BACKGROUND An acute myocardial infarction(AMI)is often treated with direct coronary intervention and requires home-based rehabilitation.Caregivers of patients with AMI need adequate social support to maintain high-qua...BACKGROUND An acute myocardial infarction(AMI)is often treated with direct coronary intervention and requires home-based rehabilitation.Caregivers of patients with AMI need adequate social support to maintain high-quality care;however,their social support function is low,and relevant indicators for intervention must be identified.AIM To analyze the correlation between social support for primary caregivers,their anxiety,and depression,when caring for patients with AMI after interventional therapy.METHODS Using convenience sampling,we selected 300 primary caregivers of patients with AMI who had undergone interventional therapy.The Social Support Rating Scale(SSRS),Self-Rating Anxiety Scale(SAS),and Self-Rating Depression Scale(SDS)were used to assess the primary caregivers.A Pearson’s correlation analysis was used to analyze the correlations between the SSRS,SAS,and SDS,and a multiple logistic regression analysis was used to analyze the factors influencing the low social support function of primary caregivers.The receiver operating characteristic curve and area under the curve(AUC)were used to evaluate the predictive ability of the SAS and SDS for low social support function in primary caregivers.RESULTS Considering the norm among Chinese people,AMI caregivers’objective support,subjective support,support utilization,and SSRS scores were lower,while their SAS and SDS scores were higher.The SSRS scores of female caregivers were higher than those of the male caregivers(t=2.123,P=0.035).The Pearson correlation analysis showed that objective support,subjective support,support utilization,and SSRS total scores were significantly correlated with both SAS(r=-0.414,-0.460,-0.416,-0.535)and SDS scores(r=-0.463,-0.379,-0.349,-0.472).Among the 300 AMI caregivers,56 cases(18.67%)had a low level of support function(SSRS≤22 points).Logistic regression model analysis showed that SAS and SDS were independent risk factors for low social support function of AMI caregivers,regardless of adjustment for other variables(P<0.05).SAS and SDS predicted that the AUC of AMI caregivers with low support function was 0.84,sensitivity was 67.9 and 71.4,and specificity was 84.0 and 70.9,respectively.CONCLUSION The social support function of the primary caregiver of patients with AMI after interventional therapy was lower and negatively correlated with anxiety and depression in the primary caregiver.展开更多
Imbalanced datasets are common in practical applications,and oversampling methods using fuzzy rules have been shown to enhance the classification performance of imbalanced data by taking into account the relationship ...Imbalanced datasets are common in practical applications,and oversampling methods using fuzzy rules have been shown to enhance the classification performance of imbalanced data by taking into account the relationship between data attributes.However,the creation of fuzzy rules typically depends on expert knowledge,which may not fully leverage the label information in training data and may be subjective.To address this issue,a novel fuzzy rule oversampling approach is developed based on the learning vector quantization(LVQ)algorithm.In this method,the label information of the training data is utilized to determine the antecedent part of If-Then fuzzy rules by dynamically dividing attribute intervals using LVQ.Subsequently,fuzzy rules are generated and adjusted to calculate rule weights.The number of new samples to be synthesized for each rule is then computed,and samples from the minority class are synthesized based on the newly generated fuzzy rules.This results in the establishment of a fuzzy rule oversampling method based on LVQ.To evaluate the effectiveness of this method,comparative experiments are conducted on 12 publicly available imbalance datasets with five other sampling techniques in combination with the support function machine.The experimental results demonstrate that the proposed method can significantly enhance the classification algorithm across seven performance indicators,including a boost of 2.15%to 12.34%in Accuracy,6.11%to 27.06%in G-mean,and 4.69%to 18.78%in AUC.These show that the proposed method is capable of more efficiently improving the classification performance of imbalanced data.展开更多
In this paper we show that the unit ball of an infinite dimensional commutative C-algebra lacks strongly exposed points, so they have no predual. Also in the second part, we use the concept of strongly exposed points ...In this paper we show that the unit ball of an infinite dimensional commutative C-algebra lacks strongly exposed points, so they have no predual. Also in the second part, we use the concept of strongly exposed points in the Frechet differentiability of support convex functions.展开更多
