A bounded linear operator T on a complex Hilbert space H is called n-normal if T^(*)T^(n)=T^(n)T^(*).By Fuglede’s theorem T is n-normal if and only if T^(n)is normal.Let k,n∈N.Then a bounded linear operator T is sai...A bounded linear operator T on a complex Hilbert space H is called n-normal if T^(*)T^(n)=T^(n)T^(*).By Fuglede’s theorem T is n-normal if and only if T^(n)is normal.Let k,n∈N.Then a bounded linear operator T is said to be of typeⅠk-quasi-n-normal if T^(*k){T^(*)T^(n)-T^(n)T^(*)}T^(k)=0,and T is said to be of typeⅡk-quasi-n-normal if T^(*k){T^(*n)T^(n)-T^(n)T^(*n)}T^(k)=0.1-quasi-n-normal is called quasi-n-normal.We shall show that(1)typeⅠquasi-2-normal and typeⅡquasi-2-normal are different classes;(2)the intersection of the class of typeⅠquasi-2-normal and the class of typeⅡquasi-2-normal is equal to the class of 2-normal.We also give some examples of type I k-quasi-n-normal and typeⅡk-quasi-n-normal.We also show that Weyl’s theorem holds for this class of operators and every k-quasi-n-normal operator has a non trivial invariant subspace.展开更多
The improvement of the Cold Filter Plugging Point (CFPP) by an additive will depend on either the characteristics of the diesel or the additive itself. The ways in which cold flow improver interacts with the constitue...The improvement of the Cold Filter Plugging Point (CFPP) by an additive will depend on either the characteristics of the diesel or the additive itself. The ways in which cold flow improver interacts with the constituents of the fuels and the reasons for their efficiencies are far from fully elucidated. In this work , the contents of the n-paraffin in five kinds of diesels were tested by urea adduction, and the carbon distribution of n-paraffins was tested by temperature programmed gas chromatograph GC-14A and computed by the software for simulating distillation. Maximum likelihood method is applied to obtain μ and σ2 of the carbon distribution, and the deviation χ2 is computed. When the degrees of freedom is 4 and significance level (α) is 0.10, χ2_ 0.90(4)=7.779. If deviation χ2 is smaller than χ2_ 0.90(4), the hypothesis that the population is normal is accepted. The results show that the distributions of n-paraffin in these five kinds of diesels are normal. It can be found that the susceptibility of the diesel DQCH is weak and the variance σ2 of the carbon distribution in n-paraffin is only 1076.21 smaller than that for other diesels. The smaller the variance σ2 is, the weaker the susceptibility is. The susceptibility of the diesel LYL is also weak. The value of the statistic test quantity χ2 on the normal distribution of the n-paraffin in the diesel LYL is 4.112 bigger than other diesels . Statistic test quantity χ2 could reflect whether the carbon distribution of n-paraffin fits the normal distribution. When the carbon distribution of n-paraffin does not fit normal well, the wax settling does not match the agglomeration of flow improver. In this situation, the flow improver can’t interact with more wax crystal so that the CFPP of diesel can not be decreased.展开更多
文摘A bounded linear operator T on a complex Hilbert space H is called n-normal if T^(*)T^(n)=T^(n)T^(*).By Fuglede’s theorem T is n-normal if and only if T^(n)is normal.Let k,n∈N.Then a bounded linear operator T is said to be of typeⅠk-quasi-n-normal if T^(*k){T^(*)T^(n)-T^(n)T^(*)}T^(k)=0,and T is said to be of typeⅡk-quasi-n-normal if T^(*k){T^(*n)T^(n)-T^(n)T^(*n)}T^(k)=0.1-quasi-n-normal is called quasi-n-normal.We shall show that(1)typeⅠquasi-2-normal and typeⅡquasi-2-normal are different classes;(2)the intersection of the class of typeⅠquasi-2-normal and the class of typeⅡquasi-2-normal is equal to the class of 2-normal.We also give some examples of type I k-quasi-n-normal and typeⅡk-quasi-n-normal.We also show that Weyl’s theorem holds for this class of operators and every k-quasi-n-normal operator has a non trivial invariant subspace.
文摘The improvement of the Cold Filter Plugging Point (CFPP) by an additive will depend on either the characteristics of the diesel or the additive itself. The ways in which cold flow improver interacts with the constituents of the fuels and the reasons for their efficiencies are far from fully elucidated. In this work , the contents of the n-paraffin in five kinds of diesels were tested by urea adduction, and the carbon distribution of n-paraffins was tested by temperature programmed gas chromatograph GC-14A and computed by the software for simulating distillation. Maximum likelihood method is applied to obtain μ and σ2 of the carbon distribution, and the deviation χ2 is computed. When the degrees of freedom is 4 and significance level (α) is 0.10, χ2_ 0.90(4)=7.779. If deviation χ2 is smaller than χ2_ 0.90(4), the hypothesis that the population is normal is accepted. The results show that the distributions of n-paraffin in these five kinds of diesels are normal. It can be found that the susceptibility of the diesel DQCH is weak and the variance σ2 of the carbon distribution in n-paraffin is only 1076.21 smaller than that for other diesels. The smaller the variance σ2 is, the weaker the susceptibility is. The susceptibility of the diesel LYL is also weak. The value of the statistic test quantity χ2 on the normal distribution of the n-paraffin in the diesel LYL is 4.112 bigger than other diesels . Statistic test quantity χ2 could reflect whether the carbon distribution of n-paraffin fits the normal distribution. When the carbon distribution of n-paraffin does not fit normal well, the wax settling does not match the agglomeration of flow improver. In this situation, the flow improver can’t interact with more wax crystal so that the CFPP of diesel can not be decreased.
