This article is not inspired by any religion or quantum many-worlds interpretation. The mathematics of multiverse is presented here. The mass operator was introduced earlier by Alnobani. This operator is used here to ...This article is not inspired by any religion or quantum many-worlds interpretation. The mathematics of multiverse is presented here. The mass operator was introduced earlier by Alnobani. This operator is used here to deduce the time state. It is found that time has four states and those four states are orthogonal. Time is the constitution of any verse. Time has direction. Every orthogonal direction of time belongs to a verse. Past and future belong to opposite directions of time and they are arbitrary. Other verses are there by their own and not a probabilities of any other verse and if any similarity it is only a coincidence. Among applications of this thesis is travelling through groups of galaxies, or more or less.展开更多
For a given compactly supported scaling fun ct ion supported over [0,3]×[0,3], we present an algorithm to construct compac t ly supported orthogonal wavelets. By this algorithm, the symbol function of the associa...For a given compactly supported scaling fun ct ion supported over [0,3]×[0,3], we present an algorithm to construct compac t ly supported orthogonal wavelets. By this algorithm, the symbol function of the associated wavelets can be constructed explicitly.展开更多
In this paper we first prove that a dual Hankel operator Rφ on the orthogonal complement of the Dirichlet space is compact for φ ∈ W^1,∞（D）, and then that a semicommutator of two Toeplitz operators on the Dirich...In this paper we first prove that a dual Hankel operator Rφ on the orthogonal complement of the Dirichlet space is compact for φ ∈ W^1,∞（D）, and then that a semicommutator of two Toeplitz operators on the Dirichlet space or two dual Toeplitz operators on the orthogonal complement of the Dirichlet space in Sobolev space is compact. We also prove that a dual Hankel operator Re with φ ∈ W^1,∞（D） is of finite rank if and only if Be is orthogonal to the Dirichlet space for some finite Blaschke product B, and give a sufficient and necessary condition for the semicommutator of two dual Toeplitz operators to be of finite rank.展开更多
文摘This article is not inspired by any religion or quantum many-worlds interpretation. The mathematics of multiverse is presented here. The mass operator was introduced earlier by Alnobani. This operator is used here to deduce the time state. It is found that time has four states and those four states are orthogonal. Time is the constitution of any verse. Time has direction. Every orthogonal direction of time belongs to a verse. Past and future belong to opposite directions of time and they are arbitrary. Other verses are there by their own and not a probabilities of any other verse and if any similarity it is only a coincidence. Among applications of this thesis is travelling through groups of galaxies, or more or less.
文摘For a given compactly supported scaling fun ct ion supported over [0,3]×[0,3], we present an algorithm to construct compac t ly supported orthogonal wavelets. By this algorithm, the symbol function of the associated wavelets can be constructed explicitly.
基金supported by National Natural Science Foundation of China (Grant Nos.10971195 and 10771064)Natural Science Foundation of Zhejiang Province (Grant Nos. Y6090689 and Y6110260)Zhejiang Innovation Project (Grant No. T200905)
文摘In this paper we first prove that a dual Hankel operator Rφ on the orthogonal complement of the Dirichlet space is compact for φ ∈ W^1,∞（D）, and then that a semicommutator of two Toeplitz operators on the Dirichlet space or two dual Toeplitz operators on the orthogonal complement of the Dirichlet space in Sobolev space is compact. We also prove that a dual Hankel operator Re with φ ∈ W^1,∞（D） is of finite rank if and only if Be is orthogonal to the Dirichlet space for some finite Blaschke product B, and give a sufficient and necessary condition for the semicommutator of two dual Toeplitz operators to be of finite rank.
