In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an a...In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.展开更多
Given a compact Hausdorff space X, U(X) denotes the compact Hausdorff space of all the upper semicontinuous functions from X to the unit interval with the dual lim inf topology. Then U is an endofunctor o...Given a compact Hausdorff space X, U(X) denotes the compact Hausdorff space of all the upper semicontinuous functions from X to the unit interval with the dual lim inf topology. Then U is an endofunctor on compact Hausdorff space. It is proved in this note that this functor preserves inverse limits.展开更多
The purpose of this paper is to introduce the notions of <em>m</em>-asymmetric semiopen sets and <em>M</em>-asymmetric semicontinuous multifunctions defined between asymmetric sets satisfying c...The purpose of this paper is to introduce the notions of <em>m</em>-asymmetric semiopen sets and <em>M</em>-asymmetric semicontinuous multifunctions defined between asymmetric sets satisfying certain minimal conditions in the framework of bitopological spaces. Some new characterizations of <em>m</em>-asymmetric semiopen sets and <em>M</em>-asymmetric semicontinuous multifunctions will be investigated and several fundamental properties will be obtained.展开更多
In this paper lower semicontinuity of the functional I(u)=∫_Ωf(x,u,Δ~ _Hu)dx is investigated for f being a Carathéodory function defined on Hn×R×R^2n and for u∈SBV_H(Ω),where Hn is the Heisenberg g...In this paper lower semicontinuity of the functional I(u)=∫_Ωf(x,u,Δ~ _Hu)dx is investigated for f being a Carathéodory function defined on Hn×R×R^2n and for u∈SBV_H(Ω),where Hn is the Heisenberg group with dimension 2n+1,ΩHn is an open set and Δ~ _Hu denotes the approximate derivative of the absolute continuous part Da_Hu with respect to D_Hu.In addition,a Lusin type approximation theorem for a SBV_H function is proved.展开更多
In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters a...In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated.展开更多
Objective: to use early rehabilitation treatment for the patients with acute stroke hemiplegia, to observe and analyze its impact on the upper and lower limb function recovery and daily life ability. Methods: in June ...Objective: to use early rehabilitation treatment for the patients with acute stroke hemiplegia, to observe and analyze its impact on the upper and lower limb function recovery and daily life ability. Methods: in June 2021-June 2022 for intercept research time interval, a total of 60 cases of acute stroke hemiplegia, random principle specification grouping, control group received 30 cases of routine treatment, observation group received 30 cases of early rehabilitation treatment, around the upper and lower limb function assessment score, daily life ability evaluation score, balance function, cognitive function scale evaluation score and complication rate data line to compare. Results: before the treatment work, the evaluation results, daily life ability, balance function, and cognitive function evaluation results showed no difference (P> 0.05), and the results were higher (P <0.05);for the complication rate, the observation group showed lower results (P <0.05). Conclusion: for acute stroke cases, early rehabilitation treatment, which can improve the function of upper and lower limbs, strengthen their living ability, balance function and cognitive function, and prevent complications in patients, which is worthy of clinical application.展开更多
In article, I present a study on upper and lower statistical convergence, and upper and lower strong fractional weighted mean convergence by moduli for triple sequences. One of the generalizations of the discrete oper...In article, I present a study on upper and lower statistical convergence, and upper and lower strong fractional weighted mean convergence by moduli for triple sequences. One of the generalizations of the discrete operator Cesàro, was weighted mean operators, which are linear operators, too. Given a modulus function f, I established that a triple sequence that is f-upper or lower strong fractional weighted mean convergent, in some supplementary conditions, is also f-lower or upper statistically convergent. The results of this paper adapt the results obtained in [1] and [2] to upper and lower strong fractional weighted mean convergence and to triple sequence concept. Furthermore, new concepts can be applied to the approximation theory, topology, Fourier analysis, analysis interdisciplinary with applications electrical engineering, robotics and other domains.展开更多
