Let Ω be a smooth bounded domian in R^(2),H_(0)^(1)(Ω)be the standard Sobolev space,and λ_(f)(Ω)be the first weighted eigenvalue of the Laplacian,namely,λ_(f)(Ω)=inf_(u∈H_(0)^(1)(Ω),∫Ωu^(2)dx=1)∫_(Ω)|∇u|^(...Let Ω be a smooth bounded domian in R^(2),H_(0)^(1)(Ω)be the standard Sobolev space,and λ_(f)(Ω)be the first weighted eigenvalue of the Laplacian,namely,λ_(f)(Ω)=inf_(u∈H_(0)^(1)(Ω),∫Ωu^(2)dx=1)∫_(Ω)|∇u|^(2)fdx,where f is a smooth positive function onΩ.In this paper,using blow-up analysis,we prove sup_(u∈H_(0)^(1)(Ω),∫^(Ω)|∇u|^(2)fdx)≤1∫_(Ω)e^(4πfu^(2)(1+α||u||_(2)^(2)))dx<+∞ for any 0≤α<λ_(f)(Ω).Furthermore,extremal functions for the above inequality exist when α>0 is chosen sufficiently small.展开更多
Let (M,g) be a compact Riemannian manifold without boundary, and (N,g) a compact Riemannian manifold with boundary. We will prove in this paper that the and can be attained. Our proof uses the blow-up analysis.
In this paper, we derive the singular Moser-Trudinger inequality which in-volves the first eigenvalue and several singular points, and further prove the existenceof the extremal functions for the relative Moser-Trudin...In this paper, we derive the singular Moser-Trudinger inequality which in-volves the first eigenvalue and several singular points, and further prove the existenceof the extremal functions for the relative Moser-Trudinger functional. Since the prob-lems involve more complicated norm and multiple singular points, not only we can＇tuse the symmetrization to deal with a one-dimensional inequality, but also the pro-cesses of the blow-up analysis become more delicate. In particular, the new inequalityis more general than that of [1, 2].展开更多
We will show in this paper that if A is very close to 1, thenI（M,λ,m） =supu∈H0^1,n（m）,∫m｜△↓u｜^ndV=1∫Ω（e^αn｜u｜^n/（n-1）-λm∑k=1｜αnun/（n-1）｜k/k!）dVcan be attained, where M is a compact-manifold ...We will show in this paper that if A is very close to 1, thenI（M,λ,m） =supu∈H0^1,n（m）,∫m｜△↓u｜^ndV=1∫Ω（e^αn｜u｜^n/（n-1）-λm∑k=1｜αnun/（n-1）｜k/k!）dVcan be attained, where M is a compact-manifold with boundary. This result gives a counter-example to the conjecture of de Figueiredo and Ruf in their paper titled ＂On an inequality by Trudinger and Moser and related elliptic equations＂ （Comm. Pure. Appl. Math., 55, 135-152, 2002）.展开更多
Let Ω (∈) R4 be a smooth bounded domain,W2,20(Ω) be the usual Sobolev space.For any positive integer e,λl(Ω) is the e-th eigenvalue of the bi-Laplacian operator.Define E(l)=Eλ1(Ω) ⊕ Eλ2(Ω)(⊕) … ⊕Eλe(Ω),...Let Ω (∈) R4 be a smooth bounded domain,W2,20(Ω) be the usual Sobolev space.For any positive integer e,λl(Ω) is the e-th eigenvalue of the bi-Laplacian operator.Define E(l)=Eλ1(Ω) ⊕ Eλ2(Ω)(⊕) … ⊕Eλe(Ω),where Eλi(Ω) is eigenfunction space associated with λi(Ω).E⊥e denotes the orthogonal complement of Ee in W2,20 (Ω).For 0 ≤ α ≤ λe+1 (Ω),we define a norm by ||u||22,α =||△u||22-α||u||22 for u ∈ E⊥e.In this paper,using the blow-up analysis,we prove the following Adams inequalities supu∈E⊥e,||u||2,α≤1∫Ω e32π2u2 dx < +∞;moreover,the above supremum can be attained by a function u0 ∈ E⊥e∩C4((Ω)) with || u0||2,α =1.This result extends that of Yang (J.Differential Equations,2015),and complements that of Lu and Yang (Adv.Math.2009) and Nguyen (arXiv: 1701.08249,2017).展开更多
Let W^(1,n)(R^(n))be the standard Sobolev space.For any T>0 and p>n>2,we denote■Define a norm in W^(1,n)(R^(n))by■where 0≤α<λ_(n,p).Using a rearrangement argument and blow-up analysis,we will prove■c...Let W^(1,n)(R^(n))be the standard Sobolev space.For any T>0 and p>n>2,we denote■Define a norm in W^(1,n)(R^(n))by■where 0≤α<λ_(n,p).Using a rearrangement argument and blow-up analysis,we will prove■can be attained by some function u_(0)∈W^(1,n)(R^(n))∩C^(1)(R^(n))with ||u_(0)||_(n,p)=1,here a_(n)=n■_(n-1)^(1/n-1) and ■_(n-1) is the measure of the unit sphere in R^(n).展开更多
Let N≥2, aN=Nω1 N-1（N-1） , where ωN-1 denotes the area of the unit sphere in RN. In this note, we prove that for any 0 〈a〈aN and any β 〉 0, the supremum sup u∈W 1,N（R N）,｜｜u｜｜W 1,N（R N）≤1 ∫ R N ｜...Let N≥2, aN=Nω1 N-1（N-1） , where ωN-1 denotes the area of the unit sphere in RN. In this note, we prove that for any 0 〈a〈aN and any β 〉 0, the supremum sup u∈W 1,N（R N）,｜｜u｜｜W 1,N（R N）≤1 ∫ R N ｜u｜β （e a ｜u｜ N/N-1 N-2 ∑j=0 aj/j!｜u｜ Ni/N-1）dx.can be attained by some function u ∈ W1, N （R N） with ｜｜ u ｜｜ W 1,N （R N ） = 1. Moreover, when a ≥ aN, the above supremum is infinity.展开更多
[Objectives]To conduct a comprehensive examination of the evidence-based impact of repetitive transcranial magnetic stimulation(rTMS)on upper extremity functionality in patients with acute stroke.[Methods]A rigorous a...[Objectives]To conduct a comprehensive examination of the evidence-based impact of repetitive transcranial magnetic stimulation(rTMS)on upper extremity functionality in patients with acute stroke.[Methods]A rigorous and systematic electronic search was conducted across the Medline,PubMed,and Web of Science databases,encompassing literature up to July 1,2024.To ensure the reliability of the in-cluded studies,an assessment of their risk of bias was conducted using RevMan 5.4 software,in accordance with the rigorous standards out-lined in the Cochrane Handbook for Systematic Revieus.Subsequently,we employed either the random-effects model or the fixed-effects model,depending on the heterogeneity of the data,to estimate the standardized mean difference(SMD)in outcomes,utilizing Stata 18.0 software for statistical analysis.