexible structure and increases the mirror surface shape error.To address this problem,we design a flexible support structure including connectors,a support plate,and flexible structures,and construct an equivalent mirror by installing connectors and a support plate on the back of the mirror.While ensuring that the neutral surface of the equivalent mirror is moved away from the mirror surface,we optimize the support structure so that the rotary center of the flexible structure is located on the neutral surface of the equivalent mirror,avoiding the tilting moment.Following design and modeling of the structure,we analyze the static and dynamic characteristics using a finite element simulation,finding a root-mean-square(RMS)value for the surface shape error of 9.28 nm under the coupled effects of 1g gravity load,4℃ temperature rise,and 0.005 mm unevenness assembly error,with a fundamental frequency of 170.75 Hz,which all meet the design requirements.Finally,we carry out a surface shape error test of the mirror assembly,confirming it to meet the design index requirement of the mirror assembly.Simulation and test results verify the reliability and effectiveness of our proposed support structure.展开更多
In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[...In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[3/4,1],then∥x^(t)y^(1-t)+ytx^(1-t)∥E(M)≤2^(2t-3/2)∥x+y∥E(M).展开更多
Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) contain...Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) containsλ^(n)-uniformly copies of l^(k)_(∞)in the case p^(*)≤n.This complete a result of S.Dineen’s from 1995.展开更多
In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zer...In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zero-points distribution of the solutions and separate the single valued analytic branch of the solutions with square roots,then convert the problem to a Riemann boundary value problem in variable exponent Lebesgue spaces and discuss the singularity of solutions at individual zeros belonging to curve.We consider two types of cases those where the coefficient is Hölder and those where it is piecewise Hölder.Then we solve the Hilbert boundary value problem with square roots in variable exponent Lebesgue spaces.By discussing the distribution of the odd-order zero-points for solutions and the method of symmetric extension,we convert the Hilbert problem to a Riemann boundary value problem.The equivalence of the transformation is discussed.Finally,we get the solvable conditions and the direct expressions of the solutions in variable exponent Lebesgue spaces.展开更多
In this paper,we studyλ-biharmonic hypersurfaces M_(r)^(5) of 6-dimensional pseudo Riemannian space form N_(p)^(6)(c)with the indexs 0≤p≤6,r=p−1 or p,and constant curvature c.It was proved that if the shape operato...In this paper,we studyλ-biharmonic hypersurfaces M_(r)^(5) of 6-dimensional pseudo Riemannian space form N_(p)^(6)(c)with the indexs 0≤p≤6,r=p−1 or p,and constant curvature c.It was proved that if the shape operator of M_(r)^(5) is diagonalizable,then the mean curvature is a constant.As an application,we find some types of biharmonic hypersurfaces of N_(p)^(6)(c)are minimal.展开更多
数字化赋能教学已成为当前教学的新趋势,本文借助Earth Space Lab程序赋能“地球的运动”教学,帮助学生从本质上理解较为抽象的地理概念,同时,基于Earth Space Lab的教学不仅能实现学生对抽象概念的熟练掌握与灵活应用,促进作业质量与...数字化赋能教学已成为当前教学的新趋势,本文借助Earth Space Lab程序赋能“地球的运动”教学,帮助学生从本质上理解较为抽象的地理概念,同时,基于Earth Space Lab的教学不仅能实现学生对抽象概念的熟练掌握与灵活应用,促进作业质量与学习效果显著提升,还能进一步提升学生学习兴趣、地理实践力与综合思维,促进其地理核心素养的培育。展开更多
文摘文章基于CNKI、Web of Science两大数据库2005—2024年收录的图书馆学习空间研究文献,运用CiteSpace、Bicomb、SPSS软件进行可视化分析。结果显示,国外研究以技术驱动创新为主导,聚焦智能化技术与跨学科应用;而国内研究呈现理论创新与实践探索并重,通过大数据、AI等技术形成本土化解决方案。文章提出通过数字技术与人文关怀的平衡发展、国际化视野与本土化创新的有机结合、理论研究与实践应用的深度融合,为我国图书馆学习空间的研究提供借鉴与参考。
基金supported by the National Natural Science Foundation of China(No.12372045)the National Key Research and the Development Program of China(Nos.2023YFC2205900,2023YFC2205901)。
文摘This paper solves the problem of model-free dual-arm space robot maneuvering after non-cooperative target capture under high control quality requirements.The explicit system model is unavailable,and the maneuvering mission is disturbed by the measurement noise and the target adversarial behavior.To address these problems,a model-free Combined Adaptive-length Datadriven Predictive Controller(CADPC)is proposed.It consists of a separated subsystem identification method and a combined predictive control strategy.The subsystem identification method is composed of an adaptive data length,thereby reducing sensitivity to undetermined measurement noises and disturbances.Based on the subsystem identification,the combined predictive controller is established,reducing calculating resource.The stability of the CADPC is rigorously proven using the Input-to-State Stable(ISS)theorem and the small-gain theorem.Simulations demonstrate that CADPC effectively handles the model-free space robot post operation in the presence of significant disturbances,state measurement noise,and control input errors.It achieves improved steady-state accuracy,reduced steady-state control consumption,and minimized control input chattering.
