We show that C∗-algebras of the form C(X)⊗Z, where X is compact and Hausdorff and Z denotes the Jiang–Su algebra, have decomposition rank at most 2. This amounts to a dimension reduction result for C∗-bundles with sufficiently regular fibres. It establishes an important case of a conjecture on the fine structure of nuclear C∗-algebras of Toms and the second named author, even in a non-simple se...

That is, a ring of rank n is a ring (commutative, associative, with unit) whose underlying additive group is isomorphic to Z. The prototypical examples of rings of rank n are, of course, orders in degree n number fields. The class of all such examples consists precisely of those rings of rank n that are integral domains. However, there are many interesting examples of rings of rank n that are n...

We investigate algebraic Zd-actions of entropy rank one, namely those for which each element has finite entropy. Such actions can be completely described in terms of diagonal actions on products of local fields using standard adelic machinery. This leads to numerous alternative characterizations of entropy rank one, both geometric and algebraic. We then compute the measure entropy of a class of...

In this paper we propose a new method for ranking Z- numbers and generalizations. This method is based on the internal structure of the artificial neural network, which suggests that the structure of this network consists of inputs weights and the transfer function linear, nonlinear and sometimes linear and nonlinear. It is shown that the proposed method while possessing the ranking properties ...

We present a new normalization condition for the axial current, which is derived from the PCAC relation with non–vanishing mass. Using this condition reduces the O(r0m) corrections to the axial current normalization constant ZA for an easier chiral extrapolation in the cases, where simulations at zero quark–mass are not possible. The method described here also serves as a preparation for a dete...

Multiple Attribute Decision Making (MADM) is one of the best candidate network selection methods used for Vertical Handover Decision (VHD) in heterogeneous wireless networks (4G). Selection of the network in MADM is predominantly decided by two steps, i.e., attribute normalization and weight calculation. This dependency in MADM results in an unreliable network selection for handover, and in a r...

We show the existence of families of elliptic curves over Q whose generic rank is at least 2 for the torsion groups Z/8Z and Z/2Z× Z/6Z. Also in both cases we prove the existence of infinitely many elliptic curves, which are parameterized by the points of an elliptic curve with positive rank, with such torsion group and rank at least 3. These results represent an improvement of previous results...

In this article, we formalize in Mizar [7] the definition of “torsion part” of Z-module and its properties. We show Z-module generated by the field of rational numbers as an example of torsion-free non free Z-modules. We also formalize the rank-nullity theorem over finite-rank free Z-modules (previously formalized in [1]). Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lo...