Series That Converge on Sets of Null Density
نویسندگان
چکیده
It is shown that a series of positive terms that converges on all sets of null density should be convergent. Using this result we construct examples of complete topological vector spaces that are proper subspaces of a Banach space, but whose dual spaces coincide with the dual space of the Banach space.
منابع مشابه
Basis Set Effects in Density Functional Calculations and BSSEcorrected on the Molybdate-Phosphonic acid Complex
In this research, this possibility was investigated the relative stablilty geometry and bindingenergies of the hydrogen bonds of Molybdate-Phosphonic Acid (MPA) complex in gas phase onthe basis of result of ab initio and DFT calculations. Three DFT methods have been applied forcalculations are B3LYP, BP86 and B3PW91 that have been studied in two series of basis sets:D95** and 6-31+G(d,p) for hy...
متن کاملA Non-Parametric Test for Continuous-Time Homogeneous Markov Process: Is It a Diffusion Process?
This paper proposes a nonparametric method to test whether an underlying continuoustime homogeneous Markov process is a diffusion process. The test statistic is based on the infinitesimal generator. Under the null hypothesis, we show that the limit distribution of the test statistic is normal. Under the alternative hypothesis, where the jump-diffusion process is assumed, the power of the test i...
متن کاملRationalizing the Strength of Hydrogen-Bonded of Molybdate-Phosphonic acid Complex (1:2): Density Functional Theory Studies
The relative stability of hydrogen-bonded of Molybdate-Phosphonic Acid (MPA) complex (1:2) ingas phase has been carried out using Density Functional Theory (DFT) methods. The methods are usedfor calculations are B3LYP, BP86 and B3PW91 that have been studied in two series of basis sets: D95**and 6-31+G(d,p) for hydrogen and oxygen atoms; LANL2DZ for Mo and Phosphorus. Predictedhydrogen-bond geom...
متن کاملDensity Dependence in Time Series Observations of Natural Populations: Estimation and Testing
We report on a new statistical test for detecting density dependence in univariate time series observations of population abundances. The test is a likelihood ratio test based on a discrete time stochastic logistic model. The null hypothesis is that the population is undergoing stochastic exponential growth. stochastic exponential decline, or random walk. The distribution of the test statistic ...
متن کاملA Density Functional Theory Study of Structure of Phosphonic Acid
The molecular structure of the stable conformation of phosphonic acid in gas phase has beencomputed by employing complete geometry optimization in Density Functional Theory(DFT) methods. The methods used for calculations are B3LYP, BP86 and B3PW91 that havebeen studied in two series of basis sets: D95** and 6-31+G(d,p) for hydrogen and oxygenatoms; LANL2DZ for phosphorus. Bond lengths and angle...
متن کامل