Related papers: Observations on the Halting Problem
In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…
It has been known for over 100 years that there is a discrepancy between Maxwell's electrodynamics and the idea of a classical electron as the ``atom'' of electricity. This incompatibility is known under the terms 4/3 problem of the…
Time does not obviously appear amongst the coordinates on the constrained phase space of general relativity in the Hamiltonian formulation. Recent work in finite-dimensional models claims that topological obstructions generically make the…
We explain the essence of perturbation problems. The key to understanding is the structure of chain homotopy equivalence -- the standard one must be replaced by a finer notion which we call a strong chain homotopy equivalence. We prove an…
We present a theory of lazy imperative timing.
The experimental findings reported in our original paper [1] (arXiv:1211.2913) have been criticized in ref.[2] (arXiv:1606.00710). We believe that the arguments brought in ref. [2] are not correct and we show evidence for this.
A new understanding of the notion of the stable solution to ill-posed problems is proposed. The new notion is more realistic than the old one and better fits the practical computational needs. A method for constructing stable solutions in…
We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems)…
The paper contains a discussion on a number of open problems in queueing theory. Some of them are known for decades, some are more recent. They relate to stability and to rare events. There is an idea to prepare a special issue of QUESTA on…
There exists a simple, didactically useful one-to-one relationship between stopping times and adapted c\`agl\`ad (LCRL) processes that are non-increasing and take the values 0 and 1 only. As a consequence, stopping times are always hitting…
The delayed choice experiments are a collection of experiments where the counterintuitive laws of quantum mechanics are manifested in a very striking way. Although the delayed choice experiments can be very accurately described with the…
The state of the superfluid He-II theory is briefly surveyed - some aspects of its history, achievements, and unsolved problems.
This note presents an interesting counterexample to a basic covering problem.
This paper has been withdrawn by the author. In this short paper I present a new approach to the problem of measurement, based on the difference between language (reality) and meta-language (meta-reality). This way, it will be shown as the…
Actual infinity in its various forms is discussed, searched and not found.
The observable universe is fundamentally inhomogeneous and anisotropic. Quantum description of the generation of these inhomogeneities and anisotropies is ill-understood and unsatisfactory. After providing a brief account of the standard…
Many new models of wave turbulence -- frozen, mesoscopic, laminated, decaying, sand-pile, etc. -- have been developed in the last decade aiming to solve problems seemingly not solvable in the framework of the existing wave turbulence theory…
We revisit the cocked hat -- an old problem from navigation -- and examine under what conditions its old solution is valid.
The Gedankenexperiment advanced by Frauchiger and Renner in their "Nature" paper was based on an implicit assumption that one can synchronize stochastic measurement intervals between two non-interacting systems. This hypothesis, the author…
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning…