This paper advances a new simplified formula for estimating variance components ,sums up the basic law to calculate the weights of observed values and a circulation method using the increaments of weights when estimat...This paper advances a new simplified formula for estimating variance components ,sums up the basic law to calculate the weights of observed values and a circulation method using the increaments of weights when estimating the variance components of traverse nets,advances the charicteristic roots method to estimate the variance components of traveres nets and presents a practical method to make two real and symmetric matrices two diagonal ones.展开更多
In the past few years,the renormalized excitonic model(REM)approach was developed as an efficient low-scaling ab initio excited state method,which assumes the low-lying excited states of the whole system are a linear ...In the past few years,the renormalized excitonic model(REM)approach was developed as an efficient low-scaling ab initio excited state method,which assumes the low-lying excited states of the whole system are a linear combination of various single monomer excitations and utilizes the effective Hamiltonian theory to derive their couplings.In this work,we further extend the REM calculations for the evaluations of first-order molecular properties(e.g.charge population and transition dipole moment)of delocalized ionic or excited states in molecular aggregates,through generalizing the effective Hamiltonian theory to effective operator representation.Results from the test calculations for four different kinds of one dimensional(1D)molecular aggregates(ammonia,formaldehyde,ethylene and pyrrole)indicate that our new scheme can efficiently describe not only the energies but also wavefunction properties of the low-lying delocalized electronic states in large systems.展开更多
This paper extends the dimension-reduced projection four-dimensional variational assimilation method(DRP-4DVar) by adding a nonlinear correction process,thereby forming the DRP-4DVar with a nonlinear correction, which...This paper extends the dimension-reduced projection four-dimensional variational assimilation method(DRP-4DVar) by adding a nonlinear correction process,thereby forming the DRP-4DVar with a nonlinear correction, which shall hereafter be referred to as the NC-DRP-4DVar. A preliminary test is conducted using the Lorenz-96 model in one single-window experiment and several multiple-window experiments. The results of the single-window experiment show that compared with the adjoint-based traditional 4DVar, the final convergence of the cost function for the NC-DRP-4DVar is almost the same as that using the traditional 4DVar, but with much less computation. Furthermore, the 30-window assimilation experiments demonstrate that the NC-DRP-4DVar can alleviate the linearity approximation error and reduce the root mean square error significantly.展开更多
In [l], a property of roots of polynomials is considered, which involves the existence of local analytic solutions of polynomial-like functional iterative equations. In this paper we discuss this property and obtain a...In [l], a property of roots of polynomials is considered, which involves the existence of local analytic solutions of polynomial-like functional iterative equations. In this paper we discuss this property and obtain a succinct condition to decide whether this property holds. Our main result is: A polynomialλnzn+''' + λ2z2 + λlz + λ0 of degree n has a root or such that inf{|λnanm +... + λ2a2m + λ1am+ λ0|: m = 2, 3,.. .} > 0 if and only if at least one of the following two conditions holds: (i) the polynomial has a root β satisfying ｜β｜ > 1; (ii) the polynomial has a root β satisfying ｜β｜ < 1, and λ0≠0展开更多
文摘This paper advances a new simplified formula for estimating variance components ,sums up the basic law to calculate the weights of observed values and a circulation method using the increaments of weights when estimating the variance components of traverse nets,advances the charicteristic roots method to estimate the variance components of traveres nets and presents a practical method to make two real and symmetric matrices two diagonal ones.
基金supported by the National Natural Science Foundation of China(No.22073045)the Fundamental Research Funds for the Central Universities。
文摘In the past few years,the renormalized excitonic model(REM)approach was developed as an efficient low-scaling ab initio excited state method,which assumes the low-lying excited states of the whole system are a linear combination of various single monomer excitations and utilizes the effective Hamiltonian theory to derive their couplings.In this work,we further extend the REM calculations for the evaluations of first-order molecular properties(e.g.charge population and transition dipole moment)of delocalized ionic or excited states in molecular aggregates,through generalizing the effective Hamiltonian theory to effective operator representation.Results from the test calculations for four different kinds of one dimensional(1D)molecular aggregates(ammonia,formaldehyde,ethylene and pyrrole)indicate that our new scheme can efficiently describe not only the energies but also wavefunction properties of the low-lying delocalized electronic states in large systems.
基金supported by the National Basic Research Program of China (973 Program, Grant No. 2010CB951604)the National Key Technologies Research and Development Program of China (Grant No. 2012BAC22B02)the National Natural Science Foundation of China (Grant No. 41105120)
文摘This paper extends the dimension-reduced projection four-dimensional variational assimilation method(DRP-4DVar) by adding a nonlinear correction process,thereby forming the DRP-4DVar with a nonlinear correction, which shall hereafter be referred to as the NC-DRP-4DVar. A preliminary test is conducted using the Lorenz-96 model in one single-window experiment and several multiple-window experiments. The results of the single-window experiment show that compared with the adjoint-based traditional 4DVar, the final convergence of the cost function for the NC-DRP-4DVar is almost the same as that using the traditional 4DVar, but with much less computation. Furthermore, the 30-window assimilation experiments demonstrate that the NC-DRP-4DVar can alleviate the linearity approximation error and reduce the root mean square error significantly.
基金Supported by the National Natural Science Foundation of China.
文摘In [l], a property of roots of polynomials is considered, which involves the existence of local analytic solutions of polynomial-like functional iterative equations. In this paper we discuss this property and obtain a succinct condition to decide whether this property holds. Our main result is: A polynomialλnzn+''' + λ2z2 + λlz + λ0 of degree n has a root or such that inf{|λnanm +... + λ2a2m + λ1am+ λ0|: m = 2, 3,.. .} > 0 if and only if at least one of the following two conditions holds: (i) the polynomial has a root β satisfying ｜β｜ > 1; (ii) the polynomial has a root β satisfying ｜β｜ < 1, and λ0≠0