Mechanical model of anchorage surrounding rock considering tray effect was established based on elastic theory,in order to study the mechanism of bolt supporting.Elastic solutions of normal force at point in the inter...Mechanical model of anchorage surrounding rock considering tray effect was established based on elastic theory,in order to study the mechanism of bolt supporting.Elastic solutions of normal force at point in the interior of a semi-infnite solid were obtained by means of classical displacement function method in elasticity.The factors which influence stress of bolted surrounding rock,such as the length of bolt and tray effect,were analyzed.The absolute value of stress along bolt axes decreased rapidly with an increase in radical distance and the maximum appeared near ends of bolt.With increasing radical distance,the value of radical stress changed from positive to negative roughly and then increased to zero,with maximum at the middle of bolt.The evolution of hoop stress as radical distance increasing was similar with stress along bolt axes.With an increase in depth,the radical effect ranges of all normal stress components were reduced.These suggest that the effect from tray on stress along bolt axes of bolted surrounding rock could be neglected,except near surface of surrounding rock.展开更多
The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Fr...The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Frechet differentiability of the support function on the extremal points.展开更多
In this paper,we study the asymptotic behavior of a class of inverse quotient curvature flow in the anti-de Sitter-Schwarzschild manifold.We prove that under suitable convex conditions for the initial hypersurface,one...In this paper,we study the asymptotic behavior of a class of inverse quotient curvature flow in the anti-de Sitter-Schwarzschild manifold.We prove that under suitable convex conditions for the initial hypersurface,one can get the long-time existence for the inverse curvature flow.Moreover,we also get that the principal curvatures of the evolving hypersurface converge to 1 when t→+∞.展开更多
Compactly supported radial basis function can enable the coefficient matrix of solving weigh linear system to have a sparse banded structure, thereby reducing the complexity of the algorithm. Firstly, based on the com...Compactly supported radial basis function can enable the coefficient matrix of solving weigh linear system to have a sparse banded structure, thereby reducing the complexity of the algorithm. Firstly, based on the compactly supported radial basis function, the paper makes the complex quadratic function （Multiquadric, MQ for short） to be transformed and proposes a class of compactly supported MQ function. Secondly, the paper describes a method that interpolates discrete motion capture data to solve the motion vectors of the interpolation points and they are used in facial expression reconstruction. Finally, according to this characteris- tic of the uneven distribution of the face markers, the markers are numbered and grouped in accordance with the density level, and then be interpolated in line with each group. The approach not only ensures the accuracy of the deformation of face local area and smoothness, but also reduces the time complexity of computing.展开更多
In this letter, on the basis of Frequent Pattern(FP) tree, the support function to update FP-tree is introduced, then an Incremental FP (IFP) algorithm for mining association rules is proposed. IFP algorithm considers...In this letter, on the basis of Frequent Pattern(FP) tree, the support function to update FP-tree is introduced, then an Incremental FP (IFP) algorithm for mining association rules is proposed. IFP algorithm considers not only adding new data into the database but also reducing old data from the database. Furthermore, it can predigest five cases to three cases.The algorithm proposed in this letter can avoid generating lots of candidate items, and it is high efficient.展开更多
Coronavirus disease 2019(COVID-19)is a highly contagious disease and a serious threat to human health.COVID-19 can cause multiple organ dysfunction,such as respiratory and circulatory failure,liver and kidney injury,d...Coronavirus disease 2019(COVID-19)is a highly contagious disease and a serious threat to human health.COVID-19 can cause multiple organ dysfunction,such as respiratory and circulatory failure,liver and kidney injury,disseminated intravascular coagulation,and thromboembolism,and even death.The World Health Organization reports that the mortality rate of severe-type COVID-19 is over 50%.Currently,the number of severe cases worldwide has increased rapidly,but the experience in the treatment of infected patients is still limited.Given the lack of specific antiviral drugs,multi-organ function support treatment is important for patients with COVID-19.To improve the cure rate and reduce the mortality of patients with severe-and critical-type COVID-19,this paper summarizes the experience of organ function support in patients with severe-and criticaltype COVID-19 in Optical Valley Branch of Tongji Hospital,Wuhan,China.This paper systematically summarizes the procedures of functional support therapies for multiple organs and systems,including respiratory,circulatory,renal,hepatic,and hematological systems,among patients with severe-and critical-type COVID-19.This paper provides a clinical reference and a new strategy for the optimal treatment of COVID-19 worldwide.展开更多