[Results]Our review encompassed a total of five studies,involving 252 patients with acute stroke.The pooled analysis of these studies revealed a statistically significant improvement in Fugl-Meyer Assessment of the Upper Extremity(FMA-UE)scores among pa-tients who received rTMS therapy(SMD=2.71,95%CI:0.85 to 4.56;P<0.0001),albeit with considerable heterogeneity(I^(2)=97.65%)across the trials.[Conclusions]The results of this systematic review and meta-analysis underscore the promising potential of rTMS in enhancing upper extremity function in patients who have experienced an acute stroke.These findings provide compelling evidence for the therapeutic benefits of rTMS in this patient population.展开更多
[Objectives]To investigate the evidence-based effect of virtual reality-based mirror therapy system(VR-MT)on upper extremity function among stroke patients.[Methods]A systematic electronic searching of the Medline,Pub...[Objectives]To investigate the evidence-based effect of virtual reality-based mirror therapy system(VR-MT)on upper extremity function among stroke patients.[Methods]A systematic electronic searching of the Medline,PubMed,Web of Science and CNKI was initially performed up to June 10,2024.The risk of bias of the included studies was evaluated using RevMan 5.4 software based on the Cochrane Handbook for Systematic Reviews.The random-effects model or fixed-effects models was employed to estimate the standardized mean difference(SMD).The subgroup analyses were conducted exploring theVR-MT type(immersive or non-immersive)and comparing with MT or control group.[Results]In total 8 studies with a total of 273 stroke patients were included in this review.The pooled analysis of these trials showed a statistically significant enhancement inFMA-UE scores(6 studies,SMD=0.72,[95%CI 0.37 to 1.06];P<0.0001,I^(2)=31%)and Box and Block Test(BBT)(3 studies,SMD=0.49,[95%C/0.05 to 0.93];P=0.03,I^(2)=0%),rather than Manual Function Test(MFT)scores(3 studies,SMD=0.38,[95%CI-0.09 to 0.84];P=0.11,I^(2)=0%)following the application of reality-based mirror therapy.Additionally,the subgroup analysis results indicated that immersive VR-MT can significantly improve FMA-UE(5studies,SMD=0.73,[95%CI 0.24 to 1.23];P=0.004,I^(2)=43%).In contrast,the overall effect of non-immersive VR-MT was non-significant(2 studies,SMD=0.33,[95%CI-0.69 to 1.34];P=0.53,I^(2)=72%).[Conclusions]In this systematic review and meta-analysis,our findings indicate that immersiveVR-MT has the potential to improve upper extremity function among stroke patients.展开更多
In the present paper, we study the polynomial approximation of analytic functions of several complex variables. The characterizations of generalized type of analytic functions of several complex variables have been ob...In the present paper, we study the polynomial approximation of analytic functions of several complex variables. The characterizations of generalized type of analytic functions of several complex variables have been obtained in terms of approximation and interpolation errors.展开更多
Wearable bioelectronic devices are rapidly evolving towards miniaturization and multifunctionality,with remarkable features such as flexibility and comfort.However,achieving a sustainable power supply for wearable bio...Wearable bioelectronic devices are rapidly evolving towards miniaturization and multifunctionality,with remarkable features such as flexibility and comfort.However,achieving a sustainable power supply for wearable bioelectronic devices is still a great challenge.Triboelectric nanogenerators(TENGs)provide an efficient solution by converting irregular,low-frequency bioenergy from the human body into electrical energy.Beyond sustainably powering wearable bioelectronics,the harvested electrical energy also carries rich information for human body sensing.In this conversion process,the choice of material plays a crucial role in affecting the output performance of the TENGs.Among various materials,silicone rubber(SR)stands out due to its exceptional plasticity,flexibility,comfortability and other favorable properties.Moreover,with appropriate treatment,SR can achieve extreme functionalities such as high robustness,good stability,self-healing capabilities,rapid response,and more.In this review,recent advances in wearable SR-based TENGs(SR-TENGs)are systematically reviewed with a focus on their application in different parts of the human body.Given that the manufacturing method of SR-TENGs largely determines its output performance and sensitivity,this paper introduces the design of SR-TENGs,including material selection,process modulation,and structure optimization.Additionally,this article discusses the current challenges in the SR-TENG fabrication technology and potential future directions,aiming to promote the effective development of SR-TENGs in biomechanical energy harvesting and self-powered sensing applications.展开更多
