Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces

In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.

Equilibria of the Abstract Economy under Almost Lower Semi-continuous Assumption

The purpose of this paper is to make a further study on the abstract economy. Here, for the constraint correspondences we assume that they are almost lower semi-continuous (n-lower semi-continuous), which is weaken than that they are lower semi-continuous. Several equilibria existence theorems are proved.

Repetitive transcranial magnetic stimulation for lower extremity motor function in patients with stroke:a systematic review and network meta-analysis

Transcranial magnetic stimulation,a type of noninvasive brain stimulation,has become an ancillary therapy for motor function rehabilitation.Most previous studies have focused on the effects of repetitive transcranial magnetic stimulation(rTMS)on motor function in stroke patients.There have been relatively few studies on the effects of different modalities of rTMS on lower extremity motor function and corticospinal excitability in patients with stroke.The MEDLINE,Embase,Cochrane Library,ISI Science Citation Index,Physiotherapy Evidence Database,China National Knowledge Infrastructure Library,and ClinicalTrials.gov databases were searched.Parallel or crossover randomized controlled trials that addressed the effectiveness of rTMS in patients with stroke,published from inception to November 28,2019,were included.Standard pairwise meta-analysis was conducted using R version 3.6.1 with the“meta”package.Bayesian network analysis using the Markov chain Monte Carlo algorithm was conducted to investigate the effectiveness of different rTMS protocol interventions.Network meta-analysis results of 18 randomized controlled trials regarding lower extremity motor function recovery revealed that low-frequency rTMS had better efficacy in promoting lower extremity motor function recovery than sham stimulation.Network meta-analysis results of five randomized controlled trials demonstrated that highfrequency rTMS led to higher amplitudes of motor evoked potentials than low-frequency rTMS or sham stimulation.These findings suggest that rTMS can improve motor function in patients with stroke,and that low-frequency rTMS mainly affects motor function,whereas high-frequency rTMS increases the amplitudes of motor evoked potentials.More highquality randomized controlled trials are needed to validate this conclusion.The work was registered in PROSPERO(registration No.CRD42020147055)on April 28,2020.

ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE

The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna＇s representation for harmonic functions in the half sphere by using HSrmander＇s theorem.

Fuzzy Semi-continuity of fuzzy number-valued function

In this paper we discuss the conecept and property of fuzzy semi continuous function.

Relationship between acute high altitude response, cardiac function injury, and high altitude de-adaptation response after returning to lower altitude

The relationship between acute high altitude response (AHAR), cardiac function injury, and high altitude de-adaptation response (HADAR) was assessed. Cardiac function indicators were assessed for 96 men (18 - 35 years old) deployed into a high altitude (3700 - 4800 m) environment requiring intense physical activity. The subjects were divided into 3 groups based on AHAR at high altitude: severe AHAR (n = 24), mild to moderate AHAR (Group B, n = 47) and non-AHAR (Group C, 25);and based on HADAR: severe HADAR (Group E, n = 19), mild to moderate HADAR (Group F, n = 40) and non-HADAR (Group G, n = 37) after return to lower altitude (1,500 m). Cardiac function indicators were measured after 50 days at high altitude and at 12 h, 15 days, and 30 days after return to lower altitude. Controls were 50 healthy volunteers (Group D, n = 50) at 1500 m. Significant differences were observed in cardiac function indicators among groups A, B, C, and D. AHAR score was positively correlated with HADAR score (r = 0.863, P < 0.001). Significant differ- ences were also observed in cardiac function indicators among groups D, E, F, and G, 12 h and15 days after return to lower altitude. There were no significant differences in cardiac function indicators among the groups, 30 days after return to lower altitude, compared to group D. The results indicated that the severity of HADAR is associated with the severity of AHAR and cardiac injury, and prolonged recovery.

