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A computationally simple method for molecular excited states, namely, the Tamm–Dancoff approximation to time-dependent density functional theory, is proposed and implemented. This method Free Run 5 yields excitation energies for several closed- and open-shell molecules that are essentially of the same quality as those obtained from time-dependent density functional theory itself, when the same exchange-correlation functional is used.
A general nonparametric density estimation problem is considered in which the data is generated by a spatial point process. Several practical problems are special cases of it, including those of estimating the Cheap Nike Roshe Run common probability density of a sequence of random vectors and estimating the product density of a stationary multivariate point process.Kernel and k-nearest neighbor estimators are defined and in each case the joint asymptotic normality and consistency of the estimates of the density at a given finite number of points is derived.
We study periodic boundary value problems relative to a general class of first-order functional differential equations. For this class of problems, we develop the monotone iterative technique. Our formulation is very general, including delay differential equations, functional differential equations with maxima and integro-differential equations, but the case where the operator defining the functional dependence is not necessarily Lipschitzian is also considered.