This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is pres...This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.展开更多
Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish...Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish our results. Results and Conclusion The results of the existence of maximal and minimal solutions of the periodic boundary value problem for functional differential equations with impulses are obtained.展开更多
The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integ...The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integrals,the relation of the upper approximation integrals,the relation of rough integrals,and the double median theorem of rough integrals are discussed.Rough integrals have finite contraction characteristic and finite extension characteristic.展开更多
The D-η-proper prequasi invexity of vector-valued functions is characterized by means of （weak） nearly convexity and density of sets. Under weaker assumptions, some equivalent conditions for D-η-proper prequasi-in...The D-η-proper prequasi invexity of vector-valued functions is characterized by means of （weak） nearly convexity and density of sets. Under weaker assumptions, some equivalent conditions for D-η-proper prequasi-invexity are derived.展开更多
Let X and Y be metrizable topological linear spaces. In this paper, the following results are proved. (1) If X and Y are complete, g: X→Y is a point closed u. s. c.,and symmetric process with F(X)=Y,then either F(X) ...Let X and Y be metrizable topological linear spaces. In this paper, the following results are proved. (1) If X and Y are complete, g: X→Y is a point closed u. s. c.,and symmetric process with F(X)=Y,then either F(X) is meager in Y,or else F is an open muRifunction with F(X)=Y. (2) If X is complete, and F: X→Y is a process with a subclosed graph, then F is I s. c.. We also discuss topological multi-homomorphisms between topological linear spaces.展开更多
We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, wher...We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs’ condition.展开更多
We obtain some theorems for real increasing functions showing that elementary fixed point theory can bring to astonishing results by assuming only a few properties, some of which intrinsically possessed from these fun...We obtain some theorems for real increasing functions showing that elementary fixed point theory can bring to astonishing results by assuming only a few properties, some of which intrinsically possessed from these functions. An application is given for a theorem of quasi-compactness and a known result in posets is also recalled and applied to real intervals.展开更多
目的:研究镜像神经元康复策略(Mirror Neuron System,MNS)联合经颅磁刺激(Transcranial Magnetic Stimulation,TMS)对卒中后神经与功能康复的作用。方法:选取2019年1月至2023年6月某部队康复中心收治的198例卒中后遗留有运动功能障碍患...目的:研究镜像神经元康复策略(Mirror Neuron System,MNS)联合经颅磁刺激(Transcranial Magnetic Stimulation,TMS)对卒中后神经与功能康复的作用。方法:选取2019年1月至2023年6月某部队康复中心收治的198例卒中后遗留有运动功能障碍患者,采用随机数字表法分为三组,各66例。三组均给予常规康复指导,磁刺激组给予TMS治疗,镜像组给予MNS治疗,联合组给予TMS+MNS治疗。比较三组干预前、干预2周后、干预4周后神经功能(NIHSS)、上下肢运动功能(FMA)、日常生活能力(ADL)、平衡能力(BBS)、上肢与下肢肌张力(MAS)、健患侧步长差、患侧负重时间百分比及语言功能。结果:联合组干预2周、4周后NIHSS评分低于磁刺激组、镜像组,差异具有统计学意义(P<0.05),磁刺激组、镜像组组间比较,差异无统计学意义(P>0.05);联合组干预2周、4周后FMA-上肢、FMA-下肢评分高于磁刺激组、镜像组,且镜像组高于磁刺激组,差异具有统计学意义(P<0.05);联合组干预2周、4周后ADL评分、BBS评分高于磁刺激组、镜像组,且镜像组高于磁刺激组,差异具有统计学意义(P<0.05);联合组干预4周后上肢和下肢MAS分级0~1级患者占比高于磁刺激组、镜像组,且磁刺激组高于镜像组,差异具有统计学意义(P<0.05);联合组干预2周、4周后健患侧步长差低于磁刺激组、镜像组,患侧负重时间百分比高于磁刺激组、镜像组,且镜像组变化幅度大于磁刺激组,差异具有统计学意义(P<0.05);联合组干预2周、4周后语言功能中阅读理解、复述、流畅度、命名评分高于磁刺激组、镜像组,且磁刺激组高于镜像组,差异具有统计学意义(P<0.05)。结论:MNS联合TMS能促进卒中后神经与功能康复,有利于改善患者日常生活能力,且二者各有优势,互相补充,联合治疗效果显著,值得临床推广。展开更多
文摘In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.
