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We give a new, simple construction of the $\alpha$-stable tree for $\alpha \in (1,2]$. We obtain it as the closure of an increasing sequence of $\mathbb{R}$-trees inductively built by gluing together line-segments one by one. The lengths of…
The 2-point correlation form factor, $K_2(\tau)$, for small values of $\tau$ is computed analytically for typical examples of pseudo-integrable systems. This is done by explicit calculation of periodic orbit contributions in the diagonal…
We define two new statistics on words: the k-connector and the gk-connector. For a word $\pi = \pi_1\pi_2\cdots\pi_n$ of length $n$ over the alphabet $[k]$, a k-connector is defined as an ordered pair $(\pi_j, \pi_{j+1})$ where $1 \leq j…
An explicit expression for the general bivariate Krawtchouk polynomials is obtained in terms of the standard Krawtchouk and dual Hahn polynomials. The bivariate Krawtchouk polynomials occur as matrix elements of the unitary reducible…
We present a new analysis of the Delta I = 1/2 rule in K --> pi pi decays and the B_K parameter. We use the 1/N_c expansion within the effective chiral lagrangian for pseudoscalar mesons and compute the hadronic matrix elements at leading…
The numbers we study in this paper are of the form $B_{n, p}(k)$, which is the number of binary words of length $n$ that contain the word $p$ (as a subsequence) exactly $k$ times. Our motivation comes from the analogous study of pattern…
Let (F_n^{(k)})_{n\geq -(k-2)} be the k-generalized Fibonacci sequence, defined as the linear recurrence sequence whose first k terms are \(0, 0, \ldots, 0, 1\), and whose subsequent terms are determined by the sum of the preceding k terms.…
Hofstadter's $G$ function is recursively defined via $G(0)=0$ and then $G(n)=n-G(G(n-1))$. Following Hofstadter, a family $(F_k)$ of similar functions is obtained by varying the number $k$ of nested recursive calls in this equation. We…
Let A be any set of positive integers and n a positive integer. A composition of n with parts in A is an ordered collection of one or more elements in A whose sum is n. We derive generating functions for the number of compositions of n with…
Statistics of Poincar\'e recurrences is studied for the base-pair breathing dynamics of an all-atom DNA molecule in realistic aqueous environment with thousands of degrees of freedom. It is found that at least over five decades in time the…
The paper represents three supplements to the source paper, q-bio/0610044 [q-bio.OT], with three new series of harmonic structures of the genetic code, determined by Gauss arithmetical algorithm; by Table of Minimal Adding, as in…
We propose strongly consistent algorithms for reconstructing the characteristic function 1_K of an unknown convex body K in R^n from possibly noisy measurements of the modulus of its Fourier transform \hat{1_K}. This represents a complete…
I propose and investigate the use of continuous functional equations for the study of meta-Fibonacci integer sequences. This exploratory study includes three sequences with quite different behavior: Conway's famous sequence $A(n)=…
Let $k,d $ be positive integers. We determine a sequence of constants that are asymptotic to the probability that the cluster at the origin in a $d$-dimensional Poisson Boolean model with balls of fixed radius is of order $k$, as the…
We are interested in stochastic processes satisfying a nonlinear recurrence relation of the form $$X_{n + k} = \Phi_0 (X_n, ..., X_{n + k - 1}) + \Theta_n$$ where $\Theta$ is a noise term. We establish the existence of an invariant measure…
Production of scalar particles by a relativistic, semi-transparent mirror in 1+3D Minkowski spacetime based on the Barton-Calogeracos (BC) action is investigated. The corresponding Bogoliubov coefficients are derived for a mirror with…
We apply the one-loop results of the $SU(3)_L\times SU(3)_R$ ChPT suplemented with the inverse amplitude method to fit the available experimental data on $\pi\pi$ and $\pi K$ scattering. With esentially only three parameters we describe…
Analogues of 1-shuffle elements for complex reflection groups of type $G(m,1,n)$ are introduced. A geometric interpretation for $G(m,1,n)$ in terms of rotational permutations of polygonal cards is given. We compute the eigenvalues, and…
The \textit{sepr-sequence} of an $n\times n$ real matrix $A$ is $(s_1,\ldots,s_n)$, where $s_k$ is the subset of those signs of $+,-,0$ that appear in the values of the $k\times k$ principal minors of $A$. The $12\times 12$ matrix…
The so called one-parameter (often called $\varkappa$) deformed $AdS$ string sigma models have attracted a lot of attention lately in the study of integrability in string theory. We construct various circular string solutions in the $(AdS_3…