Related papers: Multiple recurrence for two commuting transformati…
We survey theoretical and experimental/observational results on general-relativistic spin (rotation) effects in binary systems. A detailed discussion is given of the two-body Kepler problem and its first post-Newtonian generalization,…
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
We consider the structure of roller coaster permutations as introduced by Ahmed & Snevily[1]. A roller coaster permutation is described as a permuta- tion that maximizes the total switches from ascending to descending or visa versa for the…
It is a well-known fact that an exchangeable sequence has empirical distributions that form a reverse-martingale. This paper is devoted to proof of the converse statement. As a byproduct of the proof for the binary case, we introduce and…
We prove a transformation formula relating two determinants involving elliptic shifted factorials. Similar determinants have been applied to multiple elliptic hypergeometric series.
The purpose of this memoir is to discuss two very interesting properties of integer sequences. One is the law of apparition and the other is the law of repetition. Both have been extensively studied by mathematicians such as Ward, Lucas,…
Conditions for positive and polynomial recurrence have been proposed for a class of reliability models of two elements with transitions from working state to failure and back. As a consequence, uniqueness of stationary distribution of the…
The subject of this paper is a simulation to that in [1] but here we consider substitutions corresponding to transpositions instead of replacements.
The circular twin paradox and Thomas Precession are presented in a way that makes both accessible to students in introductory relativity courses. Both are discussed by examining what happens during travel around a polygon and then in the…
Shuffle algebra has been employed to give a proof of the duality theorem for multiple zeta-star values of height one.
Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.
The kinematical rotations of N-partical Hyperspherical basis are considered. The recurrence relation method of determination of transformation coefficients for arbitrary N-values is demonstrated.
An old conjecture claims that commuting Hamiltonians of the double-elliptic integrable system are constructed from the theta-functions associated with Riemann surfaces from the Seiberg-Witten family, with moduli treated as dynamical…
There are several approaches to study occurrences of consecutive patterns in permutations such as the inclusion-exclusion method, the tree representations of permutations, the spectral approach and others. We propose yet another approach to…
We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first…
Results concerning recurrence and ergodicity are proved in an abstract Hilbert space setting based on the proof of Khintchine's recurrence theorem for sets, and on the Hilbert space characterization of ergodicity. These results are carried…
We study the winding behavior of random walks on two oriented square lattices. One common feature of these walks is that they are bound to revolve clockwise. We also obtain quantitative results of transience/recurrence for each walk.
A short proof of the equivalence of the recurrence of non-backtracking random walk and that of simple random walk on regular infinite graphs is given. It is then shown how this proof can be extended in certain cases where the graph in…
Let $R$ be a finite ring. The commuting probability of $R$ is the probability that any two randomly chosen elements of $R$ commute. In this paper, we obtain some bounds for commuting probability of $R$.
In this article we study commutant lifting, more generally intertwining lifting, for different reproducing kernel Hilbert spaces over two domains in $\mathbb{C}^n$, namely the unit ball and the unit polydisc. The reproducing kernel Hilbert…