Proton exchange membrane fuel cells are playing an increasing role in postpandemic economic recovery and climate action plans.However,their performance,cost,and durability are significantly related to Pt-based electro...Proton exchange membrane fuel cells are playing an increasing role in postpandemic economic recovery and climate action plans.However,their performance,cost,and durability are significantly related to Pt-based electrocatalysts,hampering their large-scale commercial application.Hence,considerable efforts have been devoted to improving the activity and durability of Pt-based electrocatalysts by controlled synthesis in recent years as an effective method for decreasing Pt use,and consequently,the cost.Therefore,this review article focuses on the synthesis processes of carbon-supported Pt-based electrocatalysts,which significantly affect the nanoparticle size,shape,and dispersion on supports and thus the activity and durability of the prepared electrocatalysts.The reviewed processes include(i)the functionalization of a commercial carbon support for enhanced catalyst-support interaction and additional catalytic effects,(ii)the methods for loading Pt-based electrocatalysts onto a carbon support that impact the manufacturing costs of electrocatalysts,(iii)the preparation of spheri-cal and nonspherical Pt-based electrocatalysts(polyhedrons,nanocages,nanoframes,one-and two-dimensional nanostruc-tures),and(iv)the postsynthesis treatments of supported electrocatalysts.The influences of the supports,key experimental parameters,and postsynthesis treatments on Pt-based electrocatalysts are scrutinized in detail.Future research directions are outlined,including(i)the full exploitation of the potential functionalization of commercial carbon supports,(ii)scaled-up one-pot synthesis of carbon-supported Pt-based electrocatalysts,and(iii)simplification of postsynthesis treatments.One-pot synthesis in aqueous instead of organic reaction systems and the minimal use of organic ligands are preferred to simplify the synthesis and postsynthesis treatment processes and to promote the mass production of commercial carbon-supported Pt-based electrocatalysts.展开更多
This paper introduced a kind of functions associated with spherically convex sets and discussed their basic properties.Finally,it proved the spherical convexity/concavity of these functions in lower dimensional cases,...This paper introduced a kind of functions associated with spherically convex sets and discussed their basic properties.Finally,it proved the spherical convexity/concavity of these functions in lower dimensional cases,which provides useful information for the essential characteristics of these functions determining spherically convex sets.The results obtained here are helpful in setting up a systematic spherical convexity theory.展开更多
In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further,...In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further, we prove the existence of admissibletrajectories for evolution inclusions. Then, we extend the Fillipov's selection theoremand discuss a general Lagrange type optimal control problem. Finally, we present anexample that demonstrates the appplicability of our results.展开更多
For the p-harmonic function with strictly convex level sets,we find an auxiliary function which comes from the combination of the norm of gradient of the p-harmonic function and the Gaussian curvature of the level set...For the p-harmonic function with strictly convex level sets,we find an auxiliary function which comes from the combination of the norm of gradient of the p-harmonic function and the Gaussian curvature of the level sets of p-harmonic function.We prove that this curvature function is concave with respect to the height of the p-harmonic function.This auxiliary function is an affine function of the height when the p-harmonic function is the p-Green function on ball.展开更多
In this paper, we construct and discuss some plurisubharmonic functions of positively homogeneous of oder ρ and some weight system, which will be used in the study of the solution of Dirichlet problem for the com...In this paper, we construct and discuss some plurisubharmonic functions of positively homogeneous of oder ρ and some weight system, which will be used in the study of the solution of Dirichlet problem for the complex Monge\|Ampère equations and the Division problem in spaces of entire function.展开更多
