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We study the modificationA→A' of an affine domainA which produces another affine domainA'=A[I/f] whereI is a nontrivial ideal ofA andf is a nonzero element ofI.
      
Another proof of Joseph and Letzter's separation of variables theorem for quantum groups
      
Another interesting subset of Vλ ? Vμ is the set of decomposable tensors.
      
A similar result is proved for another class of regular 2-dimensional real algebras (the principal isotopes of the algebra ${\mbox{\bf R}}\oplus{\mbox{\bf R}}$).
      
Another generalization is obtained in the context of representations of Jordan algebras, in the spirit of Herz's previous work on matrix spaces.
      
In this article we show how to transform any basis into another basis by applying the PONS construction, thereby providing an affirmative answer to this question.
      
Specifically, for1>amp;lt;p>amp;lt;∞, we obtain sufficient conditions for the weight in one side, which guarantee that another weight exists in the other side, so that the corresponding Lp weighted inequality holds for T*.
      
The notions of localization and related approximation properties are a spectrum of ideas that quantify the degree to which elements of one frame can be approximated by elements of another frame.
      
Another pattern recognition method known as non-metric multidimensional scaling discerned finer associations that fell within categorizations by low, moderate, and higher formula weight.
      
A system receives shocks at successive random points of discrete time, and each shock causes a positive integer-valued random amount of damage which accumulates on the system one after another.
      
For an arbitrary ring A we construct quasi-P radical QP(A) with transfinite induction, and give another characterization of quasi-P radical: QP(A) = ∩ Ia ∣Ia.
      
When either a node or a link in a fault-tolerant network fails, the communication from one node to another using this faulty element must be sent via one or more intermediate nodes along a sequence of paths determined by this routing.
      
In the note the author gives a correct proof of the theorem on sunsets in spaces of bounded linear operators given in the author's another paper.
      
Also another cross ratio of the following four collinear points are suggested, i.
      
Finally, another physical meaning of the service rate is given.
      
Some properties of convex cones are obtained and are used to derive several equivalent conditions as well as another important property for nearly cone-subconvexlike set-valued functions.
      
In this paper, a new concept of an optimal complete multipartite decomposition of type 1 (type 2) of a complete n-partite graph Qn is proposed and another new concept of a normal complete multipartite decomposition of Kn is introduced.
      
Another does not have a trusted center, here, each participant plays a dual-role as the dealer and shadow (or share) provider in the whole scheme.
      
In this note, some of these conditions can be weakened to get the same results, and another simplified proof for a criterion of prequasi-invex functions established under the condition of lower semicontinuity is given.
      
The parameter estimation and the coefficient of contamination for the regression models with repeated measures are studied when its response variables are contaminated by another random variable sequence.
      
 

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