Related papers: Observations on the Halting Problem
Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value} of the stopped variable under the rule optimal…
We study the obstacle problem for the Evolutionary p-Laplace Equation when the obstacle is discontinuous and without regularity in the time variable. Two quite different procedures yield the same solution.
Notwithstanding its great influence in modern physics, the EPR thought-experiment has been explained incorrectly a surprising number of times.
In this note we introduce a notion of a generically (strongly generically) NP-complete problem and show that the randomized bounded version of the halting problem is strongly generically NP-complete.
Gray (2015) argued that the Fermi paradox (FP) is a misnomer, and it is not a valid paradox. Gray also speculated that the argument was misattributed to Fermi, whose lunchtime remarks did not pertain to the existence of extraterrestrial…
In this note, it is shown by counterexamples, theoretical analysis and simulation tests that the two types of sliding-mode controllers presented in the paper [1] fail to solve the stabilization problem of a class of under-actuated…
The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…
A variation on the splitting principle
I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…
We consider a class of discretionary stopping problems within the $G$-framework. We first establish the well-definedness of the stopping problem under the $G$-expectation, by showing the quasi-continuity of the stopped process. We then…
The use of the trading halts is a practice common to all markets. However, the advantages and the disadvantages of the measurements are regularly discussed. The partisans think that the trading suspensions or the price limits make it…
In a recent note Ellis criticizes varying speed of light theories on the grounds of a number of foundational issues. His reflections provide us with an opportunity to clarify some fundamental matters pertaining to these theories.
Fernandez Comment [1] on our pseudo-perturbative shifted-l expansion technique [2,3] is either unfounded or ambiguous.
We present an astonishingly simple and elegant proof of the celebrated Basel problem.
In the theory of hydrodynamic stability, the procedure to decompose an incompressible flow field into its basic motion and disturbances is imprecise and problematic because the disturbances, infinitesimal or finite, are ill-defined…
The paper presents a counterexample to the Hodge conjecture.
It will be shown that the comment [1] contains numerous errors, misconceptions, inaccuracies, false assumptions, misunderstandings and unjustified claims. The analysis of the comment is built on a false assumption that the terminal current…
The halting problem for Turing machines is decidable on a set of asymptotic probability one. Specifically, there is a set B of Turing machine programs such that (i) B has asymptotic probability one, so that as the number of states n…
We make remarks on Ristroph and Zhang's [{\it Phys. Rev. Lett.} {\bf 101}, 194502 (2008)] paper. We argue especially that due to the interferences the calibration procedures in [1] were not complete and this will induce some measurements'…
Reasoning about unpredicted change consists in explaining observations by events; we propose here an approach for explaining time-stamped observations by surprises, which are simple events consisting in the change of the truth value of a…