Dual number,as a special kind of plural number,hardly attracts attention although English grammar about number is so self-contained.Dual case,once an important grammar category in Old English,now has vanished in Engli...Dual number,as a special kind of plural number,hardly attracts attention although English grammar about number is so self-contained.Dual case,once an important grammar category in Old English,now has vanished in English language.A contrast was made in English and Chinese dual conceptualized nouns,verbs,prepositions,pronouns,quantifiers and affixes.It is supposed that cultural and philosophical facors do bring the common and diversed forms of dual concepts in the two languages.展开更多
For weighted sums of the form ?j = 1kn anj Xnj\sum {_{j = 1}^{k_n } } a_{nj} X_{nj} where {a nj , 1 ?j?k n ↑∞,n?1} is a real constant array and {X aj , 1≤j≤k n, n≥1} is a rowwise independent, zero mean, rando...For weighted sums of the form ?j = 1kn anj Xnj\sum {_{j = 1}^{k_n } } a_{nj} X_{nj} where {a nj , 1 ?j?k n ↑∞,n?1} is a real constant array and {X aj , 1≤j≤k n, n≥1} is a rowwise independent, zero mean, random element array in a real separable Banach space of typep, we establishL r convergence theorem and a general weak law of large numbers respectively, conversely, we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.展开更多
文摘Dual number,as a special kind of plural number,hardly attracts attention although English grammar about number is so self-contained.Dual case,once an important grammar category in Old English,now has vanished in English language.A contrast was made in English and Chinese dual conceptualized nouns,verbs,prepositions,pronouns,quantifiers and affixes.It is supposed that cultural and philosophical facors do bring the common and diversed forms of dual concepts in the two languages.
基金Supported by the National Natural Science F oundation of China( No.10 0 710 5 8)
文摘For weighted sums of the form ?j = 1kn anj Xnj\sum {_{j = 1}^{k_n } } a_{nj} X_{nj} where {a nj , 1 ?j?k n ↑∞,n?1} is a real constant array and {X aj , 1≤j≤k n, n≥1} is a rowwise independent, zero mean, random element array in a real separable Banach space of typep, we establishL r convergence theorem and a general weak law of large numbers respectively, conversely, we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.