BACKGROUND: In the natural evolution of cerebrovascular disease, unconscious use of affected extremity during drug treatment and daily life can improve the function of affected upper extremity partially, but it is ver...BACKGROUND: In the natural evolution of cerebrovascular disease, unconscious use of affected extremity during drug treatment and daily life can improve the function of affected upper extremity partially, but it is very slow and also accompanied by the formation of abnormal mode. Therefore, functional training should be emphasized in recovering the motor function of extremity. OBJECTIVE: To observe the effects of combination of motor relearning program and Bobath method on motor function of upper extremity of patients with stroke. DESIGN: Comparison of therapeutic effects taking stroke patients as observation subjects. SETTING: Department of Neurology, General Hospital of Beijing Jingmei Group. PARTICIPANTS: Totally 120 stroke patients, including 60 males and 60 females, averaged (59±3) years, who hospitalized in the Department of Neurology, General Hospital of Beijing Jingmei Group between January 2005 and June 2006 were recruited. The involved patients met the following criteria: Stroke attack within 2 weeks; diagnosis criteria of cerebral hemorrhage or infarction made in the 4th National Cerebrovascular Disease Conference; confirmed by skull CT or MRI; Informed consents of therapeutic regimen were obtained. The patients were assigned into 2 groups according to their wills: rehabilitation group and control group, with 30 males and 30 females in each group. Patients in rehabilitation group averaged (59±2)years old, and those in the control group averaged (58±2)years old. METHODS: ① Patients in two groups received routine treatment in the Department of Neurology. When the vital signs of patients in the rehabilitation group were stable, individualized treatment was conducted by combined application of motor relearning program and Bobath method. Meanwhile, training of activity of daily living was performed according to the disease condition changes of patients at different phases, including the nursing and instruction of body posture, the maintenance of good extremity position, bed exercise, bedside sit up and sitting position balance, sit up exercise, dynamic and static balance exercise, walking exercise, active training and passive training. The strength, time and speed of training were increased gradually according to their physical abilities. Patients were trained 45 to 60 minutes once, 5 times a week, within 2 weeks. ② Evaluation criteria of therapeutic effect: The motor function of upper extremity was evaluated by Fugl-Meyer method on the day of beginning and end of treatment. Higher points indicated better function of upper extremity. ③ t test and paired t test were used for comparing the difference of intergroup and intragroup measurement data, respectively. MAIN OUTCOME MEASURES: Changes in Fugl-Meyer scoring of two groups before and after treatment. RESULTS: Totally 120 stroke patients participated in the final analysis. Before treatment, Fugl-Meyer scoring was close between rehabilitation group and control group [(14.47±2.38),(14.16±2.39) points, P > 0.05]; Fugl-Meyer scoring of rehabilitation group after treatment was significantly higher than that before treatment and that of control group[(37.93±2.67),(18.36±2.43) points, t =11.053, 5.408, P < 0.01]; There were no significant differences in Fugl-Meyer scoring between before treatment in the control group and control group (P > 0.05). CONCLUSION: Combined application of motor relearning program and Bobath method can significantly improve the motor function of upper extremity of patients with stroke.展开更多
Totally three articles focusing on functional magnetic resonance imaging features of brain function in the activated brain regions of stroke patients undergoing acupuncture on the healthy limbs and healthy controls un...Totally three articles focusing on functional magnetic resonance imaging features of brain function in the activated brain regions of stroke patients undergoing acupuncture on the healthy limbs and healthy controls undergoing acupuncture on the lower extremities are published in three issues. We hope that our readers find these papers useful to their research.展开更多
Let B be a unit ball in R^(2),W_(0)^(1,2)(B)be the standard Sobolev space.For anyϵ>0,de Figueiredo,doÓ,dos Santons,Yang and Zhu proved the existence of extremals of a Trudinger-Moser inequality in the unit bal...Let B be a unit ball in R^(2),W_(0)^(1,2)(B)be the standard Sobolev space.For anyϵ>0,de Figueiredo,doÓ,dos Santons,Yang and Zhu proved the existence of extremals of a Trudinger-Moser inequality in the unit ball.Precisely,u∈W_(0)^(1,2)(B)^(sup),∫_(B)|▽u|^(2)dx≤1∫_(B)^(|x|^(2∈)e^(4π(1+∈)u^(2)dx)can be attained by some radially symmetric function u_(∈)∈W_(0)^(1,2)(B)∫_(B)with∫_(B)|▽u|^(2)dx=1.In this note,we concern the compactness of the function family{uϵ}ϵ>0 and prove that up to a subsequence uϵconverges to some function u 0 in C^(1)(B)asϵ→0.Furthermore,u_(0) is an extremal function of the supremum u∈W_(0)^(1,2)(B)^(sup),∫_(B)|▽u|^(2)dx≤1∫_(B)e^(4πu^(2)dx)Let us explain the result in geometry.Denoteω_(0)=dx_(1)^(2)+dx_(2)^(2)be the standard Euclidean metricω_(∈)|x|^(2ϵ)ω_(0)for xϵB..Then the extremal family{u_(∈)}∈>0 of the following Trudinger-Moser functionals∫_(B)e^(4π(1+∈)u^(2))dvω_(∈)under the constraint W_(0)^(1,2)(B)and∫_(B)|▽ω_∈)u|^(2)dvω_∈)≤1 is compact asϵ→0.展开更多
Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.