文摘Given a compact Hausdorff space X, U(X) denotes the compact Hausdorff space of all the upper semicontinuous functions from X to the unit interval with the dual lim inf topology. Then U is an endofunctor on compact Hausdorff space. It is proved in this note that this functor preserves inverse limits.
文摘The purpose of this paper is to introduce the notions of <em>m</em>-asymmetric semiopen sets and <em>M</em>-asymmetric semicontinuous multifunctions defined between asymmetric sets satisfying certain minimal conditions in the framework of bitopological spaces. Some new characterizations of <em>m</em>-asymmetric semiopen sets and <em>M</em>-asymmetric semicontinuous multifunctions will be investigated and several fundamental properties will be obtained.
文摘In this paper lower semicontinuity of the functional I(u)=∫_Ωf(x,u,Δ~ _Hu)dx is investigated for f being a Carathéodory function defined on Hn×R×R^2n and for u∈SBV_H(Ω),where Hn is the Heisenberg group with dimension 2n+1,ΩHn is an open set and Δ~ _Hu denotes the approximate derivative of the absolute continuous part Da_Hu with respect to D_Hu.In addition,a Lusin type approximation theorem for a SBV_H function is proved.
基金The NSF(10871226) of Chinathe NSF(ZR2009AL006) of Shandong Province
文摘In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated.
文摘Objective: to use early rehabilitation treatment for the patients with acute stroke hemiplegia, to observe and analyze its impact on the upper and lower limb function recovery and daily life ability. Methods: in June 2021-June 2022 for intercept research time interval, a total of 60 cases of acute stroke hemiplegia, random principle specification grouping, control group received 30 cases of routine treatment, observation group received 30 cases of early rehabilitation treatment, around the upper and lower limb function assessment score, daily life ability evaluation score, balance function, cognitive function scale evaluation score and complication rate data line to compare. Results: before the treatment work, the evaluation results, daily life ability, balance function, and cognitive function evaluation results showed no difference (P> 0.05), and the results were higher (P <0.05);for the complication rate, the observation group showed lower results (P <0.05). Conclusion: for acute stroke cases, early rehabilitation treatment, which can improve the function of upper and lower limbs, strengthen their living ability, balance function and cognitive function, and prevent complications in patients, which is worthy of clinical application.
文摘In article, I present a study on upper and lower statistical convergence, and upper and lower strong fractional weighted mean convergence by moduli for triple sequences. One of the generalizations of the discrete operator Cesàro, was weighted mean operators, which are linear operators, too. Given a modulus function f, I established that a triple sequence that is f-upper or lower strong fractional weighted mean convergent, in some supplementary conditions, is also f-lower or upper statistically convergent. The results of this paper adapt the results obtained in [1] and [2] to upper and lower strong fractional weighted mean convergence and to triple sequence concept. Furthermore, new concepts can be applied to the approximation theory, topology, Fourier analysis, analysis interdisciplinary with applications electrical engineering, robotics and other domains.
基金Supported by the National Natural Science Foundation of China (10571050 10871062)Hunan Provincial Innovation Foundation For Postgraduate
文摘This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.
文摘Aim To investigate the periodic boundary value problem for functional differential equations with impulses. Methods The method of upper and lower solutions and the monotone iterative technique were used to establish our results. Results and Conclusion The results of the existence of maximal and minimal solutions of the periodic boundary value problem for functional differential equations with impulses are obtained.