A Survey of Lower Limb Rehabilitation Systems and Algorithms Based on Functional Electrical Stimulation

Functional electrical stimulation is a method of repairing a dysfunctional limb in a stroke patient by using low-intensity electrical stimulation.Currently,it is widely used in smart medical treatment for limb rehabilitation in stroke patients.In this paper,the development of FES systems is sorted out and analyzed in a time order.Then,the progress of functional electrical stimulation in the field of rehabilitation is reviewed in details in two aspects,i.e.,system development and algorithm progress.In the system aspect,the development of the first FES control and stimulation system,the core of the lower limb-based neuroprosthesis system and the system based on brain-computer interface are introduced.The algorithm optimization for control strategy is introduced in the algorithm.Asynchronous stimulation to prolong the function time of the lower limbs and a method to improve the robustness of knee joint modeling using neural networks.Representative applications in each of these aspects have been investigated and analyzed.

Tailoring MXene Thickness and Functionalization for Enhanced Room‑Temperature Trace NO_(2) Sensing

In this study,precise control over the thickness and termination of Ti3C2TX MXene flakes is achieved to enhance their electrical properties,environmental stability,and gas-sensing performance.Utilizing a hybrid method involving high-pressure processing,stirring,and immiscible solutions,sub-100 nm MXene flake thickness is achieved within the MXene film on the Si-wafer.Functionalization control is achieved by defunctionalizing MXene at 650℃ under vacuum and H2 gas in a CVD furnace,followed by refunctionalization with iodine and bromine vaporization from a bubbler attached to the CVD.Notably,the introduction of iodine,which has a larger atomic size,lower electronegativity,reduce shielding effect,and lower hydrophilicity(contact angle:99°),profoundly affecting MXene.It improves the surface area(36.2 cm^(2) g^(-1)),oxidation stability in aqueous/ambient environments(21 days/80 days),and film conductivity(749 S m^(-1)).Additionally,it significantly enhances the gas-sensing performance,including the sensitivity(0.1119Ωppm^(-1)),response(0.2% and 23%to 50 ppb and 200 ppm NO_(2)),and response/recovery times(90/100 s).The reduced shielding effect of the–I-terminals and the metallic characteristics of MXene enhance the selectivity of I-MXene toward NO2.This approach paves the way for the development of stable and high-performance gas-sensing two-dimensional materials with promising prospects for future studies.

LOWER SEMICONTINUITY OF A CLASS OF FUNCTIONALSIN SBV_H

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.

Treatment of Skeletal CL II Patient with Maximum Lower Incisor Protrusion and Minimum Overjet with Rahhal Functional Appliance

Treatment of skeletal Cl II includes functional orthopedic treatment, head-gears, extraction of the upper premolars and orthognathic surgery. To treat any patient with functional appliances (bite jumping) an adequate overjet is necessary. In this case an 11 years old female patient has skeletal CLII due to mandibular deficiency with ANB angle 8 degrees, overbite: 3 mm, overjet: 1 mm, extremely convex profile and underdeveloped chin due to the hyper muscle contraction of the lower lip to obtain oral seal. To obtain an adequate overjet lower first premolars were extracted and maximum retraction using mini screws (for maximum anchorage) was applied. Afterwards Rahhal functional appliance was used by the patient 16 hours a day for 6 months and 10 hours a day for another 6 months for retention. After that fixed orthodontic treatment was completed. Lateral cephalometrics were taken, traced and analyzed. In the result Skeletal CLI was obtained (ANB 4 degree), straight facial profile, normal over bite overjet and particular chin development were noticed. As a conclusion, in skeletal CLII malocclusions, lower incisor protrusion will cause a contraindication for functional treatment. Extraction of the lower premolars and retraction of the lower incisors followed by functional orthopedic treatment is an efficient method to treat these cases instead of waiting for orthognathic surgery, also reducing the muscle pressure on the chin will change the development characteristics of it.

