Related papers: Refuting a Recent Proof of the Invariant Subspace …

In the preceding Comment it is alleged that a "hidden loophole" in the proof of Hara's theorem has been found, which purportedly invalidates the conclusions of the paper commented upon. I show that there is no such loophole in the…

In this work, we show that the proof of the main result in [An Application of Hayashi's Inequality for Differentiable Functions, Computers & Mathematics with Applications, 32 (6) (1996), 95--99, by R.P. Agarwal and S.S. Dragomir] was wrong.…

A complete characterization of near subnormality for bilateral weighted shifts is obtained. As an application of the main results, many new answers to the Hilbert space problem 160 are presented at the end of the paper.

The aim of this paper is to clarify the properties of semi-barrelled spaces (also called countably quasi-barrelled spaces in the literature). These spaces were studied by several authors, in particular in the classical book of N. Bourbaki…

Attempts to quantize light in a manifestly Lorentz covariant manner fail because of the indefinite metric problem. Here an error in the interpretation is uncovered that is at the root of this problem.

An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it…

Samuely et al. (cond-mat/0503153) make the strong claim that our letter is 'contradicting several established experimental results'. As we will show below this is not justified and the claims from are based on a misinterpretation of our…

This paper has been withdrawn, as all conjectures (and one claim) have been proven incorrect. Some of what remains may eventually reappear in a different context.

In this paper, we generalize the theory of the invariant subspace method to (m + 1)-dimensional non-linear time-fractional partial differential equations for the first time. More specifically, the applicability and efficacy of the method…

Searle's Chinese Room argument is refuted by showing that he has actually given two different versions of the room, which fail for different reasons. Hence, Searle does not achieve his stated goal of showing ``that a system could have input…

In this note we correct a paper by D. Kang ("On the Mazur-Ulam theorem in non-Archimedean fuzzy anti-2-normed spaces", Filomat, 2017). The research in that paper applies to what the author calls strictly convex spaces. Nevertheless, we…

It is pointed out that the claim made by Joshi and Joshi [1], has not been rigorously demonstrated by them. A simpler and more correct proof is provided.

We revisit the long-standing conjecture that in unitary field theories, scale invariance implies conformality. We explain why the Zamolodchikov-Polchinski proof in D=2 does not work in higher dimensions. We speculate which new ideas might…

This paper has been withdrawn due to a crucial theoretical error.

Recent proposal for counterfactual computation [Hosten et al., Nature, 439, 949 (2006)] is analyzed. It is argued that the method does not provide counterfactual computation for all possible outcomes. The explanation involves a novel…

We present a direct proof of the fact that the weak-$L^1$ and weak-$\ell^1$ spaces do not have type $1$.

This article is concerned with the representation of curves by means of integral invariants. In contrast to the classical differential invariants they have the advantage of being less sensitive with respect to noise. The integral invariant…

The traditional theory of Laplace transformation in its currently prevalent form is unsatisfactory. Its deficiencies can be traced back to a mismatch of the definition intervals of the original function and of the inverse L-transform. A new…

We discuss the claims of the comment at arXiv.org:physics/0609234. We show that A.V. Kildishev et al. misread our method of extracting of optical constants of nanostructured films. The theoretical calculations performed in the comment…

Since the experimental observation of the violation of the Bell-CHSH inequalities, much has been said about the non-local and contextual character of the underlying system. But the hypothesis from which Bell's inequalities are derived…