Incomparability of pure bipartite entangled states under deterministic LOCC is a very strange phenomena. We find two possible ways of getting our desired pure entangled state which is incomparable with the given input state, by collective LOCC with certainty. The first one is by providing some pure entanglement through the lower dimensional maximally-entangled states or using further less amoun...

* Parts of this contribution were presented as a lecture during the annual meeting of the Water Chemistry Division in the German Chemical Society (Fachgruppe Wasserchemie in der GDCh), Lindau, May 1997. ** Dr. Thomas Heberer, Dipl.-Lebensmittelchem. Kathrin Schmidt-Bäumler, Prof. Dr. Hans-Jürgen Stan, Institute of Food Chemistry, Technical University of Berlin, GustavMeyer-Allee 25, D-13355 Ber...

Let NSymm be the Hopf algebra of non-commutative symmetric functions (in an infinity of indeterminates): NSymm=Z 1 2 , ,... Z Z   . It is shown that an associative algebra A with a Hasse-Schmidt derivation 1 2 ( , , ,...) d id d d  on it is exactly the same as an NSymm module algebra. The primitives of NSymm act as ordinary derivations. There are many formulas for the generators Zi in terms ...

Josef Pochodzalla, Lech Mankiewicz, Murray Moinester, Gunther Piller , Andrzej Sandacz, Marc Vanderhaeghen Max-Planck-Institut für Kernphysik, 69029 Heidelberg, Germany Physics Department, Technical University Munich, D-85747 Garching, Germany School of Physics and Astronomy, R. and B. Sackler Faculty of Exact Sciences, Tel Aviv University, 69978 Ramat Aviv, Israel Soltan Institute for Nuclear ...

Abstract A subgroup of a group G is said to be hereditarily -permutable with B , if $AB^x = B^xA$ for some element $x \in \langle A, \rangle $ . in every In this paper, we investigate the structure finite all its Schmidt subgroups -permutable.

We consider the cohomology of two-dimensional subshifts, and develop a new approach to proving that every cocycle is trivial (i.e. cohomologous to a homomorphism). We introduce semi-safe subshifts which, roughly speaking, have the property that some symbol can surround all allowed blocks in at least one horizontal and one vertical direction. We prove that for such subshifts, every locally const...

Graphical Abstract „The greatest scientific advance of the next decade will revolve around developing technologies that harmonize human progress with ecological integrity… The most important quality a mentor is to tailor guidance fit an individual's aspirations, acknowledging one size doesn't all.“ Find out more about Andreas Benjamin Schmidt in his Introducing… Profile.

Last time we defined the minimum distance λ1(L) of a lattice L, and showed that it is upper bounded by √ n · det(L)1/n (Minkowski’s theorem), but this bound is often very loose. Some natural computational questions are: given a lattice (specified by some arbitrary basis), can we compute its minimum distance? Can we find a vector that achieves this distance? Can we find good approximations to th...

We propose a feature extraction algorithm, based on the Hilbert–Schmidt independence criterion (HSIC) and the maximum dependence – minimum redundancy approach. Experiments with classification data sets demonstrate that suggested Hilbert–Schmidt component analysis (HSCA) algorithm in certain cases may be more efficient than other considered approaches.