Effects of Water Weight-Loss Walking Training on Lower Limb Motor Function and Gait in Stroke Patients

Background: Water weight-loss walking training is an emerging physical therapy technique, which provides new ideas for improving the motor function of stroke patients and improving the quality of life of patients. However, the rehabilitation effect of water weight-loss training in stroke patients is currently unclear. Objective: To analyze the effect of water weight loss walking training in stroke patients. Methods: A total of 180 stroke patients admitted to our hospital from January 2019 to December 2021 were selected and randomly divided into two groups. The control group received routine walking training, and the research group performed weight loss walking training in water on this basis. The lower limb motor function, muscle tone grade, daily living ability, gait and balance ability were compared between the two groups before and after treatment. Results: Compared with the control group, the FMA-LE score (Fugl-Meyer motor assessment of Lower Extremity), MBI score (Modified Barthel Index) and BBS score (berg balance scale) of the study group were higher after treatment, and the muscle tone was lower (P Conclusion: Water weight loss walking training can enhance patients’ muscle tension, correct patients’ abnormal gait, improve patients’ balance and walking ability, and contribute to patients’ motor function recovery and self-care ability improvement.

Multistatic radar analysis based on ambiguity function and Cramér-Rao lower bounds

The primary goal of this work is to characterize the impact of weighting selection strategy and multistatic geometry on the multistatic radar performance. With the relationship between the multistatic ambiguity function （AF） and the multistatie Cram6r-Rao lower bound （CRLB）, the problem of calculating the multistatic AF and the multistatic CRLB as a performance metric for multistatic radar system is studied. Exactly, based on the proper selection of the system parameters, the multistatic radar performance can be significantly improved. The simulation results illustrate that the multistatic AF and the multistatic CRLB can serve as guidelines for future multistatic fusion rule development and multistatic radars deployment.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1)

In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.

Effect of Motor Relearning Combined with t DCS on Motor Function of Lower Extremities and Gait in Patients with Cerebral Infarction and 3D Gait Analysis

[Objectives]To observe the effect of motor relearning combined with transcranial direct current stimulation on the motor function of lower extremities in patients with cerebral infarction,and to observe its effect on gait by 3D gait analysis.[Methods]60 patients with cerebral infarction who met the inclusion criteria were randomly divided into 3 groups according to the order of treatment(n=20).Group A received motor relearning treatment,group B received transcranial direct current stimulation treatment,group C received motor relearning combined with transcranial direct current stimulation,and the curative effect was observed after 5 courses of treatment.[Results]Before treatment,FMA,MBI,spatio-temporal parameters for 3D gait analysis(gait frequency,gait cycle,stride length,gait speed,stride length deviation,double support)and lower limb joint motion parameters(affected side stride length,maximum hip flexion,maximum hip extension,maximum knee flexion,maximum knee extension,stance phase,swing phase)were compared among the three groups.After treatment,the FMA and MBI of the three groups increased,and the spatio-temporal parameters for 3D gait analysis(gait frequency,gait cycle,gait speed,double support)and the lower limb joint motion parameters(affected side stride length,maximum hip flexion,maximum hip extension,maximum knee flexion,swing phase)were all improved,while the spatio-temporal parameters(stride length and stride length deviation)and the lower limb joint motion parameters(maximum knee extension and stance phase)decreased.Compared with those before treatment,there were significant differences among the three groups(P<0.05).Through the comparison between groups,it was found that the FMA,MBI,spatio-temporal parameters for 3D gait analysis(gait frequency,gait cycle,gait speed,double support)and lower limb joint motion parameters(affected side stride length,maximum hip flexion,maximum hip extension,maximum knee flexion,swing phase)in group C were significantly higher than those in group A and B,while the spatio-temporal parameters(stride length and stride length deviation)and lower limb joint motion parameters(maximum knee extension and stance phase)in group C were significantly lower than those in group A and group B,and the difference was statistically significant(P<0.05).[Conclusions]Motor relearning combined with transcranial direct current stimulation could increase MBI and FMA,improve gait spatio-temporal parameters and lower limb joint motion parameters,and correct abnormal gait in patients with cerebral infarction.