In this article,we use some analytic and geometric characters of the smooth points in a sphere to study the isometric extension problem in the separable or reflexive real Banach spaces.We obtain that under some condit...In this article,we use some analytic and geometric characters of the smooth points in a sphere to study the isometric extension problem in the separable or reflexive real Banach spaces.We obtain that under some condition the answer to this problem is affirmative.展开更多
This paper extends the class of generalized type I functions introduced by Aghezzaf and Hachimi（2000） to the context of higher-order case and formulate a number of higher-order duals to a non-differentiable multi-ob...This paper extends the class of generalized type I functions introduced by Aghezzaf and Hachimi（2000） to the context of higher-order case and formulate a number of higher-order duals to a non-differentiable multi-objective programming problem and establishes higher-order duality results under the higher-order generalized type I functions introduced in the present paper, A special case that appears repeatedly in the literature is that the support function is the square root of a positive semi-definite quadratic form. This and other special cases can be readily generated from these results.展开更多
Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of tile inclusion of a function in the range of an operator. Numerical examples are given to illustr...Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of tile inclusion of a function in the range of an operator. Numerical examples are given to illustrate theoretical conclusions. Alternative methods of identification of obstacles are mentioned： the Support Function Method （SFM） and the Modified Rayleigh Conjecture （MRC） method.展开更多
It is shown that the curvature function satisfies a nonlinear evolution equation under the general curve shortening flow and a detailed asymptotic behavior of the closed curves is presented when they contract to a poi...It is shown that the curvature function satisfies a nonlinear evolution equation under the general curve shortening flow and a detailed asymptotic behavior of the closed curves is presented when they contract to a point in finite time.展开更多
In this paper, by means of support functions and distance functions, we give tow criterion theorems ofset valued martingales with values in a Banach space.
基金The study procedures were approved by the Ethics Committee of the Affiliated Hospital of Jiangnan University(approval No.WXSY-YXLL-AF/SC-02/01.0).
文摘BACKGROUND An acute myocardial infarction(AMI)is often treated with direct coronary intervention and requires home-based rehabilitation.Caregivers of patients with AMI need adequate social support to maintain high-quality care;however,their social support function is low,and relevant indicators for intervention must be identified.AIM To analyze the correlation between social support for primary caregivers,their anxiety,and depression,when caring for patients with AMI after interventional therapy.METHODS Using convenience sampling,we selected 300 primary caregivers of patients with AMI who had undergone interventional therapy.The Social Support Rating Scale(SSRS),Self-Rating Anxiety Scale(SAS),and Self-Rating Depression Scale(SDS)were used to assess the primary caregivers.A Pearson’s correlation analysis was used to analyze the correlations between the SSRS,SAS,and SDS,and a multiple logistic regression analysis was used to analyze the factors influencing the low social support function of primary caregivers.The receiver operating characteristic curve and area under the curve(AUC)were used to evaluate the predictive ability of the SAS and SDS for low social support function in primary caregivers.RESULTS Considering the norm among Chinese people,AMI caregivers’objective support,subjective support,support utilization,and SSRS scores were lower,while their SAS and SDS scores were higher.The SSRS scores of female caregivers were higher than those of the male caregivers(t=2.123,P=0.035).The Pearson correlation analysis showed that objective support,subjective support,support utilization,and SSRS total scores were significantly correlated with both SAS(r=-0.414,-0.460,-0.416,-0.535)and SDS scores(r=-0.463,-0.379,-0.349,-0.472).Among the 300 AMI caregivers,56 cases(18.67%)had a low level of support function(SSRS≤22 points).Logistic regression model analysis showed that SAS and SDS were independent risk factors for low social support function of AMI caregivers,regardless of adjustment for other variables(P<0.05).SAS and SDS predicted that the AUC of AMI caregivers with low support function was 0.84,sensitivity was 67.9 and 71.4,and specificity was 84.0 and 70.9,respectively.CONCLUSION The social support function of the primary caregiver of patients with AMI after interventional therapy was lower and negatively correlated with anxiety and depression in the primary caregiver.
