It is widely accepted that consciousness or, in other words, mental activity is in some way correlated to the behavior of the brain or, in other words, material brain activity. Since quantum theory is the most fundamental theory of matter that is currently available, it is a legitimate question to ask whether quantum theory can help us to understand consciousness. Several approaches answering t...

Let X be a compact Kähler manifold of complex dimension n, and let G be a connected solvable subgroup of the automorphism group Aut(X). Let N(G) be the normal subgroup of G of elements of null entropy. The aim of this short paper is to show that G/N(G) is a free abelian group of rank ≤ n− 1 and that the rank estimate is optimal. This proves the conjecture of Tits type in [6] affirmatively. The ...

We study transverse-tracefree (TT)-tensors on conformally flat 3-manifolds (M, g). The Cotton-York tensor linearized at g maps every symmetric tracefree tensor into one which is TT. The question as to whether this is the general solution to the TT-condition is viewed as a cohomological problem within an elliptic complex first found by Gasqui and Goldschmidt and reviewed in the present paper. Th...

E e as balls centered at the origin, provided m ∈ [0, m0) for some (potentially computable) m0 > 0; this affirmatively answers conjecture [RCBM, Conjecture 3.12] for such values of the weighted volume parameter. We also prove that the set of weighted volumes such that this characterization holds true is open, thus reducing the proof of the full conjecture to excluding the possibility of bifurca...

In 2007, Martinian and Trott presented codes for correcting a burst of erasures with a minimum decoding delay. Their construction employs [n, k] codes that can correct any burst of erasures (including wrap-around bursts) of length n− k. They raised the question if such [n, k] codes exist for all integers k and n with 1 ≤ k ≤ n and all fields (in particular, for the binary field). In this note, ...

By a regular embedding of a graph into an orientable surface we mean a 2cell embedding with the automorphism group acting regularly on arcs. In 1997 Nedela and Škoviera [Europ. J. Comb. 18, 807-823] presented a construction giving for each solution of the congruence e2 ≡ 1(mod n) a regular embedding Me of the hypercube Qn. It was conjectured that all regular embeddings of Qn can be constructed ...

For an infinite cardinal μ, MAD(μ) denotes the set of all cardinalities of nontrivial maximal almost disjoint families over μ. Erdős and Hechler proved in [7] the consistency of μ ∈ MAD(μ) for a singular cardinal μ and asked if it was ever possible for a singular μ that μ / ∈ MAD(μ), and also whether 2 μ < μ =⇒ μ ∈ MAD(μ) for every singular cardinal μ. We introduce a new method for controlling ...

We investigate Vassiliev homotopy invariants of string links, and find that in this particular case, most of the questions left unanswered in [3] can be answered affirmatively. In particular, Vassiliev invariants classify string links up to homotopy, and all Vassiliev homotopy string link invariants come from marked surfaces as in [3], using the same construction that in the case of knots gives...