This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial ra...This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial rank no more than k has a lower bound.Furthermore,if k≤1 and normal elements are commuting,then the lower bound will be better.Another result establishes a connection involving the spectrum distance operator Dc between a C^(*)-algebra of stable rank one C^(*)-algebra and its hereditary C^(*)-subalgebra.展开更多
In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→...In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.展开更多
The development of brain-computer interfaces(BCI)based on motor imagery(MI)has greatly improved patients’quality of life with movement disorders.The classification of upper limb MI has been widely studied and applied...The development of brain-computer interfaces(BCI)based on motor imagery(MI)has greatly improved patients’quality of life with movement disorders.The classification of upper limb MI has been widely studied and applied in many fields,including rehabilitation.However,the physiological representations of left and right lower limb movements are too close and activated deep in the cerebral cortex,making it difficult to distinguish their features.Therefore,classifying lower limbs motor imagery is more challenging.In this study,we propose a feature extraction method based on functional connectivity,which utilizes phase-locked values to construct a functional connectivity matrix as the features of the left and right legs,which can effectively avoid the problem of physiological representations of the left and right lower limbs being too close to each other during movement.In addition,considering the topology and the temporal characteristics of the electroencephalogram(EEG),we designed a temporal-spatial convolutional network(TSGCN)to capture the spatiotemporal information for classification.Experimental results show that the accuracy of the proposed method is higher than that of existing methods,achieving an average classification accuracy of 73.58%on the internal dataset.Finally,this study explains the network mechanism of left and right foot MI from the perspective of graph theoretic features and demonstrates the feasibility of decoding lower limb MI.展开更多
BACKGROUND The therapeutic role of neurodynamic mobilization in improving lower limb function in patients with mild post-traumatic knee osteoarthritis remains poorly understood.AIM To further elucidate the role of neu...BACKGROUND The therapeutic role of neurodynamic mobilization in improving lower limb function in patients with mild post-traumatic knee osteoarthritis remains poorly understood.AIM To further elucidate the role of neurodynamic mobilization in facilitating knee joint functional recovery.METHODS Thirty-two patients with post-traumatic knee osteoarthritis treated at Chonghua Hospital of Traditional Chinese Medicine(Guilin)from March 2024 to August 2025 were randomly assigned to a control group(n=16)or an intervention group(n=16).Both groups received eight weeks of conventional treatment;and the intervention group additionally underwent neurodynamic mobilization.Outcomes including pain assessed by the visual analogue scale,active range of motion,Lysholm score,stork stand test,single hop test,and Y-balance test were assessed before and after the intervention.RESULTS There were no significant differences between the two groups in baseline characteristics,including gender,age,body mass index,or surgical side(P>0.05).Two-way repeated-measures analysis of variance demonstrated significant time×group interaction effects for the visual analogue scale score(F=13.364,P<0.05),Lysholm knee score(F=20.385,P<0.05),stork stand test(F=103.756,P<0.05),and Y-balance test score(F=8.089,P<0.05).CONCLUSION Neurodynamic mobilization effectively reduces pain,improves knee function,and enhances lower limb balance in patients with mild post-traumatic knee osteoarthritis.展开更多
Background:Prostate cancer is a common malignancy,with many men on active surveillance for localized,low-risk disease also experiencing lower urinary tract symptoms(LUTS)from benign prostatic hyperplasia(BPH).Water Va...Background:Prostate cancer is a common malignancy,with many men on active surveillance for localized,low-risk disease also experiencing lower urinary tract symptoms(LUTS)from benign prostatic hyperplasia(BPH).Water Vapor Thermal Therapy(WVTT)is a minimally invasive BPH treatment,but its safety and efficacy in this setting are unclear.Case Description:We report three men with localized PCa on active surveillance who underwent WVTT for LUTS.Conclusions:WVTT appears safe and potentially effective in treating LUTS,especially in those with lower-risk disease and smaller prostate volumes.Further research is needed to confirm safety,efficacy,and optimal patient selection.展开更多