文摘In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and G(z)=∑^(N)_(i)=1 A_(−i)z^(i),A_(i)ae culants.
基金Supported by the National Natural Science Foundation of China(11871195)。
文摘In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale inequalities of mixed quasi-martingale Hardy spaces.Moreover,we furnish sufficient conditions for the boundedness ofσ-sublinear operators in these spaces.These findings extend the existing conclusions regarding mixed quasi-martingale Hardy spaces defined with the help of the mixed L_(p)-norm.
基金supported by Swedish Research Council(Vetenskapsradet,2023-04962).
文摘Space exploration is significant for scientific innovation,resource utilization,and planetary security.Space exploration involves several systems including satellites,space suits,communication systems,and robotics,which have to function under harsh space conditions such as extreme temperatures(−270 to 1650℃),microgravity(10^(-6)g),unhealthy humidity(<20%RH or>60%RH),high atmospheric pressure(~1450 psi),and radiation(4000–5000 mSv).Conventional energy-harvesting technologies(solar cells,fuel cells,and nuclear energy),that are normally used to power these space systems have certain limitations(e.g.,sunlight dependence,weight,degradation,big size,high cost,low capacity,radioactivity,complexity,and low efficiency).The constraints in conventional energy resources have made it imperative to look for non-conventional yet efficient alternatives.A great potential for enhancing efficiency,sustainability,and mission duration in space exploration can be offered by integrating triboelectric nanogenerators(TENGs)with existing energy sources.Recently,the potential of TENG including energy harvesting(from vibrations/movements in satellites and spacecraft),self-powered sensing,and microgravity,for multiple applications in different space missions has been discussed.This review comprehensively covers the use of TENGs for various space applications,such as planetary exploration missions(Mars environment monitoring),manned space equipment,In-orbit robotic operations/collision monitoring,spacecraft’s design and structural health monitoring,Aeronautical systems,and conventional energy harvesting(solar and nuclear).This review also discusses the use of self-powered TENG sensors for deep space object perception.At the same time,this review compares TENGs with conventional energy harvesting technologies for space systems.Lastly,this review talks about energy harvesting in satellites,TENG-based satellite communication systems,and future practical implementation challenges(with possible solutions).
基金supported by the NSFC(12301115)the Natural Science Foundation of Huzhou(2023YZ11,2024YZ37)the second author was supported by the NSFC(12071437).
文摘It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.
文摘At 11:00 p.m. on January 13, 2026, floodlights illuminated the launch pad at the Hainan Commercial Space Launch Site in Wenchang,south China’s Hainan Province. A Long March-8A (CZ-8A) carrier rocket lifted off with a steady roar, its exhaust lighting up the night sky as it delivered a satellite into its designated orbit.The development of China’s first commercial space launch site has been striking. Since its inaugural launch in2024, it has completed 11 missions in less than 14 months—each a success.
基金supported by the Zhejiang Province Natural Science Foundation of China(LY23A010003).
文摘Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).
基金supported by the National Level Project of China(No.KJSP2023020201)the Foundation of Science and Technology on Aerospace Flight Dynamics Laboratory of China(No.kjw6142210240202)+1 种基金the Beijing Institute of Technology Research Fund Program for Young Scholars of Chinathe Fundamental Research Funds for Central Universities of China。
文摘In recent years,the rapid development of mega-constellations has significantly exacerbated the deterioration of the space debris environment,posing substantial and escalating threats to the safety of spacecraft.This study aims to explore the complex evolution of the space debris environment and assess the collision risks associated with spacecraft.First,a space debris environment topological network model is proposed,which incorporates interdisciplinary methods from topological networks,fluid mechanics,and spacecraft dynamics.This model enables a structured representation of the relationships among space objects and provides rapid predictions of the space debris environment.Then,a collision probability algorithm based on the topological network model is introduced.This algorithm inherits the efficiency advantages of the topological network model and has been validated for reliability through comparison with the classical ESA’s DRAMA software.Finally,based on the above models,the collision risks of constellation satellites in Low Earth Orbit(LEO)are analyzed,including both operational and deorbit processes.The study reveals that constellation satellites face a much higher risk of internal collisions with satellites from the same constellation during operations than that with other space objects.Additionally,during the satellite deorbit process,the collision risk peaks when satellites traverse the operational region of Starlink satellites.
