A digraph G = (V; E) is primitive if, for some positive integer k, there is a u ! v walk of length k for every pair u; v of vertices of V. The minimum such k is called the exponent of G, denoted exp(G). The exponent of a vertex u 2 V , denoted exp(u), is the least integer k such that there is a u ! v walk of length k for each v 2 V. For a set X V , exp(X) is the least integer k such that for ea...

We investigate the critical temperature of an interacting Bose gas confined in a trap described by a generic isotropic power-law potential. We compare the results with respect to the non-interacting case. In particular, we derive an analytical formula for the shift of the critical temperature holding to first order in the scattering length. We show that this shift scales as N n 3(n+2) , where N...

An urban watershed in Xiamen was selected to perform the parameter uncertainty analysis for urban stormwater runoff modeling in terms of identification and sensitivity analysis based on storm water management model (SWMM) using Monte-Carlo sampling and regionalized sensitivity analysis (RSA) algorithm. Results show that Dstore-Imperv, Dstore-Perv and Curve Number (CN) are the identifiable param...

The fastest known algorithm for factoring univariate polynomials over finite fields is the KedlayaUmans [13] (fast modular composition) implementation of the Kaltofen-Shoup algorithm [12, § 2]. It is randomized and takes Õ(n3/2 log q+n log2 q) time to factor polynomials of degree n over the finite field Fq with q elements. A significant open problem is if the 3/2 exponent can be improved. We st...

In this paper we construct Baer ordered indecomposable division algebras of index pn and exponent pm for all primes p and for all n, m, with n > m ≥ 1 (n ≥ 3 if p = 2).

For every non-integral $\alpha \gt 1$, the sequence of integer parts $n^{\alpha }$ $(n=1,2,\ldots )$ is called Piatetski-Shapiro with exponent $ and let $\mathrm {PS}(\alpha denote set all terms this sequence.

We investigate the relation between trading activity—measured by the number of trades N t—and the price change G t for a given stock over a time interval [t, t + t]. We relate the time-dependent standard deviation of price changes—volatility—to two microscopic quantities: the number of transactions N t in t and the variance W 2 t of the price changes for all transactions in t . We find that N t...

We prove the existence of a positive SOLA (Solutions Obtained as Limits Approximations) to following PDE involving fractional power Laplacian ( ? ? ) s u = 1 ? + ? 2 ? ? in ? , > 0 ? N ? . Here, is bounded domain ?N, s?(0,1), 2s<N, ?,??(0,1), 2s?=2N?N?2s critical Sobolev exponent and nonnegative Radon measure ?.

We study statistics of records in a sequence of random variables. These identical and independently distributed variables are drawn from the parent distribution ρ. The running record equals the maximum of all elements in the sequence up to a given point. We define a superior sequence as one where all running records are above the average record expected for the parent distribution ρ. We find th...