In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which g...In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikantham[21 and the results obtained by Lan in [4], and [6].展开更多
In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[...In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[0,1].The process of the W-POAFD is as follows:(i)choose a dictionary and implement the pre-orthogonalization to all the dictionary elements;(ii)select points in[0,1]by the weak maximal selection principle to determine the corresponding orthonormalized dictionary elements iteratively;(iii)express the analytical solution as a linear combination of these determined dictionary elements.Convergence properties of numerical solutions are also discussed.The numerical experiments are carried out to illustrate the accuracy and efficiency of W-POAFD for solving FBVPs.展开更多
To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection techniq...To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).展开更多
Since laparoscopy was first used in cholecystectomy in 1987, it has developed quickly and has been used in most fields of traditional surgery. People have now accepted its advantages like small incision, quick recover...Since laparoscopy was first used in cholecystectomy in 1987, it has developed quickly and has been used in most fields of traditional surgery. People have now accepted its advantages like small incision, quick recovery, light pain, beauty and short hospital stays. In early times, there are still controversies about the application of laparoscopy in malignant tumor treatments, especially about the problems of oncology efficacy, incision implantation and operation security. However, these concerns have been fully eliminated by evidences on the basis of evidence-basis medicine. In recent years, new minimally invasive technologies are appearing continually, but they still have challenges and may increase the difficulties of radical dissection and the risks of potential complications, so they are confined to benign or early malignant tumors. The core value of the laparoscopic technique is to ensure the high quality of tumor's radical resection and less complications. On the basis of this, it is allowed to pursue more minimally invasive techniques. Since the development of laparoscopic colorectal surgery is rapid and unceasing, we have reasons to believe that laparoscopic surgery will become gold standard for colorectal surgery in the near future.展开更多
In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b...In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b n,n≥1} with 0<b n↑∞ ,any integer n≥1 ,there exits a constant C=C p>0 (only depending on p ) such thatP( sup j≥nji=1D ib j≥ε)≤Cε -p (∞j=n+1E‖D j‖ pb p j+nj=1E‖D j‖ pb p n) In the other direction,we prove some strong laws of large numbers and the integrability of the maximal functions for B valued random variable sequences by using this inequality and the Hajeck Renyi inequality we have obtained recently.Some known results are extended and improved.展开更多
By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential ...By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential equations in Banach spaces is proved.展开更多
The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. T...The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. This is used to give a sufficient condition of the maximal regularity in the sense of Triebel spaces for vector-valued Cauchy problems with Dirichlet boundary conditions.展开更多
Based on concave function, the problem of finding the sparse solution of absolute value equations is relaxed to a concave programming, and its corresponding algorithm is proposed, whose main part is solving a series o...Based on concave function, the problem of finding the sparse solution of absolute value equations is relaxed to a concave programming, and its corresponding algorithm is proposed, whose main part is solving a series of linear programming. It is proved that a sparse solution can be found under the assumption that the connected matrixes have range space property(RSP). Numerical experiments are also conducted to verify the efficiency of the proposed algorithm.展开更多
Cost effectiveness has been demonstrated for traditional lumbar discectomy, lumbar laminectomy as well as for instrumented and noninstrumented arthrodesis. While emerging evidence suggests that minimally invasive spin...Cost effectiveness has been demonstrated for traditional lumbar discectomy, lumbar laminectomy as well as for instrumented and noninstrumented arthrodesis. While emerging evidence suggests that minimally invasive spine surgery reduces morbidity, duration of hospitalization, and accelerates return to activites of daily living, data regarding cost effectiveness of these novel techniques is limited. The current study analyzes all available data on minimally invasive techniques for lumbar discectomy, decompression, short-segment fusion and deformity surgery. In general, minimallyinvasive spine procedures appear to hold promise in quicker patient recovery times and earlier return to work. Thus, minimally invasive lumbar spine surgery appears to have the potential to be a cost-effective intervention. Moreover, novel less invasive procedures are less destabilizing and may therefore be utilized in certain indications that traditionally required arthrodesis procedures. However, there is a lack of studies analyzing the economic impact of minimally invasive spine surgery. Future studies are necessary to confirm the durability and further define indications for minimally invasive lumbar spine procedures.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10304022,the Science-Technology Fund of Anhui Province for 0utstanding Youth under Grant No. 06042087, the General Fund of the Educational Committee of Anhui Province under Grant No. 2006KJ260B, the Key Fund of the Ministry of Education of China under Grant No. 206063. We are very grateful to Prof. Zhan-Jun Zhang for his detailed instructions and helps.
文摘In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikantham[21 and the results obtained by Lan in [4], and [6].
基金University of Macao Multi-Year Research Grant Ref.No MYRG2016-00053-FST and MYRG2018-00168-FSTthe Science and Technology Development Fund,Macao SAR FDCT/0123/2018/A3.
文摘In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[0,1].The process of the W-POAFD is as follows:(i)choose a dictionary and implement the pre-orthogonalization to all the dictionary elements;(ii)select points in[0,1]by the weak maximal selection principle to determine the corresponding orthonormalized dictionary elements iteratively;(iii)express the analytical solution as a linear combination of these determined dictionary elements.Convergence properties of numerical solutions are also discussed.The numerical experiments are carried out to illustrate the accuracy and efficiency of W-POAFD for solving FBVPs.
基金supported by the the National Science and Technology Council(Grant Number:NSTC 112-2221-E239-022).
文摘To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).
文摘Since laparoscopy was first used in cholecystectomy in 1987, it has developed quickly and has been used in most fields of traditional surgery. People have now accepted its advantages like small incision, quick recovery, light pain, beauty and short hospital stays. In early times, there are still controversies about the application of laparoscopy in malignant tumor treatments, especially about the problems of oncology efficacy, incision implantation and operation security. However, these concerns have been fully eliminated by evidences on the basis of evidence-basis medicine. In recent years, new minimally invasive technologies are appearing continually, but they still have challenges and may increase the difficulties of radical dissection and the risks of potential complications, so they are confined to benign or early malignant tumors. The core value of the laparoscopic technique is to ensure the high quality of tumor's radical resection and less complications. On the basis of this, it is allowed to pursue more minimally invasive techniques. Since the development of laparoscopic colorectal surgery is rapid and unceasing, we have reasons to believe that laparoscopic surgery will become gold standard for colorectal surgery in the near future.
文摘In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b n,n≥1} with 0<b n↑∞ ,any integer n≥1 ,there exits a constant C=C p>0 (only depending on p ) such thatP( sup j≥nji=1D ib j≥ε)≤Cε -p (∞j=n+1E‖D j‖ pb p j+nj=1E‖D j‖ pb p n) In the other direction,we prove some strong laws of large numbers and the integrability of the maximal functions for B valued random variable sequences by using this inequality and the Hajeck Renyi inequality we have obtained recently.Some known results are extended and improved.
基金theNaturalScienceFoundationofEducationalCommitteeofHainanProvince China
文摘By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential equations in Banach spaces is proved.
文摘The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. This is used to give a sufficient condition of the maximal regularity in the sense of Triebel spaces for vector-valued Cauchy problems with Dirichlet boundary conditions.
文摘Based on concave function, the problem of finding the sparse solution of absolute value equations is relaxed to a concave programming, and its corresponding algorithm is proposed, whose main part is solving a series of linear programming. It is proved that a sparse solution can be found under the assumption that the connected matrixes have range space property(RSP). Numerical experiments are also conducted to verify the efficiency of the proposed algorithm.
文摘Cost effectiveness has been demonstrated for traditional lumbar discectomy, lumbar laminectomy as well as for instrumented and noninstrumented arthrodesis. While emerging evidence suggests that minimally invasive spine surgery reduces morbidity, duration of hospitalization, and accelerates return to activites of daily living, data regarding cost effectiveness of these novel techniques is limited. The current study analyzes all available data on minimally invasive techniques for lumbar discectomy, decompression, short-segment fusion and deformity surgery. In general, minimallyinvasive spine procedures appear to hold promise in quicker patient recovery times and earlier return to work. Thus, minimally invasive lumbar spine surgery appears to have the potential to be a cost-effective intervention. Moreover, novel less invasive procedures are less destabilizing and may therefore be utilized in certain indications that traditionally required arthrodesis procedures. However, there is a lack of studies analyzing the economic impact of minimally invasive spine surgery. Future studies are necessary to confirm the durability and further define indications for minimally invasive lumbar spine procedures.