基金funded by the National Science Foundation of China(62006068)Hebei Natural Science Foundation(A2021402008),Natural Science Foundation of Scientific Research Project of Higher Education in Hebei Province(ZD2020185,QN2020188)333 Talent Supported Project of Hebei Province(C20221026).
文摘Imbalanced datasets are common in practical applications,and oversampling methods using fuzzy rules have been shown to enhance the classification performance of imbalanced data by taking into account the relationship between data attributes.However,the creation of fuzzy rules typically depends on expert knowledge,which may not fully leverage the label information in training data and may be subjective.To address this issue,a novel fuzzy rule oversampling approach is developed based on the learning vector quantization(LVQ)algorithm.In this method,the label information of the training data is utilized to determine the antecedent part of If-Then fuzzy rules by dynamically dividing attribute intervals using LVQ.Subsequently,fuzzy rules are generated and adjusted to calculate rule weights.The number of new samples to be synthesized for each rule is then computed,and samples from the minority class are synthesized based on the newly generated fuzzy rules.This results in the establishment of a fuzzy rule oversampling method based on LVQ.To evaluate the effectiveness of this method,comparative experiments are conducted on 12 publicly available imbalance datasets with five other sampling techniques in combination with the support function machine.The experimental results demonstrate that the proposed method can significantly enhance the classification algorithm across seven performance indicators,including a boost of 2.15%to 12.34%in Accuracy,6.11%to 27.06%in G-mean,and 4.69%to 18.78%in AUC.These show that the proposed method is capable of more efficiently improving the classification performance of imbalanced data.
基金Supported by the Research Institute of Fundamental Sciences, Tabriz, Iran.
文摘In this paper we show that the unit ball of an infinite dimensional commutative C-algebra lacks strongly exposed points, so they have no predual. Also in the second part, we use the concept of strongly exposed points in the Frechet differentiability of support convex functions.
基金supported by the Special Funds of the National Natural Science Foundation of China(No.51227003)the National Natural Science Foundation of China(No.51074166)the Universities Natural Science Research Project of Jiangsu Province(No.11kjd13002)
文摘Mechanical model of anchorage surrounding rock considering tray effect was established based on elastic theory,in order to study the mechanism of bolt supporting.Elastic solutions of normal force at point in the interior of a semi-infnite solid were obtained by means of classical displacement function method in elasticity.The factors which influence stress of bolted surrounding rock,such as the length of bolt and tray effect,were analyzed.The absolute value of stress along bolt axes decreased rapidly with an increase in radical distance and the maximum appeared near ends of bolt.With increasing radical distance,the value of radical stress changed from positive to negative roughly and then increased to zero,with maximum at the middle of bolt.The evolution of hoop stress as radical distance increasing was similar with stress along bolt axes.With an increase in depth,the radical effect ranges of all normal stress components were reduced.These suggest that the effect from tray on stress along bolt axes of bolted surrounding rock could be neglected,except near surface of surrounding rock.
文摘The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Frechet differentiability of the support function on the extremal points.
基金supported by the Postdoctoral Fund of Zhejiang Province,China (ZJ2022004).
文摘In this paper,we study the asymptotic behavior of a class of inverse quotient curvature flow in the anti-de Sitter-Schwarzschild manifold.We prove that under suitable convex conditions for the initial hypersurface,one can get the long-time existence for the inverse curvature flow.Moreover,we also get that the principal curvatures of the evolving hypersurface converge to 1 when t→+∞.
