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     We discussion the w-integral dependence of an extension of rings and the w-integral closure of an extension of rings, and prove that R is a UMT-domain if and only if the w-integral closure R~w of R is a w_R-multiplication domain on the star-operation w of R~w induced by the w-operation of R.
     也讨论了环的w 整相关理论与环的w 整闭包,证明了在w 整扩张下,环R的w 维数与环T的wR 维数的一致性. 还证明了一个整环R是UMT整环当且仅当R的w 整闭包Rw是wR 乘法整环.
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     On the Algebraically Dependent of Entire and Meromorphic Functions
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     和相关的一个联立不定方程
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     N( Z ) .
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  integral dependence
We establish the principle of specialization of integral dependence for submodules of finite colength of free modules, as part of the general algebraic-geometric theory of the Buchsbaum-Rim multiplicity.
      
We show the possibility of determining the variance matrix of a multivariate random process of a stochastic differential system by passing from integral dependence to a rather simple algebraic expression.
      
  integral correlation
Integral correlation results characterize the involved beta transition to be of first-forbidden non-unique type.
      
Comparison with experiments of the integral multiplicity distribution function for charged pions and of the integral correlation parameters for negative pions indicates the existence of lower and higher regimes in high-energy collisions.
      
Results from the integral correlation showed that the correlation coefficientε4 was zero within experimental errors, while those from the differential correlation experiment showed that the coefficientε2 is small and independent of energy.
      
J-integral correlation of the initiation of slow crack growth in linear polyethylene
      
Compact representation of the Hadamard function in a multidimensional space, based on the integral correlation matrix operator
      
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Let RT be an extension of domains. In this paper we introduce the star-operation w_R of T induced by w-operation over R and obtain some characterizations of a w_R-multiplication domain. We discussion the w-integral dependence of an extension of rings and the w-integral closure of an extension of rings, and prove that R is a UMT-domain if and only if the w-integral closure R~w of R is a w_R-multiplication domain on the star-operation w of R~w induced by the w-operation of R.

设R T是整环扩张,定义了T上的由R的w 算子所诱导的星型算子wR,并给出了wR 乘法整环的特征.也讨论了环的w 整相关理论与环的w 整闭包,证明了在w 整扩张下,环R的w 维数与环T的wR 维数的一致性.还证明了一个整环R是UMT整环当且仅当R的w 整闭包Rw是wR 乘法整环.

 
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