Let f be analytic in a hyperbolic region Ω. The Bloch constant β_f of f is defined by β_f=sup z∈Ω|f’(z)|/λ_Ω(z), where λ_Ω(z)|dz|is the Poincare metric in Ω. Suppose △is hyperbolic and lim inf ω→cλ△(w...Let f be analytic in a hyperbolic region Ω. The Bloch constant β_f of f is defined by β_f=sup z∈Ω|f’(z)|/λ_Ω(z), where λ_Ω(z)|dz|is the Poincare metric in Ω. Suppose △is hyperbolic and lim inf ω→cλ△(w)】λ(△)】0, (?)c∈(?)△ where λ(△)=inf w∈△ λ△(w). Then for all f with f(Ω)(?)△, we have β_f≤1/λ(△). In this paper we study the extremal functions defined by β_f=1/λ(△) and the existence of those functions.展开更多
In this paper,we consider the generalized Weinstein operator Δ_(W)^(d,α,n) we introduce new Sobolev-Weinstein spaces denoted H_(α,dn)^(s)(R_(+)^(d+1) )associated with the generalized Weinstein operator and we inves...In this paper,we consider the generalized Weinstein operator Δ_(W)^(d,α,n) we introduce new Sobolev-Weinstein spaces denoted H_(α,dn)^(s)(R_(+)^(d+1) )associated with the generalized Weinstein operator and we investigate their properties.Next,as application,we study the extremal functions on the spaces H_(α,dn)^(s)(R_(+)^(d+1)) using the theory of reproducing kernels.展开更多
OBJECTIVE： The aim of this meta-analysis was to evaluate the clinical efficacy of constraint-induced movement therapy in acute and sub-acute stroke. DATA SOURCES： The key words were stroke, cerebrovascular accident,...OBJECTIVE： The aim of this meta-analysis was to evaluate the clinical efficacy of constraint-induced movement therapy in acute and sub-acute stroke. DATA SOURCES： The key words were stroke, cerebrovascular accident, constraint-induced therapy, forced use, and randomized controlled trial. The databases, including China National Knowledge Infrastructure, WanFang, Weipu Information Resources System, Chinese Biomedical Literature Database, PubMed, Med- line, Embase, the Cochrane Central Register of Controlled Trials, and the Cochrane Database of Systematic Reviews, were searched for studies on randomized controlled trials for treating acute or sub-acute stroke published before March 2016. DATA SELECTION： We retrieved relevant randomized controlled trials that compared constraint-induced movement therapy in treatment of acute or sub-acute stroke with traditional rehabilitation therapy （tradi- tional occupational therapy）. Patients were older than 18 years, had disease courses less than 6 months, and were evaluated with at least one upper extremity function scale. Study quality was evaluated, and data that met the criteria were extracted. Stata 11.0 software was used for the meta-analysis. OUTCOME MEASURES： Fugl-Meyer motor assessment of the arm, the action research-arm test, a motor activity log for amount of use and quality of movement, the Wolf motor function test, and a modified Bar- thel index. RESULTS： A total of 16 prospective randomized controlled trials （379 patients in the constraint-induced movement-therapy group and 359 in the control group） met inclusion criteria. Analysis showed significant mean differences in favor of constraint-induced movement therapy for the Fugl-Meyer motor assessment of the arm （weighted mean difference （WMD） = 10.822; 95% confidence intervals （95% CI）： 7.419-14.226）, the action research-arm test （WMD = 10.718; 95% CI： 5.704-15.733）, the motor activity log for amount of use and quality of movement （WMD = 0.812; 95% CI： 0.331-1.293） and the modified Barthel index （WMD = 10.706; 95% CI： 4.417-16.966）. CONCLUSION： Constraint-induced movement therapy may be more beneficial than traditional rehabili- tation therapy for improving upper limb function after acute or sub-acute stroke.展开更多
A statistic method, statistics of extreme values （SEV）, was described in detail, which can esti mate the size of maximum inclusion in steel. The characteristic size of the maximum inclusion in a high clean bearing s...A statistic method, statistics of extreme values （SEV）, was described in detail, which can esti mate the size of maximum inclusion in steel. The characteristic size of the maximum inclusion in a high clean bearing steel （GCrl5） was evaluated by this method, and the morphology and corn position of large inclusions found were analyzed by scanning electron microscopy （SEM）. When standard inspection area （S0） is 280 mm2, the characteristic size of the biggest inclusion found in 30 standard inspection area is 23.93 μm, and it has a 99.9% probability of the characteristic size of maximum inclusion predicted being no larger than 36.85μm in the experimental steel. SEM result shows that large inclusions found are mainly composed of CaS, calcium-aluminate and MgO. Compositing widely exists in large inclusions in high clean bearing steel. Compared with traditional evaluation method, SEV method mainly focuses on inclusion size, and the esti- mation result is not affected by inclusion types. SEV method is suitable for the inclusion eval uation of high clean bearing steel.展开更多
