例句與用法

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1. the theorem of irregularity for markov chain fields on binary trees
   二元樹上的無規(guī)則性定理
2. some strong laws of large numbers for markov chain fields indexed by a special nonhomogeneous tree
   一類特殊非齊次樹上馬氏鏈的若干強大數(shù)定律
3. secondly, definitions of a extended bethe tree, bethe tree and cayley tree are introduced . further, the even-odd markov chain fields and markov chain fields indexed by a extended bethe tree, bethe tree and cayley tree are defined . subsequently the strong limit theorems proved above are applied to the study of all kinds of even-odd markov chain fields and markov chain fields defined above, which both extend the conclusions in [ 30 ] and [ 39 ] and prove a class of strong limit theorems for the even-odd markov chain fields and markov chain fields . as corollaries, we obtain some strong limit theorems for the frequencies of occurrence of states and ordered couples of states for the even-odd markov chain fields and markov chain fields . lastly, some coarse estimates are gained about the state occurrence frequencies for all kinds of even-odd markov chain fields and markov chain fields defined in the paper
   然后把前面所證得的一類強極限定理應(yīng)用到本文中所定義的各種奇偶馬爾可夫鏈場、馬爾可夫鏈場的研究工作中，從而推廣了[30]和[39]中的結(jié)論，獲得了本論文中所定義的各種奇偶馬爾可夫鏈場、馬爾可夫鏈場的一類強極限定理。作為這一類強極限定理的推論得到了狀態(tài)和狀態(tài)序偶出現(xiàn)頻率的一類強極限定理。最后，給出了本論文中所定義的各種奇偶馬爾可夫鏈場、馬爾可夫鏈場上狀態(tài)出現(xiàn)頻率的若干粗略估計。
4. secondly, definitions of a extended bethe tree, bethe tree and cayley tree are introduced . further, the even-odd markov chain fields and markov chain fields indexed by a extended bethe tree, bethe tree and cayley tree are defined . subsequently the strong limit theorems proved above are applied to the study of all kinds of even-odd markov chain fields and markov chain fields defined above, which both extend the conclusions in [ 30 ] and [ 39 ] and prove a class of strong limit theorems for the even-odd markov chain fields and markov chain fields . as corollaries, we obtain some strong limit theorems for the frequencies of occurrence of states and ordered couples of states for the even-odd markov chain fields and markov chain fields . lastly, some coarse estimates are gained about the state occurrence frequencies for all kinds of even-odd markov chain fields and markov chain fields defined in the paper
   然后把前面所證得的一類強極限定理應(yīng)用到本文中所定義的各種奇偶馬爾可夫鏈場、馬爾可夫鏈場的研究工作中，從而推廣了[30]和[39]中的結(jié)論，獲得了本論文中所定義的各種奇偶馬爾可夫鏈場、馬爾可夫鏈場的一類強極限定理。作為這一類強極限定理的推論得到了狀態(tài)和狀態(tài)序偶出現(xiàn)頻率的一類強極限定理。最后，給出了本論文中所定義的各種奇偶馬爾可夫鏈場、馬爾可夫鏈場上狀態(tài)出現(xiàn)頻率的若干粗略估計。
5. secondly, definitions of a extended bethe tree, bethe tree and cayley tree are introduced . further, the even-odd markov chain fields and markov chain fields indexed by a extended bethe tree, bethe tree and cayley tree are defined . subsequently the strong limit theorems proved above are applied to the study of all kinds of even-odd markov chain fields and markov chain fields defined above, which both extend the conclusions in [ 30 ] and [ 39 ] and prove a class of strong limit theorems for the even-odd markov chain fields and markov chain fields . as corollaries, we obtain some strong limit theorems for the frequencies of occurrence of states and ordered couples of states for the even-odd markov chain fields and markov chain fields . lastly, some coarse estimates are gained about the state occurrence frequencies for all kinds of even-odd markov chain fields and markov chain fields defined in the paper
   然后把前面所證得的一類強極限定理應(yīng)用到本文中所定義的各種奇偶馬爾可夫鏈場、馬爾可夫鏈場的研究工作中，從而推廣了[30]和[39]中的結(jié)論，獲得了本論文中所定義的各種奇偶馬爾可夫鏈場、馬爾可夫鏈場的一類強極限定理。作為這一類強極限定理的推論得到了狀態(tài)和狀態(tài)序偶出現(xiàn)頻率的一類強極限定理。最后，給出了本論文中所定義的各種奇偶馬爾可夫鏈場、馬爾可夫鏈場上狀態(tài)出現(xiàn)頻率的若干粗略估計。