Related papers: Refuting a Recent Proof of the Invariant Subspace …
We show that the proofs of Gill as well as of Gill, Weihs, Zeilinger and Zukowski contain serious mathematical and physical deficiencies which render them invalid.
We extend the notion of anticoherent spin states to anticoherent subspaces. An anticoherent subspace of order t, is a subspace whose unit vectors are all anticoherent states of order t. We use Klein's description of algebras of polynomials…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
We reinterpret the distribution of the Hall potential in the Hall bar-with-a-hole that has been found and interpreted by Mani and Klitzing [Appl. Phys. Lett., 64 1262 (1994)]. Our reinterpretation explains all the "paradoxes" without…
We show that recent results in the paper of Jaffe et al on evidence of vorticity and shear of the Universe are incorrect. They fit WMAP data with certain Bianchi model which is known to have a vanishing vorticity. The performed fit of the…
In this article, we briefly describe nearly $T^{-1}$ invariant subspaces with finite defect for a shift operator $T$ having finite multiplicity acting on a separable Hilbert space $\mathcal{H}$ as a generalization of nearly $T^{-1}$…
G\"odel's first and second incompleteness theorems are corner stones of modern mathematics. In this article we present a new proof of these theorems for ZFC and theories containing ZFC, using Chaitin's incompleteness theorem and a very…
In this paper we study subspaces which are invariant under squares and cubes (separately as well as jointly) of unicellular backward weighted shift operators on a separable Hilbert space. The finite-dimensional subspaces are characterized…
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
We show that a recent letter claiming to present exact cosmological solutions in Brans-Dicke theory actually uses a flawed set of equations as the starting point for their analysis. The results presented in the letter are therefore not…
Breuil et Schneider formulated a conjecture on the equivalence of the existence of invariant norms on certain locally algebraic representations of GL_d(F) and the existence of certain de Rham representations of Gal(\bar(Q_p)/F)$, where F is…
In this paper we present the following two results: we give an explicit description of the space of orderings of the field Q(x) as an inverse limit of finite spaces of orderings and we provide a new, simple proof of the fact that the class…
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
We argue that the experiment described in the recent Letter by Zu et al. [Phys. Rev. Lett. 109, 150401 (2012); arXiv:1207.0059v1] does not allow to make conclusions about contextuality, since the measurement of the observables as well as…
A recent paper (arXiv:1404.5619) claimed the presence of a loophole in the current-algebra proof of Goldstone Theorem. The enforcing of manifest covariance would lead to contradictory results also in scalar theory. We show that the argument…
In this comment we show that the approach presented by Foj\'on et al~\cite{Fojon10} is not as accurate as they claim. A straightforward calculation using the models considered buy those authors clearly shows that the spectral method, which…
We prove the existence of Hall polynomials for $x^2$-bounded invariant subspaces of nilpotent linear operators.
The content of this paper has no mathematical flaw except that the proof of the main theorem relies on the homotopy invariance of spectral invariants of topological Hamiltonian paths. Since the latter is still up in the air, the main result…
We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…
This paper has been withdrawn by the authors, because of a crucial gap in the proof of the main theorem.