Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of divisio...Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of division tends to zero. Moreover, this result can be strengthen to yield the quasi sure convergence of sums by estimating the speed of the convergence.展开更多
The purpose of this paper is to make a further study on the abstract economy. Here, for the constraint correspondences we assume that they are almost lower semi-continuous (n-lower semi-continuous), which is weaken th...The purpose of this paper is to make a further study on the abstract economy. Here, for the constraint correspondences we assume that they are almost lower semi-continuous (n-lower semi-continuous), which is weaken than that they are lower semi-continuous. Several equilibria existence theorems are proved.展开更多
Let (X,d) be a real metric linear space, with translation-invariant metric d and C a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best...Let (X,d) be a real metric linear space, with translation-invariant metric d and C a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best approximations to elements of X.We also give simultaneous characterization of elements of best approximation and also consider elements of ε-approximation.展开更多
The problem of the blind demodulation of multiuser information symbols in ahigh-rate Code Division Multiple Access (CDMA) network in the presence of InterSymbol Interference(ISI) is of considerable interest. The dispe...The problem of the blind demodulation of multiuser information symbols in ahigh-rate Code Division Multiple Access (CDMA) network in the presence of InterSymbol Interference(ISI) is of considerable interest. The dispersive CDMA channel is first cast into a Multiple-InputMultiple-Out (MIMO) signal model framework. Then , the problem of the blind channel equalization andmultiuser detection is considered. In this paper, we formulate the problem of blind channelestimation and signal detection into a quadratic programming with binary constraints. Then, theefficient ε-approximation algorithms are presented and applied to find the solution to thequadratic programming. The proposed approach does not estimate the channel directly or rely on anystatistics . Simulation results support our theoretical analysis .展开更多
In this paper,a nonlinear time-fractional coupled diffusion system is solved by using a mixed finite element(MFE)method in space combined with L1-approximation and implicit second-order backward difference scheme in t...In this paper,a nonlinear time-fractional coupled diffusion system is solved by using a mixed finite element(MFE)method in space combined with L1-approximation and implicit second-order backward difference scheme in time.The stability for nonlinear fully discrete finite element scheme is analyzed and a priori error estimates are derived.Finally,some numerical tests are shown to verify our theoretical analysis.展开更多
On the basis of primal-dual approach, we present in this paper an interior point method that gives parametric E-approximate solutions to parametric semi-definite programming problems. The method is finite, and the num...On the basis of primal-dual approach, we present in this paper an interior point method that gives parametric E-approximate solutions to parametric semi-definite programming problems. The method is finite, and the number of its iterations is quasi-polynomially bounded.展开更多
For several decades,much attention has been paid to the two-sample Behrens-Fisher(BF) problem which tests the equality of the means or mean vectors of two normal populations with unequal variance/covariance structures...For several decades,much attention has been paid to the two-sample Behrens-Fisher(BF) problem which tests the equality of the means or mean vectors of two normal populations with unequal variance/covariance structures.Little work,however,has been done for the k-sample BF problem for high dimensional data which tests the equality of the mean vectors of several high-dimensional normal populations with unequal covariance structures.In this paper we study this challenging problem via extending the famous Scheffe's transformation method,which reduces the k-sample BF problem to a one-sample problem.The induced one-sample problem can be easily tested by the classical Hotelling's T 2 test when the size of the resulting sample is very large relative to its dimensionality.For high dimensional data,however,the dimensionality of the resulting sample is often very large,and even much larger than its sample size,which makes the classical Hotelling's T 2 test not powerful or not even well defined.To overcome this diffculty,we propose and study an L2-norm based test.The asymp-totic powers of the proposed L2-norm based test and Hotelling's T 2 test are derived and theoretically compared.Methods for implementing the L2-norm based test are described.Simulation studies are conducted to compare the L2-norm based test and Hotelling's T 2 test when the latter can be well defined,and to compare the proposed implementation methods for the L2-norm based test otherwise.The methodologies are motivated and illustrated by a real data example.展开更多
文摘Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of division tends to zero. Moreover, this result can be strengthen to yield the quasi sure convergence of sums by estimating the speed of the convergence.
文摘The purpose of this paper is to make a further study on the abstract economy. Here, for the constraint correspondences we assume that they are almost lower semi-continuous (n-lower semi-continuous), which is weaken than that they are lower semi-continuous. Several equilibria existence theorems are proved.
文摘Let (X,d) be a real metric linear space, with translation-invariant metric d and C a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best approximations to elements of X.We also give simultaneous characterization of elements of best approximation and also consider elements of ε-approximation.
文摘The problem of the blind demodulation of multiuser information symbols in ahigh-rate Code Division Multiple Access (CDMA) network in the presence of InterSymbol Interference(ISI) is of considerable interest. The dispersive CDMA channel is first cast into a Multiple-InputMultiple-Out (MIMO) signal model framework. Then , the problem of the blind channel equalization andmultiuser detection is considered. In this paper, we formulate the problem of blind channelestimation and signal detection into a quadratic programming with binary constraints. Then, theefficient ε-approximation algorithms are presented and applied to find the solution to thequadratic programming. The proposed approach does not estimate the channel directly or rely on anystatistics . Simulation results support our theoretical analysis .
基金the National Natural Science Fund(11661058,11301258,11361035)the Natural Science Fund of Inner Mongolia Autonomous Region(2016MS0102,2015MS0101)+1 种基金the Scientific Research Projection of Higher Schools of Inner Mongolia(NJZZ12011)the National Undergraduate Innovative Training Project(201510126026).
文摘In this paper,a nonlinear time-fractional coupled diffusion system is solved by using a mixed finite element(MFE)method in space combined with L1-approximation and implicit second-order backward difference scheme in time.The stability for nonlinear fully discrete finite element scheme is analyzed and a priori error estimates are derived.Finally,some numerical tests are shown to verify our theoretical analysis.
基金the National Natural Science Foundation of China!19871016
文摘On the basis of primal-dual approach, we present in this paper an interior point method that gives parametric E-approximate solutions to parametric semi-definite programming problems. The method is finite, and the number of its iterations is quasi-polynomially bounded.
基金supported by the National University of Singapore Academic Research Grant (Grant No. R-155-000-085-112)
文摘For several decades,much attention has been paid to the two-sample Behrens-Fisher(BF) problem which tests the equality of the means or mean vectors of two normal populations with unequal variance/covariance structures.Little work,however,has been done for the k-sample BF problem for high dimensional data which tests the equality of the mean vectors of several high-dimensional normal populations with unequal covariance structures.In this paper we study this challenging problem via extending the famous Scheffe's transformation method,which reduces the k-sample BF problem to a one-sample problem.The induced one-sample problem can be easily tested by the classical Hotelling's T 2 test when the size of the resulting sample is very large relative to its dimensionality.For high dimensional data,however,the dimensionality of the resulting sample is often very large,and even much larger than its sample size,which makes the classical Hotelling's T 2 test not powerful or not even well defined.To overcome this diffculty,we propose and study an L2-norm based test.The asymp-totic powers of the proposed L2-norm based test and Hotelling's T 2 test are derived and theoretically compared.Methods for implementing the L2-norm based test are described.Simulation studies are conducted to compare the L2-norm based test and Hotelling's T 2 test when the latter can be well defined,and to compare the proposed implementation methods for the L2-norm based test otherwise.The methodologies are motivated and illustrated by a real data example.
