Related papers: Observations on the Halting Problem

Thanks to the interest of many people, a mistake has been found in our way of counting limit cycles. We are working on a new version.

Reasoning has long been understood as a pathway between stages of understanding. Proper reasoning leads to understanding of a given subject. This reasoning was conceptualized as a process of understanding in a particular way, i.e.,…

This paper examines the processes involved in attempting to capture the subtlest aspects of nature by the scientific method and argues on this basis that nature is fundamentally elusive and may resist grasping by the methods of science. If…

We learn mathematics subjectively and must apply it objectively. But sometimes, we apply it subjectively by using wrong intuitions which may be elusive to our eyes. The aim of this note is to disclose the secretes of two kinds of these…

We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general H\"older observables fail. We obtain limit laws for such maps and H\"older…

In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this…

The validity of non-perturbative methods is questioned. The concept of relative space is introduced.

It is shown that theories already presented as rigorous mathematical formalizations of widespread manipulations of Dirac's delta function are all unsatisfactory, and a new alternative is proposed.

In this letter, by regarding finite-time stability as an inverse problem, we reveal the essence of finite-time stability and fixed-time stability. Some necessary and sufficient conditions are given. As application, we give a new approach…

In this paper, the existence of weak solutions of a convective Cahn-Hilliard equation with degenerate mobility is studied. We first define a notion of weak solutions and establish a regularized problems. The existence of such solutions is…

In this Reply we argue that the conclusions derived in Ref. arXiv:1301.1241 are questionable.

We propose a formal proof of the undecidability of the model checking problem for alternating- time temporal logic under imperfect information and perfect recall semantics. This problem was announced to be undecidable according to a…

The possibility of stable or quasi--stable Planck mass black hole remnants as solution to the black hole information paradox is commonly believed phenomenologically unacceptable: since we have to expect a black hole remnant for every…

The paper is suspended. The reason: as was noted by prof. H. Esnault, Theorem 2.1.1 of the previous version (as well as the related Theorem 6.1.1 of http://arxiv.org/PS_cache/math/pdf/9908/9908037v2.pdf of D. Arapura and P. Sastry) is wrong…

withdrawed due to a substantial error.

An argument, perhaps originating with Feyerabend a half century ago, and repeated many times since, purporting to establish that an "ignorance interpretation" of a bipartite pure entangled state leads to logical inconsistency, is incorrect:…

The long standing issue known as the hot QCD collinear singularity problem has been proven to rely on an incorrect sequence of two mathematical operations. Here, the original derivation of this problem is entirely revisited within the…

Attempts to quantize general relativity encounter an odd problem. The Hamiltonian that normally generates time evolution vanishes in the case of general relativity as a result of diffeomorphism invariance. The theory seems to be saying that…

It is manifested that the disregard of the epistemological problems connected with the fundamental obscurity in quantum mechanics results to the misunderstanding of the essence of this positivistic theory and to both funny and grandiose…

There is a growing body of evidence that the running of $\alpha_s$ predicted by perturbation (PT) theory is not correctly describing the accelerator experiments at the highest energies. A natural explanation is provided by the authors' 1992…