Assistive Devices and Clothing: Exploring Adaptive Clothing Needs for Women with Lower Limb Prostheses Using the FEA Model

This study aimed to comprehensively investigate the essential considerations in designing adaptive clothing for women with lower limb prostheses in Saudi Arabia. Employing a qualitative methodology, the research entailed semi-structured, in-depth interviews with women utilizing lower limb prostheses and prosthetic specialists. This approach was selected to unearth pivotal design prerequisites and comprehend the specific challenges these women encounter within the realm of clothing. The utilization of selective sampling facilitated the collection of intricate and valuable insights. A Functional, Expressive, and Aesthetic (FEA) User Needs model was utilized to scrutinize participant feedback. Functional requisites encompass ease of dressing and undressing, accessibility to the prosthetic limb, comfort, mobility with the prosthesis, and appropriate fit. Additionally, participants highlighted various expressive needs, including privacy preservation, modesty, camouflaging disability appearances, maintaining alignment with non-disabled women’s fashion, and considerations about the aesthetic aspects of garments.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTION(Ⅱ)

Abstract In this paper, by using the explicit expression of the kernel of the cubic spline interpolation, the optimal error bounds for the cubic spline interpolation of lower soomth functions are obtained.

脑机接口技术在脑卒中患者下肢功能康复中的应用前景

背景:近年来,脑机接口技术通过对动作意图的识别实现对外部设备的操控,改变了人类与计算机的交互方式,可用于脑卒中后下肢功能的治疗,为脑卒中患者康复带来了新的希望。目的:分析和总结近些年脑机接口技术在脑卒中患者下肢运动功能康复中的应用,探讨脑机接口技术在脑卒中患者下肢功能康复中的临床应用价值。方法:以“脑卒中,脑机接口,下肢”为中文检索词,在中国知网进行相关文献检索;以“stroke,brain-computer interfaces,lower extremity”为英文检索词,在PubMed数据库进行相关文献检索,检索时间范围为2014年1月至2024年6月。结果与结论:脑机接口对脑卒中患者下肢运动功能恢复具有良好的应用前景,在康复医学应用领域正在不断扩大,但其机制尚未完全阐释清楚;此外,在采集患者脑电信号方面存在一定的局限,导致脑机接口系统精确识别肢体运动的能力较差,并且目前该技术的解码方法对识别步态周期存在局限性,不能精确定位到下肢各关节与肌肉的随意运动,阻碍了脑机接口技术的应用。未来的研究应该集中在阐明脑机接口技术对脑卒中患者下肢运动功能恢复的神经机制,增强大脑运动信号提取技术和设备,为个体患者制定多模态反馈实现更有效的运动康复,以期推动脑机接口技术在下肢运动功能康复领域的进一步发展,改善患者的康复效果,提高生活质量。

