Related papers: Sequentiality Restrictions in Special Relativity
In this paper, it is shown why Lorentz Transformation implies the general case where observed events are not necessarily in the inertia frame of any observer but assumes a special scenario when determining the length contraction and time…
Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…
The uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of noncommuting observables in the preparation of quantum states. Recently, many uncertainty relations were proposed with improved…
Naturalness problems such as the hierarchy problem and the origin of dark energy remain significant challenges in modern cosmology. This paper develops a rigorous mathematical framework where each observer defines their own universe, and…
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…
In a companion paper we studied field theory in the presence of a physical observer with quantum dynamics. Here we describe the most striking consequence of this assumption: new gauge and diff anomalies arise. The relevant cocycles depend…
We consider a sequence of independent random variables with the known distribution observed sequentially. The observation $n$ is assumed to be a value of one order statistics such as s:n-th, where 1 is less than s is less than n. It the…
We estimate the frequency of polynomial iterations which falls in a given multiplicative subgroup of a finite field of $p$ elements. We also give a lower bound on the size of the subgroup which is multiplicatively generated by the first $N$…
A permutation p is realized by the shift on N symbols if there is an infinite word on an N-letter alphabet whose successive left shifts by one position are lexicographically in the same relative order as p. The set of realized permutations…
In the special theory of relativity, Lorentz invariance is extended in Minkowski spacetime from ideal inertial observers to actual observers by means of the hypothesis of locality, which postulates that accelerated observers are always…
By positing a universe where all events are determined by initial conditions, superdeterminism as conceded by Bell frames correlations observed in quantum measurements as the consequence of an inherently predetermined cosmic order that…
While many production-ready and robust algorithms are available for the task of recommendation systems, many of these systems do not take the order of user's consumption into account. The order of consumption can be very useful and matters…
In this paper, we study the observability of compactly perturbed infinite dimensional systems. Assuming that a given infinite-dimensional system with self-adjoint generator is exactly observable we derive sufficient conditions on a compact…
After a brief summary of Double Special Relativity (DSR), we concentrate on a five dimensional procedure, which consistently introduce coordinates and momenta in the corresponding four-dimensional phase space, via a Hamiltonian approach.…
We consider a random permutation drawn from the set of 321-avoiding permutations of length $n$ and show that the number of occurrences of another pattern $\sigma$ has a limit distribution, after scaling by $n^{m+\ell}$ where $m$ is the…
The forbidden number $\mathrm{forb}(m,F)$, which denotes the maximum number of unique columns in an $m$-rowed $(0,1)$-matrix with no submatrix that is a row and column permutation of $F$, has been widely studied in extremal set theory.…
We bound the number of permutations with a fixed number $r$ of $321 \ominus p_0$ patterns by a constant times the number of permutations which avoid $321 \ominus p_0$. We use this new upper bound to show that the ordinary generating…
This paper discusses experiments with single-particle systems, some of whose states appear to be entangled. It shows that the interpretation of the experiments in terms of entanglement is ill-defined. Three forms of ambiguity are discussed.…
Based on symmetry consideration, quasi-one-dimensional (1D) objects, relevant to numerous observables or phenomena, can be classified into eight different types. We provide various examples of each 1D type, and discuss their Symmetry…
Complications in preparing and preserving quantum correlations stimulate recycling of a single quantum resource in information processing and communication tasks multiple times. Here, we consider a scenario involving multiple independent…