In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where ...In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where △p is the p-Laplacian operator, 1 〈 p 〈 N, M ： R＋ → R＋ and V ： RN →R＋ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik- Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.展开更多
The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exac...The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.展开更多
In this paper,we study a class of mean-reflected backward doubly stochastic differential equations(MR-BDSDEs),where the constraint depends on the law of the solution and not on its paths.The existence and uniqueness o...In this paper,we study a class of mean-reflected backward doubly stochastic differential equations(MR-BDSDEs),where the constraint depends on the law of the solution and not on its paths.The existence and uniqueness of these solutions were established.The penalization method plays an important role.We also provided a probabilistic interpretation of the classical solutions of the mean-reflected stochastic partial differential equations(MR-SPDEs)in terms of MR-BDSDEs.展开更多
We present an energy penalization method for isogeometric topology optimization using moving morphable components(ITO–MMC),propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetr...We present an energy penalization method for isogeometric topology optimization using moving morphable components(ITO–MMC),propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetric structures,and then extend the proposed energy penalization method to an ITO–MMC with a symmetric constraint.The energy penalization method can solve the problems of numerical instability and convergence for the ITO–MMC and the ITO–MMC subjected to the structural symmetric constraint with asymmetric loads.Topology optimization problems of asymmetric,bilateral symmetric,and periodic symmetric structures are discussed to validate the effectiveness of the proposed energy penalization approach.Compared with the conventional ITO–MMC,the energy penalization method for the ITO–MMC can improve the convergence rate from 18.6%to 44.5%for the optimization of the asymmetric structure.For the ITO–MMC under a bilateral symmetric constraint,the proposed method can reduce the objective value by 5.6%and obtain a final optimized topology that has a clear boundary with decreased iterations.For the ITO–MMC under a periodic symmetric constraint,the proposed energy penalization method can dramatically reduce the number of iterations and obtain a speedup of more than 2.展开更多
AIM:To compare the efficacies of patching and penalization therapies for the treatment of amblyopia patients.METHODS:The records of 64 eyes of 50 patients 7 to16y of age who had presented to our clinics with a diagnos...AIM:To compare the efficacies of patching and penalization therapies for the treatment of amblyopia patients.METHODS:The records of 64 eyes of 50 patients 7 to16y of age who had presented to our clinics with a diagnosis of amblyopia,were evaluated retrospectively.Forty eyes of 26 patients who had received patching therapy and 24 eyes of 24 patients who had received penalization therapy included in this study.The latencies and amplitudes of visual evoked potential(VEP)records and best corrected visual acuities(BCVA)of these two groups were compared before and six months after the treatment.RESULTS:In both patching and the penalization groups,the visual acuities increased significantly following the treatments(P【0.05).The latency measurements of the P100 wave obtained at 1.0°,15 arc min.Patterns of both groups significantly decreased following the 6-months-treatment.However,the amplitude measurements increased(P【0.05).CONCLUSION:The patching and the penalization methods,which are the main methods used in the treatment of amblyopia,were also effective over the age of 7y,which has been accepted as the critical age for the treatment of amblyopia.展开更多
For the purpose of achieving high-resolution optimal solutions this paper proposes a nodal design variablebased adaptive method for topology optimization of continuum structures. The analysis mesh-independent density ...For the purpose of achieving high-resolution optimal solutions this paper proposes a nodal design variablebased adaptive method for topology optimization of continuum structures. The analysis mesh-independent density field, interpolated by the nodal design variables at a given set of density points, is adaptively refined/coarsened accord- ing to a criterion regarding the gray-scale measure of local regions. New density points are added into the gray regions and redundant ones are removed from the regions occupied by purely solid/void phases for decreasing the number of de- sign variables. A penalization factor adaptivity technique is employed-to prevent premature convergence of the optimiza- tion iterations. Such an adaptive scheme not only improves the structural boundary description quality, but also allows for sufficient further topological evolution of the structural layout in higher adaptivity levels and thus essentially enables high-resolution solutions. Moreover, compared with the case with uniformly and finely distributed density points, the proposed adaptive method can achieve a higher numerical efficiency of the optimization process.展开更多
