In this lecture, we show two results dealing with lower bounds in communication complexity. The first lower bound is an Ω(n) lower bound on the distributional complexity of Disjointness due to [3, 8]. Here we will present the simplified proof presented in [8]. In the second part, we will show how to obtain lower bounds on the unbounded error probabilistic communication complexity by Forster’s m...

Three self-assembled photonic dyads comprising a zinc porphyrin donor and a free base acceptor have been studied by time-resolved fluorescence spectroscopy. The driving force of the assembly is the site selective binding of an imidazole connected to a free base porphyrin. Three spacers have been incorporated between the imidazole connector and the free base porphyrin, providing three different ...

Anatoly Yu. Smirnov, Lev G. Mourokh, and Franco Nori 1 Frontier Research System, The Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama, 351-0198, Japan 2 CREST, Japan Science and Technology Agency, Kawaguchi, Saitama, 332-0012, Japan 3 Department of Physics, Queens College, The City University of New York, Flushing, New York 11367, USA 4 Department of Engineering Science an...

I. Nemes A, Domsik P, Piros GÁ, Kalapos A, Lengyel C, Orosz A, Forster T. Relationships between three-dimensional speckle tracking echocadiography-

We introduce sheaves and sheaf cohomology and use them to prove the Riemann-Roch theorem and Serre duality. The main proofs follow the treatment in Forster [3].

Several of the fundamental theorems about algebraic K, and Kr are concerned with finding unimodular elements, that is, elements of a projective module which generate a free summand. In this paper we use the notion of a basic element (in the terminology of Swan [22]) to extend these theorems to the context of finitely generated modules. Our techniques allow a simplification and strengthening of ...