Background:Stroke is considered to be a leading cause of impairment.After experiencing strokes,patients are frequently left with impaired motor function,making it difficult to carry out daily tasks.The most extensivel...Background:Stroke is considered to be a leading cause of impairment.After experiencing strokes,patients are frequently left with impaired motor function,making it difficult to carry out daily tasks.The most extensively researched method for treating stroke patients in recent decades is CIMT(constraintinduced movement therapy),which was developed to treat upper limb deficits following stroke.CIMT entails limiting the use of the unaffected limb,altering behavior to increase the use of the affected limb,and finally,mass-training of the affected limb.Objective:The current study aimed to determine the effectiveness of CIMT through TR for upper extremity function in stroke patients.Materials and methods:Thirty post-stroke participants were selected on the basis of inclusion and exclusion criteria,and allocated into group A and group B.Group A was treated with CIMT in the physiotherapy department and group B was treated with CIMT through TR.Outcome measures were the Fugl-Meyer Assessment scale for upper extremities(FMA-UE),the Wolf Motor Function Test(WMFT),and the Motor Activity Log(MAL).Results:Both groups showed significant improvements in FMA-UE,WMFT and MAL-A0U,MAL-Q0M scores.However,there were no significant differences between groups A and B in FMA-UE,WMFT,MALAOU,and MAL-QOM scores in the inter-group analysis.Conclusion:CIMT via TR was equally effective than CIMT in physiotherapy department for upper extremity function in stroke.Further studies should be conducted to identify the long-term effectiveness of this approach.展开更多
基金supported by the Outstanding Innovative Talents Cultivation Funded Programs 2023 of Renmin University of China。
文摘Let Ω be a smooth bounded domian in R^(2),H_(0)^(1)(Ω)be the standard Sobolev space,and λ_(f)(Ω)be the first weighted eigenvalue of the Laplacian,namely,λ_(f)(Ω)=inf_(u∈H_(0)^(1)(Ω),∫Ωu^(2)dx=1)∫_(Ω)|∇u|^(2)fdx,where f is a smooth positive function onΩ.In this paper,using blow-up analysis,we prove sup_(u∈H_(0)^(1)(Ω),∫^(Ω)|∇u|^(2)fdx)≤1∫_(Ω)e^(4πfu^(2)(1+α||u||_(2)^(2)))dx<+∞ for any 0≤α<λ_(f)(Ω).Furthermore,extremal functions for the above inequality exist when α>0 is chosen sufficiently small.
文摘Let (M,g) be a compact Riemannian manifold without boundary, and (N,g) a compact Riemannian manifold with boundary. We will prove in this paper that the and can be attained. Our proof uses the blow-up analysis.
文摘In this paper, we derive the singular Moser-Trudinger inequality which in-volves the first eigenvalue and several singular points, and further prove the existenceof the extremal functions for the relative Moser-Trudinger functional. Since the prob-lems involve more complicated norm and multiple singular points, not only we can＇tuse the symmetrization to deal with a one-dimensional inequality, but also the pro-cesses of the blow-up analysis become more delicate. In particular, the new inequalityis more general than that of [1, 2].
文摘We will show in this paper that if A is very close to 1, thenI（M,λ,m） =supu∈H0^1,n（m）,∫m｜△↓u｜^ndV=1∫Ω（e^αn｜u｜^n/（n-1）-λm∑k=1｜αnun/（n-1）｜k/k!）dVcan be attained, where M is a compact-manifold with boundary. This result gives a counter-example to the conjecture of de Figueiredo and Ruf in their paper titled ＂On an inequality by Trudinger and Moser and related elliptic equations＂ （Comm. Pure. Appl. Math., 55, 135-152, 2002）.
基金This work was partly supported by the Outstanding Young Talents Program of the Education Department of Anhui Province(gxyq2018160).
文摘Let Ω (∈) R4 be a smooth bounded domain,W2,20(Ω) be the usual Sobolev space.For any positive integer e,λl(Ω) is the e-th eigenvalue of the bi-Laplacian operator.Define E(l)=Eλ1(Ω) ⊕ Eλ2(Ω)(⊕) … ⊕Eλe(Ω),where Eλi(Ω) is eigenfunction space associated with λi(Ω).E⊥e denotes the orthogonal complement of Ee in W2,20 (Ω).For 0 ≤ α ≤ λe+1 (Ω),we define a norm by ||u||22,α =||△u||22-α||u||22 for u ∈ E⊥e.In this paper,using the blow-up analysis,we prove the following Adams inequalities supu∈E⊥e,||u||2,α≤1∫Ω e32π2u2 dx < +∞;moreover,the above supremum can be attained by a function u0 ∈ E⊥e∩C4((Ω)) with || u0||2,α =1.This result extends that of Yang (J.Differential Equations,2015),and complements that of Lu and Yang (Adv.Math.2009) and Nguyen (arXiv: 1701.08249,2017).
基金supported by National Science Foundation of China(Grant No.12201234)Natural Science Foundation of Anhui Province of China(Grant No.2008085MA07)the Natural Science Foundation of the Education Department of Anhui Province(Grant No.KJ2020A1198).
文摘Let W^(1,n)(R^(n))be the standard Sobolev space.For any T>0 and p>n>2,we denote■Define a norm in W^(1,n)(R^(n))by■where 0≤α<λ_(n,p).Using a rearrangement argument and blow-up analysis,we will prove■can be attained by some function u_(0)∈W^(1,n)(R^(n))∩C^(1)(R^(n))with ||u_(0)||_(n,p)=1,here a_(n)=n■_(n-1)^(1/n-1) and ■_(n-1) is the measure of the unit sphere in R^(n).
