Partial Differential Equation(PDE)is among the most fundamental tools employed to model dynamic systems.Existing PDE modeling methods are typically derived from established knowledge and known phenomena,which are time...Partial Differential Equation(PDE)is among the most fundamental tools employed to model dynamic systems.Existing PDE modeling methods are typically derived from established knowledge and known phenomena,which are time-consuming and labor-intensive.Recently,discovering governing PDEs from collected actual data via Physics Informed Neural Networks(PINNs)provides a more efficient way to analyze fresh dynamic systems and establish PEDmodels.This study proposes Sequentially Threshold Least Squares-Lasso(STLasso),a module constructed by incorporating Lasso regression into the Sequentially Threshold Least Squares(STLS)algorithm,which can complete sparse regression of PDE coefficients with the constraints of l0 norm.It further introduces PINN-STLasso,a physics informed neural network combined with Lasso sparse regression,able to find underlying PDEs from data with reduced data requirements and better interpretability.In addition,this research conducts experiments on canonical inverse PDE problems and compares the results to several recent methods.The results demonstrated that the proposed PINN-STLasso outperforms other methods,achieving lower error rates even with less data.展开更多
Precisely quantifying transition metal(TM) redox in bulk is a key to understand the fundamental of optimizing cathode materials in secondary batteries. At present, the commonly used methods to probe TM redox are hard ...Precisely quantifying transition metal(TM) redox in bulk is a key to understand the fundamental of optimizing cathode materials in secondary batteries. At present, the commonly used methods to probe TM redox are hard X-ray absorption spectroscopy(hXAS) and soft X-ray absorption spectroscopy(sXAS).However, they are both facing challenges to precisely quantify the valence states of some transition metals such as Mn. In this paper, Mn-L iPFY(inverse partial fluorescence yield) spectra extracted from Mn-L m RIXS(mapping of resonant inelastic X-ray scattering) is adopted to quantify Mn valence states. Mn-L i PFY spectra has been considered as a bulk-sensitive, non-distorted probe of TM valence states.However, the exact precision of this method is still unclear in quantifying practical battery electrodes.Herein, a series of LiMn_(2)O_(4) electrodes with different charge and discharge states are prepared. Based on their electrochemical capacity(generally considered to be very precise), the precision of Mn iPFY in quantifying bulk Mn valence state is confirmed, and the error range is unraveled. Mn-L mRIXS iPFY thus is identified as one of the best methods to quantify the bulk Mn valence state comparing with hXAS and sXAS.展开更多
In this paper,a new model for inverse network flow problems,robust partial inverse problem is presented. For a given partial solution,the robust partial inverse problem is to modify the coefficients optimally such tha...In this paper,a new model for inverse network flow problems,robust partial inverse problem is presented. For a given partial solution,the robust partial inverse problem is to modify the coefficients optimally such that all full solutions containing the partial solution become optimal under new coefficients. It has been shown that the robust partial inverse spanning tree problem can be formulated as a combinatorial linear program,while the robust partial inverse minimum cut problem and the robust partial inverse assignment problem can be solved by combinatorial strongly polynomial algorithms.展开更多
It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a right inverse semigr...It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a right inverse semigroup. We construct partial orders on S by some kind of its subsemigroups and uncover that partial orders on S have close contact with partial orders on S/Y.展开更多
On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial ...On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.展开更多
It becomes a key technology to measure the concentration of the vehicle exhaust components with the absorption spectra. But because of the overlap of gas absorption bands, how to separate the absorption information of...It becomes a key technology to measure the concentration of the vehicle exhaust components with the absorption spectra. But because of the overlap of gas absorption bands, how to separate the absorption information of each component gas from the mixed absorption spectra has become the key point to restrict the precision of the optical detection method. In this paper, the ex-perimental platform for the absorption spectrum of vehicle exhaust components has been established. Based on the ultraviolet absorption spectra measured with the platform of exhaust gas NO & NO2, the concentration regression model for the two components has been established with weighted partial least squares regression (WPLS). Finally the each spectral characteristic information of NO & NO2 gas has been separated and the concentration of each corresponding component has been reversed successfully.展开更多
