It is known that there is a very closed connection between the set of non-isomorphic indecomposable basic Nakayama algebras and the set of admissible sequences.To determine the cardinal number of all nonisomorphic ind...It is known that there is a very closed connection between the set of non-isomorphic indecomposable basic Nakayama algebras and the set of admissible sequences.To determine the cardinal number of all nonisomorphic indecomposable basic Nakayama algebras,we describe the cardinal number of the set of all t-length admissible sequences using a new type of integers called quasi-binomial coefficients.Furthermore,we find some intrinsic relations among binomial coefficients and quasi-binomial coefficients.展开更多
Let X1,X2(where N>m)be independent Nm(μ,∑) random vectors, and putwhere T is upper- triangular with positive diagonal elements. The author considers the problemof estimating ∑,and restricts his attention to the ...Let X1,X2(where N>m)be independent Nm(μ,∑) random vectors, and putwhere T is upper- triangular with positive diagonal elements. The author considers the problemof estimating ∑,and restricts his attention to the class of estimates is any diagonal matrix and b* is any nonnegative constant} because it has the following attractive features:(a) Its elements are all quadratic forms of the sufficient and complete statistics (X, T).(b) It contains all estimates of the form(and), which constructa complete subclass of the class of nonnegative quadratic estimates (where X = (X1,…, XN)') for any strict convex loss function.(c)It contains all invariant estimates under the transformation group of upper-triangularmatrices.The author obtains the Characteristics for an estimate of the formof ∑ to be admissible in when the loss function is chosed as tr(∑-1∑-Ⅰ)2, and shows,by an example, that(and)is admissible in can not imply itsadmissibility in .展开更多
基金supported by Shandong Provincial Natural Science Foundation of China (Grant No.ZR2011AM005)National Natural Science Foundation of China (Grant No.10931006)Shanghai Municipal Natural Science Foundation (Grant No.12ZR1413200)
文摘It is known that there is a very closed connection between the set of non-isomorphic indecomposable basic Nakayama algebras and the set of admissible sequences.To determine the cardinal number of all nonisomorphic indecomposable basic Nakayama algebras,we describe the cardinal number of the set of all t-length admissible sequences using a new type of integers called quasi-binomial coefficients.Furthermore,we find some intrinsic relations among binomial coefficients and quasi-binomial coefficients.
文摘Let X1,X2(where N>m)be independent Nm(μ,∑) random vectors, and putwhere T is upper- triangular with positive diagonal elements. The author considers the problemof estimating ∑,and restricts his attention to the class of estimates is any diagonal matrix and b* is any nonnegative constant} because it has the following attractive features:(a) Its elements are all quadratic forms of the sufficient and complete statistics (X, T).(b) It contains all estimates of the form(and), which constructa complete subclass of the class of nonnegative quadratic estimates (where X = (X1,…, XN)') for any strict convex loss function.(c)It contains all invariant estimates under the transformation group of upper-triangularmatrices.The author obtains the Characteristics for an estimate of the formof ∑ to be admissible in when the loss function is chosed as tr(∑-1∑-Ⅰ)2, and shows,by an example, that(and)is admissible in can not imply itsadmissibility in .