基金The author would like to thank referee for valuable suggestions. The work is supported by the Natural Science Foundation of the Education Department of Anhui Province （KJ20 -16A641）.
文摘Let N≥2, aN=Nω1 N-1（N-1） , where ωN-1 denotes the area of the unit sphere in RN. In this note, we prove that for any 0 〈a〈aN and any β 〉 0, the supremum sup u∈W 1,N（R N）,｜｜u｜｜W 1,N（R N）≤1 ∫ R N ｜u｜β （e a ｜u｜ N/N-1 N-2 ∑j=0 aj/j!｜u｜ Ni/N-1）dx.can be attained by some function u ∈ W1, N （R N） with ｜｜ u ｜｜ W 1,N （R N ） = 1. Moreover, when a ≥ aN, the above supremum is infinity.
文摘[Objectives]To conduct a comprehensive examination of the evidence-based impact of repetitive transcranial magnetic stimulation(rTMS)on upper extremity functionality in patients with acute stroke.[Methods]A rigorous and systematic electronic search was conducted across the Medline,PubMed,and Web of Science databases,encompassing literature up to July 1,2024.To ensure the reliability of the in-cluded studies,an assessment of their risk of bias was conducted using RevMan 5.4 software,in accordance with the rigorous standards out-lined in the Cochrane Handbook for Systematic Revieus.Subsequently,we employed either the random-effects model or the fixed-effects model,depending on the heterogeneity of the data,to estimate the standardized mean difference(SMD)in outcomes,utilizing Stata 18.0 software for statistical analysis.[Results]Our review encompassed a total of five studies,involving 252 patients with acute stroke.The pooled analysis of these studies revealed a statistically significant improvement in Fugl-Meyer Assessment of the Upper Extremity(FMA-UE)scores among pa-tients who received rTMS therapy(SMD=2.71,95%CI:0.85 to 4.56;P<0.0001),albeit with considerable heterogeneity(I^(2)=97.65%)across the trials.[Conclusions]The results of this systematic review and meta-analysis underscore the promising potential of rTMS in enhancing upper extremity function in patients who have experienced an acute stroke.These findings provide compelling evidence for the therapeutic benefits of rTMS in this patient population.
文摘[Objectives]To investigate the evidence-based effect of virtual reality-based mirror therapy system(VR-MT)on upper extremity function among stroke patients.[Methods]A systematic electronic searching of the Medline,PubMed,Web of Science and CNKI was initially performed up to June 10,2024.The risk of bias of the included studies was evaluated using RevMan 5.4 software based on the Cochrane Handbook for Systematic Reviews.The random-effects model or fixed-effects models was employed to estimate the standardized mean difference(SMD).The subgroup analyses were conducted exploring theVR-MT type(immersive or non-immersive)and comparing with MT or control group.[Results]In total 8 studies with a total of 273 stroke patients were included in this review.The pooled analysis of these trials showed a statistically significant enhancement inFMA-UE scores(6 studies,SMD=0.72,[95%CI 0.37 to 1.06];P<0.0001,I^(2)=31%)and Box and Block Test(BBT)(3 studies,SMD=0.49,[95%C/0.05 to 0.93];P=0.03,I^(2)=0%),rather than Manual Function Test(MFT)scores(3 studies,SMD=0.38,[95%CI-0.09 to 0.84];P=0.11,I^(2)=0%)following the application of reality-based mirror therapy.Additionally,the subgroup analysis results indicated that immersive VR-MT can significantly improve FMA-UE(5studies,SMD=0.73,[95%CI 0.24 to 1.23];P=0.004,I^(2)=43%).In contrast,the overall effect of non-immersive VR-MT was non-significant(2 studies,SMD=0.33,[95%CI-0.69 to 1.34];P=0.53,I^(2)=72%).[Conclusions]In this systematic review and meta-analysis,our findings indicate that immersiveVR-MT has the potential to improve upper extremity function among stroke patients.
文摘In the present paper, we study the polynomial approximation of analytic functions of several complex variables. The characterizations of generalized type of analytic functions of several complex variables have been obtained in terms of approximation and interpolation errors.
基金supported by the National Natural Science Foundation of China(Grant No.52442104)the Application Research Program of Liaoning Province(Grant No.2022JH2/01300219)+1 种基金the Fundamental Research Funds for the Central Universities(Grant No.3132024210)the Scientific Research Fund of the Educational Department of Liaoning Province(Nos.LJ212410151013,LJKMZ20220359)。
文摘Wearable bioelectronic devices are rapidly evolving towards miniaturization and multifunctionality,with remarkable features such as flexibility and comfort.However,achieving a sustainable power supply for wearable bioelectronic devices is still a great challenge.Triboelectric nanogenerators(TENGs)provide an efficient solution by converting irregular,low-frequency bioenergy from the human body into electrical energy.Beyond sustainably powering wearable bioelectronics,the harvested electrical energy also carries rich information for human body sensing.In this conversion process,the choice of material plays a crucial role in affecting the output performance of the TENGs.Among various materials,silicone rubber(SR)stands out due to its exceptional plasticity,flexibility,comfortability and other favorable properties.Moreover,with appropriate treatment,SR can achieve extreme functionalities such as high robustness,good stability,self-healing capabilities,rapid response,and more.In this review,recent advances in wearable SR-based TENGs(SR-TENGs)are systematically reviewed with a focus on their application in different parts of the human body.Given that the manufacturing method of SR-TENGs largely determines its output performance and sensitivity,this paper introduces the design of SR-TENGs,including material selection,process modulation,and structure optimization.Additionally,this article discusses the current challenges in the SR-TENG fabrication technology and potential future directions,aiming to promote the effective development of SR-TENGs in biomechanical energy harvesting and self-powered sensing applications.