康复机器人训练脑性瘫痪患者:改善下肢运动功能效果的Meta分析

目的:系统评价康复机器人治疗脑性瘫痪患者下肢运动功能的临床效果,并比较不同机器人的疗效差异。方法:检索PubMed、Web of Science、Embase、Cochrane Library、中国知网、中国生物医学文献数据库、维普和万方数据库,搜集从建库至2024-04-10发表的关于康复机器人治疗脑性瘫痪患者运动功能障碍的随机对照试验。主要结局指标包括肌肉力量,肌张力、平衡功能、步速、步频、步长、步行耐力、下肢运动功能、日常生活活动能力。根据《国际功能、残疾和健康分类》对上述指标进行编码,通过Meta分析评价临床疗效并比较不同机器人的疗效差异。由2名研究人员进行文献检索与筛选,使用Cochrane 5.1.0偏倚风险评估工具对纳入文献进行质量评价。采用RevMan 5.4软件和Stata 16.0软件进行Meta分析。结果:①最终纳入15篇文献,共512例患者,试验组260例、对照组252例。②Meta分析结果显示,与常规康复疗法相比,康复机器人可以提高身体结构和功能(SMD=0.41,95%CI:0.24-0.58,P<0.05)、活动(SMD=0.53,95%CI:0.41-0.65,P<0.05)和参与能力(MD=7.86,95%CI:1.54-14.18,P<0.05)。其中,康复机器人可以改善脑性瘫痪患者下肢肌力、平衡功能、步速、步行耐力、下肢粗大运动功能和日常生活活动能力,但对步频、步长和肌张力的效果不明显。③网状Meta分析结果显示,步速:Innowalkpro>Gait trainer>Lokomat>3DCalt;6MWT评分:Gait trainer>Lokomat>Lokohelp>Innowalkro;GMFM-88D区评分:Lokohelp>Lokomat>KidGo>Innowalkpro>3DCalt;GMFM-88E区评分:Lokomat>Lokohelp>KidGo>3DCalt>Innowalkpro。结论:基于《国际功能、残疾和健康分类》,康复机器人训练可以改善脑性瘫痪患者下肢运动功能和日常生活活动能力。在改善步速方面,Innowalkpro机器人效果更优;在改善6MWT评分方面,Gait trainer机器人效果更优;在改善GMFM-D区评分方面,Lokohelp机器人效果更优;在改善GMFM-E区评分方面,Lokomat机器人效果更优。

PNF联合下肢机器人训练对脑卒中患者姿势及步行功能的影响

目的:探讨PNF联合下肢机器人训练对脑卒中患者姿势及步行功能的影响。方法:采用随机数字表法将44例脑卒中患者分成观察组和对照组各22例,两组患者均给予常规康复治疗及PNF训练,观察组在此基础上增加下肢机器人训练,分别于治疗前及治疗4周后采用脑卒中姿势量表(PASS)、功能性步行分级量表(FAC)、Berg平衡量表、肌张力改良Ashworth量表(MAS)评估患者的姿势及平衡步行功能。结果:治疗前,两组患者各量表评分差异均无统计学意义(P>0.05)。治疗4周后,两组患者PASS、FAC功能性步行分级、Berg量表评分较治疗前差异均有统计学意义(P<0.001),且观察组较对照组差异有统计学意义(P<0.001),两组患者MAS分级差异无统计学意义(P>0.05)。结论:PNF联合下肢机器人训练,有助于改善脑卒中患者姿势及平衡功能,提高其步行能力。

任务导向训练联合下肢康复机器人对脑卒中偏瘫患者下肢功能的影响

目的:探讨下肢康复机器人联合任务导向训练对脑卒中偏瘫患者的治疗效果。方法:选取我院2023年1月~12月收治的脑卒中偏瘫患者100例,随机分为对照组和观察组各50例。对照组在康复师的辅助下进行任务导向训练,观察组在对照组基础上给予下肢康复机器人训练。观察两组患者治疗前后下肢平衡、下肢肌力、运动功能、踝关节功能、膝关节屈曲活动范围及行走能力。结果:治疗后,两组患者BBS评分、股四头肌评分、腘绳肌评分、FMA-LE评分及AOFAS评分均较治疗前升高(P<0.05),且观察组治疗后的BBS评分、股四头肌评分、腘绳肌评分、FMA-LE评分及AOFAS评分均显著高于对照组(P<0.05);治疗后,两组患者的膝关节屈曲活动范围及6 min步行距离均较治疗前升高(P<0.05),且观察组治疗后的膝关节屈曲活动范围及6 min步行距离显著大于对照组(P<0.05)。结论:在脑卒中患者的临床治疗中,任务导向训练与下肢康复机器人相结合,可有效提高下肢肌力,促进平衡功能的恢复,对运动功能的恢复效果显著,可提高脑卒中患者的行走能力和膝关节屈曲的活动范围,达到较为理想的治疗效果。