This research presents a Human Lower Limb Activity Recognition(HLLAR)system that identifies specific activities and predicts the angles of the knees simultaneously,based on the EMG signals.The HLLAR systems streamline...This research presents a Human Lower Limb Activity Recognition(HLLAR)system that identifies specific activities and predicts the angles of the knees simultaneously,based on the EMG signals.The HLLAR systems streamlines the research on the lower limb activities.The HILLAR model includes Discrete Hermite Wavelets Transform-based Synchrosqueezing(DHWTS),Deep Two-Layer Multiscale Convolutional Neural Network(DTLMCNN),and Generalized Regression Neural Network(GRNN)as feature extraction,activity recognition,and knee angle prediction respectively.Electromyography signal-based automatic lower limb activity detection is crucial to rehabilitation and human movement analysis.Yet several of these methods face issues in feature extraction in complex data,overlapping signals,extraction of crucial parameters,and adaptation constraints.This research aims classify lower limb activities and predict knee joint angles from electromy-ography signals using HILLAR model.The model is validated on two datasets,comprising 26 subjects performing three classes of activities:walking,standing,and sitting.The proposed model obtained a classification accuracy of 99.95%,along with significant achievements in precision(99.93%),recall(99.91%),and F1-score(99.93%).The generalized regression neural network predicted angles of the knee joint with a root mean squared error of 1.25%.Robustness is demonstrated through consistent results in five-fold cross-validation and statistical significance testing(p-value=0.004,McNemar's test).Additionally,the proposed model showed superior performance over baseline methods by reducing error rates by 18%and decreasing processing time to 0.98 s.展开更多
The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower b...The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate （BER） for maximal ratio combining （MRC） with Gaussian distributed weighting errors on independent and identically distributed （i. i. d） fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.展开更多
Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|x...Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.展开更多
The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equation ut=△u^m＋u^p∫Ωu^qdxwith either null Dirichlet boundary condition or homogeneous Neumann boundary condi- tion is g...The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equation ut=△u^m＋u^p∫Ωu^qdxwith either null Dirichlet boundary condition or homogeneous Neumann boundary condi- tion is given in this article by using a differential inequality technique.展开更多
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 th...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.展开更多
The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee ...The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee discrepancy of fractional factorial designs with two and three mixed levels. Our new lower bound is sharper and more valid than other existing lower bounds in literature, which is a useful complement to the lower bound theory of discrepancies.展开更多
Since the features of low energy consumption and limited power supply are very impor- tant for wireless sensor networks （WSNs）, the problems of distributed state estimation with quan- tized innovations are investiga...Since the features of low energy consumption and limited power supply are very impor- tant for wireless sensor networks （WSNs）, the problems of distributed state estimation with quan- tized innovations are investigated in this paper. In the first place, the assumptions of prior and posterior probability density function （PDF） with quantized innovations in the previous papers are analyzed. After that, an innovative Gaussian mixture estimator is proposed. On this basis, this paper presents a Gaussian mixture state estimation algorithm based on quantized innovations for WSNs. In order to evaluate and compare the performance of this kind of state estimation algo- rithms for WSNs, the posterior Cram6r-Rao lower bound （CRLB） with quantized innovations is put forward. Performance analysis and simulations show that the proposed Gaussian mixture state estimation algorithm is efficient than the others under the same number of quantization levels and the performance of these algorithms can be benchmarked by the theoretical lower bound.展开更多
A lower bound approach is proposed for the first time to solve the macroscopic yield loci of porous materials.The results are then compared with Gurson's upper bound yield loci and those of the experiments.It is s...A lower bound approach is proposed for the first time to solve the macroscopic yield loci of porous materials.The results are then compared with Gurson's upper bound yield loci and those of the experiments.It is shown that the present analysis is much more in accordance with the experimen- tal results than the Gurson's.展开更多
Li et al. in [3] obtained blow-up results for a system of Petrovskey equations in some different cases. In this article we obtain lower bounds for the blow up time under some considerations on initial data.