In this puper, we consider the problem of variabie selection and model detection in varying coefficient models with longitudinM data. We propose a combined penalization procedure to select the significant variables, d...In this puper, we consider the problem of variabie selection and model detection in varying coefficient models with longitudinM data. We propose a combined penalization procedure to select the significant variables, detect the true structure of the model and estimate the unknown regression coefficients simultaneously. With appropriate selection of the tuning parameters, we show that the proposed procedure is consistent in both variable selection and the separation of varying and constant coefficients, and the penalized estimators have the oracle property. Finite sample performances of the proposed method are illustrated by some simulation studies and the real data analysis.展开更多
Background:To date,compliance to atropine penalization in amblyopic children has only been assessed through self-report.The goal of this pilot study is to measure compliance to atropine penalization objectively.Method...Background:To date,compliance to atropine penalization in amblyopic children has only been assessed through self-report.The goal of this pilot study is to measure compliance to atropine penalization objectively.Methods:Seven amblyopic children(3-8 years;20/40-20/125 in the amblyopic eye) were enrolled.None had been treated with atropine previously.Children were prescribed either a twice per week or daily atropine regimen by their physicians.Compliance was defined as the percentage of days in which the atropine eye drop was taken compared to the number of doses prescribed.We used medication event monitoring system(MEMS) caps to objectively measure compliance.The MEMS caps are designed to electronically record the time and date when the bottle is opened.The parents of the children were provided a calendar log to subjectively report compliance.Participants were scheduled for return visits at 4 and 12 weeks.Weekly compliance was analyzed.Results:At 4 weeks,objective compliance averaged 88%(range,57-100%),while subjective compliance was 98%(range,90-100%).The actual dose in grams and visual acuity(VA) response relationship(r=0.79,P=0.03) was significantly better than the relationship between regimen and response(r=0.41,P>0.05),or the relationship between actual dose in drops and response(r=0.52,P>0.05).Conclusions:Objective compliance to atropine penalization instructions can be monitored with MEMS,which may facilitate our understanding of the dose-response relationship.Objective compliance with atropine penalization decreases over time and varies with regimen.On average,subjective parental reporting of compliance is overestimated.展开更多
We give an existence result of the obstacle parabolic equations3b（x,u） div（a（x,t,u, Vu））＋div（（x,t,u））=f in QT, 3twhere b（x,u） is bounded function ot u, the term atva,x,r,u, v u）） is a Letay type operat...We give an existence result of the obstacle parabolic equations3b（x,u） div（a（x,t,u, Vu））＋div（（x,t,u））=f in QT, 3twhere b（x,u） is bounded function ot u, the term atva,x,r,u, v u）） is a Letay type operator and the function is a nonlinear lower order and satisfy only the growth condition. The second term belongs to L1 （QT）. The proof of an existence solution is based on the penalization methods.展开更多
基金supported by Natural Science Foundation of China(11371159 and 11771166)Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT_17R46
文摘In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of SchrSdinger-Kirchhoff type -εpM（εp-N∫RN｜△u｜p）△pu＋v（x｜u｜p-2u=f（u）in RN, where △p is the p-Laplacian operator, 1 〈 p 〈 N, M ： R＋ → R＋ and V ： RN →R＋ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik- Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.
文摘The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.
文摘In this paper,we study a class of mean-reflected backward doubly stochastic differential equations(MR-BDSDEs),where the constraint depends on the law of the solution and not on its paths.The existence and uniqueness of these solutions were established.The penalization method plays an important role.We also provided a probabilistic interpretation of the classical solutions of the mean-reflected stochastic partial differential equations(MR-SPDEs)in terms of MR-BDSDEs.
基金This research was supported by the National Natural Science Foundation of China(Grant Nos.51675197 and 51705158)the National Engineering Research Center of Near-Net-Shape Forming for Metallic Materials,Ministry of Education Key Laboratory of High Efficient Near-Net-Shape Forming Technology and Equipment for Metallic Materials(Category B)Opening Foundation(Grant No.2018005)The support is gratefully acknowledged.
文摘We present an energy penalization method for isogeometric topology optimization using moving morphable components(ITO–MMC),propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetric structures,and then extend the proposed energy penalization method to an ITO–MMC with a symmetric constraint.The energy penalization method can solve the problems of numerical instability and convergence for the ITO–MMC and the ITO–MMC subjected to the structural symmetric constraint with asymmetric loads.Topology optimization problems of asymmetric,bilateral symmetric,and periodic symmetric structures are discussed to validate the effectiveness of the proposed energy penalization approach.Compared with the conventional ITO–MMC,the energy penalization method for the ITO–MMC can improve the convergence rate from 18.6%to 44.5%for the optimization of the asymmetric structure.For the ITO–MMC under a bilateral symmetric constraint,the proposed method can reduce the objective value by 5.6%and obtain a final optimized topology that has a clear boundary with decreased iterations.For the ITO–MMC under a periodic symmetric constraint,the proposed energy penalization method can dramatically reduce the number of iterations and obtain a speedup of more than 2.