文摘BACKGROUND: In the natural evolution of cerebrovascular disease, unconscious use of affected extremity during drug treatment and daily life can improve the function of affected upper extremity partially, but it is very slow and also accompanied by the formation of abnormal mode. Therefore, functional training should be emphasized in recovering the motor function of extremity. OBJECTIVE: To observe the effects of combination of motor relearning program and Bobath method on motor function of upper extremity of patients with stroke. DESIGN: Comparison of therapeutic effects taking stroke patients as observation subjects. SETTING: Department of Neurology, General Hospital of Beijing Jingmei Group. PARTICIPANTS: Totally 120 stroke patients, including 60 males and 60 females, averaged (59±3) years, who hospitalized in the Department of Neurology, General Hospital of Beijing Jingmei Group between January 2005 and June 2006 were recruited. The involved patients met the following criteria: Stroke attack within 2 weeks; diagnosis criteria of cerebral hemorrhage or infarction made in the 4th National Cerebrovascular Disease Conference; confirmed by skull CT or MRI; Informed consents of therapeutic regimen were obtained. The patients were assigned into 2 groups according to their wills: rehabilitation group and control group, with 30 males and 30 females in each group. Patients in rehabilitation group averaged (59±2)years old, and those in the control group averaged (58±2)years old. METHODS: ① Patients in two groups received routine treatment in the Department of Neurology. When the vital signs of patients in the rehabilitation group were stable, individualized treatment was conducted by combined application of motor relearning program and Bobath method. Meanwhile, training of activity of daily living was performed according to the disease condition changes of patients at different phases, including the nursing and instruction of body posture, the maintenance of good extremity position, bed exercise, bedside sit up and sitting position balance, sit up exercise, dynamic and static balance exercise, walking exercise, active training and passive training. The strength, time and speed of training were increased gradually according to their physical abilities. Patients were trained 45 to 60 minutes once, 5 times a week, within 2 weeks. ② Evaluation criteria of therapeutic effect: The motor function of upper extremity was evaluated by Fugl-Meyer method on the day of beginning and end of treatment. Higher points indicated better function of upper extremity. ③ t test and paired t test were used for comparing the difference of intergroup and intragroup measurement data, respectively. MAIN OUTCOME MEASURES: Changes in Fugl-Meyer scoring of two groups before and after treatment. RESULTS: Totally 120 stroke patients participated in the final analysis. Before treatment, Fugl-Meyer scoring was close between rehabilitation group and control group [(14.47±2.38),(14.16±2.39) points, P > 0.05]; Fugl-Meyer scoring of rehabilitation group after treatment was significantly higher than that before treatment and that of control group[(37.93±2.67),(18.36±2.43) points, t =11.053, 5.408, P < 0.01]; There were no significant differences in Fugl-Meyer scoring between before treatment in the control group and control group (P > 0.05). CONCLUSION: Combined application of motor relearning program and Bobath method can significantly improve the motor function of upper extremity of patients with stroke.
文摘Totally three articles focusing on functional magnetic resonance imaging features of brain function in the activated brain regions of stroke patients undergoing acupuncture on the healthy limbs and healthy controls undergoing acupuncture on the lower extremities are published in three issues. We hope that our readers find these papers useful to their research.
基金Supported by the National Natural Science Foundation of China(Grant No.12201234)the Natural Science Foundation of Anhui Province of China(Grant No.2008085MA07)。
文摘Let B be a unit ball in R^(2),W_(0)^(1,2)(B)be the standard Sobolev space.For anyϵ>0,de Figueiredo,doÓ,dos Santons,Yang and Zhu proved the existence of extremals of a Trudinger-Moser inequality in the unit ball.Precisely,u∈W_(0)^(1,2)(B)^(sup),∫_(B)|▽u|^(2)dx≤1∫_(B)^(|x|^(2∈)e^(4π(1+∈)u^(2)dx)can be attained by some radially symmetric function u_(∈)∈W_(0)^(1,2)(B)∫_(B)with∫_(B)|▽u|^(2)dx=1.In this note,we concern the compactness of the function family{uϵ}ϵ>0 and prove that up to a subsequence uϵconverges to some function u 0 in C^(1)(B)asϵ→0.Furthermore,u_(0) is an extremal function of the supremum u∈W_(0)^(1,2)(B)^(sup),∫_(B)|▽u|^(2)dx≤1∫_(B)e^(4πu^(2)dx)Let us explain the result in geometry.Denoteω_(0)=dx_(1)^(2)+dx_(2)^(2)be the standard Euclidean metricω_(∈)|x|^(2ϵ)ω_(0)for xϵB..Then the extremal family{u_(∈)}∈>0 of the following Trudinger-Moser functionals∫_(B)e^(4π(1+∈)u^(2))dvω_(∈)under the constraint W_(0)^(1,2)(B)and∫_(B)|▽ω_∈)u|^(2)dvω_∈)≤1 is compact asϵ→0.
文摘Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.
基金Supported by the National Natural Science Foundation of China.
