let $g$ be a simple graph with vertex set $v(g) = {v_1, v_2,ldots, v_n}$ and edge set $e(g) = {e_1, e_2,ldots , e_m}$. similar tothe randi'c matrix, here we introduce the randi'c incidence matrixof a graph $g$, denoted by $i_r(g)$, which is defined as the$ntimes m$ matrix whose $(i, j)$-entry is $(d_i)^{-frac{1}{2}}$ if$v_i$ is incident to $e_j$ and $0$ otherwise. naturally, therandi'c incidenc...

We present an implemented model for discovering a class of state-space search heuristics. First, abstractions of a state-space problem are generated by dropping information from the problem definition. An optimal solution path for any such abstracted problem gives a lower bound on the true distance to the goal. This bound can be used as an admissible evaluation function for guiding the base-lev...

We examine the problem of counting the number of Hamiltonian paths and Hamiltonian cycles in outerplanar graphs and planar graphs, respectively. We give an O(nαn) upper bound and an Ω(αn) lower bound on the maximum number of Hamiltonian paths in an outerplanar graph with n vertices, where α ≈ 1.46557 is the unique real root of α = α + 1. For any positive integer n ≥ 6, we define an outerplanar ...

Sampled-data synchronization problem for singular Markovian jump systems (SMJSs) subject to aperiodic sampled-data control is investigated. Firstly, via constructing mode-dependent one-sided loop-based Lyapunov functional (LBLF) and two-sided LBLF, two different stochastically admissible conditions are suggested error SMJSs with sampled-data. It guaranteed that the slave system synchronized mas...

In this paper, we investigate the existence of random absolutely continuous invariant measures (ACIP) for expanding on average Saussol maps in higher dimensions. This is done by establishment a Lasota–Yorke inequality transfer operators space bounded oscillation. We prove that number ergodic skew product ACIPs finite and will provide an upper bound these ACIPs. work can be seen as generalizatio...

The lower bound on the period of uniform rotation of neutron stars (NS) with causal equation of state (EOS), Pmin, is shown to be determined, with a high precision, by the upper bound on the surface redshift of static neutron star models, zmax. We obtain zmax = 0.851, which turns out to be about 5% lower than upper bound obtained by Lindblom (1984). Using then the empirical formula for the maxi...

A method based on the interval Kalman filter for discrete uncertain linear systems is presented. The system under consideration is subject to bounded parameter uncertainties not only in the state and observation matrices, but also in the covariance matrices of Gaussian noises. The gain matrix provided by the filter is optimized to give a minimal upper bound on the state estimation error covaria...

The average consensus in undirected networks of multi-agent with both fixed and switching topology coupling multiple time-varying delays is studied. By using orthogonal transformation techniques, the original system can be turned into a reduced dimensional system and then LMI-based method can be applied conveniently. Convergence analysis is conducted by constructing Lyapunov-Krasovskii function...

The upper bound on the value of the surface gravity, gs, for neutron stars with equations of state respecting vsound ≤ c, is derived. This bound is inversely proportional to the maximum allowable mass Mmax, and it reads gs ≤ 1.411× 10 15 (Mmax/M⊙) −1 cm s. It implies an absolute upper bound 7.4× 10 cm s if one uses the 2σ lower bound on the neutron mass measured recently in 4U1700-37, 1.9M⊙. A ...