文摘The Pantone Color of the Year 2026,PANTONE 11-4201 Cloud Dancer,has been introduced as a soft,lofty white symbolizing calm and clarity in an increasingly noisy world.This gentle shade invites a sense of peace and spaciousness,encouraging focus and creating room for creativity and reflection.Cloud Dancer embodies a desire for simplicity and renewal-a blank canvas that allows our minds to wander and new ideas to take shape.Its expansive presence fosters environments where tranquility meets inspiration,offering visual calm that supports wellbeing and mental lightness.
基金supported by the SERB,SUR/2022/002244,Govt.India and the second author was supported by the UGC-JRF(NTA Ref.No.:201610135853)New Delhi,India,and the third author was partially supported by the JSPS KAKENHI(JP22K03363).
文摘In this paper,we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball BX of a complex Banach space X into ℂ.As applications,we will establish refined Bohr inequalities of functional type or of norm type for holomorphic mappings with lacunary series on the unit ball BX with values in higher dimensional spaces.Next,we obtain the Bohr-Rogosinski inequality for the class of holomorphic functions on BX.In addition,we establish an improved version of the Bohr inequality for holomorphic functions on BX.All the results are proved to be sharp.
基金supported by the National Natural Science Foundation of China(12473085).
文摘The neutral surface of a concave thin mirror is too close to the mirror surface,which makes it difficult to effectively mount the flexible structure and increases the mirror surface shape error.To address this problem,we design a flexible support structure including connectors,a support plate,and flexible structures,and construct an equivalent mirror by installing connectors and a support plate on the back of the mirror.While ensuring that the neutral surface of the equivalent mirror is moved away from the mirror surface,we optimize the support structure so that the rotary center of the flexible structure is located on the neutral surface of the equivalent mirror,avoiding the tilting moment.Following design and modeling of the structure,we analyze the static and dynamic characteristics using a finite element simulation,finding a root-mean-square(RMS)value for the surface shape error of 9.28 nm under the coupled effects of 1g gravity load,4℃ temperature rise,and 0.005 mm unevenness assembly error,with a fundamental frequency of 170.75 Hz,which all meet the design requirements.Finally,we carry out a surface shape error test of the mirror assembly,confirming it to meet the design index requirement of the mirror assembly.Simulation and test results verify the reliability and effectiveness of our proposed support structure.
基金supported by the Fundamental Research Program of Shanxi Province(202103021223038).
文摘In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[3/4,1],then∥x^(t)y^(1-t)+ytx^(1-t)∥E(M)≤2^(2t-3/2)∥x+y∥E(M).
文摘Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) containsλ^(n)-uniformly copies of l^(k)_(∞)in the case p^(*)≤n.This complete a result of S.Dineen’s from 1995.
基金supported by the National Natural Science Foundation of China(11601525)the Natural Science Foundation of Hunan Province(2024JJ5412),the Changsha Municipal Natural Science Foundation(kq2402193).
文摘In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zero-points distribution of the solutions and separate the single valued analytic branch of the solutions with square roots,then convert the problem to a Riemann boundary value problem in variable exponent Lebesgue spaces and discuss the singularity of solutions at individual zeros belonging to curve.We consider two types of cases those where the coefficient is Hölder and those where it is piecewise Hölder.Then we solve the Hilbert boundary value problem with square roots in variable exponent Lebesgue spaces.By discussing the distribution of the odd-order zero-points for solutions and the method of symmetric extension,we convert the Hilbert problem to a Riemann boundary value problem.The equivalence of the transformation is discussed.Finally,we get the solvable conditions and the direct expressions of the solutions in variable exponent Lebesgue spaces.
基金Supported by National Natural Science Foundation of China(12161078)Foundation for Innovative Fundamental Research Group Project of Gansu Province(24JRRA778)Project of Northwest Normal University(20240010)。
文摘In this paper,we studyλ-biharmonic hypersurfaces M_(r)^(5) of 6-dimensional pseudo Riemannian space form N_(p)^(6)(c)with the indexs 0≤p≤6,r=p−1 or p,and constant curvature c.It was proved that if the shape operator of M_(r)^(5) is diagonalizable,then the mean curvature is a constant.As an application,we find some types of biharmonic hypersurfaces of N_(p)^(6)(c)are minimal.
文摘数字化赋能教学已成为当前教学的新趋势,本文借助Earth Space Lab程序赋能“地球的运动”教学,帮助学生从本质上理解较为抽象的地理概念,同时,基于Earth Space Lab的教学不仅能实现学生对抽象概念的熟练掌握与灵活应用,促进作业质量与学习效果显著提升,还能进一步提升学生学习兴趣、地理实践力与综合思维,促进其地理核心素养的培育。