Objective:To report the recurrent spontaneous abortion that were caused by the mother's chromosomal rearrangement which was 18 chromosome inversion;and cytogenetic analysis of the fetal amniotic fluid was performe...Objective:To report the recurrent spontaneous abortion that were caused by the mother's chromosomal rearrangement which was 18 chromosome inversion;and cytogenetic analysis of the fetal amniotic fluid was performed.Methods: Traditional chromosome karyotype and whole-genome sequencing(WGS) was used to process karyotyping and genomic microdeletion and microduplication analysis.Results: the result of fetal amniotic fluid chromosome karyotype is 46,XY,rec(18),dup(18)(q12.3q23);his mother's chromosome karyotype is 46,XX,inv(18)(P11.3q12);and his father's chromosome karyotype is normal.Conclusions:A male newborn with partial trisomy 18q variation was detected in a fetus whose mother with abnormal pregnancy history, that was combined with traditional chromosome karyotype and WGS. The WGS technology has an important clinical value in the prevention of fetal birth defects of abnormal pregnancy history family in prenatal diagnosis.展开更多
In this paper, we obtain some new characterizations of the range symmetric matrices in the Minkowski Space M by using the Block representation of the matrices. These characterizations are used to establish some result...In this paper, we obtain some new characterizations of the range symmetric matrices in the Minkowski Space M by using the Block representation of the matrices. These characterizations are used to establish some results on the partial ordering of the range symmetric matrices with respect to the Minkowski adjoint. Further, we establish some results regarding the partial ordering of m-projectors with respect to the Minkowski adjoint and manipulate them to characterize some sets of range symmetric elements in the Minkowski Space M. All the results obtained in this paper are an extension to the Minkowski space of those given by A. Hernandez, et al. in [The star partial order and the eigenprojection at 0 on EP matrices, Applied Mathematics and Computation, 218: 10669-10678, 2012].展开更多
This paper presents a formula for the Drazin inverses of matrices based on a sequence of partial full-rank factorizations which theoretically extends the classic full-rank factorization method for computing the Drazin...This paper presents a formula for the Drazin inverses of matrices based on a sequence of partial full-rank factorizations which theoretically extends the classic full-rank factorization method for computing the Drazin inverses established by R.E.Cline.The result is then extended to the core-EP inverses.展开更多
文摘Partial Differential Equation(PDE)is among the most fundamental tools employed to model dynamic systems.Existing PDE modeling methods are typically derived from established knowledge and known phenomena,which are time-consuming and labor-intensive.Recently,discovering governing PDEs from collected actual data via Physics Informed Neural Networks(PINNs)provides a more efficient way to analyze fresh dynamic systems and establish PEDmodels.This study proposes Sequentially Threshold Least Squares-Lasso(STLasso),a module constructed by incorporating Lasso regression into the Sequentially Threshold Least Squares(STLS)algorithm,which can complete sparse regression of PDE coefficients with the constraints of l0 norm.It further introduces PINN-STLasso,a physics informed neural network combined with Lasso sparse regression,able to find underlying PDEs from data with reduced data requirements and better interpretability.In addition,this research conducts experiments on canonical inverse PDE problems and compares the results to several recent methods.The results demonstrated that the proposed PINN-STLasso outperforms other methods,achieving lower error rates even with less data.
基金the support from the key research and development and promotion of special projects (scientific and technological research) of Henan province (212102210188)the National Natural Science Foundation of China (51604244)the Energy Storage Materials and Processes Key Laboratory of Henan Province Open Fund (2021003)。
文摘Precisely quantifying transition metal(TM) redox in bulk is a key to understand the fundamental of optimizing cathode materials in secondary batteries. At present, the commonly used methods to probe TM redox are hard X-ray absorption spectroscopy(hXAS) and soft X-ray absorption spectroscopy(sXAS).However, they are both facing challenges to precisely quantify the valence states of some transition metals such as Mn. In this paper, Mn-L iPFY(inverse partial fluorescence yield) spectra extracted from Mn-L m RIXS(mapping of resonant inelastic X-ray scattering) is adopted to quantify Mn valence states. Mn-L i PFY spectra has been considered as a bulk-sensitive, non-distorted probe of TM valence states.However, the exact precision of this method is still unclear in quantifying practical battery electrodes.Herein, a series of LiMn_(2)O_(4) electrodes with different charge and discharge states are prepared. Based on their electrochemical capacity(generally considered to be very precise), the precision of Mn iPFY in quantifying bulk Mn valence state is confirmed, and the error range is unraveled. Mn-L mRIXS iPFY thus is identified as one of the best methods to quantify the bulk Mn valence state comparing with hXAS and sXAS.