文摘AIM:To compare the efficacies of patching and penalization therapies for the treatment of amblyopia patients.METHODS:The records of 64 eyes of 50 patients 7 to16y of age who had presented to our clinics with a diagnosis of amblyopia,were evaluated retrospectively.Forty eyes of 26 patients who had received patching therapy and 24 eyes of 24 patients who had received penalization therapy included in this study.The latencies and amplitudes of visual evoked potential(VEP)records and best corrected visual acuities(BCVA)of these two groups were compared before and six months after the treatment.RESULTS:In both patching and the penalization groups,the visual acuities increased significantly following the treatments(P【0.05).The latency measurements of the P100 wave obtained at 1.0°,15 arc min.Patterns of both groups significantly decreased following the 6-months-treatment.However,the amplitude measurements increased(P【0.05).CONCLUSION:The patching and the penalization methods,which are the main methods used in the treatment of amblyopia,were also effective over the age of 7y,which has been accepted as the critical age for the treatment of amblyopia.
基金supported by the Key Project of Chinese National Programs for Fundamental Research and Development(2010CB832703)the National Natural Science Foundation of China(11072047 and 91130025)
文摘For the purpose of achieving high-resolution optimal solutions this paper proposes a nodal design variablebased adaptive method for topology optimization of continuum structures. The analysis mesh-independent density field, interpolated by the nodal design variables at a given set of density points, is adaptively refined/coarsened accord- ing to a criterion regarding the gray-scale measure of local regions. New density points are added into the gray regions and redundant ones are removed from the regions occupied by purely solid/void phases for decreasing the number of de- sign variables. A penalization factor adaptivity technique is employed-to prevent premature convergence of the optimiza- tion iterations. Such an adaptive scheme not only improves the structural boundary description quality, but also allows for sufficient further topological evolution of the structural layout in higher adaptivity levels and thus essentially enables high-resolution solutions. Moreover, compared with the case with uniformly and finely distributed density points, the proposed adaptive method can achieve a higher numerical efficiency of the optimization process.
基金Supported by National Natural Science Foundation of China(Grant Nos.11501522,11101014,11001118 and11171012)National Statistical Research Projects(Grant No.2014LZ45)+2 种基金the Doctoral Fund of Innovation of Beijing University of Technologythe Science and Technology Project of the Faculty Adviser of Excellent PhD Degree Thesis of Beijing(Grant No.20111000503)the Beijing Municipal Education Commission Foundation(Grant No.KM201110005029)
文摘In this puper, we consider the problem of variabie selection and model detection in varying coefficient models with longitudinM data. We propose a combined penalization procedure to select the significant variables, detect the true structure of the model and estimate the unknown regression coefficients simultaneously. With appropriate selection of the tuning parameters, we show that the proposed procedure is consistent in both variable selection and the separation of varying and constant coefficients, and the penalized estimators have the oracle property. Finite sample performances of the proposed method are illustrated by some simulation studies and the real data analysis.
基金supported by a pilot grant from Indiana Clinical and Translational Sciences Institute Project Development Teams(PDT) to J Wanga Research to Prevent Blindness(RPB) unrestricted grant to the Glick Eye Institute at Indiana University
文摘Background:To date,compliance to atropine penalization in amblyopic children has only been assessed through self-report.The goal of this pilot study is to measure compliance to atropine penalization objectively.Methods:Seven amblyopic children(3-8 years;20/40-20/125 in the amblyopic eye) were enrolled.None had been treated with atropine previously.Children were prescribed either a twice per week or daily atropine regimen by their physicians.Compliance was defined as the percentage of days in which the atropine eye drop was taken compared to the number of doses prescribed.We used medication event monitoring system(MEMS) caps to objectively measure compliance.The MEMS caps are designed to electronically record the time and date when the bottle is opened.The parents of the children were provided a calendar log to subjectively report compliance.Participants were scheduled for return visits at 4 and 12 weeks.Weekly compliance was analyzed.Results:At 4 weeks,objective compliance averaged 88%(range,57-100%),while subjective compliance was 98%(range,90-100%).The actual dose in grams and visual acuity(VA) response relationship(r=0.79,P=0.03) was significantly better than the relationship between regimen and response(r=0.41,P>0.05),or the relationship between actual dose in drops and response(r=0.52,P>0.05).Conclusions:Objective compliance to atropine penalization instructions can be monitored with MEMS,which may facilitate our understanding of the dose-response relationship.Objective compliance with atropine penalization decreases over time and varies with regimen.On average,subjective parental reporting of compliance is overestimated.
文摘We give an existence result of the obstacle parabolic equations3b（x,u） div（a（x,t,u, Vu））＋div（（x,t,u））=f in QT, 3twhere b（x,u） is bounded function ot u, the term atva,x,r,u, v u）） is a Letay type operator and the function is a nonlinear lower order and satisfy only the growth condition. The second term belongs to L1 （QT）. The proof of an existence solution is based on the penalization methods.
