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.

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.

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.

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.

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.

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.

Trifecta Outcomes of Screening Detected and Patients with Lower Urinary Tract Symptoms after Open Radical Prostatectomy for Localized Prostate Cancer

Background: Many studies have reported on trifecta outcomes after radical prostatectomy. There is however paucity of studies that compares the trifecta outcome between screen detected and patients presenting with lower urinary symptoms with localized prostate cancer after radical prostatectomy. This study compares the trifecta outcomes between these two groups after an open retropubic radical prostatectomy. Methodology: This is a retrospective study, on the trifecta outcomes (urinary continence, erectile function, and cancer control) of consecutive patients that had open radical retropubic prostatectomy for localized prostate cancer by a single surgeon. Patients were grouped into screen detected and presentation with lower urinary symptoms or retention of urine. The parameters considered were the age of the patients, the total prostate specific antigen (tPSA) at presentation, the clinical T stage, the Gleason score of prostate biopsies, the risk categories using the D’Amico risk groups and the trifecta outcomes after the procedure. Results: In all, 119 patients met the criteria for inclusion. The median follow up was 63.5 months (range 12 - 156 months). Of these 40.3% of the patients were diagnosed through screening with elevated PSA while 59.7% had presented with symptoms of lower urinary tract obstruction. The mean age for the patients was 60.8 ± 6.5 years, median PSA 12.6 ng/ml (IQR 8.6 - 19.7) and median prostate weight of 50.0 (IQR 40.0 - 60 g). The urinary continence rate after the procedure was 93.3%, erection rate of 81.5%, cancer control rate of 71.4% and trifecta achieved in 57.1%. Comparing the screening and the symptomatic cases, the urinary continence rate was 91.7% vrs 94.3%;erectile function rate was 79.2% vrs 83.1%;cancer control 68.8% vrs 73.2% and trifecta achieved in 58.3% vrs 56.3%. There was no statistically significant difference between the two groups in terms of urinary continence p = 0.564, erection function p = 0.588, cancer control p = 0.595, and achieving trifecta p = 0.829. Conclusion: Patients with localized prostate cancer presenting with lower urinary symptoms compared to screen detected patients have similar outcomes in terms of urinary Continence, erectile function, cancer control and trifecta after open radical retropubic prostatectomy.

About Upper and Lower Strong Fractional Weighted Mean Convergence by Moduli for Triple Sequences

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.

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.

瑞马唑仑对肝切除术患者术后苏醒质量及认知功能的影响

目的:观察瑞马唑仑对肝切除术患者术后苏醒质量及认知功能的影响,探讨其临床价值。方法:选择赣南医学院第一附属医院2022年1月—2023年8月收治的需行肝切除手术患者60例,随机分为两组,对照组采取丙泊酚、芬太尼、顺阿曲库铵麻醉诱导,泵注丙泊酚、瑞芬太尼麻醉维持;观察组静脉注射苯磺酸瑞马唑仑、芬太尼、顺阿曲库铵麻醉诱导,泵注苯磺酸瑞马唑仑、瑞芬太尼麻醉维持。比较两组不同时刻生命体征、苏醒质量指标、术后认知功能,并测定血浆中枢神经特异性蛋白(S100β)、神经元特异性烯醇化酶(NSE)水平及统计两组不良反应发生情况。结果:两组入室后(T_(0))、麻醉诱导后(T_(1))、切皮时(T_(2))、手术1 h时(T_(3))、手术结束时(T_(4))、拔除气管导管时(T_(5))、出恢复室(T_(6))平均动脉压(MAP)及心率(HR),以及术前1 d、术后1 d、术后3 d简易智能量表(MMSE)评分、血浆S100β、NSE水平比较差异均无统计学意义(P>0.05);观察组T_(5)时刻的HR水平高于T_(0)时刻,差异有统计学意义(P<0.05)。观察组呼吸恢复时间、睁眼时间、拔管时间及恢复室停留时间均早于或者短于对照组,差异均有统计学意义(P<0.05),且观察组不良反应发生率(10.0%)低于对照组(33.3%),差异有统计学意义(P<0.05)。结论:瑞马唑仑应用于肝切除术患者苏醒时间短,且不影响认知功能,不良反应发生率更低。

虚拟现实技术对不完全脊髓损伤患者下肢功能的影响

目的探讨虚拟现实技术(VR)对不完全脊髓损伤患者下肢运动功能、平衡能力、躯干控制能力及步行能力的影响。方法选自郑州大学第一附属医院康复医学科2022年1月至2023年12月治疗的46例不完全脊髓损伤患者,采用随机数字法分成治疗组、对照组,各23例。两组接受相同的康复治疗,治疗组在此基础上增加VR 30 min,对照组在常规康复治疗的基础上继续康复训练30 min,每周5 d,疗程8周。治疗前及治疗8周后,分别采用脊髓损伤下肢功能量表(ASIA)、Berg平衡量表(BBS)、躯干控制测试量表(TCT)、Holden功能性步行量表(FAC)对患者下肢运动能力、平衡能力、躯干控制能力及步行能力进行评定。结果两组治疗前ASIA、BBS、TCT、FAC评分比较,差异无统计学意义(P>0.05);两组治疗后ASIA、BBS、TCT、FAC评分比治疗前提高,且治疗组高于对照组(P<0.05)。结论基于VR的康复治疗能改善不完全脊髓损伤患者的下肢功能,提高其平衡能力、躯干控制能力和步行能力。