Through the combing of relevant literature and the analysis of relevant psychological students’cases,the composition of family factors affecting college students’mental health is analyzed,the specific manifestations...Through the combing of relevant literature and the analysis of relevant psychological students’cases,the composition of family factors affecting college students’mental health is analyzed,the specific manifestations of college students’psychological problems are summarized,and the influence of family factors on college students’mental health status is analyzed in detail.The article finally puts forward suggestions and recommendations for strengthening college students’family education and tries to explore how to promote college students’mental health through improving family education.展开更多
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...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.展开更多
This study explores the impact of generative artificial intelligence(AI)-enabled instruction on critical thinking in English essay writing among 1,050 first-year English majors across four colleges.Pedagogical strateg...This study explores the impact of generative artificial intelligence(AI)-enabled instruction on critical thinking in English essay writing among 1,050 first-year English majors across four colleges.Pedagogical strategies,including facilitating critical responses and emphasizing real-world application,are identified to enhance generative AI’s impact.Both qualitative and quantitative analyses reveal significant post-intervention improvements in critical thinking skills.This research contributes to understanding how generative AI can effectively foster critical thinking in educational settings.展开更多
Multi-parameter mixed Hardy space Hpmix is introduced by a new discrete Calderon's identity.As an application,we obtain the Hmix^p→ L^p(R^n1+n2)boundedness of operators in the mixed Journe’s class.
In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces Fp^a,q（w;R^n1×R^n2） based on the Frazier and Jawerth＇ method in [11]. This space was firstly introduced in [18]. Then we estab...In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces Fp^a,q（w;R^n1×R^n2） based on the Frazier and Jawerth＇ method in [11]. This space was firstly introduced in [18]. Then we establish its dual space and get that （Fp＇q）＊ = CMOp^-a,q＇ for 0 ~p≤ 1.展开更多
By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive soluti...By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive solution and a negative solution are obtained respectively, so as to popularize and improve some results that have been known.展开更多
Let M be an n-dimensional complete noncompact Riemannian manifold. In this paper, we will give the elliptic gradient estimate for positive smooth solutions to the non-homogeneous heat equation(?_t-△)u(x, t) = A(x, t)...Let M be an n-dimensional complete noncompact Riemannian manifold. In this paper, we will give the elliptic gradient estimate for positive smooth solutions to the non-homogeneous heat equation(?_t-△)u(x, t) = A(x, t)when the metric evolves under the Ricci flow. As applications, we get Harnack inequalities to compare solutions at the same time.展开更多
The paper reports a survey on material evaluation on Century Business English comprehensive course of 80 students of Business English majors in Normal College.The survey covers students’and teachers’opinions and sug...The paper reports a survey on material evaluation on Century Business English comprehensive course of 80 students of Business English majors in Normal College.The survey covers students’and teachers’opinions and suggestions of the CBE.The result is helpful for Business English teachers to effectively improve the students’Business English learning.展开更多
Listening is one of the four basic abilities in English learning.Listening locates the first position of English learning.So it is obvious that listening is the most important part in English learning.In the different...Listening is one of the four basic abilities in English learning.Listening locates the first position of English learning.So it is obvious that listening is the most important part in English learning.In the different kinds of English tests in college,listening comprehension is the absolutely necessary part.In the college entrance examination,the listening comprehension is the first part in the English examination.It’s important to finish the listening part well in the exam.However,in the present middle school English teaching,not only the teachers but also the students don’t’pay more attention to the listening comprehension.They just take a mechanical training.The students can’t improve their listening ability essentially.This article will analyses the present conditions of English listening teaching in the middle school,and study the basic principles of Task-based teaching approach.And it also try to combine the essential characteristics and principles of task-based teaching approach into listening teaching.Then I will discuss the correct method of listening teaching in middle school English teaching through the experimentation according to the middle school English teaching condition.展开更多
This paper is devoted to study the atom decomposition of the weighted Hardy space on a homogeneous group X. Some results are extensions of the objects studied in Euclidean harmonic analysis.
Usually, the condition that T is bounded on L^2(R^n) is assumed to prove the boundedness of an operator T on a Hardy space. With this assumption, one only needs to prove the uniformly boundness of T on atoms, since T(...Usually, the condition that T is bounded on L^2(R^n) is assumed to prove the boundedness of an operator T on a Hardy space. With this assumption, one only needs to prove the uniformly boundness of T on atoms, since T(f)=∑iλi T(ai), provided that f =∑iλiai in L^2(R^n), where ai is an L^2 atom of this Hardy space. So far, the L^2 atomic decomposition of local Hardy spaces h^p(R^n), 0 < p ≤ 1, hasn't been established. In this paper, we will solve this problem, and also show that h^p(R^n) can also be characterized by discrete Littlewood-Paley functions.展开更多
This paper focuses on the rapid time-decay phenomenon of the 3 D incompressible NavierStokes flow in exterior domains.By using the representation of the flow in exterior domains,together with the estimates of the Gaus...This paper focuses on the rapid time-decay phenomenon of the 3 D incompressible NavierStokes flow in exterior domains.By using the representation of the flow in exterior domains,together with the estimates of the Gaussian kernel,the tensor kernel,and the Stokes semigroup,we prove that under the assumption∫0∞∫ΩT[u,p](y,t).νdSydt=0 for the body pressure tensor T[u,p],if u0∈L1(Ω)∩Lσ3(Ω)∩W2/5,5/4(Ω)with‖u0‖3≤ηfor some sufficiently small numberη>0,then rapid time-decay phenomenon of the Navier-Stokes flow appears.If additionally|x|αu0∈Lr0(Ω)for some0<α<1 and 1<r0<(1-α/3)-1 orα=1 and r0=1,then the flow exhibits higher decay rates as t→∞.展开更多
文摘Through the combing of relevant literature and the analysis of relevant psychological students’cases,the composition of family factors affecting college students’mental health is analyzed,the specific manifestations of college students’psychological problems are summarized,and the influence of family factors on college students’mental health status is analyzed in detail.The article finally puts forward suggestions and recommendations for strengthening college students’family education and tries to explore how to promote college students’mental health through improving family education.