基金Supported by the Natural Science Foundation of Shandong Province（ZR2010AL019） Supported by the Education Science Foundation of Shandong Province（2010JZ123）
文摘The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integrals,the relation of the upper approximation integrals,the relation of rough integrals,and the double median theorem of rough integrals are discussed.Rough integrals have finite contraction characteristic and finite extension characteristic.
文摘The D-η-proper prequasi invexity of vector-valued functions is characterized by means of （weak） nearly convexity and density of sets. Under weaker assumptions, some equivalent conditions for D-η-proper prequasi-invexity are derived.
基金This paper was reported at the 5th National Functional Analysis Conference held at Nanjing in Nov.,1990.
文摘Let X and Y be metrizable topological linear spaces. In this paper, the following results are proved. (1) If X and Y are complete, g: X→Y is a point closed u. s. c.,and symmetric process with F(X)=Y,then either F(X) is meager in Y,or else F is an open muRifunction with F(X)=Y. (2) If X is complete, and F: X→Y is a process with a subclosed graph, then F is I s. c.. We also discuss topological multi-homomorphisms between topological linear spaces.
基金supported by the NSF of China(11071144,11171187,11222110 and 71671104)Shandong Province(BS2011SF010,JQ201202)+4 种基金SRF for ROCS(SEM)Program for New Century Excellent Talents in University(NCET-12-0331)111 Project(B12023)the Ministry of Education of Humanities and Social Science Project(16YJA910003)Incubation Group Project of Financial Statistics and Risk Management of SDUFE
文摘We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs’ condition.
文摘We obtain some theorems for real increasing functions showing that elementary fixed point theory can bring to astonishing results by assuming only a few properties, some of which intrinsically possessed from these functions. An application is given for a theorem of quasi-compactness and a known result in posets is also recalled and applied to real intervals.
文摘目的:研究镜像神经元康复策略(Mirror Neuron System,MNS)联合经颅磁刺激(Transcranial Magnetic Stimulation,TMS)对卒中后神经与功能康复的作用。方法:选取2019年1月至2023年6月某部队康复中心收治的198例卒中后遗留有运动功能障碍患者,采用随机数字表法分为三组,各66例。三组均给予常规康复指导,磁刺激组给予TMS治疗,镜像组给予MNS治疗,联合组给予TMS+MNS治疗。比较三组干预前、干预2周后、干预4周后神经功能(NIHSS)、上下肢运动功能(FMA)、日常生活能力(ADL)、平衡能力(BBS)、上肢与下肢肌张力(MAS)、健患侧步长差、患侧负重时间百分比及语言功能。结果:联合组干预2周、4周后NIHSS评分低于磁刺激组、镜像组,差异具有统计学意义(P<0.05),磁刺激组、镜像组组间比较,差异无统计学意义(P>0.05);联合组干预2周、4周后FMA-上肢、FMA-下肢评分高于磁刺激组、镜像组,且镜像组高于磁刺激组,差异具有统计学意义(P<0.05);联合组干预2周、4周后ADL评分、BBS评分高于磁刺激组、镜像组,且镜像组高于磁刺激组,差异具有统计学意义(P<0.05);联合组干预4周后上肢和下肢MAS分级0~1级患者占比高于磁刺激组、镜像组,且磁刺激组高于镜像组,差异具有统计学意义(P<0.05);联合组干预2周、4周后健患侧步长差低于磁刺激组、镜像组,患侧负重时间百分比高于磁刺激组、镜像组,且镜像组变化幅度大于磁刺激组,差异具有统计学意义(P<0.05);联合组干预2周、4周后语言功能中阅读理解、复述、流畅度、命名评分高于磁刺激组、镜像组,且磁刺激组高于镜像组,差异具有统计学意义(P<0.05)。结论:MNS联合TMS能促进卒中后神经与功能康复,有利于改善患者日常生活能力,且二者各有优势,互相补充,联合治疗效果显著,值得临床推广。
