In this article,novel smoothness indicators are presented for calculating the nonlinear weights of the weighted essentially non-oscillatory scheme to approximate the viscosity numerical solutions of Hamilton-Jacobi eq...In this article,novel smoothness indicators are presented for calculating the nonlinear weights of the weighted essentially non-oscillatory scheme to approximate the viscosity numerical solutions of Hamilton-Jacobi equations.These novel smoothness indicators are constructed from the derivatives of reconstructed polynomials over each sub-stencil.The constructed smoothness indicators measure the arc-length of the reconstructed polynomials so that the new nonlinear weights could get less absolute truncation error and give a high-resolution numerical solution.Extensive numerical tests are conducted and presented to show the performance capability and the numerical accuracy of the proposed scheme with the comparison to the classical WENO scheme.展开更多
The nature and origin of a fundamental quantum QSPR （QQSPR） equation are discussed. In principle, as any molecular structure can be associated to quantum mechanical density functions （DF）, a molecular set can be r...The nature and origin of a fundamental quantum QSPR （QQSPR） equation are discussed. In principle, as any molecular structure can be associated to quantum mechanical density functions （DF）, a molecular set can be reconstructed as a quantum multimolecular polyhedron （QMP）, whose vertices are formed by each molecular DF. According to QQSPR theory, complicated kinds of molecular properties, like biological activity or toxicity, of molecular sets can be calculated via the quantum expectation value of an approximate Hermitian operator, which can be evaluated with the geometrical information contained in the attached QMP via quantum similarity matrices. Practical ways of solving the QQSPR problem from the point of view of QMP geometrical structure are provided. Such a development results into a powerful algorithm, which can be implemented within molecular design as an alternative to the current classical QSPR procedures.展开更多
AIM: To analyze the related indices about the prognoses of chronic liver failure caused by hepatitis virus. METHODS: Retrospectively reviewed 320 cases of chronic liver failure caused by hepatitis viruses. An improved...AIM: To analyze the related indices about the prognoses of chronic liver failure caused by hepatitis virus. METHODS: Retrospectively reviewed 320 cases of chronic liver failure caused by hepatitis viruses. An improved group and an ineffective group (IG) were made to compare and analyze their clinical manifestations, laboratory examination indices and complications. Logistic regression was also carried out. RESULTS: There were significant differences (P<0.05) between the improved group and the IG upon such indices as age, bilirubin, prothrombin time, albumin, alpha fetoprotein, the size of liver and complications (P<0.05). The regression formula was as follows: P=1/(1+e^(-y)) (y=1.7262-0.0948X_1+2.9846X_2+0.6992X_3+1.6019X_4+2.0398X_5). (Note: X_1-Prothrombin activity; X_2-digestive tract hemorrhage; X_3-hepatic encephalopathy; A_4-hepatorenal syndrome; X_5-pulmonary infection.). CONCLUSION: Laboratory examination such as bilirubin, prothrombin time and alpha fetoprotein can be regarded as indices of the prognoses of chronic liver failure caused by hepatitis. Moreover, the regression equation can evaluate prognoses more comprehensively and direct our treatments.展开更多
It is well known that the Cauchy problem for Laplace equations is an ill-posed problem in Hadamard’s sense.Small deviations in Cauchy data may lead to large errors in the solutions.It is observed that if a bound is i...It is well known that the Cauchy problem for Laplace equations is an ill-posed problem in Hadamard’s sense.Small deviations in Cauchy data may lead to large errors in the solutions.It is observed that if a bound is imposed on the solution,there exists a conditional stability estimate.This gives a reasonable way to construct stable algorithms.However,it is impossible to have good results at all points in the domain.Although numerical methods for Cauchy problems for Laplace equations have been widely studied for quite a long time,there are still some unclear points,for example,how to evaluate the numerical solutions,which means whether they can approximate the Cauchy data well and keep the bound of the solution,and at which points the numerical results are reliable?In this paper,the authors will prove the conditional stability estimate which is quantitatively related to harmonic measures.The harmonic measure can be used as an indicate function to pointwisely evaluate the numerical result,which further enables us to find a reliable subdomain where the local convergence rate is higher than a certain order.展开更多
文摘In this article,novel smoothness indicators are presented for calculating the nonlinear weights of the weighted essentially non-oscillatory scheme to approximate the viscosity numerical solutions of Hamilton-Jacobi equations.These novel smoothness indicators are constructed from the derivatives of reconstructed polynomials over each sub-stencil.The constructed smoothness indicators measure the arc-length of the reconstructed polynomials so that the new nonlinear weights could get less absolute truncation error and give a high-resolution numerical solution.Extensive numerical tests are conducted and presented to show the performance capability and the numerical accuracy of the proposed scheme with the comparison to the classical WENO scheme.
