Unipotent group actions on affine varieties

Algebraic actions of unipotent groups $U$ actions on affine $k-$varieties $X$ ($k$ an algebraically closed field of characteristic 0) for which the algebraic quotient $X//U$ has small dimension are considered$.$ In case $X$ is factorial, $O(X)^{\ast}=k^{\ast},$ and $X//U$ is one-dimensional, it is shown that $O(X)^{U}$=$k[f]$, and if some point in $X$ has trivial isotropy, then $X$ is $U$ equivariantly isomorphic to $U\times A^{1}(k).$ The main results are given distinct geometric and algebraic proofs. Links to the Abhyankar-Sathaye conjecture and a new equivalent formulation of the Sathaye conjecture are made.Comment: 10 pages. This submission comes out of an older submission ("A commuting derivations theorem on UFDs") and contains part of i

Sparse block factorization of saddle point matrices

The factorization method presented in this paper takes advantage of the special structures and properties of saddle point matrices. A variant of Gaussian elimination equivalent to the Cholesky's factorization is suggested and implemented for factorizing the saddle point matrices block-wise with small blocks of order 1 and 2. The Gaussian elimination applied to these small blocks on block level also induces a block 3 x 3 structured factorization of which the blocks have special properties. We compare the new block factorization with the Schilders' factorization in terms of the sparsity of their factors and computational efficiency. The factorization can be used as a direct method, and also anticipate for preconditioning techniques

ALGSICS - Combining physics and cryptography to enhance security and privacy in RFID systems

In this paper, we introduce several new mechanisms that are cheap to implement or integrate into RFID tags and that at the same time enhance their security and privacy properties. Our aim is to provide solutions that make use of existing (or expected) functionality on the tag or that are inherently cheap and thus, enhance the privacy friendliness of the technology "almost" for free. Our proposals, for example, make use of environmental information (presence of light temperature, humidity, etc.) to disable or enable the RFID tag. A second possibility that we explore is the use of delays in revealing a secret key used to later establish a secure communication channel. We also introduce the idea of a "sticky tag," which can be used to re-enable a disabled (or killed) tag whenever the user considers it to be safe. We discuss the security and describe usage scenarios for all solutions. Finally, we review previous works that use physical principles to provide security and privacy in RFID systems