Based on the lower bound theorem of limit analysis, a solution procedure for limit analysis of three_dimensional elastoplastic structures was established using conventional boundary element method (BEM). The elastic s...Based on the lower bound theorem of limit analysis, a solution procedure for limit analysis of three_dimensional elastoplastic structures was established using conventional boundary element method (BEM). The elastic stress field for lower bound limit analysis was computed directly by three_dimensional boundary element method (3_D BEM). The self_equilibrium stress field was constructed by the linear combination of several self_equilibrium “basis vectors” which can be computed by elastic_plastic incremental iteration of 3_D BEM analysis. The lower bound limit analysis problem was finally reduced to a series of nonlinear programming sub_problems with relatively few optimal variables. The complex method was used to solve the nonlinear programming sub_problems. The numerical results show that the present solution procedure has good accuracy and high efficiency.展开更多
The lower bounds on the maximum genus of loopless graphs are obtained according to the connectivity of these graphs. This not only answers a question of Chen, Archdeacon and Gross, but also generalizes the previous kn...The lower bounds on the maximum genus of loopless graphs are obtained according to the connectivity of these graphs. This not only answers a question of Chen, Archdeacon and Gross, but also generalizes the previous known results. Thus, a picture of the lower bounds on the maximum genus of loopless multigraphs is presented.展开更多
In this paper, the k-partitioning problem with partition matroid constraint is considered. LPT algorithm is modified to fit the problem and its worst-ease performance is analyzed. The lower bounds of optimal solution ...In this paper, the k-partitioning problem with partition matroid constraint is considered. LPT algorithm is modified to fit the problem and its worst-ease performance is analyzed. The lower bounds of optimal solution for the min-max problem are given.展开更多
In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for th...In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for the system under either homogeneous Dirichlet or nonhomogeneous Neumann boundary conditions are obtained.展开更多
We study the concurrence of arbitrary dimensional bipartite quantum systems. By using a positive but not completely positive map, we present an anaJytical lower bound of concurrence. Detailed examples are used to show...We study the concurrence of arbitrary dimensional bipartite quantum systems. By using a positive but not completely positive map, we present an anaJytical lower bound of concurrence. Detailed examples are used to show that our bound can detect entanglement better and can improve the well known existing lower bounds.展开更多
It is hard for the existing methods to obtain the expression of the system reliability for most of the practical complex systems with a large number of components and possible stales. A new regression algorithm based ...It is hard for the existing methods to obtain the expression of the system reliability for most of the practical complex systems with a large number of components and possible stales. A new regression algorithm based on the lower and upper bounds is presented in this paper, which can obtain the system reliability analytically without concerning the structure of the complex system. The method has been applied to a real system and the reliability results are compared with those acquired by the classical method and the parametric method. The effectiveness and accuracy of the proposed method have been testified.展开更多
基金Supported by Zhejiang Provincial Natural Science Foundation of China(No.ZCLQN25A0103)。
文摘This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial rank no more than k has a lower bound.Furthermore,if k≤1 and normal elements are commuting,then the lower bound will be better.Another result establishes a connection involving the spectrum distance operator Dc between a C^(*)-algebra of stable rank one C^(*)-algebra and its hereditary C^(*)-subalgebra.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12361040,12061064)the National Science Foundation of Gansu Province(Grant No.22JR5RA264)State Scholarship Fund(Grant No.20230862021).
文摘In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.
基金supported in part by the National Natural Science Foundation of China under Grant 62172368the Natural Science Foundation of Zhejiang Province under Grant LR22F020003.
文摘The development of brain-computer interfaces(BCI)based on motor imagery(MI)has greatly improved patients’quality of life with movement disorders.The classification of upper limb MI has been widely studied and applied in many fields,including rehabilitation.However,the physiological representations of left and right lower limb movements are too close and activated deep in the cerebral cortex,making it difficult to distinguish their features.Therefore,classifying lower limbs motor imagery is more challenging.In this study,we propose a feature extraction method based on functional connectivity,which utilizes phase-locked values to construct a functional connectivity matrix as the features of the left and right legs,which can effectively avoid the problem of physiological representations of the left and right lower limbs being too close to each other during movement.In addition,considering the topology and the temporal characteristics of the electroencephalogram(EEG),we designed a temporal-spatial convolutional network(TSGCN)to capture the spatiotemporal information for classification.Experimental results show that the accuracy of the proposed method is higher than that of existing methods,achieving an average classification accuracy of 73.58%on the internal dataset.Finally,this study explains the network mechanism of left and right foot MI from the perspective of graph theoretic features and demonstrates the feasibility of decoding lower limb MI.
基金Supported by the Central Guided Local Science and Technology Development Fund Project for Science and Technology Innovation Base Construction,No.Guike ZY24212046National Natural Science Foundation of China,No.U22A2092+3 种基金Guangxi Education Science“the 14th Five-Year Plan”2024 Special Project“Research on Steam Education Practice in Rehabilitation Engineering”,No.2024ZJY304the Research Basic Ability Enhancement Program for Young and Middle-aged Teachers of Guangxi,No.2025KY2255the Innovation Project of GUET Graduate Education,No.2025YCXB010Natural Science Research Project of Guilin Life and Health Career Technical College,No.2025GKKY04.
