Since the work of Kolpakov and Kucherov in [5, 6], it is known that ρ(n), the maximal number of runs in a string, is linear in the length n of the string. A lower bound of 3/(1 + √ 5)n ∼ 0.927n has been given by Franek and al. [3, 4], and upper bounds have been recently provided by Rytter, Puglisi and al., and Crochemore and Ilie (1.6n) [8, 7, 1]. However, very few properties are known for the ...

Using a theoretical framework based on the next-to-leading order QCD improved effective Hamiltonian, we have estimated the branching ratios and asymmetry parameters for the two body charmless nonleptonic decay modes of Λb baryon i.e. Λb → p(π/ρ), p(K/K) and Λ(π/ρ), within the framework of generalized factorization. The nonfactorizable contributions are parametrized in terms of the effective num...

Let π be the occupancy density of an obliquely reflected Brownian motion in half plane and let (ρ,α) polar coordinates a point upper plane. This work determines exact asymptotic behavior π(ρ,α) as ρ→∞ with α∈(0,π). We find explicit functions a, b, c such that π(ρ,α)∼ρ→∞a(α)ρb(α)e−c(α)ρ. closes open problem first stated by Professor J. Michael Harrison August 2013. also compute asymptotics for t...

Given the sensitivity of current ground-based Gravitational Wave (GW) detectors, any continuous-wave signal we can realistically expect will be at a level or below the background noise. Hence, any data analysis of detector data will need to rely on statistical techniques to separate the signal from the noise. While with the current sensitivity of our detectors we do not expect to detect any tru...