文摘Let f be analytic in a hyperbolic region Ω. The Bloch constant β_f of f is defined by β_f=sup z∈Ω|f’(z)|/λ_Ω(z), where λ_Ω(z)|dz|is the Poincare metric in Ω. Suppose △is hyperbolic and lim inf ω→cλ△(w)】λ(△)】0, (?)c∈(?)△ where λ(△)=inf w∈△ λ△(w). Then for all f with f(Ω)(?)△, we have β_f≤1/λ(△). In this paper we study the extremal functions defined by β_f=1/λ(△) and the existence of those functions.
基金Supported by Mathematics And Applications Laboratory,Faculty of Sciences,Gabes University,Tunisia。
文摘In this paper,we consider the generalized Weinstein operator Δ_(W)^(d,α,n) we introduce new Sobolev-Weinstein spaces denoted H_(α,dn)^(s)(R_(+)^(d+1) )associated with the generalized Weinstein operator and we investigate their properties.Next,as application,we study the extremal functions on the spaces H_(α,dn)^(s)(R_(+)^(d+1)) using the theory of reproducing kernels.
基金supported by the Natural Science Foundation of Shandong Province of China,No.2014ZRB14502
文摘OBJECTIVE： The aim of this meta-analysis was to evaluate the clinical efficacy of constraint-induced movement therapy in acute and sub-acute stroke. DATA SOURCES： The key words were stroke, cerebrovascular accident, constraint-induced therapy, forced use, and randomized controlled trial. The databases, including China National Knowledge Infrastructure, WanFang, Weipu Information Resources System, Chinese Biomedical Literature Database, PubMed, Med- line, Embase, the Cochrane Central Register of Controlled Trials, and the Cochrane Database of Systematic Reviews, were searched for studies on randomized controlled trials for treating acute or sub-acute stroke published before March 2016. DATA SELECTION： We retrieved relevant randomized controlled trials that compared constraint-induced movement therapy in treatment of acute or sub-acute stroke with traditional rehabilitation therapy （tradi- tional occupational therapy）. Patients were older than 18 years, had disease courses less than 6 months, and were evaluated with at least one upper extremity function scale. Study quality was evaluated, and data that met the criteria were extracted. Stata 11.0 software was used for the meta-analysis. OUTCOME MEASURES： Fugl-Meyer motor assessment of the arm, the action research-arm test, a motor activity log for amount of use and quality of movement, the Wolf motor function test, and a modified Bar- thel index. RESULTS： A total of 16 prospective randomized controlled trials （379 patients in the constraint-induced movement-therapy group and 359 in the control group） met inclusion criteria. Analysis showed significant mean differences in favor of constraint-induced movement therapy for the Fugl-Meyer motor assessment of the arm （weighted mean difference （WMD） = 10.822; 95% confidence intervals （95% CI）： 7.419-14.226）, the action research-arm test （WMD = 10.718; 95% CI： 5.704-15.733）, the motor activity log for amount of use and quality of movement （WMD = 0.812; 95% CI： 0.331-1.293） and the modified Barthel index （WMD = 10.706; 95% CI： 4.417-16.966）. CONCLUSION： Constraint-induced movement therapy may be more beneficial than traditional rehabili- tation therapy for improving upper limb function after acute or sub-acute stroke.
基金funded by National Natural Science Foundation of China(51474076)International S&T Cooperation Program(ISTCP)of China(2015DFG51950)
文摘A statistic method, statistics of extreme values （SEV）, was described in detail, which can esti mate the size of maximum inclusion in steel. The characteristic size of the maximum inclusion in a high clean bearing steel （GCrl5） was evaluated by this method, and the morphology and corn position of large inclusions found were analyzed by scanning electron microscopy （SEM）. When standard inspection area （S0） is 280 mm2, the characteristic size of the biggest inclusion found in 30 standard inspection area is 23.93 μm, and it has a 99.9% probability of the characteristic size of maximum inclusion predicted being no larger than 36.85μm in the experimental steel. SEM result shows that large inclusions found are mainly composed of CaS, calcium-aluminate and MgO. Compositing widely exists in large inclusions in high clean bearing steel. Compared with traditional evaluation method, SEV method mainly focuses on inclusion size, and the esti- mation result is not affected by inclusion types. SEV method is suitable for the inclusion eval uation of high clean bearing steel.
文摘Background:Stroke is considered to be a leading cause of impairment.After experiencing strokes,patients are frequently left with impaired motor function,making it difficult to carry out daily tasks.The most extensively researched method for treating stroke patients in recent decades is CIMT(constraintinduced movement therapy),which was developed to treat upper limb deficits following stroke.CIMT entails limiting the use of the unaffected limb,altering behavior to increase the use of the affected limb,and finally,mass-training of the affected limb.Objective:The current study aimed to determine the effectiveness of CIMT through TR for upper extremity function in stroke patients.Materials and methods:Thirty post-stroke participants were selected on the basis of inclusion and exclusion criteria,and allocated into group A and group B.Group A was treated with CIMT in the physiotherapy department and group B was treated with CIMT through TR.Outcome measures were the Fugl-Meyer Assessment scale for upper extremities(FMA-UE),the Wolf Motor Function Test(WMFT),and the Motor Activity Log(MAL).Results:Both groups showed significant improvements in FMA-UE,WMFT and MAL-A0U,MAL-Q0M scores.However,there were no significant differences between groups A and B in FMA-UE,WMFT,MALAOU,and MAL-QOM scores in the inter-group analysis.Conclusion:CIMT via TR was equally effective than CIMT in physiotherapy department for upper extremity function in stroke.Further studies should be conducted to identify the long-term effectiveness of this approach.