基金Supported by National Natural Science Foundation of China(79790 1 30 ) and National863Hi- TechProject(863- 30 6- ZT0 4 - 0 4 -
文摘In this paper,a new model for inverse network flow problems,robust partial inverse problem is presented. For a given partial solution,the robust partial inverse problem is to modify the coefficients optimally such that all full solutions containing the partial solution become optimal under new coefficients. It has been shown that the robust partial inverse spanning tree problem can be formulated as a combinatorial linear program,while the robust partial inverse minimum cut problem and the robust partial inverse assignment problem can be solved by combinatorial strongly polynomial algorithms.
基金Foundation item： Supported by NSF of China（10471112） Supported by Shaanxi Provincial Natural Science Foundation（2005A15） Acknowledgement The authors express their gratitude to the referees for very helpful and detailed comments.
文摘It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a right inverse semigroup. We construct partial orders on S by some kind of its subsemigroups and uncover that partial orders on S have close contact with partial orders on S/Y.
文摘On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.
文摘It becomes a key technology to measure the concentration of the vehicle exhaust components with the absorption spectra. But because of the overlap of gas absorption bands, how to separate the absorption information of each component gas from the mixed absorption spectra has become the key point to restrict the precision of the optical detection method. In this paper, the ex-perimental platform for the absorption spectrum of vehicle exhaust components has been established. Based on the ultraviolet absorption spectra measured with the platform of exhaust gas NO & NO2, the concentration regression model for the two components has been established with weighted partial least squares regression (WPLS). Finally the each spectral characteristic information of NO & NO2 gas has been separated and the concentration of each corresponding component has been reversed successfully.
基金Major Science and Technology Program of Hainan Province(No.ZDKJ2017007)National Natural Science Foundation of China(No.81660433,81460034,81460236)+1 种基金National Special Project for International Science and Technology Cooperation(No.2014DFA30180)2018 Natural Science Foundation of Hainan Youth Fund Project(No.818QN315).
文摘Objective:To report the recurrent spontaneous abortion that were caused by the mother's chromosomal rearrangement which was 18 chromosome inversion;and cytogenetic analysis of the fetal amniotic fluid was performed.Methods: Traditional chromosome karyotype and whole-genome sequencing(WGS) was used to process karyotyping and genomic microdeletion and microduplication analysis.Results: the result of fetal amniotic fluid chromosome karyotype is 46,XY,rec(18),dup(18)(q12.3q23);his mother's chromosome karyotype is 46,XX,inv(18)(P11.3q12);and his father's chromosome karyotype is normal.Conclusions:A male newborn with partial trisomy 18q variation was detected in a fetus whose mother with abnormal pregnancy history, that was combined with traditional chromosome karyotype and WGS. The WGS technology has an important clinical value in the prevention of fetal birth defects of abnormal pregnancy history family in prenatal diagnosis.
文摘In this paper, we obtain some new characterizations of the range symmetric matrices in the Minkowski Space M by using the Block representation of the matrices. These characterizations are used to establish some results on the partial ordering of the range symmetric matrices with respect to the Minkowski adjoint. Further, we establish some results regarding the partial ordering of m-projectors with respect to the Minkowski adjoint and manipulate them to characterize some sets of range symmetric elements in the Minkowski Space M. All the results obtained in this paper are an extension to the Minkowski space of those given by A. Hernandez, et al. in [The star partial order and the eigenprojection at 0 on EP matrices, Applied Mathematics and Computation, 218: 10669-10678, 2012].
文摘This paper presents a formula for the Drazin inverses of matrices based on a sequence of partial full-rank factorizations which theoretically extends the classic full-rank factorization method for computing the Drazin inverses established by R.E.Cline.The result is then extended to the core-EP inverses.