文摘BACKGROUND The therapeutic role of neurodynamic mobilization in improving lower limb function in patients with mild post-traumatic knee osteoarthritis remains poorly understood.AIM To further elucidate the role of neurodynamic mobilization in facilitating knee joint functional recovery.METHODS Thirty-two patients with post-traumatic knee osteoarthritis treated at Chonghua Hospital of Traditional Chinese Medicine(Guilin)from March 2024 to August 2025 were randomly assigned to a control group(n=16)or an intervention group(n=16).Both groups received eight weeks of conventional treatment;and the intervention group additionally underwent neurodynamic mobilization.Outcomes including pain assessed by the visual analogue scale,active range of motion,Lysholm score,stork stand test,single hop test,and Y-balance test were assessed before and after the intervention.RESULTS There were no significant differences between the two groups in baseline characteristics,including gender,age,body mass index,or surgical side(P>0.05).Two-way repeated-measures analysis of variance demonstrated significant time×group interaction effects for the visual analogue scale score(F=13.364,P<0.05),Lysholm knee score(F=20.385,P<0.05),stork stand test(F=103.756,P<0.05),and Y-balance test score(F=8.089,P<0.05).CONCLUSION Neurodynamic mobilization effectively reduces pain,improves knee function,and enhances lower limb balance in patients with mild post-traumatic knee osteoarthritis.
文摘Background:Prostate cancer is a common malignancy,with many men on active surveillance for localized,low-risk disease also experiencing lower urinary tract symptoms(LUTS)from benign prostatic hyperplasia(BPH).Water Vapor Thermal Therapy(WVTT)is a minimally invasive BPH treatment,but its safety and efficacy in this setting are unclear.Case Description:We report three men with localized PCa on active surveillance who underwent WVTT for LUTS.Conclusions:WVTT appears safe and potentially effective in treating LUTS,especially in those with lower-risk disease and smaller prostate volumes.Further research is needed to confirm safety,efficacy,and optimal patient selection.
文摘This research presents a Human Lower Limb Activity Recognition(HLLAR)system that identifies specific activities and predicts the angles of the knees simultaneously,based on the EMG signals.The HLLAR systems streamlines the research on the lower limb activities.The HILLAR model includes Discrete Hermite Wavelets Transform-based Synchrosqueezing(DHWTS),Deep Two-Layer Multiscale Convolutional Neural Network(DTLMCNN),and Generalized Regression Neural Network(GRNN)as feature extraction,activity recognition,and knee angle prediction respectively.Electromyography signal-based automatic lower limb activity detection is crucial to rehabilitation and human movement analysis.Yet several of these methods face issues in feature extraction in complex data,overlapping signals,extraction of crucial parameters,and adaptation constraints.This research aims classify lower limb activities and predict knee joint angles from electromy-ography signals using HILLAR model.The model is validated on two datasets,comprising 26 subjects performing three classes of activities:walking,standing,and sitting.The proposed model obtained a classification accuracy of 99.95%,along with significant achievements in precision(99.93%),recall(99.91%),and F1-score(99.93%).The generalized regression neural network predicted angles of the knee joint with a root mean squared error of 1.25%.Robustness is demonstrated through consistent results in five-fold cross-validation and statistical significance testing(p-value=0.004,McNemar's test).Additionally,the proposed model showed superior performance over baseline methods by reducing error rates by 18%and decreasing processing time to 0.98 s.
文摘The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate （BER） for maximal ratio combining （MRC） with Gaussian distributed weighting errors on independent and identically distributed （i. i. d） fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.
文摘Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.
基金supported by the Fundamental Research Funds for the Central Universities (CDJXS 11 10 00 19)Mu Chunlai is supported by NSF of China(11071266)
文摘The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equation ut=△u^m＋u^p∫Ωu^qdxwith either null Dirichlet boundary condition or homogeneous Neumann boundary condi- tion is given in this article by using a differential inequality technique.
基金Project supported by the Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (IHLB201008257)Scientific Research Common Program of Beijing Municipal Commission of Education (KM200810011005)+1 种基金PHR (IHLB 201102)research grant of University of Macao MYRG142(Y1-L2)-FST111-KKI
文摘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.
基金supported by the National Natural Science Foundation of China(11301546).supported by the National Natural Science Foundation of China(11271147,11471136)
文摘The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee discrepancy of fractional factorial designs with two and three mixed levels. Our new lower bound is sharper and more valid than other existing lower bounds in literature, which is a useful complement to the lower bound theory of discrepancies.