文摘The nature and origin of a fundamental quantum QSPR （QQSPR） equation are discussed. In principle, as any molecular structure can be associated to quantum mechanical density functions （DF）, a molecular set can be reconstructed as a quantum multimolecular polyhedron （QMP）, whose vertices are formed by each molecular DF. According to QQSPR theory, complicated kinds of molecular properties, like biological activity or toxicity, of molecular sets can be calculated via the quantum expectation value of an approximate Hermitian operator, which can be evaluated with the geometrical information contained in the attached QMP via quantum similarity matrices. Practical ways of solving the QQSPR problem from the point of view of QMP geometrical structure are provided. Such a development results into a powerful algorithm, which can be implemented within molecular design as an alternative to the current classical QSPR procedures.
文摘AIM: To analyze the related indices about the prognoses of chronic liver failure caused by hepatitis virus. METHODS: Retrospectively reviewed 320 cases of chronic liver failure caused by hepatitis viruses. An improved group and an ineffective group (IG) were made to compare and analyze their clinical manifestations, laboratory examination indices and complications. Logistic regression was also carried out. RESULTS: There were significant differences (P<0.05) between the improved group and the IG upon such indices as age, bilirubin, prothrombin time, albumin, alpha fetoprotein, the size of liver and complications (P<0.05). The regression formula was as follows: P=1/(1+e^(-y)) (y=1.7262-0.0948X_1+2.9846X_2+0.6992X_3+1.6019X_4+2.0398X_5). (Note: X_1-Prothrombin activity; X_2-digestive tract hemorrhage; X_3-hepatic encephalopathy; A_4-hepatorenal syndrome; X_5-pulmonary infection.). CONCLUSION: Laboratory examination such as bilirubin, prothrombin time and alpha fetoprotein can be regarded as indices of the prognoses of chronic liver failure caused by hepatitis. Moreover, the regression equation can evaluate prognoses more comprehensively and direct our treatments.
基金suported by the National Natural Science Foundation of China(Nos.11971121,12201386,12241103)Grant-in-Aid for Scientific Research(A)20H00117 of Japan Society for the Promotion of Science.
文摘It is well known that the Cauchy problem for Laplace equations is an ill-posed problem in Hadamard’s sense.Small deviations in Cauchy data may lead to large errors in the solutions.It is observed that if a bound is imposed on the solution,there exists a conditional stability estimate.This gives a reasonable way to construct stable algorithms.However,it is impossible to have good results at all points in the domain.Although numerical methods for Cauchy problems for Laplace equations have been widely studied for quite a long time,there are still some unclear points,for example,how to evaluate the numerical solutions,which means whether they can approximate the Cauchy data well and keep the bound of the solution,and at which points the numerical results are reliable?In this paper,the authors will prove the conditional stability estimate which is quantitatively related to harmonic measures.The harmonic measure can be used as an indicate function to pointwisely evaluate the numerical result,which further enables us to find a reliable subdomain where the local convergence rate is higher than a certain order.
