In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equation...In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed here that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax mean square or guaranteed estimates. We establish that the minimax mean square estimates are expressed via solutions of some systems of differential equations of special type and determine estimation errors.展开更多
This paper studies the initial boundary problems for semilinear strictly hyperbolic second-order equations with discontinuous data. Under the uniform Lopatinski boundary condition, the local existence theorem of disco...This paper studies the initial boundary problems for semilinear strictly hyperbolic second-order equations with discontinuous data. Under the uniform Lopatinski boundary condition, the local existence theorem of discontinuous solutions and the structure of singularities of the solutions are obtained.展开更多
分析了多类支持向量数据描述(support vector data description,SVDD)算法存在的问题,提出一种新的不平衡数据v-NSVDD多分类算法.该方法借鉴了v-SVM方法以及带有负类的SVDD的思想,并基于不同类别样本间隔最大原理,较好地克服噪声和在野...分析了多类支持向量数据描述(support vector data description,SVDD)算法存在的问题,提出一种新的不平衡数据v-NSVDD多分类算法.该方法借鉴了v-SVM方法以及带有负类的SVDD的思想,并基于不同类别样本间隔最大原理,较好地克服噪声和在野点的影响,提高了分类模型的泛化性能;通过样本加权的方法解决了不平衡类别样本预测精度低的问题,并在理论上给出了根据类别样本数量设置样本加权系数的方法.针对实际应用存在大量复杂、非线性分类数据,通过核方法把上述线性分类算法推广到非线性数据分类情形.由于现有的多分类器无法实现拒判,而且每个分类器的核函数参数不同,导致数据点与各个超球中心距离的计算结果与实际距离不相符,影响了数据判决结果的准确性和可靠性.针对上述问题,给出基于相对距离和K-NN规则相结合的多分类方法,提高了分类结果的准确性和可靠性.使用Benchmark数据集进行仿真实验,结果表明本算法能够获得较低的分类误差,能够有效处理样本不平衡问题.展开更多
In this article, our proposed kernel estimator, named as Gumbel kernel, which broadened the class of non-negative, asymmetric kernel density estimators. Such kernel estimator can be used in nonparametric estimation of...In this article, our proposed kernel estimator, named as Gumbel kernel, which broadened the class of non-negative, asymmetric kernel density estimators. Such kernel estimator can be used in nonparametric estimation of the probability density function (</span><i><span style="font-family:Verdana;">pdf</span></i><span style="font-family:Verdana;">). When the density functions have limited bounded support on [0, ∞) and they are liberated of boundary bias, always non-negative and obtain the optimal rate of convergence for the mean integrated squared error (MISE). The bias, variance and the optimal bandwidth of the proposed estimators are investigated on theoretical grounds as well as on simulation basis. Further, the applicability of the proposed estimator is compared to Weibul</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">l</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> kernel estimator, where performance of newly proposed kernel is outstanding.展开更多
For plate bending and stretching problems in piezoelectric materials,the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate mixed boundary conditions ac...For plate bending and stretching problems in piezoelectric materials,the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate mixed boundary conditions accurate to all order.A decay analysis technique is used to establish necessary conditions that the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate.For the case of axisymmetric bending and stretching of a circular plate,these decaying state conditions are obtained explicitly for the first time when the mixed conditions are imposed on the plate edge.They are then used for the correct formulation of boundary conditions for the interior solution.展开更多
文摘In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed here that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax mean square or guaranteed estimates. We establish that the minimax mean square estimates are expressed via solutions of some systems of differential equations of special type and determine estimation errors.
基金Research supported by the Natural Science Foundation of Fujian Province, China.
文摘This paper studies the initial boundary problems for semilinear strictly hyperbolic second-order equations with discontinuous data. Under the uniform Lopatinski boundary condition, the local existence theorem of discontinuous solutions and the structure of singularities of the solutions are obtained.
文摘分析了多类支持向量数据描述(support vector data description,SVDD)算法存在的问题,提出一种新的不平衡数据v-NSVDD多分类算法.该方法借鉴了v-SVM方法以及带有负类的SVDD的思想,并基于不同类别样本间隔最大原理,较好地克服噪声和在野点的影响,提高了分类模型的泛化性能;通过样本加权的方法解决了不平衡类别样本预测精度低的问题,并在理论上给出了根据类别样本数量设置样本加权系数的方法.针对实际应用存在大量复杂、非线性分类数据,通过核方法把上述线性分类算法推广到非线性数据分类情形.由于现有的多分类器无法实现拒判,而且每个分类器的核函数参数不同,导致数据点与各个超球中心距离的计算结果与实际距离不相符,影响了数据判决结果的准确性和可靠性.针对上述问题,给出基于相对距离和K-NN规则相结合的多分类方法,提高了分类结果的准确性和可靠性.使用Benchmark数据集进行仿真实验,结果表明本算法能够获得较低的分类误差,能够有效处理样本不平衡问题.
文摘In this article, our proposed kernel estimator, named as Gumbel kernel, which broadened the class of non-negative, asymmetric kernel density estimators. Such kernel estimator can be used in nonparametric estimation of the probability density function (</span><i><span style="font-family:Verdana;">pdf</span></i><span style="font-family:Verdana;">). When the density functions have limited bounded support on [0, ∞) and they are liberated of boundary bias, always non-negative and obtain the optimal rate of convergence for the mean integrated squared error (MISE). The bias, variance and the optimal bandwidth of the proposed estimators are investigated on theoretical grounds as well as on simulation basis. Further, the applicability of the proposed estimator is compared to Weibul</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">l</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> kernel estimator, where performance of newly proposed kernel is outstanding.
基金Supported by the National Natural Science Foundation of China(Grant Nos.10702077and 10602001)the Beijing Natural Science Foundation(Grant No.1083012)the Alexander von Humboldt Foundation in Germany
文摘For plate bending and stretching problems in piezoelectric materials,the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate mixed boundary conditions accurate to all order.A decay analysis technique is used to establish necessary conditions that the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate.For the case of axisymmetric bending and stretching of a circular plate,these decaying state conditions are obtained explicitly for the first time when the mixed conditions are imposed on the plate edge.They are then used for the correct formulation of boundary conditions for the interior solution.