基金jointly supported by the National Natural Science Foundation of China(No.61175008)State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System of China(No.CEMEE2014K0301A)the Natural Science Foundation of Jiangsu Province of China(No.BK20140896)
文摘Since the features of low energy consumption and limited power supply are very impor- tant for wireless sensor networks （WSNs）, the problems of distributed state estimation with quan- tized innovations are investigated in this paper. In the first place, the assumptions of prior and posterior probability density function （PDF） with quantized innovations in the previous papers are analyzed. After that, an innovative Gaussian mixture estimator is proposed. On this basis, this paper presents a Gaussian mixture state estimation algorithm based on quantized innovations for WSNs. In order to evaluate and compare the performance of this kind of state estimation algo- rithms for WSNs, the posterior Cram6r-Rao lower bound （CRLB） with quantized innovations is put forward. Performance analysis and simulations show that the proposed Gaussian mixture state estimation algorithm is efficient than the others under the same number of quantization levels and the performance of these algorithms can be benchmarked by the theoretical lower bound.
文摘A lower bound approach is proposed for the first time to solve the macroscopic yield loci of porous materials.The results are then compared with Gurson's upper bound yield loci and those of the experiments.It is shown that the present analysis is much more in accordance with the experimen- tal results than the Gurson's.
文摘Li et al. in [3] obtained blow-up results for a system of Petrovskey equations in some different cases. In this article we obtain lower bounds for the blow up time under some considerations on initial data.
文摘Based on the lower bound theorem of limit analysis, a solution procedure for limit analysis of three_dimensional elastoplastic structures was established using conventional boundary element method (BEM). The elastic stress field for lower bound limit analysis was computed directly by three_dimensional boundary element method (3_D BEM). The self_equilibrium stress field was constructed by the linear combination of several self_equilibrium “basis vectors” which can be computed by elastic_plastic incremental iteration of 3_D BEM analysis. The lower bound limit analysis problem was finally reduced to a series of nonlinear programming sub_problems with relatively few optimal variables. The complex method was used to solve the nonlinear programming sub_problems. The numerical results show that the present solution procedure has good accuracy and high efficiency.
文摘The lower bounds on the maximum genus of loopless graphs are obtained according to the connectivity of these graphs. This not only answers a question of Chen, Archdeacon and Gross, but also generalizes the previous known results. Thus, a picture of the lower bounds on the maximum genus of loopless multigraphs is presented.
基金Supported by the National Natural Science Foundation of China(10671177)
文摘In this paper, the k-partitioning problem with partition matroid constraint is considered. LPT algorithm is modified to fit the problem and its worst-ease performance is analyzed. The lower bounds of optimal solution for the min-max problem are given.
基金Supported by the Natural Science Foundation of Shaanxi Province(2019JM-534)the Youth Innovation Team of Shaanxi Universities+7 种基金the 14th Five Year Plan for Educational Science in Shaanxi Province(SGH21Y0308)Key Topic of China Higher Education Association(21DFD04)Higher Education Teaching Reform Project of Xi’an International University(2023B03)2022 Annual Planning Project of China Association of Private Education(School Development)(CANFZG22222)Project of Department of Education of Shaanxi Provincethe 2022 Annual Topic of the"14th Five-Year Plan"of Shaanxi Provincial Educational Science(SGH22Y1885)Project of Qi Fang Education Research Institute of Xi’an International University(23mjy10)Special Project of the Shaanxi Provincial Social Science Found in 2023(2023SJ12,2023LS04)。
文摘In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for the system under either homogeneous Dirichlet or nonhomogeneous Neumann boundary conditions are obtained.
基金Supported by the National Natural Science Foundation of China under Grant No.11275131
文摘We study the concurrence of arbitrary dimensional bipartite quantum systems. By using a positive but not completely positive map, we present an anaJytical lower bound of concurrence. Detailed examples are used to show that our bound can detect entanglement better and can improve the well known existing lower bounds.
基金National Natural Science Foundation of China(No.40927001)
文摘It is hard for the existing methods to obtain the expression of the system reliability for most of the practical complex systems with a large number of components and possible stales. A new regression algorithm based on the lower and upper bounds is presented in this paper, which can obtain the system reliability analytically without concerning the structure of the complex system. The method has been applied to a real system and the reliability results are compared with those acquired by the classical method and the parametric method. The effectiveness and accuracy of the proposed method have been testified.
