This paper considers wavelet transforms associated to the affine group, which is more general than the paper given by R. Murenzi, and it seems more important in mathematical theory and more natural to be used to analy...This paper considers wavelet transforms associated to the affine group, which is more general than the paper given by R. Murenzi, and it seems more important in mathematical theory and more natural to be used to analyze signals in more than 1-dimension.展开更多
Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,ea...Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,each projective transformation can be decomposed into at most three harmonic projective reflections with respect to projective lines,or equivalently,each projective spinor can be decomposed into at most three orthogonal Minkowski bispinors,each inducing a harmonic projective line reflection.In this paper,we establish the corresponding result for three-dimensional affine geometry:with each affine transformation is found a minimal decomposition into general affine reflections,where the number of general affine reflections is at most three;equivalently,each affine spinor can be decomposed into at most three affine Minkowski bispinors,each inducing a general affine line reflection.展开更多
The necessary and sufficient conditions are derived for the existence of the uniformly minimum risk equivariant (UMRE) estimator of regression coefficient matrix in normal growth carve models with arbitrary covariance...The necessary and sufficient conditions are derived for the existence of the uniformly minimum risk equivariant (UMRE) estimator of regression coefficient matrix in normal growth carve models with arbitrary covariance matrix or uniform oovananoe structure or serial covariance structure under an affine group and a transitive group of transformations for quadratic losses and matrix losses, respectively.展开更多
In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve ...In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.展开更多
文摘This paper considers wavelet transforms associated to the affine group, which is more general than the paper given by R. Murenzi, and it seems more important in mathematical theory and more natural to be used to analyze signals in more than 1-dimension.
基金Supported partially by National Key Research and Development Project(2020YFA0712300)。
文摘Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,each projective transformation can be decomposed into at most three harmonic projective reflections with respect to projective lines,or equivalently,each projective spinor can be decomposed into at most three orthogonal Minkowski bispinors,each inducing a harmonic projective line reflection.In this paper,we establish the corresponding result for three-dimensional affine geometry:with each affine transformation is found a minimal decomposition into general affine reflections,where the number of general affine reflections is at most three;equivalently,each affine spinor can be decomposed into at most three affine Minkowski bispinors,each inducing a general affine line reflection.
基金Project supported by the National Natural Science Foundation of China.
文摘The necessary and sufficient conditions are derived for the existence of the uniformly minimum risk equivariant (UMRE) estimator of regression coefficient matrix in normal growth carve models with arbitrary covariance matrix or uniform oovananoe structure or serial covariance structure under an affine group and a transitive group of transformations for quadratic losses and matrix losses, respectively.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19871088).
文摘In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.
