Related papers: A variation on the theme of Nicomachus

We analyze continuous-time quantum walks on necklace graphs - cyclical graphs consisting of many copies of a smaller graph (pearl). Using a Bloch-type ansatz for the eigenfunctions, we block-diagonalize the Hamiltonian, reducing the…

The problem of the universal form of the size spectrum is analyzed. The half-widths of two wings of spectrum is introduced and it is shown that their ratio is very close to the golden fraction. In appendix it is shown that behind the golden…

The Hamiltonian analysis for the Euler and Second-Chern classes is performed. We show that, in spite of the fact that the Second-Chern and Euler invariants give rise to the same equations of motion, their corresponding symplectic structures…

We solve the Cauchy problem for the Korteweg-de Vries equation with steplike quasi-periodic, finite-gap initial conditions under the assumption that the perturbations have a given number of derivatives with finite moments.

We give a new characterization of generalized B\"uchi sequences (sequences whose sequence of squares has constant second difference $(a)$, for some fixed integer $a$) of length 3 over the integers and a strategy for attacking B\"uchi's n…

A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…

For any integer $k\geq 1,$ define $L_k: \mathbb{R}^\mathbb{N}\to \mathbb{R}^\mathbb{N}$ by $(a_n)_{n\in\mathbb{N}}\mapsto (a'_n)_{n\in\mathbb{N}}$ where $a'_n=\det(a_{n+i+j})_{i,j=0}^{k-1}$. Previously, Zhu showed that $L_k$ preserves the…

We consider the Stokes phenomenon for the solutions of some partial differential equations with variable coefficients in two complex variables, where initial data are holomorphic. We use the theory of (moment) summability and the theory of…

This is a systematic review of the concept of indistinguishability in both classical and quantum mechanics, with particular attention to Gibbs' paradox. Section 1 is on the Gibbs paradox; section 2 is a defense of the concept of classical…

We explore the phase-space of homogeneous and anisotropic spacetimes within symmetric teleparallel $f(Q)$-gravity. Specifically, we consider the Kantowski-Sachs and locally rotational Bianchi III geometries to describe the physical space.…

Clarified certain points and related it to other work.

We generalize certain arguments in Zariski's irregularity theorem on cyclic multiple planes.

With a view to the results discussed in the first two parts of this paper, the concept of time is revisited oncemore and chosen as an example in order to demonstrate the meaning of fundamental in both physical and philosophical terms. It is…

We present new second derivative, generally covariant theories of gravity for spherically symmetric spacetimes (general covariance is in the $t-r$ plane) belonging to the class where the spherically symmetric Einstein-Hilbert theory is…

New formulas for the nth moment of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and staircase tableaux. A…

Bott periodicity for the unitary, orthogonal and symplectic groups is fundamental to topological K-theory. Analogous to unitary topological K-theory, for algebraic K-groups with finite coefficients similar periodicity results are…

We revisit a technique of S. Lehr on automata and use it to prove old and new results in a simple way. We give a very simple proof of the 1986 theorem of Honkala that it is decidable whether a given k-automatic sequence is ultimately…

The paper investigates a generalization of the classical Sitnikov problem, concentrating on the movement of a satellite along the Z-axis as it interacts with $n$ primary bodies in periodic motion. It establishes the existence of an infinite…

In this final piecemeal treatment of local Problem of Time facets, and underlying Background Independence aspects, we first reconsider the ten local facets and aspects considered so far at the quantum level. This is essential both to…

We show that whenever a closed symplectic manifold admits a Hamiltonian diffeomorphism with finitely many simple periodic orbits, the manifold has a spherical homology class of degree two with positive symplectic area and positive integral…