基金Supported by the National Natural Science Foundation of China (No.60875046)by Program for Changjiang Scholars and Innovative Research Team in University(No.IRT1109)+5 种基金the Key Project of Chinese Ministry of Education (No.209029)the Program for Liaoning Excellent Talents in University(No.LR201003)the Program for Liaoning Science and Technology Research in University (No.LS2010008,2009S008,2009S009,LS2010179)the Program for Liaoning Innovative Research Team in University(Nos.2009T005,LT2010005,LT2011018)Natural Science Foundation of Liaoning Province (201102008)by "Liaoning BaiQianWan Talents Program(2010921010,2011921009)"
文摘Compactly supported radial basis function can enable the coefficient matrix of solving weigh linear system to have a sparse banded structure, thereby reducing the complexity of the algorithm. Firstly, based on the compactly supported radial basis function, the paper makes the complex quadratic function （Multiquadric, MQ for short） to be transformed and proposes a class of compactly supported MQ function. Secondly, the paper describes a method that interpolates discrete motion capture data to solve the motion vectors of the interpolation points and they are used in facial expression reconstruction. Finally, according to this characteris- tic of the uneven distribution of the face markers, the markers are numbered and grouped in accordance with the density level, and then be interpolated in line with each group. The approach not only ensures the accuracy of the deformation of face local area and smoothness, but also reduces the time complexity of computing.
基金Supported in part by the National Natural Science Foundation of China(No.60073012),Natural Science Foundation of Jiangsu(BK2001004)
文摘In this letter, on the basis of Frequent Pattern(FP) tree, the support function to update FP-tree is introduced, then an Incremental FP (IFP) algorithm for mining association rules is proposed. IFP algorithm considers not only adding new data into the database but also reducing old data from the database. Furthermore, it can predigest five cases to three cases.The algorithm proposed in this letter can avoid generating lots of candidate items, and it is high efficient.
文摘Coronavirus disease 2019(COVID-19)is a highly contagious disease and a serious threat to human health.COVID-19 can cause multiple organ dysfunction,such as respiratory and circulatory failure,liver and kidney injury,disseminated intravascular coagulation,and thromboembolism,and even death.The World Health Organization reports that the mortality rate of severe-type COVID-19 is over 50%.Currently,the number of severe cases worldwide has increased rapidly,but the experience in the treatment of infected patients is still limited.Given the lack of specific antiviral drugs,multi-organ function support treatment is important for patients with COVID-19.To improve the cure rate and reduce the mortality of patients with severe-and critical-type COVID-19,this paper summarizes the experience of organ function support in patients with severe-and criticaltype COVID-19 in Optical Valley Branch of Tongji Hospital,Wuhan,China.This paper systematically summarizes the procedures of functional support therapies for multiple organs and systems,including respiratory,circulatory,renal,hepatic,and hematological systems,among patients with severe-and critical-type COVID-19.This paper provides a clinical reference and a new strategy for the optimal treatment of COVID-19 worldwide.
基金the Natural Sciences and Engineering Research Council of Canada(NSERC)via CRD Grant No.CRDPJ 522410-17a Discovery Grant from the Canadian Urban Transit Research&Innovation Consortium(CUTRIC)via Project No.160028Ballard Power Systems Inc.via Project No.SRA#077701.