文摘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.
基金General Project of Philosophy and Social Science Research in Jiangsu Universities in 2024“Research on the Mining and Integration Strategy of Ideological and Political Elements in Business English Major Courses”(2024SISZ0787)。
文摘This study explores the impact of generative artificial intelligence(AI)-enabled instruction on critical thinking in English essay writing among 1,050 first-year English majors across four colleges.Pedagogical strategies,including facilitating critical responses and emphasizing real-world application,are identified to enhance generative AI’s impact.Both qualitative and quantitative analyses reveal significant post-intervention improvements in critical thinking skills.This research contributes to understanding how generative AI can effectively foster critical thinking in educational settings.
基金NNSFC(11771223,11501308)Natural science foundation of Inner Mongolia(2019MS01003).
文摘Multi-parameter mixed Hardy space Hpmix is introduced by a new discrete Calderon's identity.As an application,we obtain the Hmix^p→ L^p(R^n1+n2)boundedness of operators in the mixed Journe’s class.
基金Supported by NNSF of China grants(11501308,11271209,11371370)Jiangsu Government Scholarship for Overseas Studies
文摘In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces Fp^a,q（w;R^n1×R^n2） based on the Frazier and Jawerth＇ method in [11]. This space was firstly introduced in [18]. Then we establish its dual space and get that （Fp＇q）＊ = CMOp^-a,q＇ for 0 ~p≤ 1.
文摘By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive solution and a negative solution are obtained respectively, so as to popularize and improve some results that have been known.
文摘Let M be an n-dimensional complete noncompact Riemannian manifold. In this paper, we will give the elliptic gradient estimate for positive smooth solutions to the non-homogeneous heat equation(?_t-△)u(x, t) = A(x, t)when the metric evolves under the Ricci flow. As applications, we get Harnack inequalities to compare solutions at the same time.
文摘The paper reports a survey on material evaluation on Century Business English comprehensive course of 80 students of Business English majors in Normal College.The survey covers students’and teachers’opinions and suggestions of the CBE.The result is helpful for Business English teachers to effectively improve the students’Business English learning.
文摘Listening is one of the four basic abilities in English learning.Listening locates the first position of English learning.So it is obvious that listening is the most important part in English learning.In the different kinds of English tests in college,listening comprehension is the absolutely necessary part.In the college entrance examination,the listening comprehension is the first part in the English examination.It’s important to finish the listening part well in the exam.However,in the present middle school English teaching,not only the teachers but also the students don’t’pay more attention to the listening comprehension.They just take a mechanical training.The students can’t improve their listening ability essentially.This article will analyses the present conditions of English listening teaching in the middle school,and study the basic principles of Task-based teaching approach.And it also try to combine the essential characteristics and principles of task-based teaching approach into listening teaching.Then I will discuss the correct method of listening teaching in middle school English teaching through the experimentation according to the middle school English teaching condition.
文摘This paper is devoted to study the atom decomposition of the weighted Hardy space on a homogeneous group X. Some results are extensions of the objects studied in Euclidean harmonic analysis.
基金Supported by NNSF of China(Grant Nos.11501308 and 11771223)
文摘Usually, the condition that T is bounded on L^2(R^n) is assumed to prove the boundedness of an operator T on a Hardy space. With this assumption, one only needs to prove the uniformly boundness of T on atoms, since T(f)=∑iλi T(ai), provided that f =∑iλiai in L^2(R^n), where ai is an L^2 atom of this Hardy space. So far, the L^2 atomic decomposition of local Hardy spaces h^p(R^n), 0 < p ≤ 1, hasn't been established. In this paper, we will solve this problem, and also show that h^p(R^n) can also be characterized by discrete Littlewood-Paley functions.
基金National Natural Science Foundation of China(Grant No.11771223)。
文摘This paper focuses on the rapid time-decay phenomenon of the 3 D incompressible NavierStokes flow in exterior domains.By using the representation of the flow in exterior domains,together with the estimates of the Gaussian kernel,the tensor kernel,and the Stokes semigroup,we prove that under the assumption∫0∞∫ΩT[u,p](y,t).νdSydt=0 for the body pressure tensor T[u,p],if u0∈L1(Ω)∩Lσ3(Ω)∩W2/5,5/4(Ω)with‖u0‖3≤ηfor some sufficiently small numberη>0,then rapid time-decay phenomenon of the Navier-Stokes flow appears.If additionally|x|αu0∈Lr0(Ω)for some0<α<1 and 1<r0<(1-α/3)-1 orα=1 and r0=1,then the flow exhibits higher decay rates as t→∞.
