We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure. The study of the Riemannian exponential map allows us to prove infinite-dimensional counterparts of results from classical Riemannian geometry: the Riemannian exponential map is a smooth local diffeomorphism and the...

In weakly coupled plasmas, it is common to describe the microfield using a Debye model. We examine here an “artificial” ideal one-component plasma with an infinite Debye length, which has been used for the test of line shape codes. We show that the infinite Debye length assumption can lead to a misinterpretation of numerical simulations results, in particular regarding the convergence of calcul...

We study the zero-temperature partition function of the Potts antiferromagnet (i.e., the chromatic polynomial) on a torus using a transfer-matrix approach. We consider squareand triangular-lattice strips with fixed width L, arbitrary length N , and fully periodic boundary conditions. On the mathematical side, we obtain exact expressions for the chromatic polynomial of widths L = 5, 6, 7 for the...

In this paper we study a class of infinite words on a finite alphabet A whose factors are closed under the image of an involutory antimorphism θ of the free monoid A∗. We show that given a recurrent infinite word ω ∈ AN, if there exists a positive integer K such that for each n ≥ 1 the word ω has 1) cardA + (n − 1)K distinct factors of length n, and 2) a unique right and a unique left special f...

We study the relation between the palindromic and factor complexity of infinite words. We show that for uniformly recurrent words one has P(n) + P(n + 1) ≤ ∆C(n) + 2, for all n ∈ N. For a large class of words it is a better estimate of the palindromic complexity in terms of the factor complexity then the one presented in [2]. We provide several examples of infinite words for which our estimate ...

We describe a method for proving the termination of graph transformation systems. The method is based on the fact that infinite reductions must include infinite ‘creation chains’, that is chains of edges in different graphs of the reduction sequence, such that each edge is involved in creating the next edge. In our approach, the length of such creation chains is recorded by associating with eac...

the concept of “infinite essence” that is both philosophically and theologically important, has passed many different evolutions in western history of thought. presocratics has evaluated it in two different ways. anaximender and melissus agree that the principle substance is infinite and divine, but neither absolutly transcendent nor anthropomorphic. the infinite is the fusis in its substantial...

Smooth infinite words over Σ = {1, 2} are connected to the Kolakoski word K = 221121 · · ·, defined as the fixpoint of the function ∆ that counts the length of the runs of 1’s and 2’s. In this paper we extend the notion of smooth words to arbitrary alphabets and study some of their combinatorial properties. Using the run-length encoding ∆, every word is represented by a word obtained from the i...

The causal structure of a stochastic process can be more efficiently transmitted via a quantum channel than a classical one, an advantage that increases with codeword length. While previously difficult to compute, we express the quantum advantage in closed form using spectral decomposition, leading to direct computation of the quantum communication cost at all encoding lengths, including infini...

We present numerical results obtained from a minimal relativistic model for three distinguishable particles of equal mass driven by a single bound or virtual state for each pair, which is a relativistic generalization of the zero range non-relativistic two particle scattering length model. In contrast to the non-relativistic case, the relativistic kinematics makes the three body equations conve...