文摘Proton exchange membrane fuel cells are playing an increasing role in postpandemic economic recovery and climate action plans.However,their performance,cost,and durability are significantly related to Pt-based electrocatalysts,hampering their large-scale commercial application.Hence,considerable efforts have been devoted to improving the activity and durability of Pt-based electrocatalysts by controlled synthesis in recent years as an effective method for decreasing Pt use,and consequently,the cost.Therefore,this review article focuses on the synthesis processes of carbon-supported Pt-based electrocatalysts,which significantly affect the nanoparticle size,shape,and dispersion on supports and thus the activity and durability of the prepared electrocatalysts.The reviewed processes include(i)the functionalization of a commercial carbon support for enhanced catalyst-support interaction and additional catalytic effects,(ii)the methods for loading Pt-based electrocatalysts onto a carbon support that impact the manufacturing costs of electrocatalysts,(iii)the preparation of spheri-cal and nonspherical Pt-based electrocatalysts(polyhedrons,nanocages,nanoframes,one-and two-dimensional nanostruc-tures),and(iv)the postsynthesis treatments of supported electrocatalysts.The influences of the supports,key experimental parameters,and postsynthesis treatments on Pt-based electrocatalysts are scrutinized in detail.Future research directions are outlined,including(i)the full exploitation of the potential functionalization of commercial carbon supports,(ii)scaled-up one-pot synthesis of carbon-supported Pt-based electrocatalysts,and(iii)simplification of postsynthesis treatments.One-pot synthesis in aqueous instead of organic reaction systems and the minimal use of organic ligands are preferred to simplify the synthesis and postsynthesis treatment processes and to promote the mass production of commercial carbon-supported Pt-based electrocatalysts.
文摘This paper introduced a kind of functions associated with spherically convex sets and discussed their basic properties.Finally,it proved the spherical convexity/concavity of these functions in lower dimensional cases,which provides useful information for the essential characteristics of these functions determining spherically convex sets.The results obtained here are helpful in setting up a systematic spherical convexity theory.
基金Supported by the Natural Science Foundation of Guizhou university(200101007)
文摘In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further, we prove the existence of admissibletrajectories for evolution inclusions. Then, we extend the Fillipov's selection theoremand discuss a general Lagrange type optimal control problem. Finally, we present anexample that demonstrates the appplicability of our results.
基金Research of the first author was supported by NSFC and Wu Wen-Tsun Key Laboratory of Mathematics.We finished this paper in the winter of 2009 as a part of the thesis of the second author in University of Science and Technology of China.
文摘For the p-harmonic function with strictly convex level sets,we find an auxiliary function which comes from the combination of the norm of gradient of the p-harmonic function and the Gaussian curvature of the level sets of p-harmonic function.We prove that this curvature function is concave with respect to the height of the p-harmonic function.This auxiliary function is an affine function of the height when the p-harmonic function is the p-Green function on ball.
文摘In this paper, we construct and discuss some plurisubharmonic functions of positively homogeneous of oder ρ and some weight system, which will be used in the study of the solution of Dirichlet problem for the complex Monge\|Ampère equations and the Division problem in spaces of entire function.
基金Supported by National Natural Science Foundation of China(Grant No.11371201)
文摘In this article,we use some analytic and geometric characters of the smooth points in a sphere to study the isometric extension problem in the separable or reflexive real Banach spaces.We obtain that under some condition the answer to this problem is affirmative.
文摘This paper extends the class of generalized type I functions introduced by Aghezzaf and Hachimi（2000） to the context of higher-order case and formulate a number of higher-order duals to a non-differentiable multi-objective programming problem and establishes higher-order duality results under the higher-order generalized type I functions introduced in the present paper, A special case that appears repeatedly in the literature is that the support function is the square root of a positive semi-definite quadratic form. This and other special cases can be readily generated from these results.
文摘Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of tile inclusion of a function in the range of an operator. Numerical examples are given to illustrate theoretical conclusions. Alternative methods of identification of obstacles are mentioned： the Support Function Method （SFM） and the Modified Rayleigh Conjecture （MRC） method.
基金Supported by NatiOnal Natural Science Foundation of China （Grant No. 10671022） and Doctoral Programme Foundation of Institute of Higher Education of China （Grant No. 20060027023）
文摘It is shown that the curvature function satisfies a nonlinear evolution equation under the general curve shortening flow and a detailed asymptotic behavior of the closed curves is presented when they contract to a point in finite time.
文摘In this paper, by means of support functions and distance functions, we give tow criterion theorems ofset valued martingales with values in a Banach space.
